Research Article Robust Adaptive PID Controller for a...
13
Research Article Robust Adaptive PID Controller for a Class of Uncertain Nonlinear Systems: An Application for Speed Tracking Control of an SI Engine Tossaporn Chamsai, 1 Piyoros Jirawattana, 2 and Thana Radpukdee 1 1 Department of Industrial Engineering, Khon Kaen University, Khon Kaen 40002, ailand 2 Department of Mechanical Engineering, Khon Kaen University, Khon Kaen 40002, ailand Correspondence should be addressed to ana Radpukdee; [email protected] Received 12 October 2014; Accepted 25 February 2015 Academic Editor: Kacem Chehdi Copyright © 2015 Tossaporn Chamsai et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e sliding mode control (SMC) technique with a first-order low-pass filter (LPF) is incorporated with a new adaptive PID controller. It is proposed for tracking control of an uncertain nonlinear system. In the proposed control scheme, the adaptation law is able to update the PID controller online during the control process within a short period. e chattering phenomenon of the SMC can be alleviated by incorporation of a first-order LPF, while the robustness of the control system is similar to that of the sliding mode. In the closed-loop control analysis, the convergence condition in the reaching phase and the existence condition of the sliding mode were analyzed. e stability of the closed-loop control is guaranteed in the sense of Lyapunov’s direct method. e simulations and experimental applications of a speed tracking control of a spark ignition (SI) engine via electronic throttle valve control architecture are provided to verify the effectiveness and the feasibility of the proposed control scheme. 1. Introduction e presence of uncertain nonlinearity in physical systems has been extensively studied because most of the real systems are rather complex dynamical nonlinear with large uncer- tainties which can affect inaccuracy and poor robustness of the control system. To do this, numerous control schemes have been developed; for example, sliding mode control [1– 3], intelligent control [4, 5], feedback linearization [6], and adaptive control [7–9]. On the other hand, due to its simplicity in architec- ture and simple design, the proportional-integral-derivative (PID) control is acceptable and has been extensively applied in many practical applications. e key for designing a high capability of PID controller depends on the determination of the PID gain parameters which should be properly adjusted, and this has led to the developments for self-tuning methods of the three parameters of the PID controller. Recently, adaptive control techniques are generally applied for online- tuning of the PID controller. e flexibility of the PID tuning lies in the determination of the basic PID gains that can be adjusted online according to adaptation laws and using the error signal in order to realize the online adjustable gains during a control procedure [10–13]. However, the adaptive control strategy is capable of handling only constant parametric uncertainty, inadequate robustness for against external disturbance, and an accurate system model that is required [14]. e sliding mode control (SMC) method is one of the control strategies to dominate the parametric uncertainties and external disturbances, while the control principle is without precise system model information [15–18]. Nev- ertheless, if the sliding mode exists, the chattering phe- nomenon is the main obstacle for SMC application [19–21]. In much research work, alleviations chattering phenomenon of the sliding mode incorporated with a low-pass filter has been studied [22–26] because it can make a compromise between the alleviation of the chattering and the control accuracy. Incorporation of the SMC with closed-loop filtering is capable to realize the acquisition of control signal and Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2015, Article ID 510738, 12 pages http://dx.doi.org/10.1155/2015/510738
Transcript of Research Article Robust Adaptive PID Controller for a...
Research ArticleRobust Adaptive PID Controller for a Class ofUncertain Nonlinear Systems An Application forSpeed Tracking Control of an SI Engine
Tossaporn Chamsai1 Piyoros Jirawattana2 and Thana Radpukdee1
1Department of Industrial Engineering Khon Kaen University Khon Kaen 40002 Thailand2Department of Mechanical Engineering Khon Kaen University Khon Kaen 40002 Thailand
Correspondence should be addressed toThana Radpukdee rthanakkuacth
Received 12 October 2014 Accepted 25 February 2015
Academic Editor Kacem Chehdi
Copyright copy 2015 Tossaporn Chamsai et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
The sliding mode control (SMC) technique with a first-order low-pass filter (LPF) is incorporated with a new adaptive PIDcontroller It is proposed for tracking control of an uncertain nonlinear system In the proposed control scheme the adaptationlaw is able to update the PID controller online during the control process within a short period The chattering phenomenon ofthe SMC can be alleviated by incorporation of a first-order LPF while the robustness of the control system is similar to that of thesliding mode In the closed-loop control analysis the convergence condition in the reaching phase and the existence condition ofthe slidingmode were analyzedThe stability of the closed-loop control is guaranteed in the sense of Lyapunovrsquos direct methodThesimulations and experimental applications of a speed tracking control of a spark ignition (SI) engine via electronic throttle valvecontrol architecture are provided to verify the effectiveness and the feasibility of the proposed control scheme
1 Introduction
The presence of uncertain nonlinearity in physical systemshas been extensively studied because most of the real systemsare rather complex dynamical nonlinear with large uncer-tainties which can affect inaccuracy and poor robustness ofthe control system To do this numerous control schemeshave been developed for example sliding mode control [1ndash3] intelligent control [4 5] feedback linearization [6] andadaptive control [7ndash9]
On the other hand due to its simplicity in architec-ture and simple design the proportional-integral-derivative(PID) control is acceptable and has been extensively appliedin many practical applications The key for designing a highcapability of PID controller depends on the determination ofthe PID gain parameters which should be properly adjustedand this has led to the developments for self-tuning methodsof the three parameters of the PID controller Recentlyadaptive control techniques are generally applied for online-tuning of the PID controller The flexibility of the PID tuning
lies in the determination of the basic PID gains that canbe adjusted online according to adaptation laws and usingthe error signal in order to realize the online adjustablegains during a control procedure [10ndash13] However theadaptive control strategy is capable of handling only constantparametric uncertainty inadequate robustness for againstexternal disturbance and an accurate system model that isrequired [14]
The sliding mode control (SMC) method is one of thecontrol strategies to dominate the parametric uncertaintiesand external disturbances while the control principle iswithout precise system model information [15ndash18] Nev-ertheless if the sliding mode exists the chattering phe-nomenon is the main obstacle for SMC application [19ndash21]In much research work alleviations chattering phenomenonof the sliding mode incorporated with a low-pass filter hasbeen studied [22ndash26] because it can make a compromisebetween the alleviation of the chattering and the controlaccuracy Incorporation of the SMCwith closed-loop filteringis capable to realize the acquisition of control signal and
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 510738 12 pageshttpdxdoiorg1011552015510738
2 Mathematical Problems in Engineering
the approximation of disturbances [24] while the robustnessis similar to that of the sliding mode
In this study the SMC with a first-order LPF is incor-porated with a new adaptive PID controller It is proposedfor perfect tracking control tasks of uncertain nonlinearsystems In the proposed control scheme the PID controlleris adjusted during the control procedure according to theadaptation laws while the chattering of the control signal canbe alleviated by the first-order LPFThe stability of the closed-loop control can be guaranteed in the sense of Lyapunovrsquosdirect method [27 28] The effectiveness and the feasibilityof the proposed control scheme are assessed in the problemof a speed tracking control of a spark ignition (SI) enginevia electronic throttle valve control architecture Interest isdue to the delay of the intake manifold filling dynamic andthe induction-power delay is the drawback in practice forengine speed control through the throttle valve regulationmethod [29 30] Furthermore the engine system is a rathercomplex mechanism multiactuation and largely uncertainnonlinearity phenomena which are present in the enginemechanism [31] Therefore the engine speed control is awell-known challenge in the problem of uncertain nonlinearcontrol systems [32ndash34]
Increasing transient performance and tracking accuracyof speed responses are usefulness during acceleration of thevehicle at any operating condition especially in the transitionmode of the hybrid operating system of hybrid vehicles [3536] The goal of the engine speed control resulting from thespeed response is to be able to track a desired speed at anyoperating condition [37] especially at the transient-state thathas significant effects on optimizing the maneuverability ofan engine speed control High accuracy of speed trackingcontrol leads to the achievement of an optimal engineoperating point for other applications In addition increasedengine performance reduced fuel consumption and exhaustemission are other benefits of an optimized engine speedcontrol [38 39]
The remainder of this paper is organized as followsFirstly we present the controller design and closed-loop con-trol analysis In Section 3 a description of the engine speedcontrol model is presented In Section 4 the simulations andexperimental results are presented to verify the effectivenessof the development control approach Finally the researchconclusions are presented
2 Controller Design andClosed-Loop Control Analysis
21 System Formulation In an engine system the two first-order dynamic elements which are rotational dynamics andthe manifold filling dynamics behave as a second-ordersystem [40] However the system order can be reduced due tosubstitution of the engine torque as described by the mean-value method [41] into the first-order crankshaft rotationaldynamics from Newtonrsquos law Thus for simplicity this workrealizes the system to be a first-order uncertain nonlinear
system satisfying uncoupling and matching conditions [2840] It can be described in a canonical form as
x (119905) = f (X 119905) + B (X 119905) u (119905) + B (X 119905) 120578 (X 119905)
x (1199050) = x0
(1)
where x = [
1
2
119898]
119879isin 119877
119898 is the first-order of thestate vector 119905 isin 119877 is time f(X 119905) = [119891
1 119891
119898]
119879isin 119877
119898 isthe known nonlinear function X = [119909
1 119909
119898]
119879isin 119877
119898 isthe global state vector for the nonlinear square system 119898 isthe number of independent coordinates of 119909
119894 119894 = 1 119898
u(119905) = [119906
1 119906
119898]
119879isin 119877
119898 is the control input 120578(X 119905) =
[120578
1 120578
119898]
119879isin 119877
119898 is the uncertain element that presents onlyin the highest order of the system andB(X 119905) = [119887
119894119895] isin 119877
119898times119898119894 119895 = 1 119898 is the control gain distribution matrix whichis positive definite in all arguments The aim is to force thesystem state x to reach the desired state x
119889so that the error
119909
119894= 119909
119894minus 119909
119894119889rarr 0 119894 = 1 119898 Not only does a control law
have to steer the response to the desired value but it musthave the ability to overcome a systemrsquos uncertainties also
In the work of Xu et al [24] uncertainties can beestimated by adding a second low-pass filter as a result theswitching gain is reduced to theminimum level while the firstlow-pass filter smooths out the switching control Howeverduring the filterrsquos reaching phase there are no control inputsfrom both low-pass filters and a feed forward term from anequivalent control may not have the capability to override theuncertainties If another control input during the reachingphase can be adjusted suitably better transient control canbe achievedThe assumptions below are made for control lawderivation in the next section
Assumption 1 The functions f(X 119905) B(X 119905) and 120578(X 119905) arecontinuous in X for all 119905 and continuously differentiable
Assumption 2 The uncertainties are within the range spaceof the control distribution matrix B(X 119905) and uncertaintyvariation does not affect the control direction
Assumption 3 The estimated control distribution matrixB(X 119905) is invertible and continuously dependent on paramet-ric uncertainty [28]
Assumption 4 Let B(X 119905)120578(X 119905) be upper bounded byB(X 119905)120578(X 119905) le 119872
119900and 119889(B(X 119905)120578(X 119905))119889119905 upper
bounded by 119889(B(X 119905)120578(X 119905))119889119905 le 119872
119889 where119872
119900and119872
119889
are known constants
Assumption 5 The input matrix is bounded by 0 lt 119887min le
B(X 119905) le 119887max and its derivative is upper bounded by119889(B(X 119905))119889119905 le 119887
119889 where 119887min 119887max and 119887
119889are known
constants
22 Closed-Loop Control Design To design the control law adefinition of the sliding function similar to thework of Slotineand Li [28] is adapted to the first-order system The slidingfunction can be made on each state as
119904
119894119905(119909
119894(119905)) = 119909
119894 119894 = 1 119898 (2)
Mathematical Problems in Engineering 3
SMC LPF
PlantPIDcontroller
Adaptationlaws
Adaptive PID control
+
+
+ x
+
f
usgn uL
uPIDxd minus
minus
minus
d(middot)dt
Bminus1
119854ap = minus119839 + 119857d
Figure 1 A schematic diagram of the proposed controller (LPFSMC and Adaptive PID technique)
Then the 119898-dimensional sliding function and its firstderivative for the system in (1) can be expressed as
s119905(x) = x minus x
119889
s119905(x) = C (x minus x
119889)
(3)
where s119905(x) = [119904
1119905 119904
119898119905]
119879 has components satisfying thesliding function stated earlier and C is a positive constantcoefficient119898times119898matrix with full row rank Its argument is agradient vector of the sliding function [42] which is unity ineach sliding surface due to the first-order system
From Figure 1 the control input is
u (119905) = Bminus1 [uap minus (uPID minus u119871)] (4)
where u119871is the low-frequency pass filter signal which is
a result of a first-order low-pass filter of the switchingsignal usgn = minusM
119904sgn(s) sgn(119904
119894) =
+1 if 119904119894gt0minus1 if 119904119894lt0
Let M119904=
diag(119872119900|119904
119894119905|) sgn(s) = [sgn(119904
1) sgn(119904
119898)]
119879 and uPIDdenote the control signal of the adaptive PID tuning uap isan approximation of the control input that neglects the lastterm of the RHS of (1) and is the unit matrix Thereforean approximation can be obtained similar to the idea of theequivalent control input [15] which is
uap = minusf + x119889 (5)
For the solution of u119871 it can be obtained by
119879
119891u119871+ u119871= usgn (6)
where 119879119891is the cut-off frequency The LPF is activated at the
time of 119905 = 119905reach with the zero initial condition of u119871(119905reach) =0 and given 119905reach is the reaching time For uPID it can beobtained by
uPID = k119875s + k119868int s 119889119905 + k
119863s (7)
where k119875= diag(119896
119875119894) is the proportional gain k
119868= diag(119896
119868119894)
is the integral gain and k119863= diag(119896
119863119894) is the derivative gain
119896
119875119894 119896119868119894 and 119896
119863119894isin 119877
+ which are not equal to zero
221 Reaching Phase Analysis This section presents adescription of the reaching time calculation for the closed-loop control system by the proposed control law in (4) Forthe reaching time (119905reach) the first-order LPF will be activatedwhen 119905 = 119905reach with zero initial condition of the filter inputsignal Consequently u
119871(119905reach) = 0 for 0 le 119905 le 119905reach
Therefore the control input during the reaching phase isobtained by
u = Bminus1 [uap minus uPID] (8)
Note that Assumption 5 can be extended to the gainmargin concept [28] for adaptation law derivation Forstability in the reaching phase Lyapunovrsquos theorem is chosento prove the stability of the controller and the errors canconverge to the sliding surface if u is constructed to achievethe first derivative of the Lyapunov function candidate V lt 0Choose the Lyapunov function candidate ofV gt 0ThereforeV at the reaching phase can be described as
V =
1
2
s119879s + 1
2
(k119879119875k119875+ k119879119868k119868+ k119879119863k119863) (9)
Then the derivative of the Lyapunov function (9) can berewritten as
V = s119879 s + (k119879119875k119875+ k119879119868k119868+ k119879119863k119863) (10)
To find the condition satisfying the Lyapunov stability thefirst derivative of the sliding function s must be substitutedinto (10) It can be derived by
s = C (x minus x119889)
= Cf + CB120578 minus Cx119889+ CBBminus1 (minusf + x
119889minus uPID)
= (Cf + CB120578 minus CBBminus1f) + x119889(CBBminus1 minus C)
minus CBBminus1k119875s minus CBBminus1uID
(11)
4 Mathematical Problems in Engineering
where uID = k119868int s 119889119905 + k
119863s Equation (11) shows the
fact that the control gain cannot be determined exactlyIn the following the gain margins concept [28] is adaptedwithout loss of generality due to the uncoupling andmatchingconditions From the concept the gain estimation can bedescribed by B = diag(119887) 119887 = radic119887min sdot 119887max and the boundof the control gain ratio can then be realized in the form120573
minus1le
BBminus1 le 120573 while 120573 = radic119887max119887min and the initialvalue in each argument of the three gains (k
119875 k119868 and k
119863) of
the PID portion is positive Substituting (11) into (10) yields
V = s119879 [(Cf + CB120578 minus CBBminus1f) + x119889(CBBminus1 minus C)]
minus s119879CBBminus1k119875s minus s119879CBBminus1uID + G
(12)
where G = (k119879119875k119875+ k119879119868k119868+ k119879119863k119863) which is the adaptation
term For (12) if k119875is chosen to overcome a part of the
uncertainties the adaptation law in the last term G can bedetermined to eliminate the rest of them consequently Inorder to compensate for the uncertainties in the reachingphase the proportional gain 119896
119875119894should satisfy equations
below1003817
1003817
1003817
1003817
k119875
1003817
1003817
1003817
1003817
ge
1003817
1003817
1003817
1003817
1003817
(
BBminus1f + BBminus1B120578 minus f) + (1 minus BBminus1) x119889
1003817
1003817
1003817
1003817
1003817
(13)
Then all arguments in the proportional gain are selectedto satisfy
119896
119875119894ge
1003816
1003816
1003816
1003816
120573119872
119900+ (1 minus 120573) (minus119891
119894+
119894119889)
1003816
1003816
1003816
1003816
(14)
119896
119875119894ge
1003816
1003816
1003816
1003816
120573119872
119900
1003816
1003816
1003816
1003816
+
1003816
1003816
1003816
1003816
1003816
(1 minus 120573) 119906
119894ap1003816
1003816
1003816
1003816
1003816
(15)
Equations (13) to (15) correspond to the gain margincalculationmethod [28] Even if the proportional term can bedesigned to cope with the first term in (12) its residual errorstill exists Let the residual error be the difference betweenthe first term and the second term of (12) It is bounded by apositive valueΔ = s119879[(Cf+CB120578minusCBBminus1f)+C(BBminus1minus1)x
119889]minus
s119879CBBminus1k119875s due to a bounded control input By adding the
bound of the control gain ratio (12) can be rewritten as
V le minusΔs119879s minus s119879CBBminus1k119868int s 119889119905 minus s119879CBBminus1k
119863s
+ k119879119875k119875+ k119879119868k119868+ k119879119863k119863
le minusΔs119879s minus 120573s119879Ck119868int s 119889119905 minus 120573s119879Ck
119863s
+ k119879119875k119875+ k119879119868k119868+ k119879119863k119863
(16)
Obviously to satisfy the Lyapunov stability of the condi-tion V lt 0 and the adaptation law can be designed as k
119875= 0
k119868= 120573s119879Cint s 119889119905 and k
119863= 120573s119879C s Note that the proportional
gain has a coupling effectwith the sliding gainwhich operateswith the unity boundary layer width Therefore k
119875does not
need to be updated online The adaptation gains ( k119868and
k119863) are capable of guaranteeing the stability only outside
the bound of the control gain ratio 120573 This implies thatthis technique only offers a uniform ultimate boundedness
response Additionally it is usual to have a solution when thecontrol gain magnitude is unknown Even if the control gainis known or adapted the ultimate boundedness still occursinside the vicinity around the sliding surface Notice thatat the beginning state the integral and the derivative termsof the adaptation law may be arbitrary small because theuncertainties at the beginning state can be compensated byk119875 Consequently (16) can be replaced by the adaptation law
and the new expression of (16) becomes
V le minusΔs119879s (17)
With the positive-initial value of the PID gains and thecondition of (15) and the adaptation laws the stability withinthe reaching phase can be guaranteed The reaching time(119905reach) can be obtained by
119905reach le
1003817
1003817
1003817
1003817
s(119905=0)
1003817
1003817
1003817
1003817
Δ
(18)
222 Existence of the Sliding Condition The key issue of thissection is to describe the sliding mode retention For theexistence conditions of the sliding mode at 119905 ge 119905reach thefirst-order low-pass filter (LPF) is activated and the switchingsignal is alleviated in turn To describe the existence of thesliding condition substitute the control law u(119905) = Bminus1[uap minus(uPID minus u
119871)] Therefore the derivative of the closed-loop s
dynamic at 119905 ge 119905reach can be obtained by
s = (Cf + CB120578 minus CBBminus1f) + C (BBminus1 minus 1) x119889
minus CBBminus1k119875s minus CBBminus1uID + CBBminus1u
119871
(19)
With the condition in (15) (19) can be rearranged as
minusCBBminus1k119875s = s minus (Cf + CB120578 minus CBBminus1f)
minus C (BBminus1 minus 1) x119889+ CBBminus1uID minus CBBminus1u
119871
(20)
Multiplying (20) by (CBBminus1)minus1 yields
minusk119875s = BBminus1
sdot [Cminus1 s minus (f + B120578 minus BBminus1f) minus (BBminus1 minus 1) x119889
+BBminus1uID minus BBminus1u119871]
(21)
From the condition in (15) the sliding gain can bechanged to beM
119904= diag(119896
119875119894|119904
119894119905|) and the output from the LPF
can be satisfied by 119879119891u119871+ u119871= minus diag(119896
119875119894|119904
119894119905|)sgn(s) = minusk
119875s
Therefore
119879
119891u119871+ 2u119871
=
BBminus1
sdot[Cminus1 s minus (f + B120578minusBBminus1f)minus(BBminus1 minus 1) x119889+BBminus1uID]
(22)
Mathematical Problems in Engineering 5
As the reaching phase analysis the control law in (8) andits adaptation law offer convergence regulation of the stateIntuitively the sliding function s is bounded about the slidingsurface s= 0 due to imperfection of control action in practiceThus the derivative of the sliding function s will be boundedby the boundedness of s which also implies the integralof s converges to some limit [43] Consequently the RHS of(22) can be bounded and is rewritten by a residual matrix0 = [0
1 0
119898]
119879isin 119877
119898 For each argument of the u119871 the
residual function 0119894 119894 = 1 sdot sdot sdot 119898 can be interpreted as residual
errors after the reaching phase which satisfy
119879
119891
119871119894+ 2119906
119871119894= 0
119894 (23)
Given 120574 = 2119879
119891and 120593
119894= 0
119894119879
119891 (23) is rewritten as
119871119894+ 120574119906
119871119894= 120593
119894 (24)
From (24) the bound on 120593
119894can be interpreted into a
bound on the filter output 119906119871119894 Define the bound of 120593
119894= Φ
119894
The bound of the filter output |119906119871119894| can be written as (25)
which corresponds to [28]
1003816
1003816
1003816
1003816
119906
119871119894(119905)
1003816
1003816
1003816
1003816
le (
Φ
119894
120574
) (1 minus 119890
minus120574119905) (25)
In which 119906119871119894(119905)
tends to Φ119894120574 [28] when 119905 rarr infin Thus
1003816
1003816
1003816
1003816
119906
119871119894(119905)
1003816
1003816
1003816
1003816
le
Φ
119894
120574
(26)
Consider (26) if 119879119891
and 120573 are known the residualuncertainties from the reaching phase can be compensatedby u119871 To consider the stability of the control system by using
the input according to (4) (12) can be rewritten as
V = s119879 [(Cf + CB120578 minus CBBminus1f) + C (BBminus1 minus 1) x119889]
minus s119879CBBminus1k119875s minus s119879CBBminus1uID minus s119879CBBminus1u
119871+ G
(27)
Notice that the adding of the u119871leads to uncertain of
negative definite on the Lyapunov function derivative Inorder to stabilize (27) the proportional portion has to takethe output from the LPF and the bound of uncertainty and itsderivative into account By defining119872
119905= 119872
0+ 119872
119889+ u119871
themodified proportional gain for each sliding surface can be119896
119875119894ge |120573119872
119905| + |(1 minus 120573)119906
119894ap| And together with the adaptationlaws defined in the previous section V in (27) is negativedefinite (
119881 lt 0) The sliding motion can be guaranteed for119905 isin [119905reachinfin) under the conditions stated earlier
3 Description of the Engine SpeedControl Modeling
As stated earlier a key step of the development controlscheme is based on the robust control techniques inwhich theapproach has the ability to neglect the conservatism and theneed for precise modeling [44] In addition the development
of an exact model for a real engine system is difficultbecause some parameters in the mathematical model cannotbe obtained exactly and the real plant is affected by thecomplexity of its uncertain nonlinearity [45] Consequentlythe system modeling in this work was linearized through thenominal transfer function of the real plant as the form of
119909 (119904) = 119866ta (119904) 119890minus119879119863119904
119906ta (119904) + 119866sa (119904) 119890minus119879119863119904
119906sa (119904) (28)
where 119909(119904) is the output the time delay is 119879119863 119906ta(119904) is the
control input for a throttle actuator and 119906sa(119904) is the controlinput for the spark advance system 119866ta(119904) and 119866sa(119904) are thelinearized models by 119906ta(119904) and 119906sa(119904) respectively Note thatthe symbol 119904 in this section denotes the complex argument ofthe Laplace transform which is not the sliding function
Although the conventional relevant engine dynamic forengine speed control depends on the coordination betweenthe throttle actuator and the spark advance system for theassessment in this work we have designed a controller thataims to control only the throttle actuator while the sparkadvance system is handled by conventional controller of theengine system Therefore the system modeling in this workcan be obtained by an adjustment of the throttle openingposition in degrees which is directly controlled with a DCmotor that is excited by the feed-forward control signalin DC-voltage as an input and the crankshaft speed inrevolutions perminute (rpm) as an output Consequently thelinearizationmodel at speed 900 rpm can be approximated inthe transfer function form as
119866 (119904) =
45119904
2+ 44119904 + 90
119904
3+ 15119904
2+ 25119904 + 1
(29)
where 119866(119904) is the transfer function of the real plant whichhas units of revolutions per minute (rpm) From the roughidentifications of (29) it is the third-order with relativedegree one and the system is BIBO stable because all polesare located on the left-hand side (LHS) of the 119904-plane Inaddition for the reason of low-speed control test (900 rpm)it is sensitive to any uncertain nonlinearities and externaldisturbancesTherefore the implementation of speed controlin the low-speed region is more difficult than in the high-speed control region Furthermore on average 30 percentof fuel consumption in urban city driving is spent at theidle speed range [46] As a consequence increasing theperformance of the low-speed control is able to increase fueleconomy and performance of the engine operation at anyoperating condition [32]
For simplicity to make the engine speed response asthe canonical form of (1) the rough identification model of(29) can be simplified to the first-order transfer function asfollows
119866 (119904) =
445
119904 + 0493
(30)
To make clear the acceptability of (30) the bode plotand the step response comparison between (29) and (30) aredemonstrated in Figure 2 The results make clear that thefirst-order transfer function in (30) can be employed in theperformance assessment of the proposed controller design in
6 Mathematical Problems in Engineering
0 2 4 6 8 10 120
102030405060708090
100Step response
Time (s)
Am
plitu
de
3rd order1st order
10152025303540
minus90
minus45
0
Frequency (rads)
Bode diagram
Mag
nitu
de (d
B)Ph
ase (
deg)
10minus2
10minus1
100
101
Frequency (rads)10
minus210
minus110
010
1
Figure 2 The validation of the 1st-order model
the simulations and (30) can be expressed as the time-domaindifferential equation as follows
= minus0493119909 + 445119906 (31)
where 119909 is the speed output and 119906 is the input
4 Illustrative Examples
41 Simulation Verification For the simulation verificationthe system modeling of (31) is used in order to assess theperformance of the proposed control scheme (LPFSMC andAdaptive PID) that is performed viaMATLAB-Simulink pro-gramming with a sampling period of 1ms The performanceof the proposed controller is compared with different controltechniques which are the PID control technique and the SMCtechnique The specific control parameters are chosen suchthat the sliding gain of the proposed control scheme and theconventional SMC is M
119905= 10 the cut-off frequency of the
first-order LPF is119879119891= 4 while the setting control parameters
of the PID controller are obtained by the Ziegler-Nicholstuning method
Figure 3(a) demonstrates the response results of theproposed control scheme which has a small rise time andsetting time and higher tracking accuracy than other controltechniques (PID controller and SMC) It demonstrates thatthe proposed adaptation law is capable of updating the PID
controller online during the control process within a shortperiod Furthermore the proposed control scheme can pro-vide optimal control input rapidly and has smooth controlinput which is achieved by the cut-off frequency property ofthe LPF (see Figure 3(b))
Figure 3(c) shows the error comparison among the dif-ferent controllers as the results the errors from the pro-posed control scheme can approach zero faster than othercontrol techniques and it has lower chattering than the SMCtechnique Note that although the chattering of the outputresponse control input and the errors of the PID controllerdoes not appear the results (see Figure 3) reveal that itsresponse has higher rise-time high-overshoot and longersetting time which are not satisfactory from the viewpointof a control system
42 Practical Experiment In this section we demonstrate theefficiency of the proposed control scheme in the real systemThe experimental technical data are shown in Table 1 In oursetup the functional block diagrams of the apparatus used inthe experiments are illustrated in Figure 4 which is used forperformance assessment of the proposed control schemeThesystem in Figure 4 consists of five main parts which are thecontroller unit electronic throttle valve control unit (ETC)spark-ignition (SI) engine system the power train system
Mathematical Problems in Engineering 7
Time (s)
Spee
d re
spon
se (r
pm)
ZOOM
Time (s)
Spee
d re
spon
se(r
pm)
SMCLPFSMC and adaptive PIDDesiredPID
0200400600800
10001200140016001800
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 208998995
9009005
901
(a)
Time (s)
Con
trol i
nput
(V)
SMC LPFSMC and adaptive PIDPID
minus30minus25minus20minus15minus10minus5
05
101520
2 4 6 8 10 12 14 16 18 200
(b)
Erro
rs
SMC LPFSMC and adaptive PIDPID
Time (s)
Erro
rs
ZOOM
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus1000minus800minus600minus400minus200
0200400600800
005
1
minus05minus1
0 2 4 6 8 10 12 14 16 18 20
(c)
Figure 3 Comparison of simulation results among different control techniques (a) the output response (b) the control inputs (c) the errors
PWM M
DC motor
Gear box
Throttle opening sensor
Throttle body
Control system
Electronic throttle control unit
SI engine
ADCDAC
Amplifier
Air
Speed calculation
Throttle position calculation
Fuel consumptioncomputation
Emission data logger(HC CO)
Speed sensor
Fuel flow sensor
Emission sensor
Power trainsystem
Dynamometer
Figure 4 Schematic diagram of the experiment
8 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
DesiredLPFSMC and adaptive PID
Con
trol i
nput
(V)
Time (s)
Slid
ing
varia
ble (
s)
Time (s)
Thro
ttle v
alve
ope
ning
(deg
)
Time (s)
0 20 40 60 80 100 120 140 160 180 200600650700750800850900950
1000
0
01
02
03
04
05
06
0 20 40 60 80 100 120 140 160 180 200
minus200minus150minus100minus50
050
100150200
0 20 40 60 80 100 120 140 160 180 200012345678
0 20 40 60 80 100 120 140 160 180 200
Figure 5 Experimental results of the proposed controller (LPFSMC and Adaptive PID technique)
Table 1 Experimental technical data
Item ValueSI engine (4 cylinders 900 ccgasoline type) Test range 600ndash3000 rpm
Speed sensor (rpm) Sampling speed approximately5000 ts
Throttle position sensor Measurement range 0ndash80∘
ADCDAC minus10 to 10VDC 20mA
COMPUTER Core2Duo 293GHz 4GBRAM
DCmotor 48ndash6VFuel type (experiments) Ethanol-gasoline blended (E20)
and the dynamometer which is used to generate the load-torque into the systemThe engine speed is interpreted as thecrankshaft rotation rate in revolutions per minute (rpm) andis regulated by opening the throttle In this task the throttlevalve is directly actuated by a DCmotor in which the angularmovement is handled by the control signal in the form ofPulseWidth Modulation (PWM)The exhaust emissions COandHCwere alsomeasured through a nondispersive infraredanalysis machine (Infralyt smart) in which the acquiringsampling data is 1 s while the fuel consumptionwasmeasuredby the fuel flow sensor (Hall effect-800 series) with thesampling period is 1ms The computation unit is performedwith MATLAB-Simulink programming An ADCDAC isused as an interface systembetween the computer and the realplant while the sampling period is 1ms for all experiments
As seen in Figure 5 the desired speed is chosen to rapidchange from 750 rpm to 900 rpm and 900 rpm to 750 rpmand the experiments were performed for 200 s This resultreveals that the speed response of the proposed controlscheme can reach the desired speedwithin short time and hasno overshoot and tiny oscillationThe control input is smoothand reaches an optimal value within a short time and thesliding variable can approach zero rapidly Fast convergenceof the response is a result of the updated control gains (119870
119868
and 119870119863) of the PID controller which can be adjusted rapidly
during the control process according to the adaptive lawFurthermore the characteristic of the opening position of thethrottle valve was alsomeasuredThis reveals that themotionof the actuator has smooth and tiny oscillations
43 Tracking Performance and Disturbance Rejection TestThe robust properties and the tracking performance of theproposed control schemewere also assessed because it is wellknown that the engine speed control is affected by the stateof accessory changes such as external load disturbance [41]In the experiments we compare the disturbance rejectionperformance among the proposed controller SMC techniqueand PID controller The load disturbance is generated bythe dynamometer while the speed set-point is chosen to be900 rpm Note that for the reason of low-speed test it issensitive from any disturbances therefore the implementa-tion in the low-speed region is more difficult than the high-speed control task Furthermore high performance of low-speed control leads to increase the performance of the engineoperation at any operating condition [32]
Mathematical Problems in Engineering 9
Time (s)Lo
ad (W
)
75
225
Engi
ne sp
eed
(rpm
)
DesiredLPFSMC and adaptive PID
PIDSMC
15
30
0
1000
950
900
850
800
Time (s)
120 125 130 135 140 145 150 155 160
120 125 130 135 140 145 150 155 160
Figure 6 Comparisons of tracking performance and disturbance rejection of the controllers
As seen in Figure 6 at the time 125 sec the load torquewas applied immediately into the engine speed control taskThis proposed to disturb the stability of the control system atthe steady-state condition The proposed control scheme canimprove the speed deviation rapidly and is capable of trackingthe desired speed better than other control techniques Inaddition the load torque was decreased immediately at thetime 150 sec The results show that the proposed controlscheme can decrease the speed deviation from the desiredspeed faster than other control techniques The findingsreveal that the proposed control scheme has effective ofthe robustness and fast adaptation and has better trackingperformance than other control techniques
44 Fuel Consumption andExhaust Emission Investigation Inthis section the fuel consumption and the exhaust emissionof the engine speed control by using the proposed controlscheme and different control techniques (SMC techniqueand PID controller) were investigated (see Figure 7) In theexperiments the desired speed was performed for 400 secand was rapidly changed as shown in Figure 7(a) For theaverage total fuel consumption comparison (see Figure 7(b))the proposed control scheme can attain an excellent resultwith the lowest averaged total fuel consumption whichwas obtained by the average of the fuel consumptions persecond
In addition the average exhaust emissions were alsoinvestigated (see Figure 7(c)) The CO and HC emissions arethe main pollutants contributed by the SI engines In theprinciple of the combustion process of SI engine the HCemission is appeared when fuel molecules in the engine
cannot burn or burn only partially while the CO emissionis produced when the carbon in the fuel is partially oxi-dized rather than fully oxidized to carbon dioxide Howeverincreasing efficient strategies for engine speed control viathrottle valve regulation method is capable of increasingcombustion performance as it can reduce pollutant emissionsalso [38] In the experiments effects of the controllers wereinvestigated via the constant speed set points and no addingan external engine load (small load from the unloadedhydrostatic CVT)Thus the CO
2andNO
119909which are sensitive
to speed variation and high temperature operation did notmeasure in this work (the experiments perform at coolanttemperature of 70ndash80∘C for short period) As a result bothaverages of the CO and HC emission data were calculatedby the average of emissions per second in which obtainedby the direct measurement method [43] Additionally theseresults demonstrate that high fuel consumption and exhaustemission are affected by high variation of the engine speedduring tracking of the set pointsThese results also imply thatthe performance of the SI engine at any operating conditioncan be improved by an advanced engine speed control viathe electronic throttle valve regulation method as shown inFigure 7
5 Conclusions
The incorporation of the SMC and a first-order LPF witha new adaptive PID controller is proposed for trackingthe control task of an uncertain nonlinear system Thecontroller has been successfully applied to the problem ofthe speed tracking control of an SI engine through electronic
10 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
PIDSMC
LPFSMC and adaptive PIDDesired
0 50 100 150 200 250 300 350 4000
500
1000
1500
2000
2500
(a)
00689
0071
00694
006750068
006850069
00695007
007050071
00715
LPFSMC andadaptive PID
SMC PID
Fuel consumption (Lmin)
(b)
20288 41113 20302
105977
425503
109623
0500
10001500200025003000350040004500
LPFSMC andadaptive PID
SMC PID
HC (ppm)CO (ppm)
(c)
Figure 7 Comparisons of (a) tracking performance of the controllers (b) fuel consumption rates (c) exhaust emission rates
throttle valve control architecture From the simulation andexperimental results it achieves that
(1) the proposed adaptation law is capable of optimalonline update the PID controller during the controlprocess within a short period
(2) the chattering of the SMC can be alleviated by afirst-order low pass filter while the robustness of thecontrol system similar to that of the slidingmode suchthat the load torque disturbances can be compensatedquite accurately
(3) the proposed control scheme has high performancein implementation as it can be achieved in theproblem of engine speed control in which the systemis largely uncertain nonlinear system and rathercomplex mechanisms
Conflict of Interests
The authors have no competing interests
Acknowledgment
This research is financially supported by the Office ofResearch Administration (ORA) and Farm Engineering andAutomation Technology Research Group (FEAT) of Khon
Kaen University Thailand The authors are also thankfulto the reviewers and Mr Ian Thomas for their valuablecomments and suggestions for English grammar correctionrespectively
References
[1] K-C Hsu W-Y Wang and P-Z Lin ldquoSliding mode controlfor uncertain nonlinear systemswithmultiple inputs containingsector nonlinearities and deadzonesrdquo IEEE Transactions onSystems Man and Cybernetics Part B Cybernetics vol 34 no1 pp 374ndash380 2004
[2] G Bartolini and A Ferrara ldquoMulti-input sliding mode controlof a class of uncertain nonlinear systemsrdquo IEEE Transactions onAutomatic Control vol 41 no 11 pp 1662ndash1666 1996
[3] T-C Kuo Y-J Huang and S-H Chang ldquoSliding mode controlwith self-tuning law for uncertain nonlinear systemsrdquo ISATransactions vol 47 no 2 pp 171ndash178 2008
[4] G Montaseri and M J Yazdanpanah ldquoPredictive control ofuncertain nonlinear parabolic PDE systems using a Galerkinneural-network-based modelrdquo Communications in NonlinearScience and Numerical Simulation vol 17 no 1 pp 388ndash4042012
[5] F O Tellez A G Loukianov E N Sanchez and E Jose BayroCorrochano ldquoDecentralized neural identification and controlfor uncertain nonlinear systems application to planar robotrdquoJournal of the Franklin Institute vol 347 no 6 pp 1015ndash10342010
Mathematical Problems in Engineering 11
[6] A Bazaei and V J Majd ldquoFeedback linearization of discrete-time nonlinear uncertain plants via first-principles-based serialneuro-gray-box modelsrdquo Journal of Process Control vol 13 no8 pp 819ndash830 2003
[7] T-Y Kuc and W-G Han ldquoAn adaptive PID learning controlof robot manipulatorsrdquo Automatica vol 36 no 5 pp 717ndash7252000
[8] Y Pan Y Zhou T Sun and M J Er ldquoComposite adaptivefuzzy 119867
infintracking control of uncertain nonlinear systemsrdquo
Neurocomputing vol 99 pp 15ndash24 2013[9] X Liu R Tao and M Tavakoli ldquoAdaptive control of uncertain
nonlinear teleoperation systemsrdquo Mechatronics vol 24 no 1pp 66ndash78 2014
[10] W-D Chang and J-J Yan ldquoAdaptive robust PID controllerdesign based on a sliding mode for uncertain chaotic systemsrdquoChaos Solitons amp Fractals vol 26 no 1 pp 167ndash175 2005
[11] T C Kuo Y J Huang C Y Chen and C H Chang ldquoAdaptivesliding mode control with PID tuning for uncertain systemrdquoEngineering Letters vol 16 no 3 pp 1ndash5 2008
[12] M N Howell and M C Best ldquoOn-line PID tuning forengine idle-speed control using continuous action reinforce-ment learning automatardquo Control Engineering Practice vol 8no 2 pp 147ndash154 2000
[13] C-F Hsu and B-K Lee ldquoFPGA-based adaptive PID control ofa DC motor driver via sliding-mode approachrdquo Expert Systemswith Applications vol 38 no 9 pp 11866ndash11872 2011
[14] DWMemering and PHMeckl ldquoComparison of adaptive con-trol techniques applied to diesel engine idle speed regulationrdquoJournal of Dynamic Systems Measurement and Control vol 124no 4 pp 682ndash688 2002
[15] V I Utkin ldquoSliding mode control design principles andapplications to electric drivesrdquo IEEE Transactions on IndustrialElectronics vol 40 no 1 pp 23ndash36 1993
[16] Y J Huang and T C Kuo ldquoRobust output tracking controlfor nonlinear time-varying robotic manipulatorsrdquo ElectricalEngineering vol 87 no 1 pp 47ndash55 2005
[17] M Hajatipour and M Farrokhi ldquoChattering free with noisereduction in sliding-mode observers using frequency domainanalysisrdquo Journal of Process Control vol 20 no 8 pp 912ndash9212010
[18] A Sabanovic L Fridman and S Spurgeon Variable StructureSystems From Principles to Implementation The Institution ofEngineering and Technology 2004
[19] Y Xu ldquoChattering free robust control for nonlinear systemsrdquoIEEE Transactions on Control Systems Technology vol 16 no 6pp 1352ndash1359 2008
[20] H Lee and V I Utkin ldquoChattering suppression methods insliding mode control systemsrdquo Annual Reviews in Control vol31 no 2 pp 179ndash188 2007
[21] Y Ren Z Liu L Chang and N Wen ldquoAdaptive slidingmode robust control for virtual compound-axis servo systemrdquoMathematical Problems in Engineering vol 2013 Article ID343851 9 pages 2013
[22] M-L Tseng and M-S Chen ldquoChattering reduction of slidingmode control by low-pass filtering the control signalrdquo AsianJournal of Control vol 12 no 3 pp 392ndash398 2010
[23] H Sira-RamIRez ldquoOn the dynamical sliding mode control ofnonlinear systemsrdquo International Journal of Control vol 57 no5 pp 1039ndash1061 1993
[24] J-X Xu Y-J Pan and T-H Lee ldquoSliding mode controlwith closed-loop filtering architecture for a class of nonlinear
systemsrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 51 no 4 pp 168ndash173 2004
[25] A Deenadayalan and G S Ilango ldquoPosition sensorless slidingmode observer with sigmoid function for Brushless DCmotorrdquoin Proceedings of the International Conference on Advances inPower Conversion and Energy Technologies (APCET rsquo12) pp 1ndash6IEEE August 2012
[26] Y Xia X Yu andW Oghanna ldquoAdaptive robust fast control forinduction motorsrdquo IEEE Transactions on Industrial Electronicsvol 47 no 4 pp 854ndash862 2000
[27] M Niclai Theory of Nonlinear Control Systems McGraw-Hill1969
[28] J J Slotine andW Li Applied Nonlinear Control Prentice-HallEnglewood Cliffs NJ USA 1991
[29] D Gorinevsky and L A Feldkamp ldquoRBF network feedforwardcompensation of load disturbance in idle speed controlrdquo IEEEControl Systems vol 16 no 6 pp 18ndash27 1996
[30] S Di Cairano D Yanakiev A Bemporad I V Kolmanovskyand D Hrovat ldquoModel predictive idle speed control designanalysis and experimental evaluationrdquo IEEE Transactions onControl Systems Technology vol 20 no 1 pp 84ndash97 2012
[31] P F Puleston S Spurgeon andGMonsees ldquoAutomotive enginespeed control a robust nonlinear control frameworkrdquo IEEProceedings Control Theory and Applications vol 148 no 1 pp81ndash87 2001
[32] Y Yildiz A M Annaswamy D Yanakiev and I KolmanovskyldquoSpark-ignition-engine idle speed control an adaptive controlapproachrdquo IEEE Transactions on Control Systems Technologyvol 19 no 5 pp 990ndash1002 2011
[33] A Sugeng K Baharin T Hishamuddin and J B SupriyoldquoEngine speed control using online ANN for vehicle withEMDAP-CVTrdquo Jurnal Mekanikal vol 22 pp 39ndash52 2006
[34] M K Khan K B Goh and S K Spurgeon ldquoSecond ordersliding mode control of a diesel enginerdquo Asian Journal ofControl vol 5 no 4 pp 614ndash619 2003
[35] J R Wagner D M Dawson and L Zeyu ldquoNonlinear air-to-fuel ratio and engine speed control for hybrid vehiclesrdquo IEEETransactions on Vehicular Technology vol 52 no 1 pp 184ndash1952003
[36] F Assadian S Fekri andM Hancock ldquoHybrid electric vehicleschallenges strategies for advanced engine speed controlrdquo inProceedings of the IEEE International Electric Vehicle Conference(IEVC rsquo12) March 2012
[37] A G Ulsoy H Peng and M Cakmakci Automotive ControlSystems Cambridge University Press Cambridge UK 2014
[38] C Ji and S Wang ldquoStrategies for improving the idle perfor-mance of a spark-ignited gasoline enginerdquo International Journalof Hydrogen Energy vol 37 no 4 pp 3938ndash3944 2012
[39] S Wang C Ji M Zhang and B Zhang ldquoReducing theidle speed of a spark-ignited gasoline engine with hydrogenadditionrdquo International Journal of Hydrogen Energy vol 35 no19 pp 10580ndash10588 2010
[40] DHrovat and J Sun ldquoModels and controlmethodologies for ICengine idle speed control designrdquo Control Engineering Practicevol 5 no 8 pp 1093ndash1100 1997
[41] B Alt J P Blath F Svaricek and M Schultalbers ldquoMultiplesliding surface control of idle engine speed and torque reservewith dead start assist controlrdquo IEEE Transactions on IndustrialElectronics vol 56 no 9 pp 3580ndash3592 2009
12 Mathematical Problems in Engineering
[42] T Radpukdee and P Jirawattana ldquoUncertainty learning andcompensation an application to pressure tracking of an electro-hydraulic proportional relief valverdquo Control Engineering Prac-tice vol 17 no 2 pp 291ndash301 2009
[43] P A Loannou and J Sun Robust Adaptive Control PTRPrentice-Hall 1996
[44] C D Richard and H B Robert Modern Control SystemsPrentice Hall Upper Saddle River NJ USA 2011
[45] A Jansri and P Sooraksa ldquoEnhanced model and fuzzy strategyof air to fuel ratio control for spark ignition enginesrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 922ndash9332012
[46] Z Ye ldquoModeling identification design and implementation ofnonlinear automotive idle speed control systemsmdashanoverviewrdquoIEEE Transactions on Systems Man and Cybernetics Part CApplications and Reviews vol 37 no 6 pp 1137ndash1151 2007
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
2 Mathematical Problems in Engineering
the approximation of disturbances [24] while the robustnessis similar to that of the sliding mode
In this study the SMC with a first-order LPF is incor-porated with a new adaptive PID controller It is proposedfor perfect tracking control tasks of uncertain nonlinearsystems In the proposed control scheme the PID controlleris adjusted during the control procedure according to theadaptation laws while the chattering of the control signal canbe alleviated by the first-order LPFThe stability of the closed-loop control can be guaranteed in the sense of Lyapunovrsquosdirect method [27 28] The effectiveness and the feasibilityof the proposed control scheme are assessed in the problemof a speed tracking control of a spark ignition (SI) enginevia electronic throttle valve control architecture Interest isdue to the delay of the intake manifold filling dynamic andthe induction-power delay is the drawback in practice forengine speed control through the throttle valve regulationmethod [29 30] Furthermore the engine system is a rathercomplex mechanism multiactuation and largely uncertainnonlinearity phenomena which are present in the enginemechanism [31] Therefore the engine speed control is awell-known challenge in the problem of uncertain nonlinearcontrol systems [32ndash34]
Increasing transient performance and tracking accuracyof speed responses are usefulness during acceleration of thevehicle at any operating condition especially in the transitionmode of the hybrid operating system of hybrid vehicles [3536] The goal of the engine speed control resulting from thespeed response is to be able to track a desired speed at anyoperating condition [37] especially at the transient-state thathas significant effects on optimizing the maneuverability ofan engine speed control High accuracy of speed trackingcontrol leads to the achievement of an optimal engineoperating point for other applications In addition increasedengine performance reduced fuel consumption and exhaustemission are other benefits of an optimized engine speedcontrol [38 39]
The remainder of this paper is organized as followsFirstly we present the controller design and closed-loop con-trol analysis In Section 3 a description of the engine speedcontrol model is presented In Section 4 the simulations andexperimental results are presented to verify the effectivenessof the development control approach Finally the researchconclusions are presented
2 Controller Design andClosed-Loop Control Analysis
21 System Formulation In an engine system the two first-order dynamic elements which are rotational dynamics andthe manifold filling dynamics behave as a second-ordersystem [40] However the system order can be reduced due tosubstitution of the engine torque as described by the mean-value method [41] into the first-order crankshaft rotationaldynamics from Newtonrsquos law Thus for simplicity this workrealizes the system to be a first-order uncertain nonlinear
system satisfying uncoupling and matching conditions [2840] It can be described in a canonical form as
x (119905) = f (X 119905) + B (X 119905) u (119905) + B (X 119905) 120578 (X 119905)
x (1199050) = x0
(1)
where x = [
1
2
119898]
119879isin 119877
119898 is the first-order of thestate vector 119905 isin 119877 is time f(X 119905) = [119891
1 119891
119898]
119879isin 119877
119898 isthe known nonlinear function X = [119909
1 119909
119898]
119879isin 119877
119898 isthe global state vector for the nonlinear square system 119898 isthe number of independent coordinates of 119909
119894 119894 = 1 119898
u(119905) = [119906
1 119906
119898]
119879isin 119877
119898 is the control input 120578(X 119905) =
[120578
1 120578
119898]
119879isin 119877
119898 is the uncertain element that presents onlyin the highest order of the system andB(X 119905) = [119887
119894119895] isin 119877
119898times119898119894 119895 = 1 119898 is the control gain distribution matrix whichis positive definite in all arguments The aim is to force thesystem state x to reach the desired state x
119889so that the error
119909
119894= 119909
119894minus 119909
119894119889rarr 0 119894 = 1 119898 Not only does a control law
have to steer the response to the desired value but it musthave the ability to overcome a systemrsquos uncertainties also
In the work of Xu et al [24] uncertainties can beestimated by adding a second low-pass filter as a result theswitching gain is reduced to theminimum level while the firstlow-pass filter smooths out the switching control Howeverduring the filterrsquos reaching phase there are no control inputsfrom both low-pass filters and a feed forward term from anequivalent control may not have the capability to override theuncertainties If another control input during the reachingphase can be adjusted suitably better transient control canbe achievedThe assumptions below are made for control lawderivation in the next section
Assumption 1 The functions f(X 119905) B(X 119905) and 120578(X 119905) arecontinuous in X for all 119905 and continuously differentiable
Assumption 2 The uncertainties are within the range spaceof the control distribution matrix B(X 119905) and uncertaintyvariation does not affect the control direction
Assumption 3 The estimated control distribution matrixB(X 119905) is invertible and continuously dependent on paramet-ric uncertainty [28]
Assumption 4 Let B(X 119905)120578(X 119905) be upper bounded byB(X 119905)120578(X 119905) le 119872
119900and 119889(B(X 119905)120578(X 119905))119889119905 upper
bounded by 119889(B(X 119905)120578(X 119905))119889119905 le 119872
119889 where119872
119900and119872
119889
are known constants
Assumption 5 The input matrix is bounded by 0 lt 119887min le
B(X 119905) le 119887max and its derivative is upper bounded by119889(B(X 119905))119889119905 le 119887
119889 where 119887min 119887max and 119887
119889are known
constants
22 Closed-Loop Control Design To design the control law adefinition of the sliding function similar to thework of Slotineand Li [28] is adapted to the first-order system The slidingfunction can be made on each state as
119904
119894119905(119909
119894(119905)) = 119909
119894 119894 = 1 119898 (2)
Mathematical Problems in Engineering 3
SMC LPF
PlantPIDcontroller
Adaptationlaws
Adaptive PID control
+
+
+ x
+
f
usgn uL
uPIDxd minus
minus
minus
d(middot)dt
Bminus1
119854ap = minus119839 + 119857d
Figure 1 A schematic diagram of the proposed controller (LPFSMC and Adaptive PID technique)
Then the 119898-dimensional sliding function and its firstderivative for the system in (1) can be expressed as
s119905(x) = x minus x
119889
s119905(x) = C (x minus x
119889)
(3)
where s119905(x) = [119904
1119905 119904
119898119905]
119879 has components satisfying thesliding function stated earlier and C is a positive constantcoefficient119898times119898matrix with full row rank Its argument is agradient vector of the sliding function [42] which is unity ineach sliding surface due to the first-order system
From Figure 1 the control input is
u (119905) = Bminus1 [uap minus (uPID minus u119871)] (4)
where u119871is the low-frequency pass filter signal which is
a result of a first-order low-pass filter of the switchingsignal usgn = minusM
119904sgn(s) sgn(119904
119894) =
+1 if 119904119894gt0minus1 if 119904119894lt0
Let M119904=
diag(119872119900|119904
119894119905|) sgn(s) = [sgn(119904
1) sgn(119904
119898)]
119879 and uPIDdenote the control signal of the adaptive PID tuning uap isan approximation of the control input that neglects the lastterm of the RHS of (1) and is the unit matrix Thereforean approximation can be obtained similar to the idea of theequivalent control input [15] which is
uap = minusf + x119889 (5)
For the solution of u119871 it can be obtained by
119879
119891u119871+ u119871= usgn (6)
where 119879119891is the cut-off frequency The LPF is activated at the
time of 119905 = 119905reach with the zero initial condition of u119871(119905reach) =0 and given 119905reach is the reaching time For uPID it can beobtained by
uPID = k119875s + k119868int s 119889119905 + k
119863s (7)
where k119875= diag(119896
119875119894) is the proportional gain k
119868= diag(119896
119868119894)
is the integral gain and k119863= diag(119896
119863119894) is the derivative gain
119896
119875119894 119896119868119894 and 119896
119863119894isin 119877
+ which are not equal to zero
221 Reaching Phase Analysis This section presents adescription of the reaching time calculation for the closed-loop control system by the proposed control law in (4) Forthe reaching time (119905reach) the first-order LPF will be activatedwhen 119905 = 119905reach with zero initial condition of the filter inputsignal Consequently u
119871(119905reach) = 0 for 0 le 119905 le 119905reach
Therefore the control input during the reaching phase isobtained by
u = Bminus1 [uap minus uPID] (8)
Note that Assumption 5 can be extended to the gainmargin concept [28] for adaptation law derivation Forstability in the reaching phase Lyapunovrsquos theorem is chosento prove the stability of the controller and the errors canconverge to the sliding surface if u is constructed to achievethe first derivative of the Lyapunov function candidate V lt 0Choose the Lyapunov function candidate ofV gt 0ThereforeV at the reaching phase can be described as
V =
1
2
s119879s + 1
2
(k119879119875k119875+ k119879119868k119868+ k119879119863k119863) (9)
Then the derivative of the Lyapunov function (9) can berewritten as
V = s119879 s + (k119879119875k119875+ k119879119868k119868+ k119879119863k119863) (10)
To find the condition satisfying the Lyapunov stability thefirst derivative of the sliding function s must be substitutedinto (10) It can be derived by
s = C (x minus x119889)
= Cf + CB120578 minus Cx119889+ CBBminus1 (minusf + x
119889minus uPID)
= (Cf + CB120578 minus CBBminus1f) + x119889(CBBminus1 minus C)
minus CBBminus1k119875s minus CBBminus1uID
(11)
4 Mathematical Problems in Engineering
where uID = k119868int s 119889119905 + k
119863s Equation (11) shows the
fact that the control gain cannot be determined exactlyIn the following the gain margins concept [28] is adaptedwithout loss of generality due to the uncoupling andmatchingconditions From the concept the gain estimation can bedescribed by B = diag(119887) 119887 = radic119887min sdot 119887max and the boundof the control gain ratio can then be realized in the form120573
minus1le
BBminus1 le 120573 while 120573 = radic119887max119887min and the initialvalue in each argument of the three gains (k
119875 k119868 and k
119863) of
the PID portion is positive Substituting (11) into (10) yields
V = s119879 [(Cf + CB120578 minus CBBminus1f) + x119889(CBBminus1 minus C)]
minus s119879CBBminus1k119875s minus s119879CBBminus1uID + G
(12)
where G = (k119879119875k119875+ k119879119868k119868+ k119879119863k119863) which is the adaptation
term For (12) if k119875is chosen to overcome a part of the
uncertainties the adaptation law in the last term G can bedetermined to eliminate the rest of them consequently Inorder to compensate for the uncertainties in the reachingphase the proportional gain 119896
119875119894should satisfy equations
below1003817
1003817
1003817
1003817
k119875
1003817
1003817
1003817
1003817
ge
1003817
1003817
1003817
1003817
1003817
(
BBminus1f + BBminus1B120578 minus f) + (1 minus BBminus1) x119889
1003817
1003817
1003817
1003817
1003817
(13)
Then all arguments in the proportional gain are selectedto satisfy
119896
119875119894ge
1003816
1003816
1003816
1003816
120573119872
119900+ (1 minus 120573) (minus119891
119894+
119894119889)
1003816
1003816
1003816
1003816
(14)
119896
119875119894ge
1003816
1003816
1003816
1003816
120573119872
119900
1003816
1003816
1003816
1003816
+
1003816
1003816
1003816
1003816
1003816
(1 minus 120573) 119906
119894ap1003816
1003816
1003816
1003816
1003816
(15)
Equations (13) to (15) correspond to the gain margincalculationmethod [28] Even if the proportional term can bedesigned to cope with the first term in (12) its residual errorstill exists Let the residual error be the difference betweenthe first term and the second term of (12) It is bounded by apositive valueΔ = s119879[(Cf+CB120578minusCBBminus1f)+C(BBminus1minus1)x
119889]minus
s119879CBBminus1k119875s due to a bounded control input By adding the
bound of the control gain ratio (12) can be rewritten as
V le minusΔs119879s minus s119879CBBminus1k119868int s 119889119905 minus s119879CBBminus1k
119863s
+ k119879119875k119875+ k119879119868k119868+ k119879119863k119863
le minusΔs119879s minus 120573s119879Ck119868int s 119889119905 minus 120573s119879Ck
119863s
+ k119879119875k119875+ k119879119868k119868+ k119879119863k119863
(16)
Obviously to satisfy the Lyapunov stability of the condi-tion V lt 0 and the adaptation law can be designed as k
119875= 0
k119868= 120573s119879Cint s 119889119905 and k
119863= 120573s119879C s Note that the proportional
gain has a coupling effectwith the sliding gainwhich operateswith the unity boundary layer width Therefore k
119875does not
need to be updated online The adaptation gains ( k119868and
k119863) are capable of guaranteeing the stability only outside
the bound of the control gain ratio 120573 This implies thatthis technique only offers a uniform ultimate boundedness
response Additionally it is usual to have a solution when thecontrol gain magnitude is unknown Even if the control gainis known or adapted the ultimate boundedness still occursinside the vicinity around the sliding surface Notice thatat the beginning state the integral and the derivative termsof the adaptation law may be arbitrary small because theuncertainties at the beginning state can be compensated byk119875 Consequently (16) can be replaced by the adaptation law
and the new expression of (16) becomes
V le minusΔs119879s (17)
With the positive-initial value of the PID gains and thecondition of (15) and the adaptation laws the stability withinthe reaching phase can be guaranteed The reaching time(119905reach) can be obtained by
119905reach le
1003817
1003817
1003817
1003817
s(119905=0)
1003817
1003817
1003817
1003817
Δ
(18)
222 Existence of the Sliding Condition The key issue of thissection is to describe the sliding mode retention For theexistence conditions of the sliding mode at 119905 ge 119905reach thefirst-order low-pass filter (LPF) is activated and the switchingsignal is alleviated in turn To describe the existence of thesliding condition substitute the control law u(119905) = Bminus1[uap minus(uPID minus u
119871)] Therefore the derivative of the closed-loop s
dynamic at 119905 ge 119905reach can be obtained by
s = (Cf + CB120578 minus CBBminus1f) + C (BBminus1 minus 1) x119889
minus CBBminus1k119875s minus CBBminus1uID + CBBminus1u
119871
(19)
With the condition in (15) (19) can be rearranged as
minusCBBminus1k119875s = s minus (Cf + CB120578 minus CBBminus1f)
minus C (BBminus1 minus 1) x119889+ CBBminus1uID minus CBBminus1u
119871
(20)
Multiplying (20) by (CBBminus1)minus1 yields
minusk119875s = BBminus1
sdot [Cminus1 s minus (f + B120578 minus BBminus1f) minus (BBminus1 minus 1) x119889
+BBminus1uID minus BBminus1u119871]
(21)
From the condition in (15) the sliding gain can bechanged to beM
119904= diag(119896
119875119894|119904
119894119905|) and the output from the LPF
can be satisfied by 119879119891u119871+ u119871= minus diag(119896
119875119894|119904
119894119905|)sgn(s) = minusk
119875s
Therefore
119879
119891u119871+ 2u119871
=
BBminus1
sdot[Cminus1 s minus (f + B120578minusBBminus1f)minus(BBminus1 minus 1) x119889+BBminus1uID]
(22)
Mathematical Problems in Engineering 5
As the reaching phase analysis the control law in (8) andits adaptation law offer convergence regulation of the stateIntuitively the sliding function s is bounded about the slidingsurface s= 0 due to imperfection of control action in practiceThus the derivative of the sliding function s will be boundedby the boundedness of s which also implies the integralof s converges to some limit [43] Consequently the RHS of(22) can be bounded and is rewritten by a residual matrix0 = [0
1 0
119898]
119879isin 119877
119898 For each argument of the u119871 the
residual function 0119894 119894 = 1 sdot sdot sdot 119898 can be interpreted as residual
errors after the reaching phase which satisfy
119879
119891
119871119894+ 2119906
119871119894= 0
119894 (23)
Given 120574 = 2119879
119891and 120593
119894= 0
119894119879
119891 (23) is rewritten as
119871119894+ 120574119906
119871119894= 120593
119894 (24)
From (24) the bound on 120593
119894can be interpreted into a
bound on the filter output 119906119871119894 Define the bound of 120593
119894= Φ
119894
The bound of the filter output |119906119871119894| can be written as (25)
which corresponds to [28]
1003816
1003816
1003816
1003816
119906
119871119894(119905)
1003816
1003816
1003816
1003816
le (
Φ
119894
120574
) (1 minus 119890
minus120574119905) (25)
In which 119906119871119894(119905)
tends to Φ119894120574 [28] when 119905 rarr infin Thus
1003816
1003816
1003816
1003816
119906
119871119894(119905)
1003816
1003816
1003816
1003816
le
Φ
119894
120574
(26)
Consider (26) if 119879119891
and 120573 are known the residualuncertainties from the reaching phase can be compensatedby u119871 To consider the stability of the control system by using
the input according to (4) (12) can be rewritten as
V = s119879 [(Cf + CB120578 minus CBBminus1f) + C (BBminus1 minus 1) x119889]
minus s119879CBBminus1k119875s minus s119879CBBminus1uID minus s119879CBBminus1u
119871+ G
(27)
Notice that the adding of the u119871leads to uncertain of
negative definite on the Lyapunov function derivative Inorder to stabilize (27) the proportional portion has to takethe output from the LPF and the bound of uncertainty and itsderivative into account By defining119872
119905= 119872
0+ 119872
119889+ u119871
themodified proportional gain for each sliding surface can be119896
119875119894ge |120573119872
119905| + |(1 minus 120573)119906
119894ap| And together with the adaptationlaws defined in the previous section V in (27) is negativedefinite (
119881 lt 0) The sliding motion can be guaranteed for119905 isin [119905reachinfin) under the conditions stated earlier
3 Description of the Engine SpeedControl Modeling
As stated earlier a key step of the development controlscheme is based on the robust control techniques inwhich theapproach has the ability to neglect the conservatism and theneed for precise modeling [44] In addition the development
of an exact model for a real engine system is difficultbecause some parameters in the mathematical model cannotbe obtained exactly and the real plant is affected by thecomplexity of its uncertain nonlinearity [45] Consequentlythe system modeling in this work was linearized through thenominal transfer function of the real plant as the form of
119909 (119904) = 119866ta (119904) 119890minus119879119863119904
119906ta (119904) + 119866sa (119904) 119890minus119879119863119904
119906sa (119904) (28)
where 119909(119904) is the output the time delay is 119879119863 119906ta(119904) is the
control input for a throttle actuator and 119906sa(119904) is the controlinput for the spark advance system 119866ta(119904) and 119866sa(119904) are thelinearized models by 119906ta(119904) and 119906sa(119904) respectively Note thatthe symbol 119904 in this section denotes the complex argument ofthe Laplace transform which is not the sliding function
Although the conventional relevant engine dynamic forengine speed control depends on the coordination betweenthe throttle actuator and the spark advance system for theassessment in this work we have designed a controller thataims to control only the throttle actuator while the sparkadvance system is handled by conventional controller of theengine system Therefore the system modeling in this workcan be obtained by an adjustment of the throttle openingposition in degrees which is directly controlled with a DCmotor that is excited by the feed-forward control signalin DC-voltage as an input and the crankshaft speed inrevolutions perminute (rpm) as an output Consequently thelinearizationmodel at speed 900 rpm can be approximated inthe transfer function form as
119866 (119904) =
45119904
2+ 44119904 + 90
119904
3+ 15119904
2+ 25119904 + 1
(29)
where 119866(119904) is the transfer function of the real plant whichhas units of revolutions per minute (rpm) From the roughidentifications of (29) it is the third-order with relativedegree one and the system is BIBO stable because all polesare located on the left-hand side (LHS) of the 119904-plane Inaddition for the reason of low-speed control test (900 rpm)it is sensitive to any uncertain nonlinearities and externaldisturbancesTherefore the implementation of speed controlin the low-speed region is more difficult than in the high-speed control region Furthermore on average 30 percentof fuel consumption in urban city driving is spent at theidle speed range [46] As a consequence increasing theperformance of the low-speed control is able to increase fueleconomy and performance of the engine operation at anyoperating condition [32]
For simplicity to make the engine speed response asthe canonical form of (1) the rough identification model of(29) can be simplified to the first-order transfer function asfollows
119866 (119904) =
445
119904 + 0493
(30)
To make clear the acceptability of (30) the bode plotand the step response comparison between (29) and (30) aredemonstrated in Figure 2 The results make clear that thefirst-order transfer function in (30) can be employed in theperformance assessment of the proposed controller design in
6 Mathematical Problems in Engineering
0 2 4 6 8 10 120
102030405060708090
100Step response
Time (s)
Am
plitu
de
3rd order1st order
10152025303540
minus90
minus45
0
Frequency (rads)
Bode diagram
Mag
nitu
de (d
B)Ph
ase (
deg)
10minus2
10minus1
100
101
Frequency (rads)10
minus210
minus110
010
1
Figure 2 The validation of the 1st-order model
the simulations and (30) can be expressed as the time-domaindifferential equation as follows
= minus0493119909 + 445119906 (31)
where 119909 is the speed output and 119906 is the input
4 Illustrative Examples
41 Simulation Verification For the simulation verificationthe system modeling of (31) is used in order to assess theperformance of the proposed control scheme (LPFSMC andAdaptive PID) that is performed viaMATLAB-Simulink pro-gramming with a sampling period of 1ms The performanceof the proposed controller is compared with different controltechniques which are the PID control technique and the SMCtechnique The specific control parameters are chosen suchthat the sliding gain of the proposed control scheme and theconventional SMC is M
119905= 10 the cut-off frequency of the
first-order LPF is119879119891= 4 while the setting control parameters
of the PID controller are obtained by the Ziegler-Nicholstuning method
Figure 3(a) demonstrates the response results of theproposed control scheme which has a small rise time andsetting time and higher tracking accuracy than other controltechniques (PID controller and SMC) It demonstrates thatthe proposed adaptation law is capable of updating the PID
controller online during the control process within a shortperiod Furthermore the proposed control scheme can pro-vide optimal control input rapidly and has smooth controlinput which is achieved by the cut-off frequency property ofthe LPF (see Figure 3(b))
Figure 3(c) shows the error comparison among the dif-ferent controllers as the results the errors from the pro-posed control scheme can approach zero faster than othercontrol techniques and it has lower chattering than the SMCtechnique Note that although the chattering of the outputresponse control input and the errors of the PID controllerdoes not appear the results (see Figure 3) reveal that itsresponse has higher rise-time high-overshoot and longersetting time which are not satisfactory from the viewpointof a control system
42 Practical Experiment In this section we demonstrate theefficiency of the proposed control scheme in the real systemThe experimental technical data are shown in Table 1 In oursetup the functional block diagrams of the apparatus used inthe experiments are illustrated in Figure 4 which is used forperformance assessment of the proposed control schemeThesystem in Figure 4 consists of five main parts which are thecontroller unit electronic throttle valve control unit (ETC)spark-ignition (SI) engine system the power train system
Mathematical Problems in Engineering 7
Time (s)
Spee
d re
spon
se (r
pm)
ZOOM
Time (s)
Spee
d re
spon
se(r
pm)
SMCLPFSMC and adaptive PIDDesiredPID
0200400600800
10001200140016001800
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 208998995
9009005
901
(a)
Time (s)
Con
trol i
nput
(V)
SMC LPFSMC and adaptive PIDPID
minus30minus25minus20minus15minus10minus5
05
101520
2 4 6 8 10 12 14 16 18 200
(b)
Erro
rs
SMC LPFSMC and adaptive PIDPID
Time (s)
Erro
rs
ZOOM
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus1000minus800minus600minus400minus200
0200400600800
005
1
minus05minus1
0 2 4 6 8 10 12 14 16 18 20
(c)
Figure 3 Comparison of simulation results among different control techniques (a) the output response (b) the control inputs (c) the errors
PWM M
DC motor
Gear box
Throttle opening sensor
Throttle body
Control system
Electronic throttle control unit
SI engine
ADCDAC
Amplifier
Air
Speed calculation
Throttle position calculation
Fuel consumptioncomputation
Emission data logger(HC CO)
Speed sensor
Fuel flow sensor
Emission sensor
Power trainsystem
Dynamometer
Figure 4 Schematic diagram of the experiment
8 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
DesiredLPFSMC and adaptive PID
Con
trol i
nput
(V)
Time (s)
Slid
ing
varia
ble (
s)
Time (s)
Thro
ttle v
alve
ope
ning
(deg
)
Time (s)
0 20 40 60 80 100 120 140 160 180 200600650700750800850900950
1000
0
01
02
03
04
05
06
0 20 40 60 80 100 120 140 160 180 200
minus200minus150minus100minus50
050
100150200
0 20 40 60 80 100 120 140 160 180 200012345678
0 20 40 60 80 100 120 140 160 180 200
Figure 5 Experimental results of the proposed controller (LPFSMC and Adaptive PID technique)
Table 1 Experimental technical data
Item ValueSI engine (4 cylinders 900 ccgasoline type) Test range 600ndash3000 rpm
Speed sensor (rpm) Sampling speed approximately5000 ts
Throttle position sensor Measurement range 0ndash80∘
ADCDAC minus10 to 10VDC 20mA
COMPUTER Core2Duo 293GHz 4GBRAM
DCmotor 48ndash6VFuel type (experiments) Ethanol-gasoline blended (E20)
and the dynamometer which is used to generate the load-torque into the systemThe engine speed is interpreted as thecrankshaft rotation rate in revolutions per minute (rpm) andis regulated by opening the throttle In this task the throttlevalve is directly actuated by a DCmotor in which the angularmovement is handled by the control signal in the form ofPulseWidth Modulation (PWM)The exhaust emissions COandHCwere alsomeasured through a nondispersive infraredanalysis machine (Infralyt smart) in which the acquiringsampling data is 1 s while the fuel consumptionwasmeasuredby the fuel flow sensor (Hall effect-800 series) with thesampling period is 1ms The computation unit is performedwith MATLAB-Simulink programming An ADCDAC isused as an interface systembetween the computer and the realplant while the sampling period is 1ms for all experiments
As seen in Figure 5 the desired speed is chosen to rapidchange from 750 rpm to 900 rpm and 900 rpm to 750 rpmand the experiments were performed for 200 s This resultreveals that the speed response of the proposed controlscheme can reach the desired speedwithin short time and hasno overshoot and tiny oscillationThe control input is smoothand reaches an optimal value within a short time and thesliding variable can approach zero rapidly Fast convergenceof the response is a result of the updated control gains (119870
119868
and 119870119863) of the PID controller which can be adjusted rapidly
during the control process according to the adaptive lawFurthermore the characteristic of the opening position of thethrottle valve was alsomeasuredThis reveals that themotionof the actuator has smooth and tiny oscillations
43 Tracking Performance and Disturbance Rejection TestThe robust properties and the tracking performance of theproposed control schemewere also assessed because it is wellknown that the engine speed control is affected by the stateof accessory changes such as external load disturbance [41]In the experiments we compare the disturbance rejectionperformance among the proposed controller SMC techniqueand PID controller The load disturbance is generated bythe dynamometer while the speed set-point is chosen to be900 rpm Note that for the reason of low-speed test it issensitive from any disturbances therefore the implementa-tion in the low-speed region is more difficult than the high-speed control task Furthermore high performance of low-speed control leads to increase the performance of the engineoperation at any operating condition [32]
Mathematical Problems in Engineering 9
Time (s)Lo
ad (W
)
75
225
Engi
ne sp
eed
(rpm
)
DesiredLPFSMC and adaptive PID
PIDSMC
15
30
0
1000
950
900
850
800
Time (s)
120 125 130 135 140 145 150 155 160
120 125 130 135 140 145 150 155 160
Figure 6 Comparisons of tracking performance and disturbance rejection of the controllers
As seen in Figure 6 at the time 125 sec the load torquewas applied immediately into the engine speed control taskThis proposed to disturb the stability of the control system atthe steady-state condition The proposed control scheme canimprove the speed deviation rapidly and is capable of trackingthe desired speed better than other control techniques Inaddition the load torque was decreased immediately at thetime 150 sec The results show that the proposed controlscheme can decrease the speed deviation from the desiredspeed faster than other control techniques The findingsreveal that the proposed control scheme has effective ofthe robustness and fast adaptation and has better trackingperformance than other control techniques
44 Fuel Consumption andExhaust Emission Investigation Inthis section the fuel consumption and the exhaust emissionof the engine speed control by using the proposed controlscheme and different control techniques (SMC techniqueand PID controller) were investigated (see Figure 7) In theexperiments the desired speed was performed for 400 secand was rapidly changed as shown in Figure 7(a) For theaverage total fuel consumption comparison (see Figure 7(b))the proposed control scheme can attain an excellent resultwith the lowest averaged total fuel consumption whichwas obtained by the average of the fuel consumptions persecond
In addition the average exhaust emissions were alsoinvestigated (see Figure 7(c)) The CO and HC emissions arethe main pollutants contributed by the SI engines In theprinciple of the combustion process of SI engine the HCemission is appeared when fuel molecules in the engine
cannot burn or burn only partially while the CO emissionis produced when the carbon in the fuel is partially oxi-dized rather than fully oxidized to carbon dioxide Howeverincreasing efficient strategies for engine speed control viathrottle valve regulation method is capable of increasingcombustion performance as it can reduce pollutant emissionsalso [38] In the experiments effects of the controllers wereinvestigated via the constant speed set points and no addingan external engine load (small load from the unloadedhydrostatic CVT)Thus the CO
2andNO
119909which are sensitive
to speed variation and high temperature operation did notmeasure in this work (the experiments perform at coolanttemperature of 70ndash80∘C for short period) As a result bothaverages of the CO and HC emission data were calculatedby the average of emissions per second in which obtainedby the direct measurement method [43] Additionally theseresults demonstrate that high fuel consumption and exhaustemission are affected by high variation of the engine speedduring tracking of the set pointsThese results also imply thatthe performance of the SI engine at any operating conditioncan be improved by an advanced engine speed control viathe electronic throttle valve regulation method as shown inFigure 7
5 Conclusions
The incorporation of the SMC and a first-order LPF witha new adaptive PID controller is proposed for trackingthe control task of an uncertain nonlinear system Thecontroller has been successfully applied to the problem ofthe speed tracking control of an SI engine through electronic
10 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
PIDSMC
LPFSMC and adaptive PIDDesired
0 50 100 150 200 250 300 350 4000
500
1000
1500
2000
2500
(a)
00689
0071
00694
006750068
006850069
00695007
007050071
00715
LPFSMC andadaptive PID
SMC PID
Fuel consumption (Lmin)
(b)
20288 41113 20302
105977
425503
109623
0500
10001500200025003000350040004500
LPFSMC andadaptive PID
SMC PID
HC (ppm)CO (ppm)
(c)
Figure 7 Comparisons of (a) tracking performance of the controllers (b) fuel consumption rates (c) exhaust emission rates
throttle valve control architecture From the simulation andexperimental results it achieves that
(1) the proposed adaptation law is capable of optimalonline update the PID controller during the controlprocess within a short period
(2) the chattering of the SMC can be alleviated by afirst-order low pass filter while the robustness of thecontrol system similar to that of the slidingmode suchthat the load torque disturbances can be compensatedquite accurately
(3) the proposed control scheme has high performancein implementation as it can be achieved in theproblem of engine speed control in which the systemis largely uncertain nonlinear system and rathercomplex mechanisms
Conflict of Interests
The authors have no competing interests
Acknowledgment
This research is financially supported by the Office ofResearch Administration (ORA) and Farm Engineering andAutomation Technology Research Group (FEAT) of Khon
Kaen University Thailand The authors are also thankfulto the reviewers and Mr Ian Thomas for their valuablecomments and suggestions for English grammar correctionrespectively
References
[1] K-C Hsu W-Y Wang and P-Z Lin ldquoSliding mode controlfor uncertain nonlinear systemswithmultiple inputs containingsector nonlinearities and deadzonesrdquo IEEE Transactions onSystems Man and Cybernetics Part B Cybernetics vol 34 no1 pp 374ndash380 2004
[2] G Bartolini and A Ferrara ldquoMulti-input sliding mode controlof a class of uncertain nonlinear systemsrdquo IEEE Transactions onAutomatic Control vol 41 no 11 pp 1662ndash1666 1996
[3] T-C Kuo Y-J Huang and S-H Chang ldquoSliding mode controlwith self-tuning law for uncertain nonlinear systemsrdquo ISATransactions vol 47 no 2 pp 171ndash178 2008
[4] G Montaseri and M J Yazdanpanah ldquoPredictive control ofuncertain nonlinear parabolic PDE systems using a Galerkinneural-network-based modelrdquo Communications in NonlinearScience and Numerical Simulation vol 17 no 1 pp 388ndash4042012
[5] F O Tellez A G Loukianov E N Sanchez and E Jose BayroCorrochano ldquoDecentralized neural identification and controlfor uncertain nonlinear systems application to planar robotrdquoJournal of the Franklin Institute vol 347 no 6 pp 1015ndash10342010
Mathematical Problems in Engineering 11
[6] A Bazaei and V J Majd ldquoFeedback linearization of discrete-time nonlinear uncertain plants via first-principles-based serialneuro-gray-box modelsrdquo Journal of Process Control vol 13 no8 pp 819ndash830 2003
[7] T-Y Kuc and W-G Han ldquoAn adaptive PID learning controlof robot manipulatorsrdquo Automatica vol 36 no 5 pp 717ndash7252000
[8] Y Pan Y Zhou T Sun and M J Er ldquoComposite adaptivefuzzy 119867
infintracking control of uncertain nonlinear systemsrdquo
Neurocomputing vol 99 pp 15ndash24 2013[9] X Liu R Tao and M Tavakoli ldquoAdaptive control of uncertain
nonlinear teleoperation systemsrdquo Mechatronics vol 24 no 1pp 66ndash78 2014
[10] W-D Chang and J-J Yan ldquoAdaptive robust PID controllerdesign based on a sliding mode for uncertain chaotic systemsrdquoChaos Solitons amp Fractals vol 26 no 1 pp 167ndash175 2005
[11] T C Kuo Y J Huang C Y Chen and C H Chang ldquoAdaptivesliding mode control with PID tuning for uncertain systemrdquoEngineering Letters vol 16 no 3 pp 1ndash5 2008
[12] M N Howell and M C Best ldquoOn-line PID tuning forengine idle-speed control using continuous action reinforce-ment learning automatardquo Control Engineering Practice vol 8no 2 pp 147ndash154 2000
[13] C-F Hsu and B-K Lee ldquoFPGA-based adaptive PID control ofa DC motor driver via sliding-mode approachrdquo Expert Systemswith Applications vol 38 no 9 pp 11866ndash11872 2011
[14] DWMemering and PHMeckl ldquoComparison of adaptive con-trol techniques applied to diesel engine idle speed regulationrdquoJournal of Dynamic Systems Measurement and Control vol 124no 4 pp 682ndash688 2002
[15] V I Utkin ldquoSliding mode control design principles andapplications to electric drivesrdquo IEEE Transactions on IndustrialElectronics vol 40 no 1 pp 23ndash36 1993
[16] Y J Huang and T C Kuo ldquoRobust output tracking controlfor nonlinear time-varying robotic manipulatorsrdquo ElectricalEngineering vol 87 no 1 pp 47ndash55 2005
[17] M Hajatipour and M Farrokhi ldquoChattering free with noisereduction in sliding-mode observers using frequency domainanalysisrdquo Journal of Process Control vol 20 no 8 pp 912ndash9212010
[18] A Sabanovic L Fridman and S Spurgeon Variable StructureSystems From Principles to Implementation The Institution ofEngineering and Technology 2004
[19] Y Xu ldquoChattering free robust control for nonlinear systemsrdquoIEEE Transactions on Control Systems Technology vol 16 no 6pp 1352ndash1359 2008
[20] H Lee and V I Utkin ldquoChattering suppression methods insliding mode control systemsrdquo Annual Reviews in Control vol31 no 2 pp 179ndash188 2007
[21] Y Ren Z Liu L Chang and N Wen ldquoAdaptive slidingmode robust control for virtual compound-axis servo systemrdquoMathematical Problems in Engineering vol 2013 Article ID343851 9 pages 2013
[22] M-L Tseng and M-S Chen ldquoChattering reduction of slidingmode control by low-pass filtering the control signalrdquo AsianJournal of Control vol 12 no 3 pp 392ndash398 2010
[23] H Sira-RamIRez ldquoOn the dynamical sliding mode control ofnonlinear systemsrdquo International Journal of Control vol 57 no5 pp 1039ndash1061 1993
[24] J-X Xu Y-J Pan and T-H Lee ldquoSliding mode controlwith closed-loop filtering architecture for a class of nonlinear
systemsrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 51 no 4 pp 168ndash173 2004
[25] A Deenadayalan and G S Ilango ldquoPosition sensorless slidingmode observer with sigmoid function for Brushless DCmotorrdquoin Proceedings of the International Conference on Advances inPower Conversion and Energy Technologies (APCET rsquo12) pp 1ndash6IEEE August 2012
[26] Y Xia X Yu andW Oghanna ldquoAdaptive robust fast control forinduction motorsrdquo IEEE Transactions on Industrial Electronicsvol 47 no 4 pp 854ndash862 2000
[27] M Niclai Theory of Nonlinear Control Systems McGraw-Hill1969
[28] J J Slotine andW Li Applied Nonlinear Control Prentice-HallEnglewood Cliffs NJ USA 1991
[29] D Gorinevsky and L A Feldkamp ldquoRBF network feedforwardcompensation of load disturbance in idle speed controlrdquo IEEEControl Systems vol 16 no 6 pp 18ndash27 1996
[30] S Di Cairano D Yanakiev A Bemporad I V Kolmanovskyand D Hrovat ldquoModel predictive idle speed control designanalysis and experimental evaluationrdquo IEEE Transactions onControl Systems Technology vol 20 no 1 pp 84ndash97 2012
[31] P F Puleston S Spurgeon andGMonsees ldquoAutomotive enginespeed control a robust nonlinear control frameworkrdquo IEEProceedings Control Theory and Applications vol 148 no 1 pp81ndash87 2001
[32] Y Yildiz A M Annaswamy D Yanakiev and I KolmanovskyldquoSpark-ignition-engine idle speed control an adaptive controlapproachrdquo IEEE Transactions on Control Systems Technologyvol 19 no 5 pp 990ndash1002 2011
[33] A Sugeng K Baharin T Hishamuddin and J B SupriyoldquoEngine speed control using online ANN for vehicle withEMDAP-CVTrdquo Jurnal Mekanikal vol 22 pp 39ndash52 2006
[34] M K Khan K B Goh and S K Spurgeon ldquoSecond ordersliding mode control of a diesel enginerdquo Asian Journal ofControl vol 5 no 4 pp 614ndash619 2003
[35] J R Wagner D M Dawson and L Zeyu ldquoNonlinear air-to-fuel ratio and engine speed control for hybrid vehiclesrdquo IEEETransactions on Vehicular Technology vol 52 no 1 pp 184ndash1952003
[36] F Assadian S Fekri andM Hancock ldquoHybrid electric vehicleschallenges strategies for advanced engine speed controlrdquo inProceedings of the IEEE International Electric Vehicle Conference(IEVC rsquo12) March 2012
[37] A G Ulsoy H Peng and M Cakmakci Automotive ControlSystems Cambridge University Press Cambridge UK 2014
[38] C Ji and S Wang ldquoStrategies for improving the idle perfor-mance of a spark-ignited gasoline enginerdquo International Journalof Hydrogen Energy vol 37 no 4 pp 3938ndash3944 2012
[39] S Wang C Ji M Zhang and B Zhang ldquoReducing theidle speed of a spark-ignited gasoline engine with hydrogenadditionrdquo International Journal of Hydrogen Energy vol 35 no19 pp 10580ndash10588 2010
[40] DHrovat and J Sun ldquoModels and controlmethodologies for ICengine idle speed control designrdquo Control Engineering Practicevol 5 no 8 pp 1093ndash1100 1997
[41] B Alt J P Blath F Svaricek and M Schultalbers ldquoMultiplesliding surface control of idle engine speed and torque reservewith dead start assist controlrdquo IEEE Transactions on IndustrialElectronics vol 56 no 9 pp 3580ndash3592 2009
12 Mathematical Problems in Engineering
[42] T Radpukdee and P Jirawattana ldquoUncertainty learning andcompensation an application to pressure tracking of an electro-hydraulic proportional relief valverdquo Control Engineering Prac-tice vol 17 no 2 pp 291ndash301 2009
[43] P A Loannou and J Sun Robust Adaptive Control PTRPrentice-Hall 1996
[44] C D Richard and H B Robert Modern Control SystemsPrentice Hall Upper Saddle River NJ USA 2011
[45] A Jansri and P Sooraksa ldquoEnhanced model and fuzzy strategyof air to fuel ratio control for spark ignition enginesrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 922ndash9332012
[46] Z Ye ldquoModeling identification design and implementation ofnonlinear automotive idle speed control systemsmdashanoverviewrdquoIEEE Transactions on Systems Man and Cybernetics Part CApplications and Reviews vol 37 no 6 pp 1137ndash1151 2007
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 3
SMC LPF
PlantPIDcontroller
Adaptationlaws
Adaptive PID control
+
+
+ x
+
f
usgn uL
uPIDxd minus
minus
minus
d(middot)dt
Bminus1
119854ap = minus119839 + 119857d
Figure 1 A schematic diagram of the proposed controller (LPFSMC and Adaptive PID technique)
Then the 119898-dimensional sliding function and its firstderivative for the system in (1) can be expressed as
s119905(x) = x minus x
119889
s119905(x) = C (x minus x
119889)
(3)
where s119905(x) = [119904
1119905 119904
119898119905]
119879 has components satisfying thesliding function stated earlier and C is a positive constantcoefficient119898times119898matrix with full row rank Its argument is agradient vector of the sliding function [42] which is unity ineach sliding surface due to the first-order system
From Figure 1 the control input is
u (119905) = Bminus1 [uap minus (uPID minus u119871)] (4)
where u119871is the low-frequency pass filter signal which is
a result of a first-order low-pass filter of the switchingsignal usgn = minusM
119904sgn(s) sgn(119904
119894) =
+1 if 119904119894gt0minus1 if 119904119894lt0
Let M119904=
diag(119872119900|119904
119894119905|) sgn(s) = [sgn(119904
1) sgn(119904
119898)]
119879 and uPIDdenote the control signal of the adaptive PID tuning uap isan approximation of the control input that neglects the lastterm of the RHS of (1) and is the unit matrix Thereforean approximation can be obtained similar to the idea of theequivalent control input [15] which is
uap = minusf + x119889 (5)
For the solution of u119871 it can be obtained by
119879
119891u119871+ u119871= usgn (6)
where 119879119891is the cut-off frequency The LPF is activated at the
time of 119905 = 119905reach with the zero initial condition of u119871(119905reach) =0 and given 119905reach is the reaching time For uPID it can beobtained by
uPID = k119875s + k119868int s 119889119905 + k
119863s (7)
where k119875= diag(119896
119875119894) is the proportional gain k
119868= diag(119896
119868119894)
is the integral gain and k119863= diag(119896
119863119894) is the derivative gain
119896
119875119894 119896119868119894 and 119896
119863119894isin 119877
+ which are not equal to zero
221 Reaching Phase Analysis This section presents adescription of the reaching time calculation for the closed-loop control system by the proposed control law in (4) Forthe reaching time (119905reach) the first-order LPF will be activatedwhen 119905 = 119905reach with zero initial condition of the filter inputsignal Consequently u
119871(119905reach) = 0 for 0 le 119905 le 119905reach
Therefore the control input during the reaching phase isobtained by
u = Bminus1 [uap minus uPID] (8)
Note that Assumption 5 can be extended to the gainmargin concept [28] for adaptation law derivation Forstability in the reaching phase Lyapunovrsquos theorem is chosento prove the stability of the controller and the errors canconverge to the sliding surface if u is constructed to achievethe first derivative of the Lyapunov function candidate V lt 0Choose the Lyapunov function candidate ofV gt 0ThereforeV at the reaching phase can be described as
V =
1
2
s119879s + 1
2
(k119879119875k119875+ k119879119868k119868+ k119879119863k119863) (9)
Then the derivative of the Lyapunov function (9) can berewritten as
V = s119879 s + (k119879119875k119875+ k119879119868k119868+ k119879119863k119863) (10)
To find the condition satisfying the Lyapunov stability thefirst derivative of the sliding function s must be substitutedinto (10) It can be derived by
s = C (x minus x119889)
= Cf + CB120578 minus Cx119889+ CBBminus1 (minusf + x
119889minus uPID)
= (Cf + CB120578 minus CBBminus1f) + x119889(CBBminus1 minus C)
minus CBBminus1k119875s minus CBBminus1uID
(11)
4 Mathematical Problems in Engineering
where uID = k119868int s 119889119905 + k
119863s Equation (11) shows the
fact that the control gain cannot be determined exactlyIn the following the gain margins concept [28] is adaptedwithout loss of generality due to the uncoupling andmatchingconditions From the concept the gain estimation can bedescribed by B = diag(119887) 119887 = radic119887min sdot 119887max and the boundof the control gain ratio can then be realized in the form120573
minus1le
BBminus1 le 120573 while 120573 = radic119887max119887min and the initialvalue in each argument of the three gains (k
119875 k119868 and k
119863) of
the PID portion is positive Substituting (11) into (10) yields
V = s119879 [(Cf + CB120578 minus CBBminus1f) + x119889(CBBminus1 minus C)]
minus s119879CBBminus1k119875s minus s119879CBBminus1uID + G
(12)
where G = (k119879119875k119875+ k119879119868k119868+ k119879119863k119863) which is the adaptation
term For (12) if k119875is chosen to overcome a part of the
uncertainties the adaptation law in the last term G can bedetermined to eliminate the rest of them consequently Inorder to compensate for the uncertainties in the reachingphase the proportional gain 119896
119875119894should satisfy equations
below1003817
1003817
1003817
1003817
k119875
1003817
1003817
1003817
1003817
ge
1003817
1003817
1003817
1003817
1003817
(
BBminus1f + BBminus1B120578 minus f) + (1 minus BBminus1) x119889
1003817
1003817
1003817
1003817
1003817
(13)
Then all arguments in the proportional gain are selectedto satisfy
119896
119875119894ge
1003816
1003816
1003816
1003816
120573119872
119900+ (1 minus 120573) (minus119891
119894+
119894119889)
1003816
1003816
1003816
1003816
(14)
119896
119875119894ge
1003816
1003816
1003816
1003816
120573119872
119900
1003816
1003816
1003816
1003816
+
1003816
1003816
1003816
1003816
1003816
(1 minus 120573) 119906
119894ap1003816
1003816
1003816
1003816
1003816
(15)
Equations (13) to (15) correspond to the gain margincalculationmethod [28] Even if the proportional term can bedesigned to cope with the first term in (12) its residual errorstill exists Let the residual error be the difference betweenthe first term and the second term of (12) It is bounded by apositive valueΔ = s119879[(Cf+CB120578minusCBBminus1f)+C(BBminus1minus1)x
119889]minus
s119879CBBminus1k119875s due to a bounded control input By adding the
bound of the control gain ratio (12) can be rewritten as
V le minusΔs119879s minus s119879CBBminus1k119868int s 119889119905 minus s119879CBBminus1k
119863s
+ k119879119875k119875+ k119879119868k119868+ k119879119863k119863
le minusΔs119879s minus 120573s119879Ck119868int s 119889119905 minus 120573s119879Ck
119863s
+ k119879119875k119875+ k119879119868k119868+ k119879119863k119863
(16)
Obviously to satisfy the Lyapunov stability of the condi-tion V lt 0 and the adaptation law can be designed as k
119875= 0
k119868= 120573s119879Cint s 119889119905 and k
119863= 120573s119879C s Note that the proportional
gain has a coupling effectwith the sliding gainwhich operateswith the unity boundary layer width Therefore k
119875does not
need to be updated online The adaptation gains ( k119868and
k119863) are capable of guaranteeing the stability only outside
the bound of the control gain ratio 120573 This implies thatthis technique only offers a uniform ultimate boundedness
response Additionally it is usual to have a solution when thecontrol gain magnitude is unknown Even if the control gainis known or adapted the ultimate boundedness still occursinside the vicinity around the sliding surface Notice thatat the beginning state the integral and the derivative termsof the adaptation law may be arbitrary small because theuncertainties at the beginning state can be compensated byk119875 Consequently (16) can be replaced by the adaptation law
and the new expression of (16) becomes
V le minusΔs119879s (17)
With the positive-initial value of the PID gains and thecondition of (15) and the adaptation laws the stability withinthe reaching phase can be guaranteed The reaching time(119905reach) can be obtained by
119905reach le
1003817
1003817
1003817
1003817
s(119905=0)
1003817
1003817
1003817
1003817
Δ
(18)
222 Existence of the Sliding Condition The key issue of thissection is to describe the sliding mode retention For theexistence conditions of the sliding mode at 119905 ge 119905reach thefirst-order low-pass filter (LPF) is activated and the switchingsignal is alleviated in turn To describe the existence of thesliding condition substitute the control law u(119905) = Bminus1[uap minus(uPID minus u
119871)] Therefore the derivative of the closed-loop s
dynamic at 119905 ge 119905reach can be obtained by
s = (Cf + CB120578 minus CBBminus1f) + C (BBminus1 minus 1) x119889
minus CBBminus1k119875s minus CBBminus1uID + CBBminus1u
119871
(19)
With the condition in (15) (19) can be rearranged as
minusCBBminus1k119875s = s minus (Cf + CB120578 minus CBBminus1f)
minus C (BBminus1 minus 1) x119889+ CBBminus1uID minus CBBminus1u
119871
(20)
Multiplying (20) by (CBBminus1)minus1 yields
minusk119875s = BBminus1
sdot [Cminus1 s minus (f + B120578 minus BBminus1f) minus (BBminus1 minus 1) x119889
+BBminus1uID minus BBminus1u119871]
(21)
From the condition in (15) the sliding gain can bechanged to beM
119904= diag(119896
119875119894|119904
119894119905|) and the output from the LPF
can be satisfied by 119879119891u119871+ u119871= minus diag(119896
119875119894|119904
119894119905|)sgn(s) = minusk
119875s
Therefore
119879
119891u119871+ 2u119871
=
BBminus1
sdot[Cminus1 s minus (f + B120578minusBBminus1f)minus(BBminus1 minus 1) x119889+BBminus1uID]
(22)
Mathematical Problems in Engineering 5
As the reaching phase analysis the control law in (8) andits adaptation law offer convergence regulation of the stateIntuitively the sliding function s is bounded about the slidingsurface s= 0 due to imperfection of control action in practiceThus the derivative of the sliding function s will be boundedby the boundedness of s which also implies the integralof s converges to some limit [43] Consequently the RHS of(22) can be bounded and is rewritten by a residual matrix0 = [0
1 0
119898]
119879isin 119877
119898 For each argument of the u119871 the
residual function 0119894 119894 = 1 sdot sdot sdot 119898 can be interpreted as residual
errors after the reaching phase which satisfy
119879
119891
119871119894+ 2119906
119871119894= 0
119894 (23)
Given 120574 = 2119879
119891and 120593
119894= 0
119894119879
119891 (23) is rewritten as
119871119894+ 120574119906
119871119894= 120593
119894 (24)
From (24) the bound on 120593
119894can be interpreted into a
bound on the filter output 119906119871119894 Define the bound of 120593
119894= Φ
119894
The bound of the filter output |119906119871119894| can be written as (25)
which corresponds to [28]
1003816
1003816
1003816
1003816
119906
119871119894(119905)
1003816
1003816
1003816
1003816
le (
Φ
119894
120574
) (1 minus 119890
minus120574119905) (25)
In which 119906119871119894(119905)
tends to Φ119894120574 [28] when 119905 rarr infin Thus
1003816
1003816
1003816
1003816
119906
119871119894(119905)
1003816
1003816
1003816
1003816
le
Φ
119894
120574
(26)
Consider (26) if 119879119891
and 120573 are known the residualuncertainties from the reaching phase can be compensatedby u119871 To consider the stability of the control system by using
the input according to (4) (12) can be rewritten as
V = s119879 [(Cf + CB120578 minus CBBminus1f) + C (BBminus1 minus 1) x119889]
minus s119879CBBminus1k119875s minus s119879CBBminus1uID minus s119879CBBminus1u
119871+ G
(27)
Notice that the adding of the u119871leads to uncertain of
negative definite on the Lyapunov function derivative Inorder to stabilize (27) the proportional portion has to takethe output from the LPF and the bound of uncertainty and itsderivative into account By defining119872
119905= 119872
0+ 119872
119889+ u119871
themodified proportional gain for each sliding surface can be119896
119875119894ge |120573119872
119905| + |(1 minus 120573)119906
119894ap| And together with the adaptationlaws defined in the previous section V in (27) is negativedefinite (
119881 lt 0) The sliding motion can be guaranteed for119905 isin [119905reachinfin) under the conditions stated earlier
3 Description of the Engine SpeedControl Modeling
As stated earlier a key step of the development controlscheme is based on the robust control techniques inwhich theapproach has the ability to neglect the conservatism and theneed for precise modeling [44] In addition the development
of an exact model for a real engine system is difficultbecause some parameters in the mathematical model cannotbe obtained exactly and the real plant is affected by thecomplexity of its uncertain nonlinearity [45] Consequentlythe system modeling in this work was linearized through thenominal transfer function of the real plant as the form of
119909 (119904) = 119866ta (119904) 119890minus119879119863119904
119906ta (119904) + 119866sa (119904) 119890minus119879119863119904
119906sa (119904) (28)
where 119909(119904) is the output the time delay is 119879119863 119906ta(119904) is the
control input for a throttle actuator and 119906sa(119904) is the controlinput for the spark advance system 119866ta(119904) and 119866sa(119904) are thelinearized models by 119906ta(119904) and 119906sa(119904) respectively Note thatthe symbol 119904 in this section denotes the complex argument ofthe Laplace transform which is not the sliding function
Although the conventional relevant engine dynamic forengine speed control depends on the coordination betweenthe throttle actuator and the spark advance system for theassessment in this work we have designed a controller thataims to control only the throttle actuator while the sparkadvance system is handled by conventional controller of theengine system Therefore the system modeling in this workcan be obtained by an adjustment of the throttle openingposition in degrees which is directly controlled with a DCmotor that is excited by the feed-forward control signalin DC-voltage as an input and the crankshaft speed inrevolutions perminute (rpm) as an output Consequently thelinearizationmodel at speed 900 rpm can be approximated inthe transfer function form as
119866 (119904) =
45119904
2+ 44119904 + 90
119904
3+ 15119904
2+ 25119904 + 1
(29)
where 119866(119904) is the transfer function of the real plant whichhas units of revolutions per minute (rpm) From the roughidentifications of (29) it is the third-order with relativedegree one and the system is BIBO stable because all polesare located on the left-hand side (LHS) of the 119904-plane Inaddition for the reason of low-speed control test (900 rpm)it is sensitive to any uncertain nonlinearities and externaldisturbancesTherefore the implementation of speed controlin the low-speed region is more difficult than in the high-speed control region Furthermore on average 30 percentof fuel consumption in urban city driving is spent at theidle speed range [46] As a consequence increasing theperformance of the low-speed control is able to increase fueleconomy and performance of the engine operation at anyoperating condition [32]
For simplicity to make the engine speed response asthe canonical form of (1) the rough identification model of(29) can be simplified to the first-order transfer function asfollows
119866 (119904) =
445
119904 + 0493
(30)
To make clear the acceptability of (30) the bode plotand the step response comparison between (29) and (30) aredemonstrated in Figure 2 The results make clear that thefirst-order transfer function in (30) can be employed in theperformance assessment of the proposed controller design in
6 Mathematical Problems in Engineering
0 2 4 6 8 10 120
102030405060708090
100Step response
Time (s)
Am
plitu
de
3rd order1st order
10152025303540
minus90
minus45
0
Frequency (rads)
Bode diagram
Mag
nitu
de (d
B)Ph
ase (
deg)
10minus2
10minus1
100
101
Frequency (rads)10
minus210
minus110
010
1
Figure 2 The validation of the 1st-order model
the simulations and (30) can be expressed as the time-domaindifferential equation as follows
= minus0493119909 + 445119906 (31)
where 119909 is the speed output and 119906 is the input
4 Illustrative Examples
41 Simulation Verification For the simulation verificationthe system modeling of (31) is used in order to assess theperformance of the proposed control scheme (LPFSMC andAdaptive PID) that is performed viaMATLAB-Simulink pro-gramming with a sampling period of 1ms The performanceof the proposed controller is compared with different controltechniques which are the PID control technique and the SMCtechnique The specific control parameters are chosen suchthat the sliding gain of the proposed control scheme and theconventional SMC is M
119905= 10 the cut-off frequency of the
first-order LPF is119879119891= 4 while the setting control parameters
of the PID controller are obtained by the Ziegler-Nicholstuning method
Figure 3(a) demonstrates the response results of theproposed control scheme which has a small rise time andsetting time and higher tracking accuracy than other controltechniques (PID controller and SMC) It demonstrates thatthe proposed adaptation law is capable of updating the PID
controller online during the control process within a shortperiod Furthermore the proposed control scheme can pro-vide optimal control input rapidly and has smooth controlinput which is achieved by the cut-off frequency property ofthe LPF (see Figure 3(b))
Figure 3(c) shows the error comparison among the dif-ferent controllers as the results the errors from the pro-posed control scheme can approach zero faster than othercontrol techniques and it has lower chattering than the SMCtechnique Note that although the chattering of the outputresponse control input and the errors of the PID controllerdoes not appear the results (see Figure 3) reveal that itsresponse has higher rise-time high-overshoot and longersetting time which are not satisfactory from the viewpointof a control system
42 Practical Experiment In this section we demonstrate theefficiency of the proposed control scheme in the real systemThe experimental technical data are shown in Table 1 In oursetup the functional block diagrams of the apparatus used inthe experiments are illustrated in Figure 4 which is used forperformance assessment of the proposed control schemeThesystem in Figure 4 consists of five main parts which are thecontroller unit electronic throttle valve control unit (ETC)spark-ignition (SI) engine system the power train system
Mathematical Problems in Engineering 7
Time (s)
Spee
d re
spon
se (r
pm)
ZOOM
Time (s)
Spee
d re
spon
se(r
pm)
SMCLPFSMC and adaptive PIDDesiredPID
0200400600800
10001200140016001800
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 208998995
9009005
901
(a)
Time (s)
Con
trol i
nput
(V)
SMC LPFSMC and adaptive PIDPID
minus30minus25minus20minus15minus10minus5
05
101520
2 4 6 8 10 12 14 16 18 200
(b)
Erro
rs
SMC LPFSMC and adaptive PIDPID
Time (s)
Erro
rs
ZOOM
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus1000minus800minus600minus400minus200
0200400600800
005
1
minus05minus1
0 2 4 6 8 10 12 14 16 18 20
(c)
Figure 3 Comparison of simulation results among different control techniques (a) the output response (b) the control inputs (c) the errors
PWM M
DC motor
Gear box
Throttle opening sensor
Throttle body
Control system
Electronic throttle control unit
SI engine
ADCDAC
Amplifier
Air
Speed calculation
Throttle position calculation
Fuel consumptioncomputation
Emission data logger(HC CO)
Speed sensor
Fuel flow sensor
Emission sensor
Power trainsystem
Dynamometer
Figure 4 Schematic diagram of the experiment
8 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
DesiredLPFSMC and adaptive PID
Con
trol i
nput
(V)
Time (s)
Slid
ing
varia
ble (
s)
Time (s)
Thro
ttle v
alve
ope
ning
(deg
)
Time (s)
0 20 40 60 80 100 120 140 160 180 200600650700750800850900950
1000
0
01
02
03
04
05
06
0 20 40 60 80 100 120 140 160 180 200
minus200minus150minus100minus50
050
100150200
0 20 40 60 80 100 120 140 160 180 200012345678
0 20 40 60 80 100 120 140 160 180 200
Figure 5 Experimental results of the proposed controller (LPFSMC and Adaptive PID technique)
Table 1 Experimental technical data
Item ValueSI engine (4 cylinders 900 ccgasoline type) Test range 600ndash3000 rpm
Speed sensor (rpm) Sampling speed approximately5000 ts
Throttle position sensor Measurement range 0ndash80∘
ADCDAC minus10 to 10VDC 20mA
COMPUTER Core2Duo 293GHz 4GBRAM
DCmotor 48ndash6VFuel type (experiments) Ethanol-gasoline blended (E20)
and the dynamometer which is used to generate the load-torque into the systemThe engine speed is interpreted as thecrankshaft rotation rate in revolutions per minute (rpm) andis regulated by opening the throttle In this task the throttlevalve is directly actuated by a DCmotor in which the angularmovement is handled by the control signal in the form ofPulseWidth Modulation (PWM)The exhaust emissions COandHCwere alsomeasured through a nondispersive infraredanalysis machine (Infralyt smart) in which the acquiringsampling data is 1 s while the fuel consumptionwasmeasuredby the fuel flow sensor (Hall effect-800 series) with thesampling period is 1ms The computation unit is performedwith MATLAB-Simulink programming An ADCDAC isused as an interface systembetween the computer and the realplant while the sampling period is 1ms for all experiments
As seen in Figure 5 the desired speed is chosen to rapidchange from 750 rpm to 900 rpm and 900 rpm to 750 rpmand the experiments were performed for 200 s This resultreveals that the speed response of the proposed controlscheme can reach the desired speedwithin short time and hasno overshoot and tiny oscillationThe control input is smoothand reaches an optimal value within a short time and thesliding variable can approach zero rapidly Fast convergenceof the response is a result of the updated control gains (119870
119868
and 119870119863) of the PID controller which can be adjusted rapidly
during the control process according to the adaptive lawFurthermore the characteristic of the opening position of thethrottle valve was alsomeasuredThis reveals that themotionof the actuator has smooth and tiny oscillations
43 Tracking Performance and Disturbance Rejection TestThe robust properties and the tracking performance of theproposed control schemewere also assessed because it is wellknown that the engine speed control is affected by the stateof accessory changes such as external load disturbance [41]In the experiments we compare the disturbance rejectionperformance among the proposed controller SMC techniqueand PID controller The load disturbance is generated bythe dynamometer while the speed set-point is chosen to be900 rpm Note that for the reason of low-speed test it issensitive from any disturbances therefore the implementa-tion in the low-speed region is more difficult than the high-speed control task Furthermore high performance of low-speed control leads to increase the performance of the engineoperation at any operating condition [32]
Mathematical Problems in Engineering 9
Time (s)Lo
ad (W
)
75
225
Engi
ne sp
eed
(rpm
)
DesiredLPFSMC and adaptive PID
PIDSMC
15
30
0
1000
950
900
850
800
Time (s)
120 125 130 135 140 145 150 155 160
120 125 130 135 140 145 150 155 160
Figure 6 Comparisons of tracking performance and disturbance rejection of the controllers
As seen in Figure 6 at the time 125 sec the load torquewas applied immediately into the engine speed control taskThis proposed to disturb the stability of the control system atthe steady-state condition The proposed control scheme canimprove the speed deviation rapidly and is capable of trackingthe desired speed better than other control techniques Inaddition the load torque was decreased immediately at thetime 150 sec The results show that the proposed controlscheme can decrease the speed deviation from the desiredspeed faster than other control techniques The findingsreveal that the proposed control scheme has effective ofthe robustness and fast adaptation and has better trackingperformance than other control techniques
44 Fuel Consumption andExhaust Emission Investigation Inthis section the fuel consumption and the exhaust emissionof the engine speed control by using the proposed controlscheme and different control techniques (SMC techniqueand PID controller) were investigated (see Figure 7) In theexperiments the desired speed was performed for 400 secand was rapidly changed as shown in Figure 7(a) For theaverage total fuel consumption comparison (see Figure 7(b))the proposed control scheme can attain an excellent resultwith the lowest averaged total fuel consumption whichwas obtained by the average of the fuel consumptions persecond
In addition the average exhaust emissions were alsoinvestigated (see Figure 7(c)) The CO and HC emissions arethe main pollutants contributed by the SI engines In theprinciple of the combustion process of SI engine the HCemission is appeared when fuel molecules in the engine
cannot burn or burn only partially while the CO emissionis produced when the carbon in the fuel is partially oxi-dized rather than fully oxidized to carbon dioxide Howeverincreasing efficient strategies for engine speed control viathrottle valve regulation method is capable of increasingcombustion performance as it can reduce pollutant emissionsalso [38] In the experiments effects of the controllers wereinvestigated via the constant speed set points and no addingan external engine load (small load from the unloadedhydrostatic CVT)Thus the CO
2andNO
119909which are sensitive
to speed variation and high temperature operation did notmeasure in this work (the experiments perform at coolanttemperature of 70ndash80∘C for short period) As a result bothaverages of the CO and HC emission data were calculatedby the average of emissions per second in which obtainedby the direct measurement method [43] Additionally theseresults demonstrate that high fuel consumption and exhaustemission are affected by high variation of the engine speedduring tracking of the set pointsThese results also imply thatthe performance of the SI engine at any operating conditioncan be improved by an advanced engine speed control viathe electronic throttle valve regulation method as shown inFigure 7
5 Conclusions
The incorporation of the SMC and a first-order LPF witha new adaptive PID controller is proposed for trackingthe control task of an uncertain nonlinear system Thecontroller has been successfully applied to the problem ofthe speed tracking control of an SI engine through electronic
10 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
PIDSMC
LPFSMC and adaptive PIDDesired
0 50 100 150 200 250 300 350 4000
500
1000
1500
2000
2500
(a)
00689
0071
00694
006750068
006850069
00695007
007050071
00715
LPFSMC andadaptive PID
SMC PID
Fuel consumption (Lmin)
(b)
20288 41113 20302
105977
425503
109623
0500
10001500200025003000350040004500
LPFSMC andadaptive PID
SMC PID
HC (ppm)CO (ppm)
(c)
Figure 7 Comparisons of (a) tracking performance of the controllers (b) fuel consumption rates (c) exhaust emission rates
throttle valve control architecture From the simulation andexperimental results it achieves that
(1) the proposed adaptation law is capable of optimalonline update the PID controller during the controlprocess within a short period
(2) the chattering of the SMC can be alleviated by afirst-order low pass filter while the robustness of thecontrol system similar to that of the slidingmode suchthat the load torque disturbances can be compensatedquite accurately
(3) the proposed control scheme has high performancein implementation as it can be achieved in theproblem of engine speed control in which the systemis largely uncertain nonlinear system and rathercomplex mechanisms
Conflict of Interests
The authors have no competing interests
Acknowledgment
This research is financially supported by the Office ofResearch Administration (ORA) and Farm Engineering andAutomation Technology Research Group (FEAT) of Khon
Kaen University Thailand The authors are also thankfulto the reviewers and Mr Ian Thomas for their valuablecomments and suggestions for English grammar correctionrespectively
References
[1] K-C Hsu W-Y Wang and P-Z Lin ldquoSliding mode controlfor uncertain nonlinear systemswithmultiple inputs containingsector nonlinearities and deadzonesrdquo IEEE Transactions onSystems Man and Cybernetics Part B Cybernetics vol 34 no1 pp 374ndash380 2004
[2] G Bartolini and A Ferrara ldquoMulti-input sliding mode controlof a class of uncertain nonlinear systemsrdquo IEEE Transactions onAutomatic Control vol 41 no 11 pp 1662ndash1666 1996
[3] T-C Kuo Y-J Huang and S-H Chang ldquoSliding mode controlwith self-tuning law for uncertain nonlinear systemsrdquo ISATransactions vol 47 no 2 pp 171ndash178 2008
[4] G Montaseri and M J Yazdanpanah ldquoPredictive control ofuncertain nonlinear parabolic PDE systems using a Galerkinneural-network-based modelrdquo Communications in NonlinearScience and Numerical Simulation vol 17 no 1 pp 388ndash4042012
[5] F O Tellez A G Loukianov E N Sanchez and E Jose BayroCorrochano ldquoDecentralized neural identification and controlfor uncertain nonlinear systems application to planar robotrdquoJournal of the Franklin Institute vol 347 no 6 pp 1015ndash10342010
Mathematical Problems in Engineering 11
[6] A Bazaei and V J Majd ldquoFeedback linearization of discrete-time nonlinear uncertain plants via first-principles-based serialneuro-gray-box modelsrdquo Journal of Process Control vol 13 no8 pp 819ndash830 2003
[7] T-Y Kuc and W-G Han ldquoAn adaptive PID learning controlof robot manipulatorsrdquo Automatica vol 36 no 5 pp 717ndash7252000
[8] Y Pan Y Zhou T Sun and M J Er ldquoComposite adaptivefuzzy 119867
infintracking control of uncertain nonlinear systemsrdquo
Neurocomputing vol 99 pp 15ndash24 2013[9] X Liu R Tao and M Tavakoli ldquoAdaptive control of uncertain
nonlinear teleoperation systemsrdquo Mechatronics vol 24 no 1pp 66ndash78 2014
[10] W-D Chang and J-J Yan ldquoAdaptive robust PID controllerdesign based on a sliding mode for uncertain chaotic systemsrdquoChaos Solitons amp Fractals vol 26 no 1 pp 167ndash175 2005
[11] T C Kuo Y J Huang C Y Chen and C H Chang ldquoAdaptivesliding mode control with PID tuning for uncertain systemrdquoEngineering Letters vol 16 no 3 pp 1ndash5 2008
[12] M N Howell and M C Best ldquoOn-line PID tuning forengine idle-speed control using continuous action reinforce-ment learning automatardquo Control Engineering Practice vol 8no 2 pp 147ndash154 2000
[13] C-F Hsu and B-K Lee ldquoFPGA-based adaptive PID control ofa DC motor driver via sliding-mode approachrdquo Expert Systemswith Applications vol 38 no 9 pp 11866ndash11872 2011
[14] DWMemering and PHMeckl ldquoComparison of adaptive con-trol techniques applied to diesel engine idle speed regulationrdquoJournal of Dynamic Systems Measurement and Control vol 124no 4 pp 682ndash688 2002
[15] V I Utkin ldquoSliding mode control design principles andapplications to electric drivesrdquo IEEE Transactions on IndustrialElectronics vol 40 no 1 pp 23ndash36 1993
[16] Y J Huang and T C Kuo ldquoRobust output tracking controlfor nonlinear time-varying robotic manipulatorsrdquo ElectricalEngineering vol 87 no 1 pp 47ndash55 2005
[17] M Hajatipour and M Farrokhi ldquoChattering free with noisereduction in sliding-mode observers using frequency domainanalysisrdquo Journal of Process Control vol 20 no 8 pp 912ndash9212010
[18] A Sabanovic L Fridman and S Spurgeon Variable StructureSystems From Principles to Implementation The Institution ofEngineering and Technology 2004
[19] Y Xu ldquoChattering free robust control for nonlinear systemsrdquoIEEE Transactions on Control Systems Technology vol 16 no 6pp 1352ndash1359 2008
[20] H Lee and V I Utkin ldquoChattering suppression methods insliding mode control systemsrdquo Annual Reviews in Control vol31 no 2 pp 179ndash188 2007
[21] Y Ren Z Liu L Chang and N Wen ldquoAdaptive slidingmode robust control for virtual compound-axis servo systemrdquoMathematical Problems in Engineering vol 2013 Article ID343851 9 pages 2013
[22] M-L Tseng and M-S Chen ldquoChattering reduction of slidingmode control by low-pass filtering the control signalrdquo AsianJournal of Control vol 12 no 3 pp 392ndash398 2010
[23] H Sira-RamIRez ldquoOn the dynamical sliding mode control ofnonlinear systemsrdquo International Journal of Control vol 57 no5 pp 1039ndash1061 1993
[24] J-X Xu Y-J Pan and T-H Lee ldquoSliding mode controlwith closed-loop filtering architecture for a class of nonlinear
systemsrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 51 no 4 pp 168ndash173 2004
[25] A Deenadayalan and G S Ilango ldquoPosition sensorless slidingmode observer with sigmoid function for Brushless DCmotorrdquoin Proceedings of the International Conference on Advances inPower Conversion and Energy Technologies (APCET rsquo12) pp 1ndash6IEEE August 2012
[26] Y Xia X Yu andW Oghanna ldquoAdaptive robust fast control forinduction motorsrdquo IEEE Transactions on Industrial Electronicsvol 47 no 4 pp 854ndash862 2000
[27] M Niclai Theory of Nonlinear Control Systems McGraw-Hill1969
[28] J J Slotine andW Li Applied Nonlinear Control Prentice-HallEnglewood Cliffs NJ USA 1991
[29] D Gorinevsky and L A Feldkamp ldquoRBF network feedforwardcompensation of load disturbance in idle speed controlrdquo IEEEControl Systems vol 16 no 6 pp 18ndash27 1996
[30] S Di Cairano D Yanakiev A Bemporad I V Kolmanovskyand D Hrovat ldquoModel predictive idle speed control designanalysis and experimental evaluationrdquo IEEE Transactions onControl Systems Technology vol 20 no 1 pp 84ndash97 2012
[31] P F Puleston S Spurgeon andGMonsees ldquoAutomotive enginespeed control a robust nonlinear control frameworkrdquo IEEProceedings Control Theory and Applications vol 148 no 1 pp81ndash87 2001
[32] Y Yildiz A M Annaswamy D Yanakiev and I KolmanovskyldquoSpark-ignition-engine idle speed control an adaptive controlapproachrdquo IEEE Transactions on Control Systems Technologyvol 19 no 5 pp 990ndash1002 2011
[33] A Sugeng K Baharin T Hishamuddin and J B SupriyoldquoEngine speed control using online ANN for vehicle withEMDAP-CVTrdquo Jurnal Mekanikal vol 22 pp 39ndash52 2006
[34] M K Khan K B Goh and S K Spurgeon ldquoSecond ordersliding mode control of a diesel enginerdquo Asian Journal ofControl vol 5 no 4 pp 614ndash619 2003
[35] J R Wagner D M Dawson and L Zeyu ldquoNonlinear air-to-fuel ratio and engine speed control for hybrid vehiclesrdquo IEEETransactions on Vehicular Technology vol 52 no 1 pp 184ndash1952003
[36] F Assadian S Fekri andM Hancock ldquoHybrid electric vehicleschallenges strategies for advanced engine speed controlrdquo inProceedings of the IEEE International Electric Vehicle Conference(IEVC rsquo12) March 2012
[37] A G Ulsoy H Peng and M Cakmakci Automotive ControlSystems Cambridge University Press Cambridge UK 2014
[38] C Ji and S Wang ldquoStrategies for improving the idle perfor-mance of a spark-ignited gasoline enginerdquo International Journalof Hydrogen Energy vol 37 no 4 pp 3938ndash3944 2012
[39] S Wang C Ji M Zhang and B Zhang ldquoReducing theidle speed of a spark-ignited gasoline engine with hydrogenadditionrdquo International Journal of Hydrogen Energy vol 35 no19 pp 10580ndash10588 2010
[40] DHrovat and J Sun ldquoModels and controlmethodologies for ICengine idle speed control designrdquo Control Engineering Practicevol 5 no 8 pp 1093ndash1100 1997
[41] B Alt J P Blath F Svaricek and M Schultalbers ldquoMultiplesliding surface control of idle engine speed and torque reservewith dead start assist controlrdquo IEEE Transactions on IndustrialElectronics vol 56 no 9 pp 3580ndash3592 2009
12 Mathematical Problems in Engineering
[42] T Radpukdee and P Jirawattana ldquoUncertainty learning andcompensation an application to pressure tracking of an electro-hydraulic proportional relief valverdquo Control Engineering Prac-tice vol 17 no 2 pp 291ndash301 2009
[43] P A Loannou and J Sun Robust Adaptive Control PTRPrentice-Hall 1996
[44] C D Richard and H B Robert Modern Control SystemsPrentice Hall Upper Saddle River NJ USA 2011
[45] A Jansri and P Sooraksa ldquoEnhanced model and fuzzy strategyof air to fuel ratio control for spark ignition enginesrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 922ndash9332012
[46] Z Ye ldquoModeling identification design and implementation ofnonlinear automotive idle speed control systemsmdashanoverviewrdquoIEEE Transactions on Systems Man and Cybernetics Part CApplications and Reviews vol 37 no 6 pp 1137ndash1151 2007
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
4 Mathematical Problems in Engineering
where uID = k119868int s 119889119905 + k
119863s Equation (11) shows the
fact that the control gain cannot be determined exactlyIn the following the gain margins concept [28] is adaptedwithout loss of generality due to the uncoupling andmatchingconditions From the concept the gain estimation can bedescribed by B = diag(119887) 119887 = radic119887min sdot 119887max and the boundof the control gain ratio can then be realized in the form120573
minus1le
BBminus1 le 120573 while 120573 = radic119887max119887min and the initialvalue in each argument of the three gains (k
119875 k119868 and k
119863) of
the PID portion is positive Substituting (11) into (10) yields
V = s119879 [(Cf + CB120578 minus CBBminus1f) + x119889(CBBminus1 minus C)]
minus s119879CBBminus1k119875s minus s119879CBBminus1uID + G
(12)
where G = (k119879119875k119875+ k119879119868k119868+ k119879119863k119863) which is the adaptation
term For (12) if k119875is chosen to overcome a part of the
uncertainties the adaptation law in the last term G can bedetermined to eliminate the rest of them consequently Inorder to compensate for the uncertainties in the reachingphase the proportional gain 119896
119875119894should satisfy equations
below1003817
1003817
1003817
1003817
k119875
1003817
1003817
1003817
1003817
ge
1003817
1003817
1003817
1003817
1003817
(
BBminus1f + BBminus1B120578 minus f) + (1 minus BBminus1) x119889
1003817
1003817
1003817
1003817
1003817
(13)
Then all arguments in the proportional gain are selectedto satisfy
119896
119875119894ge
1003816
1003816
1003816
1003816
120573119872
119900+ (1 minus 120573) (minus119891
119894+
119894119889)
1003816
1003816
1003816
1003816
(14)
119896
119875119894ge
1003816
1003816
1003816
1003816
120573119872
119900
1003816
1003816
1003816
1003816
+
1003816
1003816
1003816
1003816
1003816
(1 minus 120573) 119906
119894ap1003816
1003816
1003816
1003816
1003816
(15)
Equations (13) to (15) correspond to the gain margincalculationmethod [28] Even if the proportional term can bedesigned to cope with the first term in (12) its residual errorstill exists Let the residual error be the difference betweenthe first term and the second term of (12) It is bounded by apositive valueΔ = s119879[(Cf+CB120578minusCBBminus1f)+C(BBminus1minus1)x
119889]minus
s119879CBBminus1k119875s due to a bounded control input By adding the
bound of the control gain ratio (12) can be rewritten as
V le minusΔs119879s minus s119879CBBminus1k119868int s 119889119905 minus s119879CBBminus1k
119863s
+ k119879119875k119875+ k119879119868k119868+ k119879119863k119863
le minusΔs119879s minus 120573s119879Ck119868int s 119889119905 minus 120573s119879Ck
119863s
+ k119879119875k119875+ k119879119868k119868+ k119879119863k119863
(16)
Obviously to satisfy the Lyapunov stability of the condi-tion V lt 0 and the adaptation law can be designed as k
119875= 0
k119868= 120573s119879Cint s 119889119905 and k
119863= 120573s119879C s Note that the proportional
gain has a coupling effectwith the sliding gainwhich operateswith the unity boundary layer width Therefore k
119875does not
need to be updated online The adaptation gains ( k119868and
k119863) are capable of guaranteeing the stability only outside
the bound of the control gain ratio 120573 This implies thatthis technique only offers a uniform ultimate boundedness
response Additionally it is usual to have a solution when thecontrol gain magnitude is unknown Even if the control gainis known or adapted the ultimate boundedness still occursinside the vicinity around the sliding surface Notice thatat the beginning state the integral and the derivative termsof the adaptation law may be arbitrary small because theuncertainties at the beginning state can be compensated byk119875 Consequently (16) can be replaced by the adaptation law
and the new expression of (16) becomes
V le minusΔs119879s (17)
With the positive-initial value of the PID gains and thecondition of (15) and the adaptation laws the stability withinthe reaching phase can be guaranteed The reaching time(119905reach) can be obtained by
119905reach le
1003817
1003817
1003817
1003817
s(119905=0)
1003817
1003817
1003817
1003817
Δ
(18)
222 Existence of the Sliding Condition The key issue of thissection is to describe the sliding mode retention For theexistence conditions of the sliding mode at 119905 ge 119905reach thefirst-order low-pass filter (LPF) is activated and the switchingsignal is alleviated in turn To describe the existence of thesliding condition substitute the control law u(119905) = Bminus1[uap minus(uPID minus u
119871)] Therefore the derivative of the closed-loop s
dynamic at 119905 ge 119905reach can be obtained by
s = (Cf + CB120578 minus CBBminus1f) + C (BBminus1 minus 1) x119889
minus CBBminus1k119875s minus CBBminus1uID + CBBminus1u
119871
(19)
With the condition in (15) (19) can be rearranged as
minusCBBminus1k119875s = s minus (Cf + CB120578 minus CBBminus1f)
minus C (BBminus1 minus 1) x119889+ CBBminus1uID minus CBBminus1u
119871
(20)
Multiplying (20) by (CBBminus1)minus1 yields
minusk119875s = BBminus1
sdot [Cminus1 s minus (f + B120578 minus BBminus1f) minus (BBminus1 minus 1) x119889
+BBminus1uID minus BBminus1u119871]
(21)
From the condition in (15) the sliding gain can bechanged to beM
119904= diag(119896
119875119894|119904
119894119905|) and the output from the LPF
can be satisfied by 119879119891u119871+ u119871= minus diag(119896
119875119894|119904
119894119905|)sgn(s) = minusk
119875s
Therefore
119879
119891u119871+ 2u119871
=
BBminus1
sdot[Cminus1 s minus (f + B120578minusBBminus1f)minus(BBminus1 minus 1) x119889+BBminus1uID]
(22)
Mathematical Problems in Engineering 5
As the reaching phase analysis the control law in (8) andits adaptation law offer convergence regulation of the stateIntuitively the sliding function s is bounded about the slidingsurface s= 0 due to imperfection of control action in practiceThus the derivative of the sliding function s will be boundedby the boundedness of s which also implies the integralof s converges to some limit [43] Consequently the RHS of(22) can be bounded and is rewritten by a residual matrix0 = [0
1 0
119898]
119879isin 119877
119898 For each argument of the u119871 the
residual function 0119894 119894 = 1 sdot sdot sdot 119898 can be interpreted as residual
errors after the reaching phase which satisfy
119879
119891
119871119894+ 2119906
119871119894= 0
119894 (23)
Given 120574 = 2119879
119891and 120593
119894= 0
119894119879
119891 (23) is rewritten as
119871119894+ 120574119906
119871119894= 120593
119894 (24)
From (24) the bound on 120593
119894can be interpreted into a
bound on the filter output 119906119871119894 Define the bound of 120593
119894= Φ
119894
The bound of the filter output |119906119871119894| can be written as (25)
which corresponds to [28]
1003816
1003816
1003816
1003816
119906
119871119894(119905)
1003816
1003816
1003816
1003816
le (
Φ
119894
120574
) (1 minus 119890
minus120574119905) (25)
In which 119906119871119894(119905)
tends to Φ119894120574 [28] when 119905 rarr infin Thus
1003816
1003816
1003816
1003816
119906
119871119894(119905)
1003816
1003816
1003816
1003816
le
Φ
119894
120574
(26)
Consider (26) if 119879119891
and 120573 are known the residualuncertainties from the reaching phase can be compensatedby u119871 To consider the stability of the control system by using
the input according to (4) (12) can be rewritten as
V = s119879 [(Cf + CB120578 minus CBBminus1f) + C (BBminus1 minus 1) x119889]
minus s119879CBBminus1k119875s minus s119879CBBminus1uID minus s119879CBBminus1u
119871+ G
(27)
Notice that the adding of the u119871leads to uncertain of
negative definite on the Lyapunov function derivative Inorder to stabilize (27) the proportional portion has to takethe output from the LPF and the bound of uncertainty and itsderivative into account By defining119872
119905= 119872
0+ 119872
119889+ u119871
themodified proportional gain for each sliding surface can be119896
119875119894ge |120573119872
119905| + |(1 minus 120573)119906
119894ap| And together with the adaptationlaws defined in the previous section V in (27) is negativedefinite (
119881 lt 0) The sliding motion can be guaranteed for119905 isin [119905reachinfin) under the conditions stated earlier
3 Description of the Engine SpeedControl Modeling
As stated earlier a key step of the development controlscheme is based on the robust control techniques inwhich theapproach has the ability to neglect the conservatism and theneed for precise modeling [44] In addition the development
of an exact model for a real engine system is difficultbecause some parameters in the mathematical model cannotbe obtained exactly and the real plant is affected by thecomplexity of its uncertain nonlinearity [45] Consequentlythe system modeling in this work was linearized through thenominal transfer function of the real plant as the form of
119909 (119904) = 119866ta (119904) 119890minus119879119863119904
119906ta (119904) + 119866sa (119904) 119890minus119879119863119904
119906sa (119904) (28)
where 119909(119904) is the output the time delay is 119879119863 119906ta(119904) is the
control input for a throttle actuator and 119906sa(119904) is the controlinput for the spark advance system 119866ta(119904) and 119866sa(119904) are thelinearized models by 119906ta(119904) and 119906sa(119904) respectively Note thatthe symbol 119904 in this section denotes the complex argument ofthe Laplace transform which is not the sliding function
Although the conventional relevant engine dynamic forengine speed control depends on the coordination betweenthe throttle actuator and the spark advance system for theassessment in this work we have designed a controller thataims to control only the throttle actuator while the sparkadvance system is handled by conventional controller of theengine system Therefore the system modeling in this workcan be obtained by an adjustment of the throttle openingposition in degrees which is directly controlled with a DCmotor that is excited by the feed-forward control signalin DC-voltage as an input and the crankshaft speed inrevolutions perminute (rpm) as an output Consequently thelinearizationmodel at speed 900 rpm can be approximated inthe transfer function form as
119866 (119904) =
45119904
2+ 44119904 + 90
119904
3+ 15119904
2+ 25119904 + 1
(29)
where 119866(119904) is the transfer function of the real plant whichhas units of revolutions per minute (rpm) From the roughidentifications of (29) it is the third-order with relativedegree one and the system is BIBO stable because all polesare located on the left-hand side (LHS) of the 119904-plane Inaddition for the reason of low-speed control test (900 rpm)it is sensitive to any uncertain nonlinearities and externaldisturbancesTherefore the implementation of speed controlin the low-speed region is more difficult than in the high-speed control region Furthermore on average 30 percentof fuel consumption in urban city driving is spent at theidle speed range [46] As a consequence increasing theperformance of the low-speed control is able to increase fueleconomy and performance of the engine operation at anyoperating condition [32]
For simplicity to make the engine speed response asthe canonical form of (1) the rough identification model of(29) can be simplified to the first-order transfer function asfollows
119866 (119904) =
445
119904 + 0493
(30)
To make clear the acceptability of (30) the bode plotand the step response comparison between (29) and (30) aredemonstrated in Figure 2 The results make clear that thefirst-order transfer function in (30) can be employed in theperformance assessment of the proposed controller design in
6 Mathematical Problems in Engineering
0 2 4 6 8 10 120
102030405060708090
100Step response
Time (s)
Am
plitu
de
3rd order1st order
10152025303540
minus90
minus45
0
Frequency (rads)
Bode diagram
Mag
nitu
de (d
B)Ph
ase (
deg)
10minus2
10minus1
100
101
Frequency (rads)10
minus210
minus110
010
1
Figure 2 The validation of the 1st-order model
the simulations and (30) can be expressed as the time-domaindifferential equation as follows
= minus0493119909 + 445119906 (31)
where 119909 is the speed output and 119906 is the input
4 Illustrative Examples
41 Simulation Verification For the simulation verificationthe system modeling of (31) is used in order to assess theperformance of the proposed control scheme (LPFSMC andAdaptive PID) that is performed viaMATLAB-Simulink pro-gramming with a sampling period of 1ms The performanceof the proposed controller is compared with different controltechniques which are the PID control technique and the SMCtechnique The specific control parameters are chosen suchthat the sliding gain of the proposed control scheme and theconventional SMC is M
119905= 10 the cut-off frequency of the
first-order LPF is119879119891= 4 while the setting control parameters
of the PID controller are obtained by the Ziegler-Nicholstuning method
Figure 3(a) demonstrates the response results of theproposed control scheme which has a small rise time andsetting time and higher tracking accuracy than other controltechniques (PID controller and SMC) It demonstrates thatthe proposed adaptation law is capable of updating the PID
controller online during the control process within a shortperiod Furthermore the proposed control scheme can pro-vide optimal control input rapidly and has smooth controlinput which is achieved by the cut-off frequency property ofthe LPF (see Figure 3(b))
Figure 3(c) shows the error comparison among the dif-ferent controllers as the results the errors from the pro-posed control scheme can approach zero faster than othercontrol techniques and it has lower chattering than the SMCtechnique Note that although the chattering of the outputresponse control input and the errors of the PID controllerdoes not appear the results (see Figure 3) reveal that itsresponse has higher rise-time high-overshoot and longersetting time which are not satisfactory from the viewpointof a control system
42 Practical Experiment In this section we demonstrate theefficiency of the proposed control scheme in the real systemThe experimental technical data are shown in Table 1 In oursetup the functional block diagrams of the apparatus used inthe experiments are illustrated in Figure 4 which is used forperformance assessment of the proposed control schemeThesystem in Figure 4 consists of five main parts which are thecontroller unit electronic throttle valve control unit (ETC)spark-ignition (SI) engine system the power train system
Mathematical Problems in Engineering 7
Time (s)
Spee
d re
spon
se (r
pm)
ZOOM
Time (s)
Spee
d re
spon
se(r
pm)
SMCLPFSMC and adaptive PIDDesiredPID
0200400600800
10001200140016001800
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 208998995
9009005
901
(a)
Time (s)
Con
trol i
nput
(V)
SMC LPFSMC and adaptive PIDPID
minus30minus25minus20minus15minus10minus5
05
101520
2 4 6 8 10 12 14 16 18 200
(b)
Erro
rs
SMC LPFSMC and adaptive PIDPID
Time (s)
Erro
rs
ZOOM
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus1000minus800minus600minus400minus200
0200400600800
005
1
minus05minus1
0 2 4 6 8 10 12 14 16 18 20
(c)
Figure 3 Comparison of simulation results among different control techniques (a) the output response (b) the control inputs (c) the errors
PWM M
DC motor
Gear box
Throttle opening sensor
Throttle body
Control system
Electronic throttle control unit
SI engine
ADCDAC
Amplifier
Air
Speed calculation
Throttle position calculation
Fuel consumptioncomputation
Emission data logger(HC CO)
Speed sensor
Fuel flow sensor
Emission sensor
Power trainsystem
Dynamometer
Figure 4 Schematic diagram of the experiment
8 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
DesiredLPFSMC and adaptive PID
Con
trol i
nput
(V)
Time (s)
Slid
ing
varia
ble (
s)
Time (s)
Thro
ttle v
alve
ope
ning
(deg
)
Time (s)
0 20 40 60 80 100 120 140 160 180 200600650700750800850900950
1000
0
01
02
03
04
05
06
0 20 40 60 80 100 120 140 160 180 200
minus200minus150minus100minus50
050
100150200
0 20 40 60 80 100 120 140 160 180 200012345678
0 20 40 60 80 100 120 140 160 180 200
Figure 5 Experimental results of the proposed controller (LPFSMC and Adaptive PID technique)
Table 1 Experimental technical data
Item ValueSI engine (4 cylinders 900 ccgasoline type) Test range 600ndash3000 rpm
Speed sensor (rpm) Sampling speed approximately5000 ts
Throttle position sensor Measurement range 0ndash80∘
ADCDAC minus10 to 10VDC 20mA
COMPUTER Core2Duo 293GHz 4GBRAM
DCmotor 48ndash6VFuel type (experiments) Ethanol-gasoline blended (E20)
and the dynamometer which is used to generate the load-torque into the systemThe engine speed is interpreted as thecrankshaft rotation rate in revolutions per minute (rpm) andis regulated by opening the throttle In this task the throttlevalve is directly actuated by a DCmotor in which the angularmovement is handled by the control signal in the form ofPulseWidth Modulation (PWM)The exhaust emissions COandHCwere alsomeasured through a nondispersive infraredanalysis machine (Infralyt smart) in which the acquiringsampling data is 1 s while the fuel consumptionwasmeasuredby the fuel flow sensor (Hall effect-800 series) with thesampling period is 1ms The computation unit is performedwith MATLAB-Simulink programming An ADCDAC isused as an interface systembetween the computer and the realplant while the sampling period is 1ms for all experiments
As seen in Figure 5 the desired speed is chosen to rapidchange from 750 rpm to 900 rpm and 900 rpm to 750 rpmand the experiments were performed for 200 s This resultreveals that the speed response of the proposed controlscheme can reach the desired speedwithin short time and hasno overshoot and tiny oscillationThe control input is smoothand reaches an optimal value within a short time and thesliding variable can approach zero rapidly Fast convergenceof the response is a result of the updated control gains (119870
119868
and 119870119863) of the PID controller which can be adjusted rapidly
during the control process according to the adaptive lawFurthermore the characteristic of the opening position of thethrottle valve was alsomeasuredThis reveals that themotionof the actuator has smooth and tiny oscillations
43 Tracking Performance and Disturbance Rejection TestThe robust properties and the tracking performance of theproposed control schemewere also assessed because it is wellknown that the engine speed control is affected by the stateof accessory changes such as external load disturbance [41]In the experiments we compare the disturbance rejectionperformance among the proposed controller SMC techniqueand PID controller The load disturbance is generated bythe dynamometer while the speed set-point is chosen to be900 rpm Note that for the reason of low-speed test it issensitive from any disturbances therefore the implementa-tion in the low-speed region is more difficult than the high-speed control task Furthermore high performance of low-speed control leads to increase the performance of the engineoperation at any operating condition [32]
Mathematical Problems in Engineering 9
Time (s)Lo
ad (W
)
75
225
Engi
ne sp
eed
(rpm
)
DesiredLPFSMC and adaptive PID
PIDSMC
15
30
0
1000
950
900
850
800
Time (s)
120 125 130 135 140 145 150 155 160
120 125 130 135 140 145 150 155 160
Figure 6 Comparisons of tracking performance and disturbance rejection of the controllers
As seen in Figure 6 at the time 125 sec the load torquewas applied immediately into the engine speed control taskThis proposed to disturb the stability of the control system atthe steady-state condition The proposed control scheme canimprove the speed deviation rapidly and is capable of trackingthe desired speed better than other control techniques Inaddition the load torque was decreased immediately at thetime 150 sec The results show that the proposed controlscheme can decrease the speed deviation from the desiredspeed faster than other control techniques The findingsreveal that the proposed control scheme has effective ofthe robustness and fast adaptation and has better trackingperformance than other control techniques
44 Fuel Consumption andExhaust Emission Investigation Inthis section the fuel consumption and the exhaust emissionof the engine speed control by using the proposed controlscheme and different control techniques (SMC techniqueand PID controller) were investigated (see Figure 7) In theexperiments the desired speed was performed for 400 secand was rapidly changed as shown in Figure 7(a) For theaverage total fuel consumption comparison (see Figure 7(b))the proposed control scheme can attain an excellent resultwith the lowest averaged total fuel consumption whichwas obtained by the average of the fuel consumptions persecond
In addition the average exhaust emissions were alsoinvestigated (see Figure 7(c)) The CO and HC emissions arethe main pollutants contributed by the SI engines In theprinciple of the combustion process of SI engine the HCemission is appeared when fuel molecules in the engine
cannot burn or burn only partially while the CO emissionis produced when the carbon in the fuel is partially oxi-dized rather than fully oxidized to carbon dioxide Howeverincreasing efficient strategies for engine speed control viathrottle valve regulation method is capable of increasingcombustion performance as it can reduce pollutant emissionsalso [38] In the experiments effects of the controllers wereinvestigated via the constant speed set points and no addingan external engine load (small load from the unloadedhydrostatic CVT)Thus the CO
2andNO
119909which are sensitive
to speed variation and high temperature operation did notmeasure in this work (the experiments perform at coolanttemperature of 70ndash80∘C for short period) As a result bothaverages of the CO and HC emission data were calculatedby the average of emissions per second in which obtainedby the direct measurement method [43] Additionally theseresults demonstrate that high fuel consumption and exhaustemission are affected by high variation of the engine speedduring tracking of the set pointsThese results also imply thatthe performance of the SI engine at any operating conditioncan be improved by an advanced engine speed control viathe electronic throttle valve regulation method as shown inFigure 7
5 Conclusions
The incorporation of the SMC and a first-order LPF witha new adaptive PID controller is proposed for trackingthe control task of an uncertain nonlinear system Thecontroller has been successfully applied to the problem ofthe speed tracking control of an SI engine through electronic
10 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
PIDSMC
LPFSMC and adaptive PIDDesired
0 50 100 150 200 250 300 350 4000
500
1000
1500
2000
2500
(a)
00689
0071
00694
006750068
006850069
00695007
007050071
00715
LPFSMC andadaptive PID
SMC PID
Fuel consumption (Lmin)
(b)
20288 41113 20302
105977
425503
109623
0500
10001500200025003000350040004500
LPFSMC andadaptive PID
SMC PID
HC (ppm)CO (ppm)
(c)
Figure 7 Comparisons of (a) tracking performance of the controllers (b) fuel consumption rates (c) exhaust emission rates
throttle valve control architecture From the simulation andexperimental results it achieves that
(1) the proposed adaptation law is capable of optimalonline update the PID controller during the controlprocess within a short period
(2) the chattering of the SMC can be alleviated by afirst-order low pass filter while the robustness of thecontrol system similar to that of the slidingmode suchthat the load torque disturbances can be compensatedquite accurately
(3) the proposed control scheme has high performancein implementation as it can be achieved in theproblem of engine speed control in which the systemis largely uncertain nonlinear system and rathercomplex mechanisms
Conflict of Interests
The authors have no competing interests
Acknowledgment
This research is financially supported by the Office ofResearch Administration (ORA) and Farm Engineering andAutomation Technology Research Group (FEAT) of Khon
Kaen University Thailand The authors are also thankfulto the reviewers and Mr Ian Thomas for their valuablecomments and suggestions for English grammar correctionrespectively
References
[1] K-C Hsu W-Y Wang and P-Z Lin ldquoSliding mode controlfor uncertain nonlinear systemswithmultiple inputs containingsector nonlinearities and deadzonesrdquo IEEE Transactions onSystems Man and Cybernetics Part B Cybernetics vol 34 no1 pp 374ndash380 2004
[2] G Bartolini and A Ferrara ldquoMulti-input sliding mode controlof a class of uncertain nonlinear systemsrdquo IEEE Transactions onAutomatic Control vol 41 no 11 pp 1662ndash1666 1996
[3] T-C Kuo Y-J Huang and S-H Chang ldquoSliding mode controlwith self-tuning law for uncertain nonlinear systemsrdquo ISATransactions vol 47 no 2 pp 171ndash178 2008
[4] G Montaseri and M J Yazdanpanah ldquoPredictive control ofuncertain nonlinear parabolic PDE systems using a Galerkinneural-network-based modelrdquo Communications in NonlinearScience and Numerical Simulation vol 17 no 1 pp 388ndash4042012
[5] F O Tellez A G Loukianov E N Sanchez and E Jose BayroCorrochano ldquoDecentralized neural identification and controlfor uncertain nonlinear systems application to planar robotrdquoJournal of the Franklin Institute vol 347 no 6 pp 1015ndash10342010
Mathematical Problems in Engineering 11
[6] A Bazaei and V J Majd ldquoFeedback linearization of discrete-time nonlinear uncertain plants via first-principles-based serialneuro-gray-box modelsrdquo Journal of Process Control vol 13 no8 pp 819ndash830 2003
[7] T-Y Kuc and W-G Han ldquoAn adaptive PID learning controlof robot manipulatorsrdquo Automatica vol 36 no 5 pp 717ndash7252000
[8] Y Pan Y Zhou T Sun and M J Er ldquoComposite adaptivefuzzy 119867
infintracking control of uncertain nonlinear systemsrdquo
Neurocomputing vol 99 pp 15ndash24 2013[9] X Liu R Tao and M Tavakoli ldquoAdaptive control of uncertain
nonlinear teleoperation systemsrdquo Mechatronics vol 24 no 1pp 66ndash78 2014
[10] W-D Chang and J-J Yan ldquoAdaptive robust PID controllerdesign based on a sliding mode for uncertain chaotic systemsrdquoChaos Solitons amp Fractals vol 26 no 1 pp 167ndash175 2005
[11] T C Kuo Y J Huang C Y Chen and C H Chang ldquoAdaptivesliding mode control with PID tuning for uncertain systemrdquoEngineering Letters vol 16 no 3 pp 1ndash5 2008
[12] M N Howell and M C Best ldquoOn-line PID tuning forengine idle-speed control using continuous action reinforce-ment learning automatardquo Control Engineering Practice vol 8no 2 pp 147ndash154 2000
[13] C-F Hsu and B-K Lee ldquoFPGA-based adaptive PID control ofa DC motor driver via sliding-mode approachrdquo Expert Systemswith Applications vol 38 no 9 pp 11866ndash11872 2011
[14] DWMemering and PHMeckl ldquoComparison of adaptive con-trol techniques applied to diesel engine idle speed regulationrdquoJournal of Dynamic Systems Measurement and Control vol 124no 4 pp 682ndash688 2002
[15] V I Utkin ldquoSliding mode control design principles andapplications to electric drivesrdquo IEEE Transactions on IndustrialElectronics vol 40 no 1 pp 23ndash36 1993
[16] Y J Huang and T C Kuo ldquoRobust output tracking controlfor nonlinear time-varying robotic manipulatorsrdquo ElectricalEngineering vol 87 no 1 pp 47ndash55 2005
[17] M Hajatipour and M Farrokhi ldquoChattering free with noisereduction in sliding-mode observers using frequency domainanalysisrdquo Journal of Process Control vol 20 no 8 pp 912ndash9212010
[18] A Sabanovic L Fridman and S Spurgeon Variable StructureSystems From Principles to Implementation The Institution ofEngineering and Technology 2004
[19] Y Xu ldquoChattering free robust control for nonlinear systemsrdquoIEEE Transactions on Control Systems Technology vol 16 no 6pp 1352ndash1359 2008
[20] H Lee and V I Utkin ldquoChattering suppression methods insliding mode control systemsrdquo Annual Reviews in Control vol31 no 2 pp 179ndash188 2007
[21] Y Ren Z Liu L Chang and N Wen ldquoAdaptive slidingmode robust control for virtual compound-axis servo systemrdquoMathematical Problems in Engineering vol 2013 Article ID343851 9 pages 2013
[22] M-L Tseng and M-S Chen ldquoChattering reduction of slidingmode control by low-pass filtering the control signalrdquo AsianJournal of Control vol 12 no 3 pp 392ndash398 2010
[23] H Sira-RamIRez ldquoOn the dynamical sliding mode control ofnonlinear systemsrdquo International Journal of Control vol 57 no5 pp 1039ndash1061 1993
[24] J-X Xu Y-J Pan and T-H Lee ldquoSliding mode controlwith closed-loop filtering architecture for a class of nonlinear
systemsrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 51 no 4 pp 168ndash173 2004
[25] A Deenadayalan and G S Ilango ldquoPosition sensorless slidingmode observer with sigmoid function for Brushless DCmotorrdquoin Proceedings of the International Conference on Advances inPower Conversion and Energy Technologies (APCET rsquo12) pp 1ndash6IEEE August 2012
[26] Y Xia X Yu andW Oghanna ldquoAdaptive robust fast control forinduction motorsrdquo IEEE Transactions on Industrial Electronicsvol 47 no 4 pp 854ndash862 2000
[27] M Niclai Theory of Nonlinear Control Systems McGraw-Hill1969
[28] J J Slotine andW Li Applied Nonlinear Control Prentice-HallEnglewood Cliffs NJ USA 1991
[29] D Gorinevsky and L A Feldkamp ldquoRBF network feedforwardcompensation of load disturbance in idle speed controlrdquo IEEEControl Systems vol 16 no 6 pp 18ndash27 1996
[30] S Di Cairano D Yanakiev A Bemporad I V Kolmanovskyand D Hrovat ldquoModel predictive idle speed control designanalysis and experimental evaluationrdquo IEEE Transactions onControl Systems Technology vol 20 no 1 pp 84ndash97 2012
[31] P F Puleston S Spurgeon andGMonsees ldquoAutomotive enginespeed control a robust nonlinear control frameworkrdquo IEEProceedings Control Theory and Applications vol 148 no 1 pp81ndash87 2001
[32] Y Yildiz A M Annaswamy D Yanakiev and I KolmanovskyldquoSpark-ignition-engine idle speed control an adaptive controlapproachrdquo IEEE Transactions on Control Systems Technologyvol 19 no 5 pp 990ndash1002 2011
[33] A Sugeng K Baharin T Hishamuddin and J B SupriyoldquoEngine speed control using online ANN for vehicle withEMDAP-CVTrdquo Jurnal Mekanikal vol 22 pp 39ndash52 2006
[34] M K Khan K B Goh and S K Spurgeon ldquoSecond ordersliding mode control of a diesel enginerdquo Asian Journal ofControl vol 5 no 4 pp 614ndash619 2003
[35] J R Wagner D M Dawson and L Zeyu ldquoNonlinear air-to-fuel ratio and engine speed control for hybrid vehiclesrdquo IEEETransactions on Vehicular Technology vol 52 no 1 pp 184ndash1952003
[36] F Assadian S Fekri andM Hancock ldquoHybrid electric vehicleschallenges strategies for advanced engine speed controlrdquo inProceedings of the IEEE International Electric Vehicle Conference(IEVC rsquo12) March 2012
[37] A G Ulsoy H Peng and M Cakmakci Automotive ControlSystems Cambridge University Press Cambridge UK 2014
[38] C Ji and S Wang ldquoStrategies for improving the idle perfor-mance of a spark-ignited gasoline enginerdquo International Journalof Hydrogen Energy vol 37 no 4 pp 3938ndash3944 2012
[39] S Wang C Ji M Zhang and B Zhang ldquoReducing theidle speed of a spark-ignited gasoline engine with hydrogenadditionrdquo International Journal of Hydrogen Energy vol 35 no19 pp 10580ndash10588 2010
[40] DHrovat and J Sun ldquoModels and controlmethodologies for ICengine idle speed control designrdquo Control Engineering Practicevol 5 no 8 pp 1093ndash1100 1997
[41] B Alt J P Blath F Svaricek and M Schultalbers ldquoMultiplesliding surface control of idle engine speed and torque reservewith dead start assist controlrdquo IEEE Transactions on IndustrialElectronics vol 56 no 9 pp 3580ndash3592 2009
12 Mathematical Problems in Engineering
[42] T Radpukdee and P Jirawattana ldquoUncertainty learning andcompensation an application to pressure tracking of an electro-hydraulic proportional relief valverdquo Control Engineering Prac-tice vol 17 no 2 pp 291ndash301 2009
[43] P A Loannou and J Sun Robust Adaptive Control PTRPrentice-Hall 1996
[44] C D Richard and H B Robert Modern Control SystemsPrentice Hall Upper Saddle River NJ USA 2011
[45] A Jansri and P Sooraksa ldquoEnhanced model and fuzzy strategyof air to fuel ratio control for spark ignition enginesrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 922ndash9332012
[46] Z Ye ldquoModeling identification design and implementation ofnonlinear automotive idle speed control systemsmdashanoverviewrdquoIEEE Transactions on Systems Man and Cybernetics Part CApplications and Reviews vol 37 no 6 pp 1137ndash1151 2007
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 5
As the reaching phase analysis the control law in (8) andits adaptation law offer convergence regulation of the stateIntuitively the sliding function s is bounded about the slidingsurface s= 0 due to imperfection of control action in practiceThus the derivative of the sliding function s will be boundedby the boundedness of s which also implies the integralof s converges to some limit [43] Consequently the RHS of(22) can be bounded and is rewritten by a residual matrix0 = [0
1 0
119898]
119879isin 119877
119898 For each argument of the u119871 the
residual function 0119894 119894 = 1 sdot sdot sdot 119898 can be interpreted as residual
errors after the reaching phase which satisfy
119879
119891
119871119894+ 2119906
119871119894= 0
119894 (23)
Given 120574 = 2119879
119891and 120593
119894= 0
119894119879
119891 (23) is rewritten as
119871119894+ 120574119906
119871119894= 120593
119894 (24)
From (24) the bound on 120593
119894can be interpreted into a
bound on the filter output 119906119871119894 Define the bound of 120593
119894= Φ
119894
The bound of the filter output |119906119871119894| can be written as (25)
which corresponds to [28]
1003816
1003816
1003816
1003816
119906
119871119894(119905)
1003816
1003816
1003816
1003816
le (
Φ
119894
120574
) (1 minus 119890
minus120574119905) (25)
In which 119906119871119894(119905)
tends to Φ119894120574 [28] when 119905 rarr infin Thus
1003816
1003816
1003816
1003816
119906
119871119894(119905)
1003816
1003816
1003816
1003816
le
Φ
119894
120574
(26)
Consider (26) if 119879119891
and 120573 are known the residualuncertainties from the reaching phase can be compensatedby u119871 To consider the stability of the control system by using
the input according to (4) (12) can be rewritten as
V = s119879 [(Cf + CB120578 minus CBBminus1f) + C (BBminus1 minus 1) x119889]
minus s119879CBBminus1k119875s minus s119879CBBminus1uID minus s119879CBBminus1u
119871+ G
(27)
Notice that the adding of the u119871leads to uncertain of
negative definite on the Lyapunov function derivative Inorder to stabilize (27) the proportional portion has to takethe output from the LPF and the bound of uncertainty and itsderivative into account By defining119872
119905= 119872
0+ 119872
119889+ u119871
themodified proportional gain for each sliding surface can be119896
119875119894ge |120573119872
119905| + |(1 minus 120573)119906
119894ap| And together with the adaptationlaws defined in the previous section V in (27) is negativedefinite (
119881 lt 0) The sliding motion can be guaranteed for119905 isin [119905reachinfin) under the conditions stated earlier
3 Description of the Engine SpeedControl Modeling
As stated earlier a key step of the development controlscheme is based on the robust control techniques inwhich theapproach has the ability to neglect the conservatism and theneed for precise modeling [44] In addition the development
of an exact model for a real engine system is difficultbecause some parameters in the mathematical model cannotbe obtained exactly and the real plant is affected by thecomplexity of its uncertain nonlinearity [45] Consequentlythe system modeling in this work was linearized through thenominal transfer function of the real plant as the form of
119909 (119904) = 119866ta (119904) 119890minus119879119863119904
119906ta (119904) + 119866sa (119904) 119890minus119879119863119904
119906sa (119904) (28)
where 119909(119904) is the output the time delay is 119879119863 119906ta(119904) is the
control input for a throttle actuator and 119906sa(119904) is the controlinput for the spark advance system 119866ta(119904) and 119866sa(119904) are thelinearized models by 119906ta(119904) and 119906sa(119904) respectively Note thatthe symbol 119904 in this section denotes the complex argument ofthe Laplace transform which is not the sliding function
Although the conventional relevant engine dynamic forengine speed control depends on the coordination betweenthe throttle actuator and the spark advance system for theassessment in this work we have designed a controller thataims to control only the throttle actuator while the sparkadvance system is handled by conventional controller of theengine system Therefore the system modeling in this workcan be obtained by an adjustment of the throttle openingposition in degrees which is directly controlled with a DCmotor that is excited by the feed-forward control signalin DC-voltage as an input and the crankshaft speed inrevolutions perminute (rpm) as an output Consequently thelinearizationmodel at speed 900 rpm can be approximated inthe transfer function form as
119866 (119904) =
45119904
2+ 44119904 + 90
119904
3+ 15119904
2+ 25119904 + 1
(29)
where 119866(119904) is the transfer function of the real plant whichhas units of revolutions per minute (rpm) From the roughidentifications of (29) it is the third-order with relativedegree one and the system is BIBO stable because all polesare located on the left-hand side (LHS) of the 119904-plane Inaddition for the reason of low-speed control test (900 rpm)it is sensitive to any uncertain nonlinearities and externaldisturbancesTherefore the implementation of speed controlin the low-speed region is more difficult than in the high-speed control region Furthermore on average 30 percentof fuel consumption in urban city driving is spent at theidle speed range [46] As a consequence increasing theperformance of the low-speed control is able to increase fueleconomy and performance of the engine operation at anyoperating condition [32]
For simplicity to make the engine speed response asthe canonical form of (1) the rough identification model of(29) can be simplified to the first-order transfer function asfollows
119866 (119904) =
445
119904 + 0493
(30)
To make clear the acceptability of (30) the bode plotand the step response comparison between (29) and (30) aredemonstrated in Figure 2 The results make clear that thefirst-order transfer function in (30) can be employed in theperformance assessment of the proposed controller design in
6 Mathematical Problems in Engineering
0 2 4 6 8 10 120
102030405060708090
100Step response
Time (s)
Am
plitu
de
3rd order1st order
10152025303540
minus90
minus45
0
Frequency (rads)
Bode diagram
Mag
nitu
de (d
B)Ph
ase (
deg)
10minus2
10minus1
100
101
Frequency (rads)10
minus210
minus110
010
1
Figure 2 The validation of the 1st-order model
the simulations and (30) can be expressed as the time-domaindifferential equation as follows
= minus0493119909 + 445119906 (31)
where 119909 is the speed output and 119906 is the input
4 Illustrative Examples
41 Simulation Verification For the simulation verificationthe system modeling of (31) is used in order to assess theperformance of the proposed control scheme (LPFSMC andAdaptive PID) that is performed viaMATLAB-Simulink pro-gramming with a sampling period of 1ms The performanceof the proposed controller is compared with different controltechniques which are the PID control technique and the SMCtechnique The specific control parameters are chosen suchthat the sliding gain of the proposed control scheme and theconventional SMC is M
119905= 10 the cut-off frequency of the
first-order LPF is119879119891= 4 while the setting control parameters
of the PID controller are obtained by the Ziegler-Nicholstuning method
Figure 3(a) demonstrates the response results of theproposed control scheme which has a small rise time andsetting time and higher tracking accuracy than other controltechniques (PID controller and SMC) It demonstrates thatthe proposed adaptation law is capable of updating the PID
controller online during the control process within a shortperiod Furthermore the proposed control scheme can pro-vide optimal control input rapidly and has smooth controlinput which is achieved by the cut-off frequency property ofthe LPF (see Figure 3(b))
Figure 3(c) shows the error comparison among the dif-ferent controllers as the results the errors from the pro-posed control scheme can approach zero faster than othercontrol techniques and it has lower chattering than the SMCtechnique Note that although the chattering of the outputresponse control input and the errors of the PID controllerdoes not appear the results (see Figure 3) reveal that itsresponse has higher rise-time high-overshoot and longersetting time which are not satisfactory from the viewpointof a control system
42 Practical Experiment In this section we demonstrate theefficiency of the proposed control scheme in the real systemThe experimental technical data are shown in Table 1 In oursetup the functional block diagrams of the apparatus used inthe experiments are illustrated in Figure 4 which is used forperformance assessment of the proposed control schemeThesystem in Figure 4 consists of five main parts which are thecontroller unit electronic throttle valve control unit (ETC)spark-ignition (SI) engine system the power train system
Mathematical Problems in Engineering 7
Time (s)
Spee
d re
spon
se (r
pm)
ZOOM
Time (s)
Spee
d re
spon
se(r
pm)
SMCLPFSMC and adaptive PIDDesiredPID
0200400600800
10001200140016001800
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 208998995
9009005
901
(a)
Time (s)
Con
trol i
nput
(V)
SMC LPFSMC and adaptive PIDPID
minus30minus25minus20minus15minus10minus5
05
101520
2 4 6 8 10 12 14 16 18 200
(b)
Erro
rs
SMC LPFSMC and adaptive PIDPID
Time (s)
Erro
rs
ZOOM
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus1000minus800minus600minus400minus200
0200400600800
005
1
minus05minus1
0 2 4 6 8 10 12 14 16 18 20
(c)
Figure 3 Comparison of simulation results among different control techniques (a) the output response (b) the control inputs (c) the errors
PWM M
DC motor
Gear box
Throttle opening sensor
Throttle body
Control system
Electronic throttle control unit
SI engine
ADCDAC
Amplifier
Air
Speed calculation
Throttle position calculation
Fuel consumptioncomputation
Emission data logger(HC CO)
Speed sensor
Fuel flow sensor
Emission sensor
Power trainsystem
Dynamometer
Figure 4 Schematic diagram of the experiment
8 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
DesiredLPFSMC and adaptive PID
Con
trol i
nput
(V)
Time (s)
Slid
ing
varia
ble (
s)
Time (s)
Thro
ttle v
alve
ope
ning
(deg
)
Time (s)
0 20 40 60 80 100 120 140 160 180 200600650700750800850900950
1000
0
01
02
03
04
05
06
0 20 40 60 80 100 120 140 160 180 200
minus200minus150minus100minus50
050
100150200
0 20 40 60 80 100 120 140 160 180 200012345678
0 20 40 60 80 100 120 140 160 180 200
Figure 5 Experimental results of the proposed controller (LPFSMC and Adaptive PID technique)
Table 1 Experimental technical data
Item ValueSI engine (4 cylinders 900 ccgasoline type) Test range 600ndash3000 rpm
Speed sensor (rpm) Sampling speed approximately5000 ts
Throttle position sensor Measurement range 0ndash80∘
ADCDAC minus10 to 10VDC 20mA
COMPUTER Core2Duo 293GHz 4GBRAM
DCmotor 48ndash6VFuel type (experiments) Ethanol-gasoline blended (E20)
and the dynamometer which is used to generate the load-torque into the systemThe engine speed is interpreted as thecrankshaft rotation rate in revolutions per minute (rpm) andis regulated by opening the throttle In this task the throttlevalve is directly actuated by a DCmotor in which the angularmovement is handled by the control signal in the form ofPulseWidth Modulation (PWM)The exhaust emissions COandHCwere alsomeasured through a nondispersive infraredanalysis machine (Infralyt smart) in which the acquiringsampling data is 1 s while the fuel consumptionwasmeasuredby the fuel flow sensor (Hall effect-800 series) with thesampling period is 1ms The computation unit is performedwith MATLAB-Simulink programming An ADCDAC isused as an interface systembetween the computer and the realplant while the sampling period is 1ms for all experiments
As seen in Figure 5 the desired speed is chosen to rapidchange from 750 rpm to 900 rpm and 900 rpm to 750 rpmand the experiments were performed for 200 s This resultreveals that the speed response of the proposed controlscheme can reach the desired speedwithin short time and hasno overshoot and tiny oscillationThe control input is smoothand reaches an optimal value within a short time and thesliding variable can approach zero rapidly Fast convergenceof the response is a result of the updated control gains (119870
119868
and 119870119863) of the PID controller which can be adjusted rapidly
during the control process according to the adaptive lawFurthermore the characteristic of the opening position of thethrottle valve was alsomeasuredThis reveals that themotionof the actuator has smooth and tiny oscillations
43 Tracking Performance and Disturbance Rejection TestThe robust properties and the tracking performance of theproposed control schemewere also assessed because it is wellknown that the engine speed control is affected by the stateof accessory changes such as external load disturbance [41]In the experiments we compare the disturbance rejectionperformance among the proposed controller SMC techniqueand PID controller The load disturbance is generated bythe dynamometer while the speed set-point is chosen to be900 rpm Note that for the reason of low-speed test it issensitive from any disturbances therefore the implementa-tion in the low-speed region is more difficult than the high-speed control task Furthermore high performance of low-speed control leads to increase the performance of the engineoperation at any operating condition [32]
Mathematical Problems in Engineering 9
Time (s)Lo
ad (W
)
75
225
Engi
ne sp
eed
(rpm
)
DesiredLPFSMC and adaptive PID
PIDSMC
15
30
0
1000
950
900
850
800
Time (s)
120 125 130 135 140 145 150 155 160
120 125 130 135 140 145 150 155 160
Figure 6 Comparisons of tracking performance and disturbance rejection of the controllers
As seen in Figure 6 at the time 125 sec the load torquewas applied immediately into the engine speed control taskThis proposed to disturb the stability of the control system atthe steady-state condition The proposed control scheme canimprove the speed deviation rapidly and is capable of trackingthe desired speed better than other control techniques Inaddition the load torque was decreased immediately at thetime 150 sec The results show that the proposed controlscheme can decrease the speed deviation from the desiredspeed faster than other control techniques The findingsreveal that the proposed control scheme has effective ofthe robustness and fast adaptation and has better trackingperformance than other control techniques
44 Fuel Consumption andExhaust Emission Investigation Inthis section the fuel consumption and the exhaust emissionof the engine speed control by using the proposed controlscheme and different control techniques (SMC techniqueand PID controller) were investigated (see Figure 7) In theexperiments the desired speed was performed for 400 secand was rapidly changed as shown in Figure 7(a) For theaverage total fuel consumption comparison (see Figure 7(b))the proposed control scheme can attain an excellent resultwith the lowest averaged total fuel consumption whichwas obtained by the average of the fuel consumptions persecond
In addition the average exhaust emissions were alsoinvestigated (see Figure 7(c)) The CO and HC emissions arethe main pollutants contributed by the SI engines In theprinciple of the combustion process of SI engine the HCemission is appeared when fuel molecules in the engine
cannot burn or burn only partially while the CO emissionis produced when the carbon in the fuel is partially oxi-dized rather than fully oxidized to carbon dioxide Howeverincreasing efficient strategies for engine speed control viathrottle valve regulation method is capable of increasingcombustion performance as it can reduce pollutant emissionsalso [38] In the experiments effects of the controllers wereinvestigated via the constant speed set points and no addingan external engine load (small load from the unloadedhydrostatic CVT)Thus the CO
2andNO
119909which are sensitive
to speed variation and high temperature operation did notmeasure in this work (the experiments perform at coolanttemperature of 70ndash80∘C for short period) As a result bothaverages of the CO and HC emission data were calculatedby the average of emissions per second in which obtainedby the direct measurement method [43] Additionally theseresults demonstrate that high fuel consumption and exhaustemission are affected by high variation of the engine speedduring tracking of the set pointsThese results also imply thatthe performance of the SI engine at any operating conditioncan be improved by an advanced engine speed control viathe electronic throttle valve regulation method as shown inFigure 7
5 Conclusions
The incorporation of the SMC and a first-order LPF witha new adaptive PID controller is proposed for trackingthe control task of an uncertain nonlinear system Thecontroller has been successfully applied to the problem ofthe speed tracking control of an SI engine through electronic
10 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
PIDSMC
LPFSMC and adaptive PIDDesired
0 50 100 150 200 250 300 350 4000
500
1000
1500
2000
2500
(a)
00689
0071
00694
006750068
006850069
00695007
007050071
00715
LPFSMC andadaptive PID
SMC PID
Fuel consumption (Lmin)
(b)
20288 41113 20302
105977
425503
109623
0500
10001500200025003000350040004500
LPFSMC andadaptive PID
SMC PID
HC (ppm)CO (ppm)
(c)
Figure 7 Comparisons of (a) tracking performance of the controllers (b) fuel consumption rates (c) exhaust emission rates
throttle valve control architecture From the simulation andexperimental results it achieves that
(1) the proposed adaptation law is capable of optimalonline update the PID controller during the controlprocess within a short period
(2) the chattering of the SMC can be alleviated by afirst-order low pass filter while the robustness of thecontrol system similar to that of the slidingmode suchthat the load torque disturbances can be compensatedquite accurately
(3) the proposed control scheme has high performancein implementation as it can be achieved in theproblem of engine speed control in which the systemis largely uncertain nonlinear system and rathercomplex mechanisms
Conflict of Interests
The authors have no competing interests
Acknowledgment
This research is financially supported by the Office ofResearch Administration (ORA) and Farm Engineering andAutomation Technology Research Group (FEAT) of Khon
Kaen University Thailand The authors are also thankfulto the reviewers and Mr Ian Thomas for their valuablecomments and suggestions for English grammar correctionrespectively
References
[1] K-C Hsu W-Y Wang and P-Z Lin ldquoSliding mode controlfor uncertain nonlinear systemswithmultiple inputs containingsector nonlinearities and deadzonesrdquo IEEE Transactions onSystems Man and Cybernetics Part B Cybernetics vol 34 no1 pp 374ndash380 2004
[2] G Bartolini and A Ferrara ldquoMulti-input sliding mode controlof a class of uncertain nonlinear systemsrdquo IEEE Transactions onAutomatic Control vol 41 no 11 pp 1662ndash1666 1996
[3] T-C Kuo Y-J Huang and S-H Chang ldquoSliding mode controlwith self-tuning law for uncertain nonlinear systemsrdquo ISATransactions vol 47 no 2 pp 171ndash178 2008
[4] G Montaseri and M J Yazdanpanah ldquoPredictive control ofuncertain nonlinear parabolic PDE systems using a Galerkinneural-network-based modelrdquo Communications in NonlinearScience and Numerical Simulation vol 17 no 1 pp 388ndash4042012
[5] F O Tellez A G Loukianov E N Sanchez and E Jose BayroCorrochano ldquoDecentralized neural identification and controlfor uncertain nonlinear systems application to planar robotrdquoJournal of the Franklin Institute vol 347 no 6 pp 1015ndash10342010
Mathematical Problems in Engineering 11
[6] A Bazaei and V J Majd ldquoFeedback linearization of discrete-time nonlinear uncertain plants via first-principles-based serialneuro-gray-box modelsrdquo Journal of Process Control vol 13 no8 pp 819ndash830 2003
[7] T-Y Kuc and W-G Han ldquoAn adaptive PID learning controlof robot manipulatorsrdquo Automatica vol 36 no 5 pp 717ndash7252000
[8] Y Pan Y Zhou T Sun and M J Er ldquoComposite adaptivefuzzy 119867
infintracking control of uncertain nonlinear systemsrdquo
Neurocomputing vol 99 pp 15ndash24 2013[9] X Liu R Tao and M Tavakoli ldquoAdaptive control of uncertain
nonlinear teleoperation systemsrdquo Mechatronics vol 24 no 1pp 66ndash78 2014
[10] W-D Chang and J-J Yan ldquoAdaptive robust PID controllerdesign based on a sliding mode for uncertain chaotic systemsrdquoChaos Solitons amp Fractals vol 26 no 1 pp 167ndash175 2005
[11] T C Kuo Y J Huang C Y Chen and C H Chang ldquoAdaptivesliding mode control with PID tuning for uncertain systemrdquoEngineering Letters vol 16 no 3 pp 1ndash5 2008
[12] M N Howell and M C Best ldquoOn-line PID tuning forengine idle-speed control using continuous action reinforce-ment learning automatardquo Control Engineering Practice vol 8no 2 pp 147ndash154 2000
[13] C-F Hsu and B-K Lee ldquoFPGA-based adaptive PID control ofa DC motor driver via sliding-mode approachrdquo Expert Systemswith Applications vol 38 no 9 pp 11866ndash11872 2011
[14] DWMemering and PHMeckl ldquoComparison of adaptive con-trol techniques applied to diesel engine idle speed regulationrdquoJournal of Dynamic Systems Measurement and Control vol 124no 4 pp 682ndash688 2002
[15] V I Utkin ldquoSliding mode control design principles andapplications to electric drivesrdquo IEEE Transactions on IndustrialElectronics vol 40 no 1 pp 23ndash36 1993
[16] Y J Huang and T C Kuo ldquoRobust output tracking controlfor nonlinear time-varying robotic manipulatorsrdquo ElectricalEngineering vol 87 no 1 pp 47ndash55 2005
[17] M Hajatipour and M Farrokhi ldquoChattering free with noisereduction in sliding-mode observers using frequency domainanalysisrdquo Journal of Process Control vol 20 no 8 pp 912ndash9212010
[18] A Sabanovic L Fridman and S Spurgeon Variable StructureSystems From Principles to Implementation The Institution ofEngineering and Technology 2004
[19] Y Xu ldquoChattering free robust control for nonlinear systemsrdquoIEEE Transactions on Control Systems Technology vol 16 no 6pp 1352ndash1359 2008
[20] H Lee and V I Utkin ldquoChattering suppression methods insliding mode control systemsrdquo Annual Reviews in Control vol31 no 2 pp 179ndash188 2007
[21] Y Ren Z Liu L Chang and N Wen ldquoAdaptive slidingmode robust control for virtual compound-axis servo systemrdquoMathematical Problems in Engineering vol 2013 Article ID343851 9 pages 2013
[22] M-L Tseng and M-S Chen ldquoChattering reduction of slidingmode control by low-pass filtering the control signalrdquo AsianJournal of Control vol 12 no 3 pp 392ndash398 2010
[23] H Sira-RamIRez ldquoOn the dynamical sliding mode control ofnonlinear systemsrdquo International Journal of Control vol 57 no5 pp 1039ndash1061 1993
[24] J-X Xu Y-J Pan and T-H Lee ldquoSliding mode controlwith closed-loop filtering architecture for a class of nonlinear
systemsrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 51 no 4 pp 168ndash173 2004
[25] A Deenadayalan and G S Ilango ldquoPosition sensorless slidingmode observer with sigmoid function for Brushless DCmotorrdquoin Proceedings of the International Conference on Advances inPower Conversion and Energy Technologies (APCET rsquo12) pp 1ndash6IEEE August 2012
[26] Y Xia X Yu andW Oghanna ldquoAdaptive robust fast control forinduction motorsrdquo IEEE Transactions on Industrial Electronicsvol 47 no 4 pp 854ndash862 2000
[27] M Niclai Theory of Nonlinear Control Systems McGraw-Hill1969
[28] J J Slotine andW Li Applied Nonlinear Control Prentice-HallEnglewood Cliffs NJ USA 1991
[29] D Gorinevsky and L A Feldkamp ldquoRBF network feedforwardcompensation of load disturbance in idle speed controlrdquo IEEEControl Systems vol 16 no 6 pp 18ndash27 1996
[30] S Di Cairano D Yanakiev A Bemporad I V Kolmanovskyand D Hrovat ldquoModel predictive idle speed control designanalysis and experimental evaluationrdquo IEEE Transactions onControl Systems Technology vol 20 no 1 pp 84ndash97 2012
[31] P F Puleston S Spurgeon andGMonsees ldquoAutomotive enginespeed control a robust nonlinear control frameworkrdquo IEEProceedings Control Theory and Applications vol 148 no 1 pp81ndash87 2001
[32] Y Yildiz A M Annaswamy D Yanakiev and I KolmanovskyldquoSpark-ignition-engine idle speed control an adaptive controlapproachrdquo IEEE Transactions on Control Systems Technologyvol 19 no 5 pp 990ndash1002 2011
[33] A Sugeng K Baharin T Hishamuddin and J B SupriyoldquoEngine speed control using online ANN for vehicle withEMDAP-CVTrdquo Jurnal Mekanikal vol 22 pp 39ndash52 2006
[34] M K Khan K B Goh and S K Spurgeon ldquoSecond ordersliding mode control of a diesel enginerdquo Asian Journal ofControl vol 5 no 4 pp 614ndash619 2003
[35] J R Wagner D M Dawson and L Zeyu ldquoNonlinear air-to-fuel ratio and engine speed control for hybrid vehiclesrdquo IEEETransactions on Vehicular Technology vol 52 no 1 pp 184ndash1952003
[36] F Assadian S Fekri andM Hancock ldquoHybrid electric vehicleschallenges strategies for advanced engine speed controlrdquo inProceedings of the IEEE International Electric Vehicle Conference(IEVC rsquo12) March 2012
[37] A G Ulsoy H Peng and M Cakmakci Automotive ControlSystems Cambridge University Press Cambridge UK 2014
[38] C Ji and S Wang ldquoStrategies for improving the idle perfor-mance of a spark-ignited gasoline enginerdquo International Journalof Hydrogen Energy vol 37 no 4 pp 3938ndash3944 2012
[39] S Wang C Ji M Zhang and B Zhang ldquoReducing theidle speed of a spark-ignited gasoline engine with hydrogenadditionrdquo International Journal of Hydrogen Energy vol 35 no19 pp 10580ndash10588 2010
[40] DHrovat and J Sun ldquoModels and controlmethodologies for ICengine idle speed control designrdquo Control Engineering Practicevol 5 no 8 pp 1093ndash1100 1997
[41] B Alt J P Blath F Svaricek and M Schultalbers ldquoMultiplesliding surface control of idle engine speed and torque reservewith dead start assist controlrdquo IEEE Transactions on IndustrialElectronics vol 56 no 9 pp 3580ndash3592 2009
12 Mathematical Problems in Engineering
[42] T Radpukdee and P Jirawattana ldquoUncertainty learning andcompensation an application to pressure tracking of an electro-hydraulic proportional relief valverdquo Control Engineering Prac-tice vol 17 no 2 pp 291ndash301 2009
[43] P A Loannou and J Sun Robust Adaptive Control PTRPrentice-Hall 1996
[44] C D Richard and H B Robert Modern Control SystemsPrentice Hall Upper Saddle River NJ USA 2011
[45] A Jansri and P Sooraksa ldquoEnhanced model and fuzzy strategyof air to fuel ratio control for spark ignition enginesrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 922ndash9332012
[46] Z Ye ldquoModeling identification design and implementation ofnonlinear automotive idle speed control systemsmdashanoverviewrdquoIEEE Transactions on Systems Man and Cybernetics Part CApplications and Reviews vol 37 no 6 pp 1137ndash1151 2007
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
6 Mathematical Problems in Engineering
0 2 4 6 8 10 120
102030405060708090
100Step response
Time (s)
Am
plitu
de
3rd order1st order
10152025303540
minus90
minus45
0
Frequency (rads)
Bode diagram
Mag
nitu
de (d
B)Ph
ase (
deg)
10minus2
10minus1
100
101
Frequency (rads)10
minus210
minus110
010
1
Figure 2 The validation of the 1st-order model
the simulations and (30) can be expressed as the time-domaindifferential equation as follows
= minus0493119909 + 445119906 (31)
where 119909 is the speed output and 119906 is the input
4 Illustrative Examples
41 Simulation Verification For the simulation verificationthe system modeling of (31) is used in order to assess theperformance of the proposed control scheme (LPFSMC andAdaptive PID) that is performed viaMATLAB-Simulink pro-gramming with a sampling period of 1ms The performanceof the proposed controller is compared with different controltechniques which are the PID control technique and the SMCtechnique The specific control parameters are chosen suchthat the sliding gain of the proposed control scheme and theconventional SMC is M
119905= 10 the cut-off frequency of the
first-order LPF is119879119891= 4 while the setting control parameters
of the PID controller are obtained by the Ziegler-Nicholstuning method
Figure 3(a) demonstrates the response results of theproposed control scheme which has a small rise time andsetting time and higher tracking accuracy than other controltechniques (PID controller and SMC) It demonstrates thatthe proposed adaptation law is capable of updating the PID
controller online during the control process within a shortperiod Furthermore the proposed control scheme can pro-vide optimal control input rapidly and has smooth controlinput which is achieved by the cut-off frequency property ofthe LPF (see Figure 3(b))
Figure 3(c) shows the error comparison among the dif-ferent controllers as the results the errors from the pro-posed control scheme can approach zero faster than othercontrol techniques and it has lower chattering than the SMCtechnique Note that although the chattering of the outputresponse control input and the errors of the PID controllerdoes not appear the results (see Figure 3) reveal that itsresponse has higher rise-time high-overshoot and longersetting time which are not satisfactory from the viewpointof a control system
42 Practical Experiment In this section we demonstrate theefficiency of the proposed control scheme in the real systemThe experimental technical data are shown in Table 1 In oursetup the functional block diagrams of the apparatus used inthe experiments are illustrated in Figure 4 which is used forperformance assessment of the proposed control schemeThesystem in Figure 4 consists of five main parts which are thecontroller unit electronic throttle valve control unit (ETC)spark-ignition (SI) engine system the power train system
Mathematical Problems in Engineering 7
Time (s)
Spee
d re
spon
se (r
pm)
ZOOM
Time (s)
Spee
d re
spon
se(r
pm)
SMCLPFSMC and adaptive PIDDesiredPID
0200400600800
10001200140016001800
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 208998995
9009005
901
(a)
Time (s)
Con
trol i
nput
(V)
SMC LPFSMC and adaptive PIDPID
minus30minus25minus20minus15minus10minus5
05
101520
2 4 6 8 10 12 14 16 18 200
(b)
Erro
rs
SMC LPFSMC and adaptive PIDPID
Time (s)
Erro
rs
ZOOM
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus1000minus800minus600minus400minus200
0200400600800
005
1
minus05minus1
0 2 4 6 8 10 12 14 16 18 20
(c)
Figure 3 Comparison of simulation results among different control techniques (a) the output response (b) the control inputs (c) the errors
PWM M
DC motor
Gear box
Throttle opening sensor
Throttle body
Control system
Electronic throttle control unit
SI engine
ADCDAC
Amplifier
Air
Speed calculation
Throttle position calculation
Fuel consumptioncomputation
Emission data logger(HC CO)
Speed sensor
Fuel flow sensor
Emission sensor
Power trainsystem
Dynamometer
Figure 4 Schematic diagram of the experiment
8 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
DesiredLPFSMC and adaptive PID
Con
trol i
nput
(V)
Time (s)
Slid
ing
varia
ble (
s)
Time (s)
Thro
ttle v
alve
ope
ning
(deg
)
Time (s)
0 20 40 60 80 100 120 140 160 180 200600650700750800850900950
1000
0
01
02
03
04
05
06
0 20 40 60 80 100 120 140 160 180 200
minus200minus150minus100minus50
050
100150200
0 20 40 60 80 100 120 140 160 180 200012345678
0 20 40 60 80 100 120 140 160 180 200
Figure 5 Experimental results of the proposed controller (LPFSMC and Adaptive PID technique)
Table 1 Experimental technical data
Item ValueSI engine (4 cylinders 900 ccgasoline type) Test range 600ndash3000 rpm
Speed sensor (rpm) Sampling speed approximately5000 ts
Throttle position sensor Measurement range 0ndash80∘
ADCDAC minus10 to 10VDC 20mA
COMPUTER Core2Duo 293GHz 4GBRAM
DCmotor 48ndash6VFuel type (experiments) Ethanol-gasoline blended (E20)
and the dynamometer which is used to generate the load-torque into the systemThe engine speed is interpreted as thecrankshaft rotation rate in revolutions per minute (rpm) andis regulated by opening the throttle In this task the throttlevalve is directly actuated by a DCmotor in which the angularmovement is handled by the control signal in the form ofPulseWidth Modulation (PWM)The exhaust emissions COandHCwere alsomeasured through a nondispersive infraredanalysis machine (Infralyt smart) in which the acquiringsampling data is 1 s while the fuel consumptionwasmeasuredby the fuel flow sensor (Hall effect-800 series) with thesampling period is 1ms The computation unit is performedwith MATLAB-Simulink programming An ADCDAC isused as an interface systembetween the computer and the realplant while the sampling period is 1ms for all experiments
As seen in Figure 5 the desired speed is chosen to rapidchange from 750 rpm to 900 rpm and 900 rpm to 750 rpmand the experiments were performed for 200 s This resultreveals that the speed response of the proposed controlscheme can reach the desired speedwithin short time and hasno overshoot and tiny oscillationThe control input is smoothand reaches an optimal value within a short time and thesliding variable can approach zero rapidly Fast convergenceof the response is a result of the updated control gains (119870
119868
and 119870119863) of the PID controller which can be adjusted rapidly
during the control process according to the adaptive lawFurthermore the characteristic of the opening position of thethrottle valve was alsomeasuredThis reveals that themotionof the actuator has smooth and tiny oscillations
43 Tracking Performance and Disturbance Rejection TestThe robust properties and the tracking performance of theproposed control schemewere also assessed because it is wellknown that the engine speed control is affected by the stateof accessory changes such as external load disturbance [41]In the experiments we compare the disturbance rejectionperformance among the proposed controller SMC techniqueand PID controller The load disturbance is generated bythe dynamometer while the speed set-point is chosen to be900 rpm Note that for the reason of low-speed test it issensitive from any disturbances therefore the implementa-tion in the low-speed region is more difficult than the high-speed control task Furthermore high performance of low-speed control leads to increase the performance of the engineoperation at any operating condition [32]
Mathematical Problems in Engineering 9
Time (s)Lo
ad (W
)
75
225
Engi
ne sp
eed
(rpm
)
DesiredLPFSMC and adaptive PID
PIDSMC
15
30
0
1000
950
900
850
800
Time (s)
120 125 130 135 140 145 150 155 160
120 125 130 135 140 145 150 155 160
Figure 6 Comparisons of tracking performance and disturbance rejection of the controllers
As seen in Figure 6 at the time 125 sec the load torquewas applied immediately into the engine speed control taskThis proposed to disturb the stability of the control system atthe steady-state condition The proposed control scheme canimprove the speed deviation rapidly and is capable of trackingthe desired speed better than other control techniques Inaddition the load torque was decreased immediately at thetime 150 sec The results show that the proposed controlscheme can decrease the speed deviation from the desiredspeed faster than other control techniques The findingsreveal that the proposed control scheme has effective ofthe robustness and fast adaptation and has better trackingperformance than other control techniques
44 Fuel Consumption andExhaust Emission Investigation Inthis section the fuel consumption and the exhaust emissionof the engine speed control by using the proposed controlscheme and different control techniques (SMC techniqueand PID controller) were investigated (see Figure 7) In theexperiments the desired speed was performed for 400 secand was rapidly changed as shown in Figure 7(a) For theaverage total fuel consumption comparison (see Figure 7(b))the proposed control scheme can attain an excellent resultwith the lowest averaged total fuel consumption whichwas obtained by the average of the fuel consumptions persecond
In addition the average exhaust emissions were alsoinvestigated (see Figure 7(c)) The CO and HC emissions arethe main pollutants contributed by the SI engines In theprinciple of the combustion process of SI engine the HCemission is appeared when fuel molecules in the engine
cannot burn or burn only partially while the CO emissionis produced when the carbon in the fuel is partially oxi-dized rather than fully oxidized to carbon dioxide Howeverincreasing efficient strategies for engine speed control viathrottle valve regulation method is capable of increasingcombustion performance as it can reduce pollutant emissionsalso [38] In the experiments effects of the controllers wereinvestigated via the constant speed set points and no addingan external engine load (small load from the unloadedhydrostatic CVT)Thus the CO
2andNO
119909which are sensitive
to speed variation and high temperature operation did notmeasure in this work (the experiments perform at coolanttemperature of 70ndash80∘C for short period) As a result bothaverages of the CO and HC emission data were calculatedby the average of emissions per second in which obtainedby the direct measurement method [43] Additionally theseresults demonstrate that high fuel consumption and exhaustemission are affected by high variation of the engine speedduring tracking of the set pointsThese results also imply thatthe performance of the SI engine at any operating conditioncan be improved by an advanced engine speed control viathe electronic throttle valve regulation method as shown inFigure 7
5 Conclusions
The incorporation of the SMC and a first-order LPF witha new adaptive PID controller is proposed for trackingthe control task of an uncertain nonlinear system Thecontroller has been successfully applied to the problem ofthe speed tracking control of an SI engine through electronic
10 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
PIDSMC
LPFSMC and adaptive PIDDesired
0 50 100 150 200 250 300 350 4000
500
1000
1500
2000
2500
(a)
00689
0071
00694
006750068
006850069
00695007
007050071
00715
LPFSMC andadaptive PID
SMC PID
Fuel consumption (Lmin)
(b)
20288 41113 20302
105977
425503
109623
0500
10001500200025003000350040004500
LPFSMC andadaptive PID
SMC PID
HC (ppm)CO (ppm)
(c)
Figure 7 Comparisons of (a) tracking performance of the controllers (b) fuel consumption rates (c) exhaust emission rates
throttle valve control architecture From the simulation andexperimental results it achieves that
(1) the proposed adaptation law is capable of optimalonline update the PID controller during the controlprocess within a short period
(2) the chattering of the SMC can be alleviated by afirst-order low pass filter while the robustness of thecontrol system similar to that of the slidingmode suchthat the load torque disturbances can be compensatedquite accurately
(3) the proposed control scheme has high performancein implementation as it can be achieved in theproblem of engine speed control in which the systemis largely uncertain nonlinear system and rathercomplex mechanisms
Conflict of Interests
The authors have no competing interests
Acknowledgment
This research is financially supported by the Office ofResearch Administration (ORA) and Farm Engineering andAutomation Technology Research Group (FEAT) of Khon
Kaen University Thailand The authors are also thankfulto the reviewers and Mr Ian Thomas for their valuablecomments and suggestions for English grammar correctionrespectively
References
[1] K-C Hsu W-Y Wang and P-Z Lin ldquoSliding mode controlfor uncertain nonlinear systemswithmultiple inputs containingsector nonlinearities and deadzonesrdquo IEEE Transactions onSystems Man and Cybernetics Part B Cybernetics vol 34 no1 pp 374ndash380 2004
[2] G Bartolini and A Ferrara ldquoMulti-input sliding mode controlof a class of uncertain nonlinear systemsrdquo IEEE Transactions onAutomatic Control vol 41 no 11 pp 1662ndash1666 1996
[3] T-C Kuo Y-J Huang and S-H Chang ldquoSliding mode controlwith self-tuning law for uncertain nonlinear systemsrdquo ISATransactions vol 47 no 2 pp 171ndash178 2008
[4] G Montaseri and M J Yazdanpanah ldquoPredictive control ofuncertain nonlinear parabolic PDE systems using a Galerkinneural-network-based modelrdquo Communications in NonlinearScience and Numerical Simulation vol 17 no 1 pp 388ndash4042012
[5] F O Tellez A G Loukianov E N Sanchez and E Jose BayroCorrochano ldquoDecentralized neural identification and controlfor uncertain nonlinear systems application to planar robotrdquoJournal of the Franklin Institute vol 347 no 6 pp 1015ndash10342010
Mathematical Problems in Engineering 11
[6] A Bazaei and V J Majd ldquoFeedback linearization of discrete-time nonlinear uncertain plants via first-principles-based serialneuro-gray-box modelsrdquo Journal of Process Control vol 13 no8 pp 819ndash830 2003
[7] T-Y Kuc and W-G Han ldquoAn adaptive PID learning controlof robot manipulatorsrdquo Automatica vol 36 no 5 pp 717ndash7252000
[8] Y Pan Y Zhou T Sun and M J Er ldquoComposite adaptivefuzzy 119867
infintracking control of uncertain nonlinear systemsrdquo
Neurocomputing vol 99 pp 15ndash24 2013[9] X Liu R Tao and M Tavakoli ldquoAdaptive control of uncertain
nonlinear teleoperation systemsrdquo Mechatronics vol 24 no 1pp 66ndash78 2014
[10] W-D Chang and J-J Yan ldquoAdaptive robust PID controllerdesign based on a sliding mode for uncertain chaotic systemsrdquoChaos Solitons amp Fractals vol 26 no 1 pp 167ndash175 2005
[11] T C Kuo Y J Huang C Y Chen and C H Chang ldquoAdaptivesliding mode control with PID tuning for uncertain systemrdquoEngineering Letters vol 16 no 3 pp 1ndash5 2008
[12] M N Howell and M C Best ldquoOn-line PID tuning forengine idle-speed control using continuous action reinforce-ment learning automatardquo Control Engineering Practice vol 8no 2 pp 147ndash154 2000
[13] C-F Hsu and B-K Lee ldquoFPGA-based adaptive PID control ofa DC motor driver via sliding-mode approachrdquo Expert Systemswith Applications vol 38 no 9 pp 11866ndash11872 2011
[14] DWMemering and PHMeckl ldquoComparison of adaptive con-trol techniques applied to diesel engine idle speed regulationrdquoJournal of Dynamic Systems Measurement and Control vol 124no 4 pp 682ndash688 2002
[15] V I Utkin ldquoSliding mode control design principles andapplications to electric drivesrdquo IEEE Transactions on IndustrialElectronics vol 40 no 1 pp 23ndash36 1993
[16] Y J Huang and T C Kuo ldquoRobust output tracking controlfor nonlinear time-varying robotic manipulatorsrdquo ElectricalEngineering vol 87 no 1 pp 47ndash55 2005
[17] M Hajatipour and M Farrokhi ldquoChattering free with noisereduction in sliding-mode observers using frequency domainanalysisrdquo Journal of Process Control vol 20 no 8 pp 912ndash9212010
[18] A Sabanovic L Fridman and S Spurgeon Variable StructureSystems From Principles to Implementation The Institution ofEngineering and Technology 2004
[19] Y Xu ldquoChattering free robust control for nonlinear systemsrdquoIEEE Transactions on Control Systems Technology vol 16 no 6pp 1352ndash1359 2008
[20] H Lee and V I Utkin ldquoChattering suppression methods insliding mode control systemsrdquo Annual Reviews in Control vol31 no 2 pp 179ndash188 2007
[21] Y Ren Z Liu L Chang and N Wen ldquoAdaptive slidingmode robust control for virtual compound-axis servo systemrdquoMathematical Problems in Engineering vol 2013 Article ID343851 9 pages 2013
[22] M-L Tseng and M-S Chen ldquoChattering reduction of slidingmode control by low-pass filtering the control signalrdquo AsianJournal of Control vol 12 no 3 pp 392ndash398 2010
[23] H Sira-RamIRez ldquoOn the dynamical sliding mode control ofnonlinear systemsrdquo International Journal of Control vol 57 no5 pp 1039ndash1061 1993
[24] J-X Xu Y-J Pan and T-H Lee ldquoSliding mode controlwith closed-loop filtering architecture for a class of nonlinear
systemsrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 51 no 4 pp 168ndash173 2004
[25] A Deenadayalan and G S Ilango ldquoPosition sensorless slidingmode observer with sigmoid function for Brushless DCmotorrdquoin Proceedings of the International Conference on Advances inPower Conversion and Energy Technologies (APCET rsquo12) pp 1ndash6IEEE August 2012
[26] Y Xia X Yu andW Oghanna ldquoAdaptive robust fast control forinduction motorsrdquo IEEE Transactions on Industrial Electronicsvol 47 no 4 pp 854ndash862 2000
[27] M Niclai Theory of Nonlinear Control Systems McGraw-Hill1969
[28] J J Slotine andW Li Applied Nonlinear Control Prentice-HallEnglewood Cliffs NJ USA 1991
[29] D Gorinevsky and L A Feldkamp ldquoRBF network feedforwardcompensation of load disturbance in idle speed controlrdquo IEEEControl Systems vol 16 no 6 pp 18ndash27 1996
[30] S Di Cairano D Yanakiev A Bemporad I V Kolmanovskyand D Hrovat ldquoModel predictive idle speed control designanalysis and experimental evaluationrdquo IEEE Transactions onControl Systems Technology vol 20 no 1 pp 84ndash97 2012
[31] P F Puleston S Spurgeon andGMonsees ldquoAutomotive enginespeed control a robust nonlinear control frameworkrdquo IEEProceedings Control Theory and Applications vol 148 no 1 pp81ndash87 2001
[32] Y Yildiz A M Annaswamy D Yanakiev and I KolmanovskyldquoSpark-ignition-engine idle speed control an adaptive controlapproachrdquo IEEE Transactions on Control Systems Technologyvol 19 no 5 pp 990ndash1002 2011
[33] A Sugeng K Baharin T Hishamuddin and J B SupriyoldquoEngine speed control using online ANN for vehicle withEMDAP-CVTrdquo Jurnal Mekanikal vol 22 pp 39ndash52 2006
[34] M K Khan K B Goh and S K Spurgeon ldquoSecond ordersliding mode control of a diesel enginerdquo Asian Journal ofControl vol 5 no 4 pp 614ndash619 2003
[35] J R Wagner D M Dawson and L Zeyu ldquoNonlinear air-to-fuel ratio and engine speed control for hybrid vehiclesrdquo IEEETransactions on Vehicular Technology vol 52 no 1 pp 184ndash1952003
[36] F Assadian S Fekri andM Hancock ldquoHybrid electric vehicleschallenges strategies for advanced engine speed controlrdquo inProceedings of the IEEE International Electric Vehicle Conference(IEVC rsquo12) March 2012
[37] A G Ulsoy H Peng and M Cakmakci Automotive ControlSystems Cambridge University Press Cambridge UK 2014
[38] C Ji and S Wang ldquoStrategies for improving the idle perfor-mance of a spark-ignited gasoline enginerdquo International Journalof Hydrogen Energy vol 37 no 4 pp 3938ndash3944 2012
[39] S Wang C Ji M Zhang and B Zhang ldquoReducing theidle speed of a spark-ignited gasoline engine with hydrogenadditionrdquo International Journal of Hydrogen Energy vol 35 no19 pp 10580ndash10588 2010
[40] DHrovat and J Sun ldquoModels and controlmethodologies for ICengine idle speed control designrdquo Control Engineering Practicevol 5 no 8 pp 1093ndash1100 1997
[41] B Alt J P Blath F Svaricek and M Schultalbers ldquoMultiplesliding surface control of idle engine speed and torque reservewith dead start assist controlrdquo IEEE Transactions on IndustrialElectronics vol 56 no 9 pp 3580ndash3592 2009
12 Mathematical Problems in Engineering
[42] T Radpukdee and P Jirawattana ldquoUncertainty learning andcompensation an application to pressure tracking of an electro-hydraulic proportional relief valverdquo Control Engineering Prac-tice vol 17 no 2 pp 291ndash301 2009
[43] P A Loannou and J Sun Robust Adaptive Control PTRPrentice-Hall 1996
[44] C D Richard and H B Robert Modern Control SystemsPrentice Hall Upper Saddle River NJ USA 2011
[45] A Jansri and P Sooraksa ldquoEnhanced model and fuzzy strategyof air to fuel ratio control for spark ignition enginesrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 922ndash9332012
[46] Z Ye ldquoModeling identification design and implementation ofnonlinear automotive idle speed control systemsmdashanoverviewrdquoIEEE Transactions on Systems Man and Cybernetics Part CApplications and Reviews vol 37 no 6 pp 1137ndash1151 2007
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 7
Time (s)
Spee
d re
spon
se (r
pm)
ZOOM
Time (s)
Spee
d re
spon
se(r
pm)
SMCLPFSMC and adaptive PIDDesiredPID
0200400600800
10001200140016001800
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 208998995
9009005
901
(a)
Time (s)
Con
trol i
nput
(V)
SMC LPFSMC and adaptive PIDPID
minus30minus25minus20minus15minus10minus5
05
101520
2 4 6 8 10 12 14 16 18 200
(b)
Erro
rs
SMC LPFSMC and adaptive PIDPID
Time (s)
Erro
rs
ZOOM
0 2 4 6 8 10 12 14 16 18 20Time (s)
minus1000minus800minus600minus400minus200
0200400600800
005
1
minus05minus1
0 2 4 6 8 10 12 14 16 18 20
(c)
Figure 3 Comparison of simulation results among different control techniques (a) the output response (b) the control inputs (c) the errors
PWM M
DC motor
Gear box
Throttle opening sensor
Throttle body
Control system
Electronic throttle control unit
SI engine
ADCDAC
Amplifier
Air
Speed calculation
Throttle position calculation
Fuel consumptioncomputation
Emission data logger(HC CO)
Speed sensor
Fuel flow sensor
Emission sensor
Power trainsystem
Dynamometer
Figure 4 Schematic diagram of the experiment
8 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
DesiredLPFSMC and adaptive PID
Con
trol i
nput
(V)
Time (s)
Slid
ing
varia
ble (
s)
Time (s)
Thro
ttle v
alve
ope
ning
(deg
)
Time (s)
0 20 40 60 80 100 120 140 160 180 200600650700750800850900950
1000
0
01
02
03
04
05
06
0 20 40 60 80 100 120 140 160 180 200
minus200minus150minus100minus50
050
100150200
0 20 40 60 80 100 120 140 160 180 200012345678
0 20 40 60 80 100 120 140 160 180 200
Figure 5 Experimental results of the proposed controller (LPFSMC and Adaptive PID technique)
Table 1 Experimental technical data
Item ValueSI engine (4 cylinders 900 ccgasoline type) Test range 600ndash3000 rpm
Speed sensor (rpm) Sampling speed approximately5000 ts
Throttle position sensor Measurement range 0ndash80∘
ADCDAC minus10 to 10VDC 20mA
COMPUTER Core2Duo 293GHz 4GBRAM
DCmotor 48ndash6VFuel type (experiments) Ethanol-gasoline blended (E20)
and the dynamometer which is used to generate the load-torque into the systemThe engine speed is interpreted as thecrankshaft rotation rate in revolutions per minute (rpm) andis regulated by opening the throttle In this task the throttlevalve is directly actuated by a DCmotor in which the angularmovement is handled by the control signal in the form ofPulseWidth Modulation (PWM)The exhaust emissions COandHCwere alsomeasured through a nondispersive infraredanalysis machine (Infralyt smart) in which the acquiringsampling data is 1 s while the fuel consumptionwasmeasuredby the fuel flow sensor (Hall effect-800 series) with thesampling period is 1ms The computation unit is performedwith MATLAB-Simulink programming An ADCDAC isused as an interface systembetween the computer and the realplant while the sampling period is 1ms for all experiments
As seen in Figure 5 the desired speed is chosen to rapidchange from 750 rpm to 900 rpm and 900 rpm to 750 rpmand the experiments were performed for 200 s This resultreveals that the speed response of the proposed controlscheme can reach the desired speedwithin short time and hasno overshoot and tiny oscillationThe control input is smoothand reaches an optimal value within a short time and thesliding variable can approach zero rapidly Fast convergenceof the response is a result of the updated control gains (119870
119868
and 119870119863) of the PID controller which can be adjusted rapidly
during the control process according to the adaptive lawFurthermore the characteristic of the opening position of thethrottle valve was alsomeasuredThis reveals that themotionof the actuator has smooth and tiny oscillations
43 Tracking Performance and Disturbance Rejection TestThe robust properties and the tracking performance of theproposed control schemewere also assessed because it is wellknown that the engine speed control is affected by the stateof accessory changes such as external load disturbance [41]In the experiments we compare the disturbance rejectionperformance among the proposed controller SMC techniqueand PID controller The load disturbance is generated bythe dynamometer while the speed set-point is chosen to be900 rpm Note that for the reason of low-speed test it issensitive from any disturbances therefore the implementa-tion in the low-speed region is more difficult than the high-speed control task Furthermore high performance of low-speed control leads to increase the performance of the engineoperation at any operating condition [32]
Mathematical Problems in Engineering 9
Time (s)Lo
ad (W
)
75
225
Engi
ne sp
eed
(rpm
)
DesiredLPFSMC and adaptive PID
PIDSMC
15
30
0
1000
950
900
850
800
Time (s)
120 125 130 135 140 145 150 155 160
120 125 130 135 140 145 150 155 160
Figure 6 Comparisons of tracking performance and disturbance rejection of the controllers
As seen in Figure 6 at the time 125 sec the load torquewas applied immediately into the engine speed control taskThis proposed to disturb the stability of the control system atthe steady-state condition The proposed control scheme canimprove the speed deviation rapidly and is capable of trackingthe desired speed better than other control techniques Inaddition the load torque was decreased immediately at thetime 150 sec The results show that the proposed controlscheme can decrease the speed deviation from the desiredspeed faster than other control techniques The findingsreveal that the proposed control scheme has effective ofthe robustness and fast adaptation and has better trackingperformance than other control techniques
44 Fuel Consumption andExhaust Emission Investigation Inthis section the fuel consumption and the exhaust emissionof the engine speed control by using the proposed controlscheme and different control techniques (SMC techniqueand PID controller) were investigated (see Figure 7) In theexperiments the desired speed was performed for 400 secand was rapidly changed as shown in Figure 7(a) For theaverage total fuel consumption comparison (see Figure 7(b))the proposed control scheme can attain an excellent resultwith the lowest averaged total fuel consumption whichwas obtained by the average of the fuel consumptions persecond
In addition the average exhaust emissions were alsoinvestigated (see Figure 7(c)) The CO and HC emissions arethe main pollutants contributed by the SI engines In theprinciple of the combustion process of SI engine the HCemission is appeared when fuel molecules in the engine
cannot burn or burn only partially while the CO emissionis produced when the carbon in the fuel is partially oxi-dized rather than fully oxidized to carbon dioxide Howeverincreasing efficient strategies for engine speed control viathrottle valve regulation method is capable of increasingcombustion performance as it can reduce pollutant emissionsalso [38] In the experiments effects of the controllers wereinvestigated via the constant speed set points and no addingan external engine load (small load from the unloadedhydrostatic CVT)Thus the CO
2andNO
119909which are sensitive
to speed variation and high temperature operation did notmeasure in this work (the experiments perform at coolanttemperature of 70ndash80∘C for short period) As a result bothaverages of the CO and HC emission data were calculatedby the average of emissions per second in which obtainedby the direct measurement method [43] Additionally theseresults demonstrate that high fuel consumption and exhaustemission are affected by high variation of the engine speedduring tracking of the set pointsThese results also imply thatthe performance of the SI engine at any operating conditioncan be improved by an advanced engine speed control viathe electronic throttle valve regulation method as shown inFigure 7
5 Conclusions
The incorporation of the SMC and a first-order LPF witha new adaptive PID controller is proposed for trackingthe control task of an uncertain nonlinear system Thecontroller has been successfully applied to the problem ofthe speed tracking control of an SI engine through electronic
10 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
PIDSMC
LPFSMC and adaptive PIDDesired
0 50 100 150 200 250 300 350 4000
500
1000
1500
2000
2500
(a)
00689
0071
00694
006750068
006850069
00695007
007050071
00715
LPFSMC andadaptive PID
SMC PID
Fuel consumption (Lmin)
(b)
20288 41113 20302
105977
425503
109623
0500
10001500200025003000350040004500
LPFSMC andadaptive PID
SMC PID
HC (ppm)CO (ppm)
(c)
Figure 7 Comparisons of (a) tracking performance of the controllers (b) fuel consumption rates (c) exhaust emission rates
throttle valve control architecture From the simulation andexperimental results it achieves that
(1) the proposed adaptation law is capable of optimalonline update the PID controller during the controlprocess within a short period
(2) the chattering of the SMC can be alleviated by afirst-order low pass filter while the robustness of thecontrol system similar to that of the slidingmode suchthat the load torque disturbances can be compensatedquite accurately
(3) the proposed control scheme has high performancein implementation as it can be achieved in theproblem of engine speed control in which the systemis largely uncertain nonlinear system and rathercomplex mechanisms
Conflict of Interests
The authors have no competing interests
Acknowledgment
This research is financially supported by the Office ofResearch Administration (ORA) and Farm Engineering andAutomation Technology Research Group (FEAT) of Khon
Kaen University Thailand The authors are also thankfulto the reviewers and Mr Ian Thomas for their valuablecomments and suggestions for English grammar correctionrespectively
References
[1] K-C Hsu W-Y Wang and P-Z Lin ldquoSliding mode controlfor uncertain nonlinear systemswithmultiple inputs containingsector nonlinearities and deadzonesrdquo IEEE Transactions onSystems Man and Cybernetics Part B Cybernetics vol 34 no1 pp 374ndash380 2004
[2] G Bartolini and A Ferrara ldquoMulti-input sliding mode controlof a class of uncertain nonlinear systemsrdquo IEEE Transactions onAutomatic Control vol 41 no 11 pp 1662ndash1666 1996
[3] T-C Kuo Y-J Huang and S-H Chang ldquoSliding mode controlwith self-tuning law for uncertain nonlinear systemsrdquo ISATransactions vol 47 no 2 pp 171ndash178 2008
[4] G Montaseri and M J Yazdanpanah ldquoPredictive control ofuncertain nonlinear parabolic PDE systems using a Galerkinneural-network-based modelrdquo Communications in NonlinearScience and Numerical Simulation vol 17 no 1 pp 388ndash4042012
[5] F O Tellez A G Loukianov E N Sanchez and E Jose BayroCorrochano ldquoDecentralized neural identification and controlfor uncertain nonlinear systems application to planar robotrdquoJournal of the Franklin Institute vol 347 no 6 pp 1015ndash10342010
Mathematical Problems in Engineering 11
[6] A Bazaei and V J Majd ldquoFeedback linearization of discrete-time nonlinear uncertain plants via first-principles-based serialneuro-gray-box modelsrdquo Journal of Process Control vol 13 no8 pp 819ndash830 2003
[7] T-Y Kuc and W-G Han ldquoAn adaptive PID learning controlof robot manipulatorsrdquo Automatica vol 36 no 5 pp 717ndash7252000
[8] Y Pan Y Zhou T Sun and M J Er ldquoComposite adaptivefuzzy 119867
infintracking control of uncertain nonlinear systemsrdquo
Neurocomputing vol 99 pp 15ndash24 2013[9] X Liu R Tao and M Tavakoli ldquoAdaptive control of uncertain
nonlinear teleoperation systemsrdquo Mechatronics vol 24 no 1pp 66ndash78 2014
[10] W-D Chang and J-J Yan ldquoAdaptive robust PID controllerdesign based on a sliding mode for uncertain chaotic systemsrdquoChaos Solitons amp Fractals vol 26 no 1 pp 167ndash175 2005
[11] T C Kuo Y J Huang C Y Chen and C H Chang ldquoAdaptivesliding mode control with PID tuning for uncertain systemrdquoEngineering Letters vol 16 no 3 pp 1ndash5 2008
[12] M N Howell and M C Best ldquoOn-line PID tuning forengine idle-speed control using continuous action reinforce-ment learning automatardquo Control Engineering Practice vol 8no 2 pp 147ndash154 2000
[13] C-F Hsu and B-K Lee ldquoFPGA-based adaptive PID control ofa DC motor driver via sliding-mode approachrdquo Expert Systemswith Applications vol 38 no 9 pp 11866ndash11872 2011
[14] DWMemering and PHMeckl ldquoComparison of adaptive con-trol techniques applied to diesel engine idle speed regulationrdquoJournal of Dynamic Systems Measurement and Control vol 124no 4 pp 682ndash688 2002
[15] V I Utkin ldquoSliding mode control design principles andapplications to electric drivesrdquo IEEE Transactions on IndustrialElectronics vol 40 no 1 pp 23ndash36 1993
[16] Y J Huang and T C Kuo ldquoRobust output tracking controlfor nonlinear time-varying robotic manipulatorsrdquo ElectricalEngineering vol 87 no 1 pp 47ndash55 2005
[17] M Hajatipour and M Farrokhi ldquoChattering free with noisereduction in sliding-mode observers using frequency domainanalysisrdquo Journal of Process Control vol 20 no 8 pp 912ndash9212010
[18] A Sabanovic L Fridman and S Spurgeon Variable StructureSystems From Principles to Implementation The Institution ofEngineering and Technology 2004
[19] Y Xu ldquoChattering free robust control for nonlinear systemsrdquoIEEE Transactions on Control Systems Technology vol 16 no 6pp 1352ndash1359 2008
[20] H Lee and V I Utkin ldquoChattering suppression methods insliding mode control systemsrdquo Annual Reviews in Control vol31 no 2 pp 179ndash188 2007
[21] Y Ren Z Liu L Chang and N Wen ldquoAdaptive slidingmode robust control for virtual compound-axis servo systemrdquoMathematical Problems in Engineering vol 2013 Article ID343851 9 pages 2013
[22] M-L Tseng and M-S Chen ldquoChattering reduction of slidingmode control by low-pass filtering the control signalrdquo AsianJournal of Control vol 12 no 3 pp 392ndash398 2010
[23] H Sira-RamIRez ldquoOn the dynamical sliding mode control ofnonlinear systemsrdquo International Journal of Control vol 57 no5 pp 1039ndash1061 1993
[24] J-X Xu Y-J Pan and T-H Lee ldquoSliding mode controlwith closed-loop filtering architecture for a class of nonlinear
systemsrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 51 no 4 pp 168ndash173 2004
[25] A Deenadayalan and G S Ilango ldquoPosition sensorless slidingmode observer with sigmoid function for Brushless DCmotorrdquoin Proceedings of the International Conference on Advances inPower Conversion and Energy Technologies (APCET rsquo12) pp 1ndash6IEEE August 2012
[26] Y Xia X Yu andW Oghanna ldquoAdaptive robust fast control forinduction motorsrdquo IEEE Transactions on Industrial Electronicsvol 47 no 4 pp 854ndash862 2000
[27] M Niclai Theory of Nonlinear Control Systems McGraw-Hill1969
[28] J J Slotine andW Li Applied Nonlinear Control Prentice-HallEnglewood Cliffs NJ USA 1991
[29] D Gorinevsky and L A Feldkamp ldquoRBF network feedforwardcompensation of load disturbance in idle speed controlrdquo IEEEControl Systems vol 16 no 6 pp 18ndash27 1996
[30] S Di Cairano D Yanakiev A Bemporad I V Kolmanovskyand D Hrovat ldquoModel predictive idle speed control designanalysis and experimental evaluationrdquo IEEE Transactions onControl Systems Technology vol 20 no 1 pp 84ndash97 2012
[31] P F Puleston S Spurgeon andGMonsees ldquoAutomotive enginespeed control a robust nonlinear control frameworkrdquo IEEProceedings Control Theory and Applications vol 148 no 1 pp81ndash87 2001
[32] Y Yildiz A M Annaswamy D Yanakiev and I KolmanovskyldquoSpark-ignition-engine idle speed control an adaptive controlapproachrdquo IEEE Transactions on Control Systems Technologyvol 19 no 5 pp 990ndash1002 2011
[33] A Sugeng K Baharin T Hishamuddin and J B SupriyoldquoEngine speed control using online ANN for vehicle withEMDAP-CVTrdquo Jurnal Mekanikal vol 22 pp 39ndash52 2006
[34] M K Khan K B Goh and S K Spurgeon ldquoSecond ordersliding mode control of a diesel enginerdquo Asian Journal ofControl vol 5 no 4 pp 614ndash619 2003
[35] J R Wagner D M Dawson and L Zeyu ldquoNonlinear air-to-fuel ratio and engine speed control for hybrid vehiclesrdquo IEEETransactions on Vehicular Technology vol 52 no 1 pp 184ndash1952003
[36] F Assadian S Fekri andM Hancock ldquoHybrid electric vehicleschallenges strategies for advanced engine speed controlrdquo inProceedings of the IEEE International Electric Vehicle Conference(IEVC rsquo12) March 2012
[37] A G Ulsoy H Peng and M Cakmakci Automotive ControlSystems Cambridge University Press Cambridge UK 2014
[38] C Ji and S Wang ldquoStrategies for improving the idle perfor-mance of a spark-ignited gasoline enginerdquo International Journalof Hydrogen Energy vol 37 no 4 pp 3938ndash3944 2012
[39] S Wang C Ji M Zhang and B Zhang ldquoReducing theidle speed of a spark-ignited gasoline engine with hydrogenadditionrdquo International Journal of Hydrogen Energy vol 35 no19 pp 10580ndash10588 2010
[40] DHrovat and J Sun ldquoModels and controlmethodologies for ICengine idle speed control designrdquo Control Engineering Practicevol 5 no 8 pp 1093ndash1100 1997
[41] B Alt J P Blath F Svaricek and M Schultalbers ldquoMultiplesliding surface control of idle engine speed and torque reservewith dead start assist controlrdquo IEEE Transactions on IndustrialElectronics vol 56 no 9 pp 3580ndash3592 2009
12 Mathematical Problems in Engineering
[42] T Radpukdee and P Jirawattana ldquoUncertainty learning andcompensation an application to pressure tracking of an electro-hydraulic proportional relief valverdquo Control Engineering Prac-tice vol 17 no 2 pp 291ndash301 2009
[43] P A Loannou and J Sun Robust Adaptive Control PTRPrentice-Hall 1996
[44] C D Richard and H B Robert Modern Control SystemsPrentice Hall Upper Saddle River NJ USA 2011
[45] A Jansri and P Sooraksa ldquoEnhanced model and fuzzy strategyof air to fuel ratio control for spark ignition enginesrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 922ndash9332012
[46] Z Ye ldquoModeling identification design and implementation ofnonlinear automotive idle speed control systemsmdashanoverviewrdquoIEEE Transactions on Systems Man and Cybernetics Part CApplications and Reviews vol 37 no 6 pp 1137ndash1151 2007
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
8 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
DesiredLPFSMC and adaptive PID
Con
trol i
nput
(V)
Time (s)
Slid
ing
varia
ble (
s)
Time (s)
Thro
ttle v
alve
ope
ning
(deg
)
Time (s)
0 20 40 60 80 100 120 140 160 180 200600650700750800850900950
1000
0
01
02
03
04
05
06
0 20 40 60 80 100 120 140 160 180 200
minus200minus150minus100minus50
050
100150200
0 20 40 60 80 100 120 140 160 180 200012345678
0 20 40 60 80 100 120 140 160 180 200
Figure 5 Experimental results of the proposed controller (LPFSMC and Adaptive PID technique)
Table 1 Experimental technical data
Item ValueSI engine (4 cylinders 900 ccgasoline type) Test range 600ndash3000 rpm
Speed sensor (rpm) Sampling speed approximately5000 ts
Throttle position sensor Measurement range 0ndash80∘
ADCDAC minus10 to 10VDC 20mA
COMPUTER Core2Duo 293GHz 4GBRAM
DCmotor 48ndash6VFuel type (experiments) Ethanol-gasoline blended (E20)
and the dynamometer which is used to generate the load-torque into the systemThe engine speed is interpreted as thecrankshaft rotation rate in revolutions per minute (rpm) andis regulated by opening the throttle In this task the throttlevalve is directly actuated by a DCmotor in which the angularmovement is handled by the control signal in the form ofPulseWidth Modulation (PWM)The exhaust emissions COandHCwere alsomeasured through a nondispersive infraredanalysis machine (Infralyt smart) in which the acquiringsampling data is 1 s while the fuel consumptionwasmeasuredby the fuel flow sensor (Hall effect-800 series) with thesampling period is 1ms The computation unit is performedwith MATLAB-Simulink programming An ADCDAC isused as an interface systembetween the computer and the realplant while the sampling period is 1ms for all experiments
As seen in Figure 5 the desired speed is chosen to rapidchange from 750 rpm to 900 rpm and 900 rpm to 750 rpmand the experiments were performed for 200 s This resultreveals that the speed response of the proposed controlscheme can reach the desired speedwithin short time and hasno overshoot and tiny oscillationThe control input is smoothand reaches an optimal value within a short time and thesliding variable can approach zero rapidly Fast convergenceof the response is a result of the updated control gains (119870
119868
and 119870119863) of the PID controller which can be adjusted rapidly
during the control process according to the adaptive lawFurthermore the characteristic of the opening position of thethrottle valve was alsomeasuredThis reveals that themotionof the actuator has smooth and tiny oscillations
43 Tracking Performance and Disturbance Rejection TestThe robust properties and the tracking performance of theproposed control schemewere also assessed because it is wellknown that the engine speed control is affected by the stateof accessory changes such as external load disturbance [41]In the experiments we compare the disturbance rejectionperformance among the proposed controller SMC techniqueand PID controller The load disturbance is generated bythe dynamometer while the speed set-point is chosen to be900 rpm Note that for the reason of low-speed test it issensitive from any disturbances therefore the implementa-tion in the low-speed region is more difficult than the high-speed control task Furthermore high performance of low-speed control leads to increase the performance of the engineoperation at any operating condition [32]
Mathematical Problems in Engineering 9
Time (s)Lo
ad (W
)
75
225
Engi
ne sp
eed
(rpm
)
DesiredLPFSMC and adaptive PID
PIDSMC
15
30
0
1000
950
900
850
800
Time (s)
120 125 130 135 140 145 150 155 160
120 125 130 135 140 145 150 155 160
Figure 6 Comparisons of tracking performance and disturbance rejection of the controllers
As seen in Figure 6 at the time 125 sec the load torquewas applied immediately into the engine speed control taskThis proposed to disturb the stability of the control system atthe steady-state condition The proposed control scheme canimprove the speed deviation rapidly and is capable of trackingthe desired speed better than other control techniques Inaddition the load torque was decreased immediately at thetime 150 sec The results show that the proposed controlscheme can decrease the speed deviation from the desiredspeed faster than other control techniques The findingsreveal that the proposed control scheme has effective ofthe robustness and fast adaptation and has better trackingperformance than other control techniques
44 Fuel Consumption andExhaust Emission Investigation Inthis section the fuel consumption and the exhaust emissionof the engine speed control by using the proposed controlscheme and different control techniques (SMC techniqueand PID controller) were investigated (see Figure 7) In theexperiments the desired speed was performed for 400 secand was rapidly changed as shown in Figure 7(a) For theaverage total fuel consumption comparison (see Figure 7(b))the proposed control scheme can attain an excellent resultwith the lowest averaged total fuel consumption whichwas obtained by the average of the fuel consumptions persecond
In addition the average exhaust emissions were alsoinvestigated (see Figure 7(c)) The CO and HC emissions arethe main pollutants contributed by the SI engines In theprinciple of the combustion process of SI engine the HCemission is appeared when fuel molecules in the engine
cannot burn or burn only partially while the CO emissionis produced when the carbon in the fuel is partially oxi-dized rather than fully oxidized to carbon dioxide Howeverincreasing efficient strategies for engine speed control viathrottle valve regulation method is capable of increasingcombustion performance as it can reduce pollutant emissionsalso [38] In the experiments effects of the controllers wereinvestigated via the constant speed set points and no addingan external engine load (small load from the unloadedhydrostatic CVT)Thus the CO
2andNO
119909which are sensitive
to speed variation and high temperature operation did notmeasure in this work (the experiments perform at coolanttemperature of 70ndash80∘C for short period) As a result bothaverages of the CO and HC emission data were calculatedby the average of emissions per second in which obtainedby the direct measurement method [43] Additionally theseresults demonstrate that high fuel consumption and exhaustemission are affected by high variation of the engine speedduring tracking of the set pointsThese results also imply thatthe performance of the SI engine at any operating conditioncan be improved by an advanced engine speed control viathe electronic throttle valve regulation method as shown inFigure 7
5 Conclusions
The incorporation of the SMC and a first-order LPF witha new adaptive PID controller is proposed for trackingthe control task of an uncertain nonlinear system Thecontroller has been successfully applied to the problem ofthe speed tracking control of an SI engine through electronic
10 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
PIDSMC
LPFSMC and adaptive PIDDesired
0 50 100 150 200 250 300 350 4000
500
1000
1500
2000
2500
(a)
00689
0071
00694
006750068
006850069
00695007
007050071
00715
LPFSMC andadaptive PID
SMC PID
Fuel consumption (Lmin)
(b)
20288 41113 20302
105977
425503
109623
0500
10001500200025003000350040004500
LPFSMC andadaptive PID
SMC PID
HC (ppm)CO (ppm)
(c)
Figure 7 Comparisons of (a) tracking performance of the controllers (b) fuel consumption rates (c) exhaust emission rates
throttle valve control architecture From the simulation andexperimental results it achieves that
(1) the proposed adaptation law is capable of optimalonline update the PID controller during the controlprocess within a short period
(2) the chattering of the SMC can be alleviated by afirst-order low pass filter while the robustness of thecontrol system similar to that of the slidingmode suchthat the load torque disturbances can be compensatedquite accurately
(3) the proposed control scheme has high performancein implementation as it can be achieved in theproblem of engine speed control in which the systemis largely uncertain nonlinear system and rathercomplex mechanisms
Conflict of Interests
The authors have no competing interests
Acknowledgment
This research is financially supported by the Office ofResearch Administration (ORA) and Farm Engineering andAutomation Technology Research Group (FEAT) of Khon
Kaen University Thailand The authors are also thankfulto the reviewers and Mr Ian Thomas for their valuablecomments and suggestions for English grammar correctionrespectively
References
[1] K-C Hsu W-Y Wang and P-Z Lin ldquoSliding mode controlfor uncertain nonlinear systemswithmultiple inputs containingsector nonlinearities and deadzonesrdquo IEEE Transactions onSystems Man and Cybernetics Part B Cybernetics vol 34 no1 pp 374ndash380 2004
[2] G Bartolini and A Ferrara ldquoMulti-input sliding mode controlof a class of uncertain nonlinear systemsrdquo IEEE Transactions onAutomatic Control vol 41 no 11 pp 1662ndash1666 1996
[3] T-C Kuo Y-J Huang and S-H Chang ldquoSliding mode controlwith self-tuning law for uncertain nonlinear systemsrdquo ISATransactions vol 47 no 2 pp 171ndash178 2008
[4] G Montaseri and M J Yazdanpanah ldquoPredictive control ofuncertain nonlinear parabolic PDE systems using a Galerkinneural-network-based modelrdquo Communications in NonlinearScience and Numerical Simulation vol 17 no 1 pp 388ndash4042012
[5] F O Tellez A G Loukianov E N Sanchez and E Jose BayroCorrochano ldquoDecentralized neural identification and controlfor uncertain nonlinear systems application to planar robotrdquoJournal of the Franklin Institute vol 347 no 6 pp 1015ndash10342010
Mathematical Problems in Engineering 11
[6] A Bazaei and V J Majd ldquoFeedback linearization of discrete-time nonlinear uncertain plants via first-principles-based serialneuro-gray-box modelsrdquo Journal of Process Control vol 13 no8 pp 819ndash830 2003
[7] T-Y Kuc and W-G Han ldquoAn adaptive PID learning controlof robot manipulatorsrdquo Automatica vol 36 no 5 pp 717ndash7252000
[8] Y Pan Y Zhou T Sun and M J Er ldquoComposite adaptivefuzzy 119867
infintracking control of uncertain nonlinear systemsrdquo
Neurocomputing vol 99 pp 15ndash24 2013[9] X Liu R Tao and M Tavakoli ldquoAdaptive control of uncertain
nonlinear teleoperation systemsrdquo Mechatronics vol 24 no 1pp 66ndash78 2014
[10] W-D Chang and J-J Yan ldquoAdaptive robust PID controllerdesign based on a sliding mode for uncertain chaotic systemsrdquoChaos Solitons amp Fractals vol 26 no 1 pp 167ndash175 2005
[11] T C Kuo Y J Huang C Y Chen and C H Chang ldquoAdaptivesliding mode control with PID tuning for uncertain systemrdquoEngineering Letters vol 16 no 3 pp 1ndash5 2008
[12] M N Howell and M C Best ldquoOn-line PID tuning forengine idle-speed control using continuous action reinforce-ment learning automatardquo Control Engineering Practice vol 8no 2 pp 147ndash154 2000
[13] C-F Hsu and B-K Lee ldquoFPGA-based adaptive PID control ofa DC motor driver via sliding-mode approachrdquo Expert Systemswith Applications vol 38 no 9 pp 11866ndash11872 2011
[14] DWMemering and PHMeckl ldquoComparison of adaptive con-trol techniques applied to diesel engine idle speed regulationrdquoJournal of Dynamic Systems Measurement and Control vol 124no 4 pp 682ndash688 2002
[15] V I Utkin ldquoSliding mode control design principles andapplications to electric drivesrdquo IEEE Transactions on IndustrialElectronics vol 40 no 1 pp 23ndash36 1993
[16] Y J Huang and T C Kuo ldquoRobust output tracking controlfor nonlinear time-varying robotic manipulatorsrdquo ElectricalEngineering vol 87 no 1 pp 47ndash55 2005
[17] M Hajatipour and M Farrokhi ldquoChattering free with noisereduction in sliding-mode observers using frequency domainanalysisrdquo Journal of Process Control vol 20 no 8 pp 912ndash9212010
[18] A Sabanovic L Fridman and S Spurgeon Variable StructureSystems From Principles to Implementation The Institution ofEngineering and Technology 2004
[19] Y Xu ldquoChattering free robust control for nonlinear systemsrdquoIEEE Transactions on Control Systems Technology vol 16 no 6pp 1352ndash1359 2008
[20] H Lee and V I Utkin ldquoChattering suppression methods insliding mode control systemsrdquo Annual Reviews in Control vol31 no 2 pp 179ndash188 2007
[21] Y Ren Z Liu L Chang and N Wen ldquoAdaptive slidingmode robust control for virtual compound-axis servo systemrdquoMathematical Problems in Engineering vol 2013 Article ID343851 9 pages 2013
[22] M-L Tseng and M-S Chen ldquoChattering reduction of slidingmode control by low-pass filtering the control signalrdquo AsianJournal of Control vol 12 no 3 pp 392ndash398 2010
[23] H Sira-RamIRez ldquoOn the dynamical sliding mode control ofnonlinear systemsrdquo International Journal of Control vol 57 no5 pp 1039ndash1061 1993
[24] J-X Xu Y-J Pan and T-H Lee ldquoSliding mode controlwith closed-loop filtering architecture for a class of nonlinear
systemsrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 51 no 4 pp 168ndash173 2004
[25] A Deenadayalan and G S Ilango ldquoPosition sensorless slidingmode observer with sigmoid function for Brushless DCmotorrdquoin Proceedings of the International Conference on Advances inPower Conversion and Energy Technologies (APCET rsquo12) pp 1ndash6IEEE August 2012
[26] Y Xia X Yu andW Oghanna ldquoAdaptive robust fast control forinduction motorsrdquo IEEE Transactions on Industrial Electronicsvol 47 no 4 pp 854ndash862 2000
[27] M Niclai Theory of Nonlinear Control Systems McGraw-Hill1969
[28] J J Slotine andW Li Applied Nonlinear Control Prentice-HallEnglewood Cliffs NJ USA 1991
[29] D Gorinevsky and L A Feldkamp ldquoRBF network feedforwardcompensation of load disturbance in idle speed controlrdquo IEEEControl Systems vol 16 no 6 pp 18ndash27 1996
[30] S Di Cairano D Yanakiev A Bemporad I V Kolmanovskyand D Hrovat ldquoModel predictive idle speed control designanalysis and experimental evaluationrdquo IEEE Transactions onControl Systems Technology vol 20 no 1 pp 84ndash97 2012
[31] P F Puleston S Spurgeon andGMonsees ldquoAutomotive enginespeed control a robust nonlinear control frameworkrdquo IEEProceedings Control Theory and Applications vol 148 no 1 pp81ndash87 2001
[32] Y Yildiz A M Annaswamy D Yanakiev and I KolmanovskyldquoSpark-ignition-engine idle speed control an adaptive controlapproachrdquo IEEE Transactions on Control Systems Technologyvol 19 no 5 pp 990ndash1002 2011
[33] A Sugeng K Baharin T Hishamuddin and J B SupriyoldquoEngine speed control using online ANN for vehicle withEMDAP-CVTrdquo Jurnal Mekanikal vol 22 pp 39ndash52 2006
[34] M K Khan K B Goh and S K Spurgeon ldquoSecond ordersliding mode control of a diesel enginerdquo Asian Journal ofControl vol 5 no 4 pp 614ndash619 2003
[35] J R Wagner D M Dawson and L Zeyu ldquoNonlinear air-to-fuel ratio and engine speed control for hybrid vehiclesrdquo IEEETransactions on Vehicular Technology vol 52 no 1 pp 184ndash1952003
[36] F Assadian S Fekri andM Hancock ldquoHybrid electric vehicleschallenges strategies for advanced engine speed controlrdquo inProceedings of the IEEE International Electric Vehicle Conference(IEVC rsquo12) March 2012
[37] A G Ulsoy H Peng and M Cakmakci Automotive ControlSystems Cambridge University Press Cambridge UK 2014
[38] C Ji and S Wang ldquoStrategies for improving the idle perfor-mance of a spark-ignited gasoline enginerdquo International Journalof Hydrogen Energy vol 37 no 4 pp 3938ndash3944 2012
[39] S Wang C Ji M Zhang and B Zhang ldquoReducing theidle speed of a spark-ignited gasoline engine with hydrogenadditionrdquo International Journal of Hydrogen Energy vol 35 no19 pp 10580ndash10588 2010
[40] DHrovat and J Sun ldquoModels and controlmethodologies for ICengine idle speed control designrdquo Control Engineering Practicevol 5 no 8 pp 1093ndash1100 1997
[41] B Alt J P Blath F Svaricek and M Schultalbers ldquoMultiplesliding surface control of idle engine speed and torque reservewith dead start assist controlrdquo IEEE Transactions on IndustrialElectronics vol 56 no 9 pp 3580ndash3592 2009
12 Mathematical Problems in Engineering
[42] T Radpukdee and P Jirawattana ldquoUncertainty learning andcompensation an application to pressure tracking of an electro-hydraulic proportional relief valverdquo Control Engineering Prac-tice vol 17 no 2 pp 291ndash301 2009
[43] P A Loannou and J Sun Robust Adaptive Control PTRPrentice-Hall 1996
[44] C D Richard and H B Robert Modern Control SystemsPrentice Hall Upper Saddle River NJ USA 2011
[45] A Jansri and P Sooraksa ldquoEnhanced model and fuzzy strategyof air to fuel ratio control for spark ignition enginesrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 922ndash9332012
[46] Z Ye ldquoModeling identification design and implementation ofnonlinear automotive idle speed control systemsmdashanoverviewrdquoIEEE Transactions on Systems Man and Cybernetics Part CApplications and Reviews vol 37 no 6 pp 1137ndash1151 2007
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 9
Time (s)Lo
ad (W
)
75
225
Engi
ne sp
eed
(rpm
)
DesiredLPFSMC and adaptive PID
PIDSMC
15
30
0
1000
950
900
850
800
Time (s)
120 125 130 135 140 145 150 155 160
120 125 130 135 140 145 150 155 160
Figure 6 Comparisons of tracking performance and disturbance rejection of the controllers
As seen in Figure 6 at the time 125 sec the load torquewas applied immediately into the engine speed control taskThis proposed to disturb the stability of the control system atthe steady-state condition The proposed control scheme canimprove the speed deviation rapidly and is capable of trackingthe desired speed better than other control techniques Inaddition the load torque was decreased immediately at thetime 150 sec The results show that the proposed controlscheme can decrease the speed deviation from the desiredspeed faster than other control techniques The findingsreveal that the proposed control scheme has effective ofthe robustness and fast adaptation and has better trackingperformance than other control techniques
44 Fuel Consumption andExhaust Emission Investigation Inthis section the fuel consumption and the exhaust emissionof the engine speed control by using the proposed controlscheme and different control techniques (SMC techniqueand PID controller) were investigated (see Figure 7) In theexperiments the desired speed was performed for 400 secand was rapidly changed as shown in Figure 7(a) For theaverage total fuel consumption comparison (see Figure 7(b))the proposed control scheme can attain an excellent resultwith the lowest averaged total fuel consumption whichwas obtained by the average of the fuel consumptions persecond
In addition the average exhaust emissions were alsoinvestigated (see Figure 7(c)) The CO and HC emissions arethe main pollutants contributed by the SI engines In theprinciple of the combustion process of SI engine the HCemission is appeared when fuel molecules in the engine
cannot burn or burn only partially while the CO emissionis produced when the carbon in the fuel is partially oxi-dized rather than fully oxidized to carbon dioxide Howeverincreasing efficient strategies for engine speed control viathrottle valve regulation method is capable of increasingcombustion performance as it can reduce pollutant emissionsalso [38] In the experiments effects of the controllers wereinvestigated via the constant speed set points and no addingan external engine load (small load from the unloadedhydrostatic CVT)Thus the CO
2andNO
119909which are sensitive
to speed variation and high temperature operation did notmeasure in this work (the experiments perform at coolanttemperature of 70ndash80∘C for short period) As a result bothaverages of the CO and HC emission data were calculatedby the average of emissions per second in which obtainedby the direct measurement method [43] Additionally theseresults demonstrate that high fuel consumption and exhaustemission are affected by high variation of the engine speedduring tracking of the set pointsThese results also imply thatthe performance of the SI engine at any operating conditioncan be improved by an advanced engine speed control viathe electronic throttle valve regulation method as shown inFigure 7
5 Conclusions
The incorporation of the SMC and a first-order LPF witha new adaptive PID controller is proposed for trackingthe control task of an uncertain nonlinear system Thecontroller has been successfully applied to the problem ofthe speed tracking control of an SI engine through electronic
10 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
PIDSMC
LPFSMC and adaptive PIDDesired
0 50 100 150 200 250 300 350 4000
500
1000
1500
2000
2500
(a)
00689
0071
00694
006750068
006850069
00695007
007050071
00715
LPFSMC andadaptive PID
SMC PID
Fuel consumption (Lmin)
(b)
20288 41113 20302
105977
425503
109623
0500
10001500200025003000350040004500
LPFSMC andadaptive PID
SMC PID
HC (ppm)CO (ppm)
(c)
Figure 7 Comparisons of (a) tracking performance of the controllers (b) fuel consumption rates (c) exhaust emission rates
throttle valve control architecture From the simulation andexperimental results it achieves that
(1) the proposed adaptation law is capable of optimalonline update the PID controller during the controlprocess within a short period
(2) the chattering of the SMC can be alleviated by afirst-order low pass filter while the robustness of thecontrol system similar to that of the slidingmode suchthat the load torque disturbances can be compensatedquite accurately
(3) the proposed control scheme has high performancein implementation as it can be achieved in theproblem of engine speed control in which the systemis largely uncertain nonlinear system and rathercomplex mechanisms
Conflict of Interests
The authors have no competing interests
Acknowledgment
This research is financially supported by the Office ofResearch Administration (ORA) and Farm Engineering andAutomation Technology Research Group (FEAT) of Khon
Kaen University Thailand The authors are also thankfulto the reviewers and Mr Ian Thomas for their valuablecomments and suggestions for English grammar correctionrespectively
References
[1] K-C Hsu W-Y Wang and P-Z Lin ldquoSliding mode controlfor uncertain nonlinear systemswithmultiple inputs containingsector nonlinearities and deadzonesrdquo IEEE Transactions onSystems Man and Cybernetics Part B Cybernetics vol 34 no1 pp 374ndash380 2004
[2] G Bartolini and A Ferrara ldquoMulti-input sliding mode controlof a class of uncertain nonlinear systemsrdquo IEEE Transactions onAutomatic Control vol 41 no 11 pp 1662ndash1666 1996
[3] T-C Kuo Y-J Huang and S-H Chang ldquoSliding mode controlwith self-tuning law for uncertain nonlinear systemsrdquo ISATransactions vol 47 no 2 pp 171ndash178 2008
[4] G Montaseri and M J Yazdanpanah ldquoPredictive control ofuncertain nonlinear parabolic PDE systems using a Galerkinneural-network-based modelrdquo Communications in NonlinearScience and Numerical Simulation vol 17 no 1 pp 388ndash4042012
[5] F O Tellez A G Loukianov E N Sanchez and E Jose BayroCorrochano ldquoDecentralized neural identification and controlfor uncertain nonlinear systems application to planar robotrdquoJournal of the Franklin Institute vol 347 no 6 pp 1015ndash10342010
Mathematical Problems in Engineering 11
[6] A Bazaei and V J Majd ldquoFeedback linearization of discrete-time nonlinear uncertain plants via first-principles-based serialneuro-gray-box modelsrdquo Journal of Process Control vol 13 no8 pp 819ndash830 2003
[7] T-Y Kuc and W-G Han ldquoAn adaptive PID learning controlof robot manipulatorsrdquo Automatica vol 36 no 5 pp 717ndash7252000
[8] Y Pan Y Zhou T Sun and M J Er ldquoComposite adaptivefuzzy 119867
infintracking control of uncertain nonlinear systemsrdquo
Neurocomputing vol 99 pp 15ndash24 2013[9] X Liu R Tao and M Tavakoli ldquoAdaptive control of uncertain
nonlinear teleoperation systemsrdquo Mechatronics vol 24 no 1pp 66ndash78 2014
[10] W-D Chang and J-J Yan ldquoAdaptive robust PID controllerdesign based on a sliding mode for uncertain chaotic systemsrdquoChaos Solitons amp Fractals vol 26 no 1 pp 167ndash175 2005
[11] T C Kuo Y J Huang C Y Chen and C H Chang ldquoAdaptivesliding mode control with PID tuning for uncertain systemrdquoEngineering Letters vol 16 no 3 pp 1ndash5 2008
[12] M N Howell and M C Best ldquoOn-line PID tuning forengine idle-speed control using continuous action reinforce-ment learning automatardquo Control Engineering Practice vol 8no 2 pp 147ndash154 2000
[13] C-F Hsu and B-K Lee ldquoFPGA-based adaptive PID control ofa DC motor driver via sliding-mode approachrdquo Expert Systemswith Applications vol 38 no 9 pp 11866ndash11872 2011
[14] DWMemering and PHMeckl ldquoComparison of adaptive con-trol techniques applied to diesel engine idle speed regulationrdquoJournal of Dynamic Systems Measurement and Control vol 124no 4 pp 682ndash688 2002
[15] V I Utkin ldquoSliding mode control design principles andapplications to electric drivesrdquo IEEE Transactions on IndustrialElectronics vol 40 no 1 pp 23ndash36 1993
[16] Y J Huang and T C Kuo ldquoRobust output tracking controlfor nonlinear time-varying robotic manipulatorsrdquo ElectricalEngineering vol 87 no 1 pp 47ndash55 2005
[17] M Hajatipour and M Farrokhi ldquoChattering free with noisereduction in sliding-mode observers using frequency domainanalysisrdquo Journal of Process Control vol 20 no 8 pp 912ndash9212010
[18] A Sabanovic L Fridman and S Spurgeon Variable StructureSystems From Principles to Implementation The Institution ofEngineering and Technology 2004
[19] Y Xu ldquoChattering free robust control for nonlinear systemsrdquoIEEE Transactions on Control Systems Technology vol 16 no 6pp 1352ndash1359 2008
[20] H Lee and V I Utkin ldquoChattering suppression methods insliding mode control systemsrdquo Annual Reviews in Control vol31 no 2 pp 179ndash188 2007
[21] Y Ren Z Liu L Chang and N Wen ldquoAdaptive slidingmode robust control for virtual compound-axis servo systemrdquoMathematical Problems in Engineering vol 2013 Article ID343851 9 pages 2013
[22] M-L Tseng and M-S Chen ldquoChattering reduction of slidingmode control by low-pass filtering the control signalrdquo AsianJournal of Control vol 12 no 3 pp 392ndash398 2010
[23] H Sira-RamIRez ldquoOn the dynamical sliding mode control ofnonlinear systemsrdquo International Journal of Control vol 57 no5 pp 1039ndash1061 1993
[24] J-X Xu Y-J Pan and T-H Lee ldquoSliding mode controlwith closed-loop filtering architecture for a class of nonlinear
systemsrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 51 no 4 pp 168ndash173 2004
[25] A Deenadayalan and G S Ilango ldquoPosition sensorless slidingmode observer with sigmoid function for Brushless DCmotorrdquoin Proceedings of the International Conference on Advances inPower Conversion and Energy Technologies (APCET rsquo12) pp 1ndash6IEEE August 2012
[26] Y Xia X Yu andW Oghanna ldquoAdaptive robust fast control forinduction motorsrdquo IEEE Transactions on Industrial Electronicsvol 47 no 4 pp 854ndash862 2000
[27] M Niclai Theory of Nonlinear Control Systems McGraw-Hill1969
[28] J J Slotine andW Li Applied Nonlinear Control Prentice-HallEnglewood Cliffs NJ USA 1991
[29] D Gorinevsky and L A Feldkamp ldquoRBF network feedforwardcompensation of load disturbance in idle speed controlrdquo IEEEControl Systems vol 16 no 6 pp 18ndash27 1996
[30] S Di Cairano D Yanakiev A Bemporad I V Kolmanovskyand D Hrovat ldquoModel predictive idle speed control designanalysis and experimental evaluationrdquo IEEE Transactions onControl Systems Technology vol 20 no 1 pp 84ndash97 2012
[31] P F Puleston S Spurgeon andGMonsees ldquoAutomotive enginespeed control a robust nonlinear control frameworkrdquo IEEProceedings Control Theory and Applications vol 148 no 1 pp81ndash87 2001
[32] Y Yildiz A M Annaswamy D Yanakiev and I KolmanovskyldquoSpark-ignition-engine idle speed control an adaptive controlapproachrdquo IEEE Transactions on Control Systems Technologyvol 19 no 5 pp 990ndash1002 2011
[33] A Sugeng K Baharin T Hishamuddin and J B SupriyoldquoEngine speed control using online ANN for vehicle withEMDAP-CVTrdquo Jurnal Mekanikal vol 22 pp 39ndash52 2006
[34] M K Khan K B Goh and S K Spurgeon ldquoSecond ordersliding mode control of a diesel enginerdquo Asian Journal ofControl vol 5 no 4 pp 614ndash619 2003
[35] J R Wagner D M Dawson and L Zeyu ldquoNonlinear air-to-fuel ratio and engine speed control for hybrid vehiclesrdquo IEEETransactions on Vehicular Technology vol 52 no 1 pp 184ndash1952003
[36] F Assadian S Fekri andM Hancock ldquoHybrid electric vehicleschallenges strategies for advanced engine speed controlrdquo inProceedings of the IEEE International Electric Vehicle Conference(IEVC rsquo12) March 2012
[37] A G Ulsoy H Peng and M Cakmakci Automotive ControlSystems Cambridge University Press Cambridge UK 2014
[38] C Ji and S Wang ldquoStrategies for improving the idle perfor-mance of a spark-ignited gasoline enginerdquo International Journalof Hydrogen Energy vol 37 no 4 pp 3938ndash3944 2012
[39] S Wang C Ji M Zhang and B Zhang ldquoReducing theidle speed of a spark-ignited gasoline engine with hydrogenadditionrdquo International Journal of Hydrogen Energy vol 35 no19 pp 10580ndash10588 2010
[40] DHrovat and J Sun ldquoModels and controlmethodologies for ICengine idle speed control designrdquo Control Engineering Practicevol 5 no 8 pp 1093ndash1100 1997
[41] B Alt J P Blath F Svaricek and M Schultalbers ldquoMultiplesliding surface control of idle engine speed and torque reservewith dead start assist controlrdquo IEEE Transactions on IndustrialElectronics vol 56 no 9 pp 3580ndash3592 2009
12 Mathematical Problems in Engineering
[42] T Radpukdee and P Jirawattana ldquoUncertainty learning andcompensation an application to pressure tracking of an electro-hydraulic proportional relief valverdquo Control Engineering Prac-tice vol 17 no 2 pp 291ndash301 2009
[43] P A Loannou and J Sun Robust Adaptive Control PTRPrentice-Hall 1996
[44] C D Richard and H B Robert Modern Control SystemsPrentice Hall Upper Saddle River NJ USA 2011
[45] A Jansri and P Sooraksa ldquoEnhanced model and fuzzy strategyof air to fuel ratio control for spark ignition enginesrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 922ndash9332012
[46] Z Ye ldquoModeling identification design and implementation ofnonlinear automotive idle speed control systemsmdashanoverviewrdquoIEEE Transactions on Systems Man and Cybernetics Part CApplications and Reviews vol 37 no 6 pp 1137ndash1151 2007
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
10 Mathematical Problems in Engineering
Time (s)
Engi
ne sp
eed
(rpm
)
PIDSMC
LPFSMC and adaptive PIDDesired
0 50 100 150 200 250 300 350 4000
500
1000
1500
2000
2500
(a)
00689
0071
00694
006750068
006850069
00695007
007050071
00715
LPFSMC andadaptive PID
SMC PID
Fuel consumption (Lmin)
(b)
20288 41113 20302
105977
425503
109623
0500
10001500200025003000350040004500
LPFSMC andadaptive PID
SMC PID
HC (ppm)CO (ppm)
(c)
Figure 7 Comparisons of (a) tracking performance of the controllers (b) fuel consumption rates (c) exhaust emission rates
throttle valve control architecture From the simulation andexperimental results it achieves that
(1) the proposed adaptation law is capable of optimalonline update the PID controller during the controlprocess within a short period
(2) the chattering of the SMC can be alleviated by afirst-order low pass filter while the robustness of thecontrol system similar to that of the slidingmode suchthat the load torque disturbances can be compensatedquite accurately
(3) the proposed control scheme has high performancein implementation as it can be achieved in theproblem of engine speed control in which the systemis largely uncertain nonlinear system and rathercomplex mechanisms
Conflict of Interests
The authors have no competing interests
Acknowledgment
This research is financially supported by the Office ofResearch Administration (ORA) and Farm Engineering andAutomation Technology Research Group (FEAT) of Khon
Kaen University Thailand The authors are also thankfulto the reviewers and Mr Ian Thomas for their valuablecomments and suggestions for English grammar correctionrespectively
References
[1] K-C Hsu W-Y Wang and P-Z Lin ldquoSliding mode controlfor uncertain nonlinear systemswithmultiple inputs containingsector nonlinearities and deadzonesrdquo IEEE Transactions onSystems Man and Cybernetics Part B Cybernetics vol 34 no1 pp 374ndash380 2004
[2] G Bartolini and A Ferrara ldquoMulti-input sliding mode controlof a class of uncertain nonlinear systemsrdquo IEEE Transactions onAutomatic Control vol 41 no 11 pp 1662ndash1666 1996
[3] T-C Kuo Y-J Huang and S-H Chang ldquoSliding mode controlwith self-tuning law for uncertain nonlinear systemsrdquo ISATransactions vol 47 no 2 pp 171ndash178 2008
[4] G Montaseri and M J Yazdanpanah ldquoPredictive control ofuncertain nonlinear parabolic PDE systems using a Galerkinneural-network-based modelrdquo Communications in NonlinearScience and Numerical Simulation vol 17 no 1 pp 388ndash4042012
[5] F O Tellez A G Loukianov E N Sanchez and E Jose BayroCorrochano ldquoDecentralized neural identification and controlfor uncertain nonlinear systems application to planar robotrdquoJournal of the Franklin Institute vol 347 no 6 pp 1015ndash10342010
Mathematical Problems in Engineering 11
[6] A Bazaei and V J Majd ldquoFeedback linearization of discrete-time nonlinear uncertain plants via first-principles-based serialneuro-gray-box modelsrdquo Journal of Process Control vol 13 no8 pp 819ndash830 2003
[7] T-Y Kuc and W-G Han ldquoAn adaptive PID learning controlof robot manipulatorsrdquo Automatica vol 36 no 5 pp 717ndash7252000
[8] Y Pan Y Zhou T Sun and M J Er ldquoComposite adaptivefuzzy 119867
infintracking control of uncertain nonlinear systemsrdquo
Neurocomputing vol 99 pp 15ndash24 2013[9] X Liu R Tao and M Tavakoli ldquoAdaptive control of uncertain
nonlinear teleoperation systemsrdquo Mechatronics vol 24 no 1pp 66ndash78 2014
[10] W-D Chang and J-J Yan ldquoAdaptive robust PID controllerdesign based on a sliding mode for uncertain chaotic systemsrdquoChaos Solitons amp Fractals vol 26 no 1 pp 167ndash175 2005
[11] T C Kuo Y J Huang C Y Chen and C H Chang ldquoAdaptivesliding mode control with PID tuning for uncertain systemrdquoEngineering Letters vol 16 no 3 pp 1ndash5 2008
[12] M N Howell and M C Best ldquoOn-line PID tuning forengine idle-speed control using continuous action reinforce-ment learning automatardquo Control Engineering Practice vol 8no 2 pp 147ndash154 2000
[13] C-F Hsu and B-K Lee ldquoFPGA-based adaptive PID control ofa DC motor driver via sliding-mode approachrdquo Expert Systemswith Applications vol 38 no 9 pp 11866ndash11872 2011
[14] DWMemering and PHMeckl ldquoComparison of adaptive con-trol techniques applied to diesel engine idle speed regulationrdquoJournal of Dynamic Systems Measurement and Control vol 124no 4 pp 682ndash688 2002
[15] V I Utkin ldquoSliding mode control design principles andapplications to electric drivesrdquo IEEE Transactions on IndustrialElectronics vol 40 no 1 pp 23ndash36 1993
[16] Y J Huang and T C Kuo ldquoRobust output tracking controlfor nonlinear time-varying robotic manipulatorsrdquo ElectricalEngineering vol 87 no 1 pp 47ndash55 2005
[17] M Hajatipour and M Farrokhi ldquoChattering free with noisereduction in sliding-mode observers using frequency domainanalysisrdquo Journal of Process Control vol 20 no 8 pp 912ndash9212010
[18] A Sabanovic L Fridman and S Spurgeon Variable StructureSystems From Principles to Implementation The Institution ofEngineering and Technology 2004
[19] Y Xu ldquoChattering free robust control for nonlinear systemsrdquoIEEE Transactions on Control Systems Technology vol 16 no 6pp 1352ndash1359 2008
[20] H Lee and V I Utkin ldquoChattering suppression methods insliding mode control systemsrdquo Annual Reviews in Control vol31 no 2 pp 179ndash188 2007
[21] Y Ren Z Liu L Chang and N Wen ldquoAdaptive slidingmode robust control for virtual compound-axis servo systemrdquoMathematical Problems in Engineering vol 2013 Article ID343851 9 pages 2013
[22] M-L Tseng and M-S Chen ldquoChattering reduction of slidingmode control by low-pass filtering the control signalrdquo AsianJournal of Control vol 12 no 3 pp 392ndash398 2010
[23] H Sira-RamIRez ldquoOn the dynamical sliding mode control ofnonlinear systemsrdquo International Journal of Control vol 57 no5 pp 1039ndash1061 1993
[24] J-X Xu Y-J Pan and T-H Lee ldquoSliding mode controlwith closed-loop filtering architecture for a class of nonlinear
systemsrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 51 no 4 pp 168ndash173 2004
[25] A Deenadayalan and G S Ilango ldquoPosition sensorless slidingmode observer with sigmoid function for Brushless DCmotorrdquoin Proceedings of the International Conference on Advances inPower Conversion and Energy Technologies (APCET rsquo12) pp 1ndash6IEEE August 2012
[26] Y Xia X Yu andW Oghanna ldquoAdaptive robust fast control forinduction motorsrdquo IEEE Transactions on Industrial Electronicsvol 47 no 4 pp 854ndash862 2000
[27] M Niclai Theory of Nonlinear Control Systems McGraw-Hill1969
[28] J J Slotine andW Li Applied Nonlinear Control Prentice-HallEnglewood Cliffs NJ USA 1991
[29] D Gorinevsky and L A Feldkamp ldquoRBF network feedforwardcompensation of load disturbance in idle speed controlrdquo IEEEControl Systems vol 16 no 6 pp 18ndash27 1996
[30] S Di Cairano D Yanakiev A Bemporad I V Kolmanovskyand D Hrovat ldquoModel predictive idle speed control designanalysis and experimental evaluationrdquo IEEE Transactions onControl Systems Technology vol 20 no 1 pp 84ndash97 2012
[31] P F Puleston S Spurgeon andGMonsees ldquoAutomotive enginespeed control a robust nonlinear control frameworkrdquo IEEProceedings Control Theory and Applications vol 148 no 1 pp81ndash87 2001
[32] Y Yildiz A M Annaswamy D Yanakiev and I KolmanovskyldquoSpark-ignition-engine idle speed control an adaptive controlapproachrdquo IEEE Transactions on Control Systems Technologyvol 19 no 5 pp 990ndash1002 2011
[33] A Sugeng K Baharin T Hishamuddin and J B SupriyoldquoEngine speed control using online ANN for vehicle withEMDAP-CVTrdquo Jurnal Mekanikal vol 22 pp 39ndash52 2006
[34] M K Khan K B Goh and S K Spurgeon ldquoSecond ordersliding mode control of a diesel enginerdquo Asian Journal ofControl vol 5 no 4 pp 614ndash619 2003
[35] J R Wagner D M Dawson and L Zeyu ldquoNonlinear air-to-fuel ratio and engine speed control for hybrid vehiclesrdquo IEEETransactions on Vehicular Technology vol 52 no 1 pp 184ndash1952003
[36] F Assadian S Fekri andM Hancock ldquoHybrid electric vehicleschallenges strategies for advanced engine speed controlrdquo inProceedings of the IEEE International Electric Vehicle Conference(IEVC rsquo12) March 2012
[37] A G Ulsoy H Peng and M Cakmakci Automotive ControlSystems Cambridge University Press Cambridge UK 2014
[38] C Ji and S Wang ldquoStrategies for improving the idle perfor-mance of a spark-ignited gasoline enginerdquo International Journalof Hydrogen Energy vol 37 no 4 pp 3938ndash3944 2012
[39] S Wang C Ji M Zhang and B Zhang ldquoReducing theidle speed of a spark-ignited gasoline engine with hydrogenadditionrdquo International Journal of Hydrogen Energy vol 35 no19 pp 10580ndash10588 2010
[40] DHrovat and J Sun ldquoModels and controlmethodologies for ICengine idle speed control designrdquo Control Engineering Practicevol 5 no 8 pp 1093ndash1100 1997
[41] B Alt J P Blath F Svaricek and M Schultalbers ldquoMultiplesliding surface control of idle engine speed and torque reservewith dead start assist controlrdquo IEEE Transactions on IndustrialElectronics vol 56 no 9 pp 3580ndash3592 2009
12 Mathematical Problems in Engineering
[42] T Radpukdee and P Jirawattana ldquoUncertainty learning andcompensation an application to pressure tracking of an electro-hydraulic proportional relief valverdquo Control Engineering Prac-tice vol 17 no 2 pp 291ndash301 2009
[43] P A Loannou and J Sun Robust Adaptive Control PTRPrentice-Hall 1996
[44] C D Richard and H B Robert Modern Control SystemsPrentice Hall Upper Saddle River NJ USA 2011
[45] A Jansri and P Sooraksa ldquoEnhanced model and fuzzy strategyof air to fuel ratio control for spark ignition enginesrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 922ndash9332012
[46] Z Ye ldquoModeling identification design and implementation ofnonlinear automotive idle speed control systemsmdashanoverviewrdquoIEEE Transactions on Systems Man and Cybernetics Part CApplications and Reviews vol 37 no 6 pp 1137ndash1151 2007
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 11
[6] A Bazaei and V J Majd ldquoFeedback linearization of discrete-time nonlinear uncertain plants via first-principles-based serialneuro-gray-box modelsrdquo Journal of Process Control vol 13 no8 pp 819ndash830 2003
[7] T-Y Kuc and W-G Han ldquoAn adaptive PID learning controlof robot manipulatorsrdquo Automatica vol 36 no 5 pp 717ndash7252000
[8] Y Pan Y Zhou T Sun and M J Er ldquoComposite adaptivefuzzy 119867
infintracking control of uncertain nonlinear systemsrdquo
Neurocomputing vol 99 pp 15ndash24 2013[9] X Liu R Tao and M Tavakoli ldquoAdaptive control of uncertain
nonlinear teleoperation systemsrdquo Mechatronics vol 24 no 1pp 66ndash78 2014
[10] W-D Chang and J-J Yan ldquoAdaptive robust PID controllerdesign based on a sliding mode for uncertain chaotic systemsrdquoChaos Solitons amp Fractals vol 26 no 1 pp 167ndash175 2005
[11] T C Kuo Y J Huang C Y Chen and C H Chang ldquoAdaptivesliding mode control with PID tuning for uncertain systemrdquoEngineering Letters vol 16 no 3 pp 1ndash5 2008
[12] M N Howell and M C Best ldquoOn-line PID tuning forengine idle-speed control using continuous action reinforce-ment learning automatardquo Control Engineering Practice vol 8no 2 pp 147ndash154 2000
[13] C-F Hsu and B-K Lee ldquoFPGA-based adaptive PID control ofa DC motor driver via sliding-mode approachrdquo Expert Systemswith Applications vol 38 no 9 pp 11866ndash11872 2011
[14] DWMemering and PHMeckl ldquoComparison of adaptive con-trol techniques applied to diesel engine idle speed regulationrdquoJournal of Dynamic Systems Measurement and Control vol 124no 4 pp 682ndash688 2002
[15] V I Utkin ldquoSliding mode control design principles andapplications to electric drivesrdquo IEEE Transactions on IndustrialElectronics vol 40 no 1 pp 23ndash36 1993
[16] Y J Huang and T C Kuo ldquoRobust output tracking controlfor nonlinear time-varying robotic manipulatorsrdquo ElectricalEngineering vol 87 no 1 pp 47ndash55 2005
[17] M Hajatipour and M Farrokhi ldquoChattering free with noisereduction in sliding-mode observers using frequency domainanalysisrdquo Journal of Process Control vol 20 no 8 pp 912ndash9212010
[18] A Sabanovic L Fridman and S Spurgeon Variable StructureSystems From Principles to Implementation The Institution ofEngineering and Technology 2004
[19] Y Xu ldquoChattering free robust control for nonlinear systemsrdquoIEEE Transactions on Control Systems Technology vol 16 no 6pp 1352ndash1359 2008
[20] H Lee and V I Utkin ldquoChattering suppression methods insliding mode control systemsrdquo Annual Reviews in Control vol31 no 2 pp 179ndash188 2007
[21] Y Ren Z Liu L Chang and N Wen ldquoAdaptive slidingmode robust control for virtual compound-axis servo systemrdquoMathematical Problems in Engineering vol 2013 Article ID343851 9 pages 2013
[22] M-L Tseng and M-S Chen ldquoChattering reduction of slidingmode control by low-pass filtering the control signalrdquo AsianJournal of Control vol 12 no 3 pp 392ndash398 2010
[23] H Sira-RamIRez ldquoOn the dynamical sliding mode control ofnonlinear systemsrdquo International Journal of Control vol 57 no5 pp 1039ndash1061 1993
[24] J-X Xu Y-J Pan and T-H Lee ldquoSliding mode controlwith closed-loop filtering architecture for a class of nonlinear
systemsrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 51 no 4 pp 168ndash173 2004
[25] A Deenadayalan and G S Ilango ldquoPosition sensorless slidingmode observer with sigmoid function for Brushless DCmotorrdquoin Proceedings of the International Conference on Advances inPower Conversion and Energy Technologies (APCET rsquo12) pp 1ndash6IEEE August 2012
[26] Y Xia X Yu andW Oghanna ldquoAdaptive robust fast control forinduction motorsrdquo IEEE Transactions on Industrial Electronicsvol 47 no 4 pp 854ndash862 2000
[27] M Niclai Theory of Nonlinear Control Systems McGraw-Hill1969
[28] J J Slotine andW Li Applied Nonlinear Control Prentice-HallEnglewood Cliffs NJ USA 1991
[29] D Gorinevsky and L A Feldkamp ldquoRBF network feedforwardcompensation of load disturbance in idle speed controlrdquo IEEEControl Systems vol 16 no 6 pp 18ndash27 1996
[30] S Di Cairano D Yanakiev A Bemporad I V Kolmanovskyand D Hrovat ldquoModel predictive idle speed control designanalysis and experimental evaluationrdquo IEEE Transactions onControl Systems Technology vol 20 no 1 pp 84ndash97 2012
[31] P F Puleston S Spurgeon andGMonsees ldquoAutomotive enginespeed control a robust nonlinear control frameworkrdquo IEEProceedings Control Theory and Applications vol 148 no 1 pp81ndash87 2001
[32] Y Yildiz A M Annaswamy D Yanakiev and I KolmanovskyldquoSpark-ignition-engine idle speed control an adaptive controlapproachrdquo IEEE Transactions on Control Systems Technologyvol 19 no 5 pp 990ndash1002 2011
[33] A Sugeng K Baharin T Hishamuddin and J B SupriyoldquoEngine speed control using online ANN for vehicle withEMDAP-CVTrdquo Jurnal Mekanikal vol 22 pp 39ndash52 2006
[34] M K Khan K B Goh and S K Spurgeon ldquoSecond ordersliding mode control of a diesel enginerdquo Asian Journal ofControl vol 5 no 4 pp 614ndash619 2003
[35] J R Wagner D M Dawson and L Zeyu ldquoNonlinear air-to-fuel ratio and engine speed control for hybrid vehiclesrdquo IEEETransactions on Vehicular Technology vol 52 no 1 pp 184ndash1952003
[36] F Assadian S Fekri andM Hancock ldquoHybrid electric vehicleschallenges strategies for advanced engine speed controlrdquo inProceedings of the IEEE International Electric Vehicle Conference(IEVC rsquo12) March 2012
[37] A G Ulsoy H Peng and M Cakmakci Automotive ControlSystems Cambridge University Press Cambridge UK 2014
[38] C Ji and S Wang ldquoStrategies for improving the idle perfor-mance of a spark-ignited gasoline enginerdquo International Journalof Hydrogen Energy vol 37 no 4 pp 3938ndash3944 2012
[39] S Wang C Ji M Zhang and B Zhang ldquoReducing theidle speed of a spark-ignited gasoline engine with hydrogenadditionrdquo International Journal of Hydrogen Energy vol 35 no19 pp 10580ndash10588 2010
[40] DHrovat and J Sun ldquoModels and controlmethodologies for ICengine idle speed control designrdquo Control Engineering Practicevol 5 no 8 pp 1093ndash1100 1997
[41] B Alt J P Blath F Svaricek and M Schultalbers ldquoMultiplesliding surface control of idle engine speed and torque reservewith dead start assist controlrdquo IEEE Transactions on IndustrialElectronics vol 56 no 9 pp 3580ndash3592 2009
12 Mathematical Problems in Engineering
[42] T Radpukdee and P Jirawattana ldquoUncertainty learning andcompensation an application to pressure tracking of an electro-hydraulic proportional relief valverdquo Control Engineering Prac-tice vol 17 no 2 pp 291ndash301 2009
[43] P A Loannou and J Sun Robust Adaptive Control PTRPrentice-Hall 1996
[44] C D Richard and H B Robert Modern Control SystemsPrentice Hall Upper Saddle River NJ USA 2011
[45] A Jansri and P Sooraksa ldquoEnhanced model and fuzzy strategyof air to fuel ratio control for spark ignition enginesrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 922ndash9332012
[46] Z Ye ldquoModeling identification design and implementation ofnonlinear automotive idle speed control systemsmdashanoverviewrdquoIEEE Transactions on Systems Man and Cybernetics Part CApplications and Reviews vol 37 no 6 pp 1137ndash1151 2007
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
12 Mathematical Problems in Engineering
[42] T Radpukdee and P Jirawattana ldquoUncertainty learning andcompensation an application to pressure tracking of an electro-hydraulic proportional relief valverdquo Control Engineering Prac-tice vol 17 no 2 pp 291ndash301 2009
[43] P A Loannou and J Sun Robust Adaptive Control PTRPrentice-Hall 1996
[44] C D Richard and H B Robert Modern Control SystemsPrentice Hall Upper Saddle River NJ USA 2011
[45] A Jansri and P Sooraksa ldquoEnhanced model and fuzzy strategyof air to fuel ratio control for spark ignition enginesrdquoComputersamp Mathematics with Applications vol 64 no 5 pp 922ndash9332012
[46] Z Ye ldquoModeling identification design and implementation ofnonlinear automotive idle speed control systemsmdashanoverviewrdquoIEEE Transactions on Systems Man and Cybernetics Part CApplications and Reviews vol 37 no 6 pp 1137ndash1151 2007
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
