Mohammed H. Mohammed 1 PID Controller of...

Journal of Advanced Sciences and Engineering Technologies (2018) Vol 2 No1 1-12 1

ISSN:2617-2070(Print);2617-2070(Online)

Journal of Advanced Sciences and Engineering Technologies

available online at: http://www.jaset.isnra.org

Mohammed H. Mohammed 1

Adel M Bash 2

1 Department of Mechanical Engineering/ Tikrit University/Iraq [email protected] 2 Department of Mechanical Engineering/ Tikrit University/Iraq [email protected]

Keywords: Suspension, Quarter car model, Active suspension, Passive suspension, PID controller A R T I C L E I N F O

Article history: Received01jan2018Accepted15-Jan-2019Availableonline02febuary2019 DOI:http://dx.doi.org/10.32441/jaset.02.01.01

Copyright©2018byauthor(s)andThisworkislicensedundertheCreativeCommonsAttributionInternationalLicense(CCBY4.0).

http://creativecommons.org/licenses/by/4.0/

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Invest PID Controller of Quarter CarModelofActiveSuspensionSystem

A B S T R A C T

A Suspension system can be defined as the mechanism thatphysically separates the car body from the car wheels. Thepurposeofanysuspensionsystemisto increase the ridecomfort, road handling andstabilityof closed loopsystem.The suspension design must becompensate theeffectofconflictingcriteriaofroadholding, load carryingandpassengercomfort. An active suspension system has been proposed. Aquarter-car two degree-of-freedom (2DOF) system is designedandconstructedtosimulatetheactionsofanactivequartercarsuspension system.White noise input is introduced to a givensystemtoexpressedunpavedroadandbothstepinputandsinewaveinputarestudiedaswell.Thecontrolstrategy isbasedontwo degree of freedom PID controller. (MATLAB/ Simulink) isusedtoverifytheproposedalgorithm.Thecomparisonbetweenthepassiveandactivesuspensionandtheresultsobtainedfroma range of road input simulations in the proposed algorithmshows the effectiveness of the proposed algorithm and bestresultsareobtained.

© 2019 JASET, International Scholars and Researchers Association

Introduction

Thedesign of car advanced systemhasbeenimprovedefficientlysincethelastthree decades using individual controlsystems, algorithms and activeactuators.The changing inthesystemscomponents’ properties can bepredicted widely which improving

their efficiency, safety and comfort ofthe car [1]. The reduction in theinducedgroundvariation,tiredeflection, dynamic characteristics and provideride comfort are the maincharacteristics in the design of passivesuspension is designed [2]. The draw

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Mohammed H. Mohammed, Adel M Bash. / Journal of Advanced Sciences and Engineering Technologies

2

backs ofthepassivesuspensiondesignwithinerterhasbeenconsideredby[3].In the vehicles, the multipleperformance is required such as tiregrip,ride comfort suspension deflection[4]. The semi-active and activesuspensions are used in many vehiclesapplications. The passive suspensionperformance is restricted due to theabsence of feedback control action. Anew structure for a semi-activesuspension to obtain performancespecifications has been introduced by[5].Theactivesuspensionsystemshavebeen utilized in linear and non-linearcontrolmethodsforactiveseat[6].Theactive suspension system is consideredas improvement achieved in thesystem performance, which deliver ahigher power to generate suspensionforces to achieve the performance.Different models for vehiclessuspensionsystemcanbeunderstooddue to their dynamical performance.Theremaydifferentdegreeoffreedom(DOF)asshownintheFig.1.

Fig.1.ClassificationofSuspensionModels

Allpowersofvehicleshaveamountanddirection depends on the size of bumpthat hits the wheel, where the wheelsare exposed to a vertical height whenpassing the road curves [7]. In fact, thevehiclesuspensionsystemispartofthestructure and combines all importantsystems at the bottom of the vehiclewhich includes the Frame, suspensionsystem, guidance system [8]-[9]. Thusthe system should provide appropriate

conditions for increasing the ability ofvehicle to change its direction andmaintain a high level of quality. Thesearetwoopposites;wheretheprocessofsuspension system tuning isrepresented by finding the rightsolution for the required application[10].

Independent suspension system anddependentsuspensionsystem,aremostimportant types of suspensionsystems.Dependent system allowslinking all vehicle wheels with vehiclestructurethroughsuspensionsystemsothateachwheelisseparatedfromotherwheels, instead of linking the wheelswithajointaxisandcanbedividedintofront independent suspension systemand rear Independent suspensionsystem[11]. Suspension systems canbeclassifiedalsodependingonthetypeofdamper used into passive suspensionsystem, semi-active suspension systemandactivesuspensionsystem[12].

Passive suspension system cannotprovide ride comfort and ride safetybecauseitcannotadjustthecoefficientsof springs and dampers throughactuators[13]-[14].Theseactuatorsandsensorshavegoodpractical resultsandare significantly spreading in markets[15].Tocontrol thesemiactivesystem,there aremany strategies tomaintain,thecoefficientofdamperused likesky-hook [16], groundhook [17] and thehybrid [18], the best strategy amongthesetypescanbefoundin[19].

The active suspension system consistsof sensors, actuators, control unit andsome hydraulic components. Thissystemworkselectronicallyandcanbecontrolled electronically according tothe road condition in many modernvehicles, such as BMW, Mercedes-Benzand Volvo [20]. The Simulink/Matlab


programhastheabilitytosimulateandseparate unspring mass from springmassandmakeitspowerwhichfocuseson suspension system to suit roaddisorder [21].The amount and powercreated by actuator on theireffectiveness to reduce vibrationresulting from the different roadroughness, how actuator (PID) workson active suspension system and theinfluence of power on basic and rearwheels and passengers presentedin[22].

Theeffectofroadsignalsinputsontheability of active control system and onreducing vibration capacity by 27.3%presented in[23].The purpose of thisstudy is to design an active suspensionsystem by building an actuator of2DOFPID controller for suspensionsystem and simulating passive andactive suspension systems that werebuilt.

MATHEMATICAL MODEL OF ACTIVESUSPENSIONSYSTEMDevelop a system good characteristicsinbothroadholdingandridecomfortispassive suspensionbehavior but thesetwo indicators conflict each other andmotivate different spring and damperphenomena. The considerableimprovement in power consumptionand variable damping characteristicswill lead to the semi-active suspensionsystems[24]-[25].

In thisworkdifferent assumptions of a¼ car modelling are considered asfollows:

1.The tires is considered as linearspringwithoutdamping,

2.The wheel and body has norotational,

3.There is no gap between the tire andtheroadsurface,

4.Thefrictionisneglected.

for active suspension system of a 1/4carmodel,parametersthatdescribethesystem are: (x(t), D, k2, k1, m2, m1,x0(t),x2(t),x1(t)).

The suspension of the quarter carvehicle can be shown in Fig.2.

Fig.2. The suspension of quarter carvehicle

These are considered as parameters oftraditional suspension system .However,whatraisesaquestioninthisfigure is actuator represented by (u)which gives controlled power to thesystemandthatpowerhasbeencreatedbyactuatorinactivesuspensionsystem.Based on this model in Fig.2, dynamicactive suspension system will beanalyzed. This system is a DE with a2DOFasinthefollowingequations:

( ) ( ) ( )

( ) ( )0

0

¨

1 0 2

1 2

m x t D x t x t

k x t x t u

⎡ ⎤+ −⎣ ⎦

⎡ ⎤+ − =⎣ ⎦

& & (1)

( ) ( ) ( )

( ) ( )

( ) ( )

¨22 0 2

1 2 0

2 2 1

m x t D x t x t

k x t x t

k x t x t u

⎡ ⎤− − +⎣ ⎦

⎡ ⎤− +⎣ ⎦

⎡ ⎤− = −⎣ ⎦

& &

(2)

( ) ( )( ) ( )

1 2 2 0

3 2 4 0

x x t , x x t ,

x x t , x x t

= =

= =& & (3)

Systemstatespacecanbewritteninthisway:

dX AX BU dt

= + (4)


4

Variables of state space can bewrittenin the form of a matrix(A) which is asystemmatrixandmatrix (B) is inputmatrixare:

1 2 1

2 2 2 2

1 1

1 11 1

0 0 1 00 0 0 1

k k k D DA

m m m mk k D D

m mm m

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥+− −= ⎢ ⎥⎢ ⎥⎢ ⎥

−−⎢ ⎥⎢ ⎥⎣ ⎦

(5)

22

2

1

0 0

0 01

B km

m1

0m

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥

= ⎢ ⎥⎢ ⎥⎢ ⎥

−⎢ ⎥⎣ ⎦ (6)

System variables introduced to thematrixare:

( )T

iU x t u ⎡ ⎤= ⎣ ⎦ (7)

Systemoutputsofsuspensionsystemofvehicleinthematrixformare:

Y=CX+DU (8)

Variablesofequation(8)are

( ) ( ) ( ) ( )¨

02 i 2 oY k x t x t x t x t⎧ ⎫⎡ ⎤= −⎨ ⎬⎣ ⎦

⎩ ⎭(9)

EquationYcanbewrittenasin(10)

( )¨

22 i 1 2Y k x t x x x⎧ ⎫⎡ ⎤= −⎨ ⎬⎣ ⎦

⎩ ⎭ (10)

Matrices(C) and (D) are output matrixand feedforward matrices respectivelyasshownbelow:

2

1 1

1 1 1 1

k 0 0 0 k k D D

Cm m m m0 1 0 0

−⎡ ⎤⎢ ⎥⎢ ⎥− −=⎢ ⎥⎢ ⎥⎣ ⎦ (11)

2

1

K 01

D 0m

00

⎡ ⎤⎢ ⎥⎢ ⎥−=⎢ ⎥⎢ ⎥⎣ ⎦ (12)

Thetransferfunction(TF)ofthe1/4carmodel in the active suspension systemcan be shown as in (13).

4 3 21.2 e 0 4 s+1.8 e0 6

s +28 s +4.2 s +1.G (s ) =

8 e0 6

(13)

The parameters used in the simulationarelistedintable1.

Table 1. Simulation parameters and itsmeaning


The spring and damper circuit in thesuspension system can be shown inFig.3.

Fig.3. Block diagram of the generalsuspensionsystem.

There are eight standard levels toassessment the roads optimality (A-H)ascanbeshownintable2.Inthisstudy,levelhasbeenchosen.

Table2.Standardlevelsoftheroads

(σq/10-3m)

0.01m-1< n

>2.83m-1

(Gq(no)/10-

6m3)

no=0.1m-1

Road

level

Geometric

average

Geometric

average

3.81 16 A

7.61 64 B

15.23 256 C

30.45 1024 D

60.90 4096 E

121.80 16384 F

243.61 65536 G

487.22 262144 H

Asmentioned earlier, despite the largevolume of studies in this area, andalthough the TAM andD&M have beenconsidered as well-recognized modelsin the field of IS (Gefen, et al., 2003),reviews of the most basic version ofTAM routinely find that it accounts for30%to40%ofITacceptance,despiteitsrelativesimplicity(Lee,Kozar,&Larsen,2003; Legris, Ingham, & Collerette,2003). However, systematic researchwithin the context of health careremains lacking, thus indicating asignificantgapinknowledge.Therefore,developing the TAM and gainingempirical support for it within healthorganizations, as well as adopting aWeb-based system for improvingcollaborationinmedicalresearchbased

Symbols forsuspensionsystem

Values Meaning Unit

m1 300 Vehiclemass Kg

m2 40 Excelandwheelsmass Kg

k1 15000 Spring connects the vehicle bodyandwheels

m/N

k2 150000

Framem/N

D 1000 Damper m/N*s


6

on privacy protection, are essential.Further replication studies arenecessary. In this study, we haveemployedqualitative researchmethodsto support theoutcomeof thepreviousproposalandtoperceiveHISacceptanceproblemsandrequirement


SUSPENSIONCONTROLSTRATEGY

The nonlinear control ,optimal control andback stepping control are most usefulcontrolschemes inthe investigationof the1/4 car model. Different behaviouralcharacteristics dependent upon variousroad conditions should be provided byactivesuspensionwithoutgoingbeyond itstravellimits[26].

Whitenoise,sinewavesignalandunitstepinput signals are the three types that canexplain road ruggedness, periodicinstability and random road roughnessaddedtotheintensityofthepowerresultedfrom a hole or bump against the vehiclewhiledriving.

The classical PID controller normally usedinthisfield.ThemathematicalmodelofthePIDcontrollercanbeexpressedasin(14)

t

p i d0

de( t )u( t ) k e( t ) k e( )d kdt

τ τ= + +∫ (14)

In this paper a two degree of freedom(2DoF)PIDcontroller isusedas in(15)forthemathematicalmodelofthiscontroller.

1 ND1s 1 Ns

y ( t ) P I ++

= +

(15)

Where

Nissmoothingcoefficientofthefilter.

Include the PID parameters with thesmoothing parameters of the filter yield.

1 500.95213 0.9 6.41s 1 50s

y ( t ) ++

= +

(16)

The new controller composed of theclassicalPIDandsmoothingfilterascanbeshowninFig.4.

In this work, the advanced PID controlalgorithmusedMatlab/2018bfeaturessuchas anti-windup, external reset, and signaltracking, tune the PID gainsautomatically[27].

Fig.4.TheadvancedPIDcontrollerused.

RESULTSANDDISCUSSIONSTo understand dynamics, the quarter carmodelcanbesimulatedinMatlab/Simulinkto governing DE ofmotion for the sprungand unsprung masses of the passive andactivequartercar.

The effect of white noise input on thesystem is simulated by Simulinkimplementation of the circuit shown inFig.5.

Fig.5.Simulinkofthesuspensionsystemtotestwhitenoiseeffect

The active force of both sine wave input(smooth fluctuation road) and the stepinput (sudden change in the road) can beexpressedasin(17)

iu( t ) px ( t )= − (17)


8

From(17), theactive force (u) is relative tothe road input signal xi(t) and for whitenoise signal( unpaved road), the equationcanbetransformedinto(18):

t

n0

u( t ) p w ( t )d tΔ

Δ= − ∫ (18)

Fig.6 and Fig.7, shows the vehicledisplacement without and with proposedPID controller for the three types of theinputs respectively. When the systempassing at a constant speed, it will beexposed torandomroadroughness.Hence,the vibration capacity of signal resultedfrom passive suspension system is largerthangain representedbywhitenoise sincethere is no actuator in the system. Thevehicle has received these disordersroutinelyandputoutaftera longperiodoftime;whilethesignalgeneratedfromactivesuspension system is more controlled andless vibration capacity and even less thanthe signal of gain and will be improvedcompletelywith theproposedalgorithmasin Fig.7.

Fig.6.Suspensiondisplacementindifferentsituation

Fig.7. Suspension displacement with thewhitenoisesignal

The active suspension system accelerationresponsewith thewhitenoise input signal,and compare with passive suspensionsystem can be shown in Fig.8.

Fig.8. Active suspension accelerationresponse

Fig.9 and Fig.10 shows the activesuspension and passive systemscomparison vehicle without and with PIDcontroller when the input is sine waverespectively. The proposed method whenpassingontheroadwithregularmeandersas the signal which resulted from passivesuspension system has no enough powerand flexibility to withstand suchfluctuations; adding to that vibrationcapacity is very high. However, the signalthatresultedfromactivesuspensionsystemshowed high flexibility to overcome theseperiodicfluctuationsandvibrationcapacityislessthanactivesuspensionsystemsanditwill be improved as in Fig.10 withapplication of the proposed algorithm.

Fig.9.Activeandpassive suspension whensubjected to sine wave in case of active


suspension

Fig.10. Active and passive suspensionwiththeproposedalgorithm

Fig. 11 and Fig.12, shows the active andpassive vehicle suspension without andwith the proposed algorithm when theinputissteprespectively.Whenthesystempassing on the road and is exposed to ajump, the signal resulted from gain of theunit step stimulates the power intensityresulted when facing a particular bumpwhile driving. One can observe how largeamplitude vibration produced by passivesuspension system and compare it withvibration created by active suspensionsystem,andthencanseethevastdifferencein vibration capacity and again it will beimproved to be more comfortable forpassengersintheFig.12.

Fig.11. Active and passive suspension instepinputsystem

Fig.12.Active suspension compare withpassive suspension displacement of unitstepsignal

The reduction in the acceleration value ofthe active suspension(red) is 50%. Whilethe other two curve have slight change inthe amplitude. The improvement in thesettling time(6 sec into 2.5sec) . Smallvalues of acceleration and displacementensurebetteroperationandrodecomfort.

The acceleration response of the activesuspension system with step input signal,and compare it with acceleration of thepassivesuspensioncanbeshowninFig.13.

Fig.13. Active suspension systemacceleration

STABILITYANALYSISStability means that the input and outputsignalsremainbounded.Thisisboundinputbounded output stability(BIBO). Theavoidanceofsysteminstability is themainrequirement for control systems with thedamagepreventing of the equipment.Thelocation of the system TF poles in the s-plane is theoneof thestabilityassessmentofanylinearfeedbacksystems.


10

Intherealsystems,itisveyusefultoknowhowthesystembehaveagainstthe systemfailure. The loop gain changing is anindication of the system rigidity before thesystem become unstable. The root locusplotcanbeusedtoestimatetherangeof(k)values for which the loop is stable as inFig.14.

Fig.14.Rootlocusofthesuspensionsystem

The robust stability depends on thechanging in the loopgainasoneaspect tojudge the systemperformance. If bothgainandphaseareunknown,theplantorsystemprocesscannotbe modelledprecisely.Thefrequencywhereopen-loopgainis0dBwillbe consideredashighest errors regionandit may damage the system and this occurnear the gain crossover frequencycombined with phase variation at thisfrequency[28].

The phase variation needed can bemeasured by the phasemargin at the gaincrossover frequency before the systemunstability. The gain margin assesses therelative system gain needed at the gaincrossoverfrequencybeforetheunstability.The gain and phase margins signs is anindication of stability of the closed loopsystem . The highest values with positivevalues, refer to high system stability. Thegainmarginthestableclosedsystemare(-1.07 and 116.48 )dB The correspondingphasemargin is (6.230and -1000)and the

peak gain to ensure stable closed loopsystemis4.2dB.

The generalized proposed algorithmwhichcontains all the suspension types isdevelopedinthisstudyascanbeshowninFig.15.

Fig.15.thecompletesuspensionsystem

The vehicle with the new algorithm istested with extra deflection to check theride comfort in both displacement andacceleration effects, the results can beshown as in fig.16 andFig.17. respectively.

Fig.16. Displacement deflection effects onthe ride comfort

Fig.17. Acceleration effects on the ridecomfort


Comparison of all the suspension systemswhentheinputissinewaveprovesthattheproposed suspension system with PIDcontroller isbetter thantheotherswithoutPIDcontrollerascanbeshowninFig.18.fortheaccelerationresponseandFig.19forthedisplacement response respectively.

Fig.18. Acceleration response of thesuspension systems with sinewave inputsignal

Fig.19. Displacement response of thesuspension systems with sinewave inputsignal

With the random input signal the responseproves the effectivness of the proposedalgorithm as shown for the displacementresponseoftheallsuspensionsystem.Inallfigurestheoutputresponseoftheproposedalgorithm is much smaller values as anindication of the satifactory implemintaionof the new algothm in the control systemtechniques as can be shown in Fig.20.

Fig.20. Displacement response of thesuspension systems with randam inputsignal

Theridecomfortcanbemeasuredasin

RMS of the accelerationRide Comfort ( RC ) 20 log( )Re ference Acceleration( RAcc )

=(19)

t

2

t T

1RMS (f( t )) f( t )T −

= ∫ (20)

Where

f(t)),1/T is the input signal , the effectivefrequencyrespectively.

Thereferenceacceleration(RAcc) value is(1x10-6 ) according to the Koreanstandards can be used to find therelationship between the ride comfort andthe acceleration level in the suspensionsystemascanbeshownintable3.

Table3.Ridecomfortlevels

RClevel RC

Verycomfort43

Comfort43-69

Middle 69-83

Notcomfort 83- 120

Bad120

CONCLUSIONDesign of a sufficient and efficientsuspension system is adifficultdue to theconflict between the componentscharacteristics . Active suspension systemprovides a greater improvement inperformance of vehicle and improve ride


12

comfort compared to traditional passivesuspensionsystems.

Byconsideringandexpectingtypesofroadsrepresentedbyinputsignalsofwhitenoise,sine wave and unit step, a new algorithmwith the best performance but does nothave the expertise to be tested with apractice system; however, the method ofcombining PID controller represented bythis new algorithm with control ofconventional suspension systems has theability to compete as it has demonstratedbetter stability and reliability. This alsodramatically improves the properties ofdisplacement and acceleration and makestheresponsemoresmoothly.

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