730 IEEE TRANSACTIONS ON CONTROL SYSTEMS … · 2016-08-11 · 730 IEEE TRANSACTIONS ON CONTROL...

730 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 19, NO. 4, JULY 2011

Adaptive Control of a Pneumatic Valve Actuator foran Internal Combustion Engine

Jia Ma, Guoming G. Zhu, and Harold Schock

Abstract—Electro-pneumatic valve actuators are used to elim-inate the cam shafts of a traditional internal combustion engine.They are used to control the opening timing, duration, and lift ofboth intake and exhaust valves. In order to develop model-basedcontrol strategies, a control oriented model was developed by piece-wisely linearizing the physics-based nonlinear system model. Inthis paper, an adaptive valve lift control strategy was developedto improve the intake valve lift repeatability. The model referenceadaptive system identification technique was employed to estimatesystem parameters needed for generating feedforward control sig-nals for the closed-loop control scheme. The closed-loop lift con-trol strategies, along with the model reference feedforward con-trol, were developed and implemented in a prototype controller,and validated on a valve test bench with multiple reference valvelifts at both 1200 and 5000 r/min engine speeds. The experimentresults showed that the actual valve lift reached the reference liftwithin 0.5 mm of lift error in one cycle at 1200 r/min and in two cy-cles at 5000 r/min. The maximum steady-state lift errors were lessthan 0.4 mm at high valve lift and less than 1.3 mm at low valve lift.Furthermore, the closed-loop valve lift control improved valve liftrepeatability with more than 30% reduction of standard deviationover the open-loop control.

Index Terms—Adaptive control, adaptive estimation, engines,valves.

I. INTRODUCTION

V ARIABLE intake and/or exhaust valve actuation iscapable of significantly improving the fuel economy,

emissions, and power output of internal combustion (IC)engines. Variable valve actuation can be achieved with me-chanical (cam-based), electro-magnetic (electric mechanical),electro-hydraulic, and electro-pneumatic valvetrain mech-anisms. The cam-based variable valve actuation is able toprovide either a multiple stepping or a continuously changingvalve timing phase shift. The Honda mechanism [1] is a mul-tiple-step actuator that allows a switch between two cams.The Toyota system [2] allows the intake and exhaust cams toshift continuously without the flexibility of varying the valvelift and duration. BMW’s valvetronic system [3] combines

Manuscript received August 31, 2009; revised January 29, 2010; acceptedMay 16, 2010. Manuscript received in final form June 18, 2010. Date of publi-cation July 19, 2010; date of current version June 17, 2011. Recommended byAssociate Editor P. Meckl. This work was supported in part by the U.S. Depart-ment of Energy under Grant FC26-05NT42481.

J. Ma was with Michigan State University, East Lansing, MI 48326 USA.She is now with the Delphi Powertrain Systems, Auburn Hill, MI 48326 USA(email: [email protected]).

G. Zhu and H. Schock are with the Mechanical Engineering Department,Michigan State University, East Lansing, MI 48824 USA (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCST.2010.2054091

variable cam phasing with a continuously variable valve liftand duration actuation.

A significant amount of research has been conducted todemonstrate the advantage of variable valve actuation (VVA)over the traditional cam-based valve-train of both gasoline anddiesel engines. The investigation of intake valve timing controlof a spark ignited (SI) engine was conducted in [4]. It wasfound that at low and partial load conditions, engine pumpingloss was reduced between 20% and 80% due to throttle-lessoperation. Fuel consumption was improved up to 10% at idle.Through simulation and experiments, [5] shows that SI engineefficiency can be improved up to 29% due to variable valvetiming (VVT), compared to a classic (throttled) engine. Theengine torque output is also improved by up to 8% at lowspeed with wide open throttle. Research carried out in [6]demonstrated how VVT and VVL (variable valve lift) affectedthe partial load fuel economy of a light-duty diesel engine. Inthis case, the indicated and brake-specific fuel consumptionswere improved up to 6% and 19%, respectively. The operationof an Otto-Atkinson cycle engine by late intake valve closingto have a larger expansion ratio than compression ratio wasstudied in [7]. A significant improvement of Carbon-Monoxide(CO) and Nitrogen Oxide (NOx) was obtained. Reference [8]also showed that the operational range of a homogeneouslycharged compression ignition (HCCI) engine can be expandedto both high and low load ranges through the adoption of VVTand VVL. The advantages of VVT and VVL engines lead tothe development of their optimization over engine operationalrange. For example, [9] developed the VVT and VVL opti-mization methodology for an I4 2.0L camless ZETEC engineat various operational conditions including cold starts, cylinderdeactivation, full load, idle, and transient operations.

Infinitely variable valvetrain, often referred to camlessvalvetrain, includes electro-magnetic, electro-hydraulic, andelectro-pneumatic actuation. The electro-magnetic systems,such as GM Magnavalve [10], FEV ([11] and [12]), and Visteon[13] systems, are capable of generating variable valve timingand duration but with fixed lift operation. The electro-hydraulicsystems, such as the Sturman system [14], Ford and GM“camless” systems [15]–[17], provide infinitely variable valvetiming, duration, and lift. The electro-pneumatic valve actuator(EPVA) [18], shown in Fig. 1, utilizes supplied compressedair to actuate either the intake or exhaust valve by electroni-cally controlling two solenoids. For both electro-hydraulic andelectro-pneumatic valves, there is a potential issue of having arepeatable valve lift over the life of an engine.

Valve lift control for electro-hydraulic valvetrain actuationhas been investigated by number of researchers. Adaptive peaklift control was presented in [19], and digital valve technology

1063-6536/$26.00 © 2010 IEEE

MA et al.: ADAPTIVE CONTROL OF A PNEUMATIC VALVE ACTUATOR FOR AN INTERNAL COMBUSTION ENGINE 731

Fig. 1. Electro-pneumatic valve actuator.

was applied to control of a hydraulic valve actuator in [20]. Thispaper proposed an adaptive lift control scheme for the electro-pneumatic valve actuator to improve the EPVA intake valve liftrepeatability. A control oriented electro-pneumatic valve modelwas developed and used for adaptive parameter identification;and a closed-loop control scheme of valve lift was developed,utilizing the identified parameters in real-time. The main controltechniques used in the process include model reference adapta-tion and MIT rule that can be found in [21].

This paper is organized as follows. First, a control orientedmodel is presented in Section II. Next, the valve actuator pa-rameter identification and its closed-loop control are discussedin Section III. Third, the open-loop statistical response analysisresults are presented in Section IV and the experimental vali-dation results are shown in Section V, where the adaptive pa-rameter identification convergence was verified with test benchdata. Finally, conclusions are drawn in Section VI.

II. MODELING

A physics-based nonlinear mathematical model was builtcomponent by component where the flow and fluid dynamicswere considered. The details of the nonlinear dynamic modeland its verification can be found in [18]. This model providesan insight into the hydraulic-mechanical system. The under-standing of the system gained from this modeling processhelped to develop a simplified control oriented model forcontrol development purpose in the next step.

A. System Dynamics

The EPVA consists of two control solenoids, two spoolvalves, two port valves, an actuator piston, an actuator cylinder,and a hydraulic latch-damper system. An actuator piston pushesthe back of the engine poppet valve stem, causing the valveto open. Solenoid-controlled spool valves 1 and 2 are used tocontrol the flow of the compressed air that enters and exits theactuator cylinder. In order to reduce the energy consumption,EPVA uses a hydraulic latch which allows the actuator toextract the full expansion work out of the air that is drawn intothe actuator cylinder. Meanwhile, the actuator is still capable ofholding the valve open over the desired opening duration. Thehydraulic latch also behaviors as a hydraulic damping mech-anism during valve closing to provide a soft seating velocity.According to the events taking place in the actuator cylinder,the system dynamics are divided into three stages: air charging,expansion and dwell, and air discharging stages.

Fig. 2. EPVA hydraulic diagram.

Fig. 2 shows a schematic diagram of an EPVA when bothsolenoids are inactive. During the air charging stage, solenoid1 is activated, causing spool valve 1 to move right and closeon-off valve . As a result, the outlet port valve closes and theinlet port valve opens. The supply compressed air now chargesthe cylinder, the actuator piston starts moving down and opensthe poppet valve. During the expansion and dwell stage, bothsolenoids 1 and 2 are activated, which causes spool valve 2 tobe pushed slightly to the left, and as a result, the inlet spool valvecloses. Meanwhile, the on-off valve is closed when solenoid2 is activated to prevent the high pressure air from escaping tothe atmosphere through spool valve 1. The actuator piston andpoppet valve both reach their maximum displacements at steadystate. During the discharging stage, both solenoids 1 and 2 aredeactivated and both spool valves 1 and 2 return to their defaultpositions shown in Fig. 2. Note that in this stage both on-offvalves and are activated. Since the oil in the hydrauliclatch is now able to flow back up to its reservoir, the actuatorpiston returns to its rest position due to the valve spring force.A detailed description of the EPVA dynamics and nonlinear dy-namic model can be found in [18].

B. Control Oriented Dynamic Model

The control oriented modeling work concentrates on the ac-tuator piston (end actuator) dynamics and omits the nonlinearflow dynamics. As illustrated in Fig. 3, the valve response canbe divided into three stages. They are the opening stage between

and , dwell stage between and , and closing stage after.1) Opening Stage: During the opening stage, solenoid 1 is

activated at time to open the air supply valve (see Figs. 3 and4), which induces a high air pressure force at time to pushthe valve open.

The time difference between and is due to the electro-magnetic delay of solenoid 1. Solenoid 2 is then activated at time

to close the air supply valve and open air outlet valve, whichremoves the air pressure force at time . Again, the time dif-ference between and is due to the electro-magnetic delay ofsolenoid 2. Note that the interplay between two solenoids resultsin a pulse force to the actuator betweenand . The increment of the pulse width increases valve


Fig. 3. Valve lift profile and its control signals.

lift. With the air pressure force removed, the valve movementcontinues until it reaches its peak lift at time (the valve equi-librium). In this stage the valve actuator is modeled as a secondorder mass-spring-damper system with zero initial conditions

(1)and

ifif

(2)where ; is the summation of actuatorpiston mass , the intake valve mass , valve stemcap mass , and effective valve spring mass . (Theeffective spring mass equals one third of the total spring mass[22]); , where and are the radius ofthe actuator piston and oil passage; is the damping ratioapproximating energy dissipation due to flow loss and frictionalloss; and are the stiffness of the valve spring and thepreload of the valve spring, respectively; , , andare the actuator air, oil pressure, and the air supply pressure;

is the area of the cap on the top of the actuator piston stem;and last, is the lag between the activation of solenoids 1 and 2without solenoid electromagnetic delays as illustrated in Fig. 3.

2) Expansion and Dwell Stage: During the dwell stage be-tween and , the valve is held open by a hydraulic latchmechanism (see Figs. 3 and 4). The equation of motion at stageII is described as follows:

(3)

where since the supply pressure has been removedand the piston is fully extended at this stage, is the total massof the actuator system as described in (1), is the dampingratio approximating energy dissipation due to frictional loss atdwell (lock) stage, and is the oil pressure applied to

Fig. 4. EPVA piston model.

piston stem in dwell stage. The state equation,constant, is used to obtain the expression for , where alarge was chosen to represent the low compressibility of oil

(4)

Substituting and into (4) to obtain

(5)

where is the maximum valve displacement, is the volumeof the fluid at the maximum valve displacement , and is theoil pressure at the peak valve lift height .

3) Closing Stage: At the end of the dwell stage, solenoid1 is deactivated at time (see Fig. 3), resulting the release ofthe hydraulic latch and the valve starts returning at time . Thetime difference between and is due to the electro-magneticdelay of solenoid 1. The close stage starts at time (free re-turn) and the hydraulic latch activated at the end of closing stageto have a soft landing of intake valve [12]. Dynamic motion inthe closing stage was divided into sub-stages 1 and 2 as illus-trated in Fig. 3, where sub-stage 1 is between and , andsub-stage 2 is after . Sub-stage 1 can again be separated intotwo segments. The first segment is from (when the pistonstarts returning) to ; and the second segment is from towhen the hydraulic damper becomes effective. During the firstsegment, valve piston motion is a free return, however, in thesecond segment, the piston returns against certain pressure dueto in-cylinder compressed residual air. For simplicity, both seg-ments were modeled as free returns. In sub-stage 2, the pistonreturns against largely increased hydraulic damping force thatacts on the piston stem. The governing equations at this stageare described in (6) and (7). Equation (6) describes the responsebetween and (see Figs. 3 and 4)

(6)

where , and . The response after inhydraulic damping region follows (7)

(7)


Fig. 5. Control oriented model simulation and experiment responses.

where is a constant in sub-stage 1. But it is a function offlow out area in the hydraulic damper in sub-stage 2. The detailderivation of can be found in [18].

C. Control Oriented Dynamic Model Validation

The simulation and experimental responses of the control ori-ented model are compared in Fig. 5, where the dashed line isthe experimental response and the solid one is the simulated re-sponse using control oriented model.

Damping ratio at opening stage, , and damping ratioat closing stage, , are identified manually by trial anderror in this simulation. In the real-time implementation, thetwo damping coefficients will be adaptively identified onlinesince they vary significantly with respect to temperature, fluidviscosity, and engine operational conditions. Fig. 5 also showsthe measured solenoid currents, where the solid line is thedwell current of solenoid 1 and the dash line is that of solenoid2. There are delays between the activation of the solenoidsand the actual mechanical motions. The total delay associatedwith solenoids 1 and 2 are defined as and

(see Fig. 3), respectively. As shown in Fig. 5,total delay of each solenoid rises in two steps. Taking solenoid1 current as an example, the first rise is from the starting pointto the first peak, which represents the electrical delay; and thesecond rise is from the first peak to the second peak, whichrepresents the magnetic delay. Algorithms were developed todetect and online for each cycle. was used tofollow reference opening timing by compensating the valveopening delay. Both and were used to modify thepulse width of air pressure force input associated with thevalve lift control. Note that is used to control the valveopening timing and is one of the variables for the liftcontrol. This will be discussed in Section III.

III. CONTROL STRATEGY

The goal of VVT and VVL control is to control valve openingtiming, duration, and lift, or in other words, to control the valvelift, opening, and closing timings. The strategy of achieving thisgoal is addressed in this section. An adaptive parameter iden-tification algorithm using model reference technique and MITrule [21] were utilized to estimate the two damping coefficientsat both opening and closing stages. The identified parameters

are used to modify the feedforward control of the closed-loopPI controller. Certain approximations were used to obtain ana-lytical solutions of control inputs in terms of the estimated pa-rameters. Only opening and closing stages of the control ori-ented model were used in the real-time control scheme to reducethe computational throughput. The closed-loop control schemeaimed at real-time implementation is discussed in this section.

A. Variable Definition

Fig. 3 defines the control signals and variables involved inthe control strategy. At low engine speed, the valve lift profilehas all three stages as shown in Fig. 3, where the holding periodexists. As engine speed increases, the holding period reduces.At certain engine speed, the holding period disappears, and thevalve lift profile consists of only the open and close stages. Inthis case, solenoid 1 is deactivated shortly after its activation.It discharges the cylinder and allows the valve to return beforethe hydraulic latch can be engaged. In these two cases, bothsolenoids 1 and 2 are needed to control the valve event and theair supply pressure remains unchanged throughout the process.There is another special case in which only solenoid 1 is used.The cylinder is simply charged with supply air when solenoid1 is energized and discharged when solenoid 1 is de-energized.This occurs when the engine speed is so high that the activa-tion duration of solenoid 1 becomes very small. The valve liftcontrol needs to be accomplished through regulating air supplypressure. This special case is not discussed in this paper.

For a given engine operational condition, the desired intakevalve lift, opening, and closing timings are provided by the en-gine controller to optimize engine fuel economy with satisfac-tory emissions. Therefore, as displayed in Fig. 3, time points

and can be determined by the desired valve opening andclosing timings provided by engine controller. To accuratelycontrol the intake valve opening and closing timings, the keycontrol parameters are for opening timing and

for closing timing assuming is a constant;and the control parameter for valve lift control is .Note that is the time delay between the activation oftwo solenoids; and represents the time needed for the valveto return after the deactivation of solenoid 1 (at valve returnpoint). Activation of solenoids 1 and 2 begins their impact onthe system after their time delays and , respectively.The air pressure in the piston cylinder increases and forms apulse force input to the system with a pulse width of .

and can be obtained from the identified parametersand of opening and closing control oriented models. Thecontrol variable conventions for the other cases are similar tothis case and are not repeated. The Table I summarizes the con-trol variables.

B. Adaptive Parameter Identification

The architecture of the model reference adaptive system(MRAS) for parameter identification is illustrated in Fig. 6,where is the control oriented model and is thephysical plant (EPVA). This adaptive estimator is applied toidentify the damping ratios and , where is for theopen stage and is for the close stage. The error betweenmodel and plant outputs reduces as the estimated parameterconverges. Note that in this case the excitation force is a pulse


Fig. 6. Model reference adaptive parameter identification scheme.

input with PE (persistency of excitation) of order infinity. TheMIT rule uses the error between the model and plant outputsto generate the estimated (or ) corresponding to

(or ), where (or ) is updated at every valveevent. Note that for the adaptive parameter identification algo-rithm, a second order linear model was used to represent thevalve dynamics and the robustness of the adaptive parameteridentification algorithm against modeling error was not studiedin this paper.

The MIT rule (gradient method) is used for real-time param-eter identification. Consider the following cost function, where

(8)

(9)

Note that valve displacement is the plant output and is thesimulated valve displacement based upon the control orientedmodel, is the error between the model and plant outputs, isthe estimated parameter, and is the adaptive gain. In thiscase

for opening stagefor closing stage. (10)

The adaptive law at opening and closing stage is developedbased upon the MIT rule. The governing equation of the systemat this stage is expressed in (11)

(11)

where , , and by(1). To change the coordinate, let

(12)

Equation (11) can be rewritten in coordinate as follows:

(13)

where . Laplace transform of (13) results inthe following equation:

(14)

The error between the model and the plant outputs in Laplacedomain can be expressed in the followingequation:

(15)

where and are the plant and model outputs, respec-tively, and and are the plant and model damping ra-tios. Then

(16)

where . The inverse Laplace transform of (16)results the adaptation law of as follows:

(17)

The adaptation law of at opening stage can be summarizedin the following:

(18)

where is the selected adaptive gain and is themodel damping ratio (or estimated ). The adaptive algorithmutilizes the sampled data between and from the valve re-sponse shown in Fig. 3. For the closing stage

(19)

where is the selected adaptive gain and is themodel damping ratio (or estimated ). The adaptive algorithmuses the sampled data between and from the valve responseshown in Fig. 3 due to free return characteristics of the valveresponse.

C. Feedforward Valve Lift and Timing Control

The purpose of the closed-loop control is to make the valvelift, opening, and closing timings track the references with fasttransient responses as well as repeatable steady state responses.The closed-loop valve lift and closing timing controls are cre-ated based upon the identified damping ratios and .Let and denote the estimated values of and de-fined in Table I. It is desirable to have analytical solutions ofand from estimated and . Test data shows thatthe second-order system dynamics for both opening and closingstages are between over-damped and slightly under-damped,which indicated that both system responses could be approxi-mated by the first-order responses, especially when the systemis over-damped. Note that when the system is over damped, itstime response is the summation of two corresponding first-ordersystem ones. The approximation is realized by constructing a


TABLE ICONTROL PARAMETERS FOR VALVE LIFT, OPENING AND CLOSING TIMINGS

first-order system such that its time constant is associated withthe dominated pole of the over-damped second-order systemdescribed in (1) and its steady-state response matches the cor-responding second-order system one. Therefore, for openingstage, the first-order approximated time response is

(20)

where is definedby (1) and is defined by

.(21)

Note that is the inverse of the largest time constant of theopening stage system model (11). When the system is criti-cally or under damped, is selected to be the real portionof the second order system pole locations. Therefore, for thegiven identified parameters and , the analytical so-lutions of and can be developed basedupon the first-order approximated system. Referring to Fig. 3, byignoring the small time delay between and and assumingthat is fixed, the parameter can be approxi-mated by the following equations as a function of :

(22)

where can be calculated based upon (23) and (24) with thegiven desired lift

(23)

(24)

Similarly assuming that is fixed and at thevalve is closed, the parameter can be approximated by thefollowing equations as a function of :

(25)

where can be calculated based upon (26) with the actual valvelift since in this case the response governing equation is

(26)

where is a function of and is defined as follows:

.(27)

Fig. 7. Feedforward and closed-loop valve lift control scheme.

D. Closed-Loop Lift, Opening, and Closing Timing Control

The architecture of the closed-loop valve lift control is de-picted in Fig. 7, where only the valve lift control scheme isshown inside the dotted box. The control system is mainly di-vided in three portions: 1) adaptive parameter estimation; 2)feedforward control parameter calculation; 3) and feedforwardand closed-loop proportional and integral (PI) control. The feed-forward control is aimed to have fast transient response and theclosed-loop control is used to eliminate the steady-state error.

Adaptive parameter estimation block shown in Fig. 7 uses thetwo solenoid control pulses and and valve displacementsignal, shown in Fig. 3, as input signals; and the estimation algo-rithm are based upon both (18) and (19) to obtain the estimatedsystem damping coefficients and . The estimatedparameters are updated every valve event. Since the adaptiveparameter estimation takes certain iterations to converge, theclosed-loop control system starts with open-loop control untilthe estimation converges, where the parameter difference be-tween two estimation steps is used as the convergence criterion.In order to achieve initial fast convergence, both parameters

and are estimated using high adaptive gains and thegains are reduced after the parameter estimations are converged.The initial convergence may take up to 50 valve events. Note thatthe estimation algorithm is executed at a relatively high samplerate to capture the valve displacement dynamics. For the datapresented in the paper, the estimation scheme was sampled at40 s.

Feedforward parameter estimation of both and , shownin Fig. 7, is based upon (22) and (25) using the estimated systemdamping coefficients and , along with the desiredvalve lift and actual valve lift . The feedforward param-eter estimation strategy is executed every valve event. For theengine operated at 1500 r/min, this algorithm is executed at a12.5 Hz sample rate.

As a summary, the adaptive valve control scheme was exe-cuted in dual sampling periods: one sampled during the valveoperation period with a fast sample period of 40 s and the othersampled at every valve event. From Fig. 7, the “Adaptive Pa-rameter Estimation” and “Solenoid Signal Construction” blockswere executed every 40 s and the rest of blocks were executedevery valve event after the valve was fully closed. As shown inFig. 3, it is worth mentioning that time parameters , , andare required to construct both solenoid control signals andassuming that the desired valve lift, opening, and closing timing( , , and ) are known.


Fig. 8. PI controller architecture.

1) Feedforward and Closed-Loop Valve Lift Control: Thefeedforward and closed-loop valve control strategy is executedonce after the valve event to provide control parameter . Thefeedforward term of is calculated based upon the followingequation:

(28)

where parameter was obtained from “Feedforward Param-eter Calculation” block based upon estimation results of adap-tive estimation system. The actual valve lift control parameter

is the summation of the feedforward control and the PIfeedback control signal as a function of the error signal

between the reference and actual valve lift. The PI controlarchitecture is shown in Fig. 8, where both proportional and in-tegral gains ( and ) are a function of PI input error (seeequation below)

(29)

The constant gains ( and ) were selected to be 0.06and 0.4, respectively. The other important feature of the PI con-troller is the anti-windup feature, which prevents the PI con-troller over and under flow. When the composite control signal

is within the given upper limit and lower limit, the anti-windup logic output will be one and other-

wise it will be zero.2) Closed-Loop Opening Timing Control: Opening timing

is controlled by a closed-loop PI controller with a fixed feedfor-ward control , where is the desired valve openingtiming. We assume that the solenoid magnetic delay does notchange cycle-by-cycle, and therefore, is a constant. In prac-tical application, does change as the oil temperature, supplyair temperature, and pressure vary and it can be corrected usingthe solenoid current measurements. A closed-loop PI controlleris used to compensate for the valve opening timing control. Thiscontrol strategy executes every valve event.

3) Feedforward and Closed-Loop Closing Timing Control:The feedforward and closed-loop valve closing timing controlis similar to the valve lift control schemes shown in Fig. 7. Thefeedforward term of is calculated based upon the followingequation:

(30)

where parameter was obtained from “Feedforward Param-eter Calculation” block based upon estimation results of adap-tive estimation system and is assumed to bea fixed electrical-magnetic delay. The “Lift Calculation” block

Fig. 9. Closed-loop valve opening timing control scheme.

Fig. 10. Control system architecture.

will be replaced by a block calculating the valve closing timing;and the PI controller reference signal is changed to desired valveclosing timing . The summation of both feedforward and PIclosed-loop control outputs are connected to the input of the“Solenoid Signal Construction” block.

IV. EXPERIMENTAL SETUP AND OPEN-LOOP TESTS

This section discusses the experimental setup for the pro-posed model reference adaptive control (MRAC) scheme andits open-loop experimental results.

A. Test Setup

A real-time dual-CPU control system was employed as a pro-totype controller for the EPVA bench tests. Fig. 10 shows thearchitecture of the prototype control system. CPU #1 was as-signed to engine and valve event based control and CPU #2 wasdedicated to the valve actuator (EPVA) control for adaptive pa-rameter estimation and solenoid signal construction. An IEEE1934 firewire serial bus was used for communication betweenCPU #1 and CPU #2. CPU #1 was configured to be updatedevery 1 ms and executed the engine and valve control strate-gies every combustion event. This means that this CPU updatesinput and output signals every 1 ms but calculates the engineand valve control variables every engine combustion event. Thedigital outputs of CPU #1, used to generate both solenoid con-trol signals and , were synchronized with the engine crankangle with one-third crank degree resolution. The crank anglecalculation was accomplished utilizing the field-programmablegate array (FPGA) digital I/O board associated with CPU #1based upon engine cam and crank encoder signals.

CPU #2 was mainly used for adaptive parameter estimationas part of MRAC scheme. This CPU was configured to operatewith a 40 s sample rate, which is about one crank degree at4000 r/min. The valve displacement signal is sampled every 40

s and the adaptive parameter estimation algorithms were exe-cuted at the same sample rate. The estimated valve damping co-efficients and were updated within 1 ms to CPU #1via IEEE 1934 serial bus. The other valve sensor signals, such


Fig. 11. Test bench setup.

as supply air pressure and solenoid currents of and , werealso be sampled into CPU #2 for parameter estimations.

A Ford 4.6 liter four-valve V8 engine head was used for thevalve test, see Fig. 11. The camshaft was removed from the in-take valve side and an EPVA was installed above one of the in-take valves. A Micro-Epsilon point range laser sensor was usedto measure the intake valve displacement with a resolution about15 m. This laser sensor uses the triangulation principle for a2-D acquisition of a height profile of various target surfaces. Thelaser sensor was mounted on an angle such that the laser beamfrom the emitter of the laser sensor would be perpendicular tothe surface of the end of the valve stem. Note that this measure-ment approach is accuracy for the bench tests but is not fea-sible in a production engine environment. For a production en-gine, a non-contact differential variable reluctance transformer(DVRT) position sensor is under investigation for measuring thevalve displacement.

Also note that this experimental setup is suitable for val-idating engine intake valve lift, opening and closing timingsince the engine intake valve opens against the in-cylinderpressure close to engine intake manifold one with relativelysmall cycle-to-cycle variation. But it is not suitable for engineexhaust valve performance validation since in this case, thevalve opens against an in-cylinder pressure that varies as afunction of the engine operational conditions with fairly largecycle-to-cycle combustion variation. The in-cylinder pressuredisturbance slows down the pneumatic valve actuator response,and as a result, it increases the variation of valve opening delay,and therefore, makes it difficult to maintain repeatable valveopening timing and lift. Reference [24] utilizes model basedpredictive techniques to overcome the in-cylinder pressuredisturbance for improved repeatability.

B. Open-Loop Statistical Analysis

Before the closed-loop valve lift and timing control benchtests were conducted, a statistical study focusing on the valveresponse repeatability was performed on test bench at both highand low engine speeds. Results of this study are used to com-pare with those of the closed-loop valve lift tests to evaluatethe steady state closed-loop lift control performance in the nextsection. The valve repeatability has a great impact on the adap-tive parameter estimation and steady state response. Since the

Fig. 12. OL and CL valve lift histogram at 1200 r/min.

MRAC of valve closing timing control is similar to the valvelift control, both open and closed-loop control experimental re-sults for valve closing control are not discussed in this paperand only the valve lift MRAC results are presented. To comparewith the closed-loop experimental results, the operational con-ditions for the open-loop tests were selected to be identical tothe closed-loop ones. All test data were collected in the proto-type controller with a sample rate of 25 kHz. To hold a desiredlift, the lag between the activation of solenoids 1 and2 was set to be a constant value, where andwas selected to maintain a desired lift. The solenoid pulse pe-riod (a function of engine speed) and pulse width, the air supplypressure and the oil pressure were held constant in both typesof experiments. Since the valve closing timing MRAS controlis fairly close to the valve lift control, only the valve lift experi-mental results are presented in this section.

1) Low Speed Open-Loop Valve Tests: Five bench tests wereconducted using 80 psi air supply pressure, 90 psi oil pressure,100 ms solenoid period, which corresponds to the engine speedat 1200 r/min, with 25% pulse duty cycle and a lag of5 ms between the activation of two solenoids. The valve lift wastargeted to be around 9 mm and there was a holding period onthe valve lift profile under this experiment configuration (seeTable II). The main purpose of these tests is to obtain the statis-tical characteristics of the valve responses. Two hundred-cycledata was collected for each experiment. The experimental dataof valve lift was plotted as histograms and the mean and standarddeviation of responses were calculated. The top row of Fig. 12shows the histograms of data group #3 (with the largest devia-tion) shown in Table II, where the top left plot is the valve lifthistogram which reflects the valve lift repeatability and the topright one is the histogram of the valve lift integral during thevalve opening which is associated with the repeatability of theengine charged air. For the valve lift diagram, the horizontal axisis the valve lift ranging from 8.4 to 10.0 mm and the vertical axisis the number of occurrence for each valve lift; and for the in-tegral diagram, the horizontal axis is the integral area and thevertical axis is the number of occurrence. The mean and thestandard deviation over 200 test cycles were calculated, andthe mean of integral area of the valve lift was normalized to one.Note that the region between and contains about95% occurrence of valve lift.


Fig. 13. OL and CL valve lift histogram at 5000 r/min.

TABLE IISTATISTICAL STUDY OF OL VALVE TEST AT 1200 r/min

The statistical information of five data groups are summa-rized in Table II. For the valve lift, group #1 has the largest liftmean at 9.69 mm and group #2 has the smallest mean at 8.83mm. The largest three-time deviation of valve lift, 0.86mm, comes from data group #3. The smallest three-time devia-tion of valve lift (0.44 mm) is from data group #1. For thenormalized lift integral area, the mean values were normalizedto one and the three-time deviations are calculated basedupon the normalized data. This leads to the percentage of thearea deviation. Among the five data groups, group #2 has thelargest value of 10.87%. Group #3 data provided the largestdeviations of valve lift and the second largest integral area. Theirhistograms are shown in the top row of Fig. 12, and comparedwith the correspondent closed-loop histograms, see the bottomrow of Fig. 12, with the largest deviations at the same opera-tional conditions as the open-loop ones.

2) High Speed Open-Loop Valve Tests: Similar to the lowengine speed case, five bench tests were conducted using 80 psiair supply pressure, 90 psi oil pressure, 24 ms solenoid period(which corresponds to the engine speed at 5000 r/min) with a25% pulse duty cycle and a lag of 5 ms between theactivation of two solenoids. This is corresponding to the desiredvalve lift of 9 mm for all five tests (see Table III). As to the highspeed case, two hundred-cycle data was collected for each test.The mean and the standard deviation were calculated.

TABLE IIISTATISTICAL STUDY OF OL VALVE TEST AT 5000 r/min

Table III summarizes the statistical analysis results of five testdata groups. For the valve lift, data group #1 has the largest meanvalve lift at 9.14 mm and group #5 has the smallest mean valvelift at 8.59 mm. The largest three-time deviation of valvelift (0.63 mm) comes from data group #4 which is less than thelargest three-time deviation of valve lift (0.86 mm) at lowengine speed (1200 r/min). The smallest three-time deviation

of valve lift is 0.17 mm from data group #2. It is less thanthe smallest three-time deviation of valve lift 0.44 mm, seeTable II, at 1200 r/min. This indicates that the valve lift repeata-bility improves at high engine speed. For the integral area, datagroup #4 has the largest three-time deviation of 11.7%.

The group #4 test results show the largest deviations of bothvalve lift and the integral area. The corresponding histogramsare shown in the top row of Fig. 13, where the top left histogramis for the valve lift and the top right one is for the integral area.The histograms of bottom row of Fig. 13 are the closed-loophistograms for comparison purpose.

3) Low Valve Lift Open-Loop Valve Tests: The EPVA is ca-pable of providing a valve lift as low as 3 mm. This subsectionstudies statistical low lift properties to determine if the low valvelift operation is acceptable for engine operation. Since the valvelift repeatability improves as engine speed increases, see the re-sults from previous two subsections, we studied the low valvelift operation only at low engine speed (1200 r/min). Similar tothe previous studies, five bench tests were conducted using the


TABLE IVSTATISTICAL STUDY OF OL VALVE TEST AT 1200 r/min (3 mm LIFT)

same experimental setup as high lift case at 1200 r/min enginespeed except the lag between the activation of two solenoids wasreduced to 3.4 ms to obtain the targeted valve lift at 3 mm. Thestatistical results were shown in Table IV. The mean valve liftvaries between 2.68 and 3.51 mm. The largest three-time devi-ation of valve lift is 2.5 mm from data group #3 and the

value is less than 2.5 mm among the rest of the data groups.Consequently, data group #3 has a integral area value as highas 73.19%. Therefore, although the actuator is capable of pro-viding a lift as low as 3 mm, its repeatability is not good enoughto deliver a stable air flow when engine is operated at light loadconditions. For future engine control applications, the valve liftoperational range will be limited between 5 and 11 mm to ensurethe desired repeatability. When the required valve lift is below5 mm at light load condition, a flap valve or a throttle will beused to reduce the intake air flow.

V. CLOSED-LOOP VALVE LIFT EXPERIMENTAL RESPONSES

The closed-loop valve control strategies were verified on thevalve test bench using the same setup as the open-loop tests.The experimental responses at both low and high engine speedsare discussed in this section. Air and oil supply pressures forall tests are 80 and 90 psi, respectively. Two solenoid periodswere selected: one was 100 ms with 25 ms solenoid active dura-tion (25% duty cycle) corresponding to 1200 r/min in low speedopen-loop tests; and the other was 24 with 6 ms solenoid activeduration (25% duty cycle) corresponding to 5000 r/min in highengine speed open-loop tests.

Before the closed-loop tests were conducted, the character-istics of parameter system identification are studied. Since theidentification process of is identical to , only re-sults are presented. For parameter identification of , the lag

between the activation of solenoids 1 and 2 duringthe open-loop parameter identification period was 5 ms at bothlow and high speed tests. Fig. 14 shows the first 80 cycle valvelift response (top plot), where for the first 60 cycles the controlsystem was operated in an open-loop to make sure that the iden-tified (mid plot) is accurate enough for feedforward con-trol. After the identification error (bottom plot) converges to agiven tolerance the valve control was switched into closed-loopcontrol at the 61st cycle with a step reference signal change.From Fig. 14 it can also be observed that the parameter estima-tion reaches 90% of its converged target within first 25 cycles.

A. Experimental Results at Low Engine Speeds

For the valve lift tests at 1200 r/min, the open-loop parameteridentification was converged in the first 25 cycles. After both pa-rameters were converged, the closed-loop valve lift control was

Fig. 14. OL parameter identification at 1200 r/min.

enabled and 2500 cycles of valve responses were recorded withstep reference valve lifts changed every 500 engine cycles. Thefive reference valve lifts are 9.3, 6.0, 10, 7.0, and 9.0 mm. Notethat proper selection of the opening and closing damping coef-ficient initial conditions (e.g., using lookup tables as a functionof engine coolant temperature) could reduce parameter identifi-cation convergence time significantly.

The steady-state valve lift responses are presented in Figs. 15and 16. For Fig. 15, the top row diagrams show both referenceand actual valve lift responses from 9.3 to 6 mm and from 6to 10 mm; the middle diagrams display the difference betweenthe reference and actual valve lift; and the bottom plots showthe feedforward portion of and the combined controlvariable that is the summation of both the feedforwardand closed-loop PI control. The feedforward control portion of

remains relatively steady since the parameter identifica-tion convergence is preserved during the closed-loop lift control.Since the valve solenoid control signals updated every 40 s, thecontrol variable is digitized at the same sample rate withsteps shown in the bottom row of Fig. 15. One can see that atthe steady state the valve lift oscillated around its reference liftand most of the lift errors are within 0.5 mm.

Fig. 16 shows the transient valve lift responses from 10 to7 mm and from 7 to 9 mm. The difference between Figs. 15and 16 is that Fig. 16 depicts the magnified step responses withmagnified time axis in the bottom row of the figure, while thetop row of the figures provides both reference and actual valvelifts and the middle row shows the control signals. From thebottom row of Fig. 16 it can be clearly observed that the valvelift transition was accomplished within next valve event withless than 0.5 mm of lift error. This is very important for tran-sient air charge control since for the internal combustion engineoperated in HCCI (Homogenous Charge Compression Ignition)combustion mode, cycle-to-cycle valve timing control is a ne-cessity. The one step valve lift control is the result of the pro-posed model reference predictive control. Note that 0.5 mm lifterror leads to less that 0.5% IMEP variation for an engine op-erated at 1500 r/min with 5 bar IMEP based upon GT-Powersimulations.


Fig. 15. Steady state and transient responses (valve lift: 9 to 6 and 6 to 10 mm).

TABLE VMAX SS ABSOLUTE LIFT ERROR (1200 r/min)

Next, steady state valve lift performance will be evaluated bytheir mean and standard deviations and compared with open-loop results. From both Figs. 15 and 16, it can be seen that duringthe steady state operations, the valve lift tracks the referencevalve lift. The actual valve lift responses show good repeata-bility at high valve lifts. The maximum absolute valve lift errorwas 0.4 mm with 10 mm lift and 0.5 mm with 9 mm lift, respec-tively. The valve lift repeatability reduces as the lift decreasesin general. This is partially due to the fact that the controlla-bility of the pneumatic valve actuator decreases as valve lift re-duces, which results in a high steady state lift error with lowvalve lift. The maximum absolute steady-state errors at thesefour set points are listed in Table V.

The statistical performance of the valve lift responses with theclosed-loop controller is also important to study. The statisticalcharacteristics of the open-loop valve lift are analyzed in thethird subsection of Section IV. The open-loop statistical anal-ysis results of the valve lift at 1200 r/min are shown in Fig. 12(top row) and Table II. They provides three time deviationof the worst 9 mm lift at 0.86 mm and the worst integral area

of 9 mm lift at 10.87% over five test data set. The samestatistical analysis was conducted for the closed-loop lift con-trol results. Five 200 cycle steady-state valve lift responses at 9mm were obtained and used to calculate the closed-loop means

TABLE VISTATISTICAL STUDY OF CL VALVE TEST AT 1200 r/min

and standard deviations of the valve lift and its integrated area.The closed-loop statistical analysis results are compared withthe corresponding open-loop results in Fig. 12 that depicts thehistograms of the lift and integral area of the valve lift profile forboth open and closed-loop control. The closed-loop lift statisticsdata were obtained from the data set with the largest variationsamong the five data sets (see group #1 in Table VI). Note thatthe axes ranges and the bin width of the valve lift (left) and in-tegral area (right) histograms in Fig. 12 are the same for bothopen and closed-loop results for easy comparison.

The five sets of closed-loop means and values of valve liftand integral area were summarized in Table VI. The worstvalue of the valve lift reduced from open-loop of 0.86 mm toclosed-loop of 0.45 mm, and the worst integral area valuereduced from 10.87% to 5.45% (comparing both Tables II andVI). In other words, the worst case values of both valve liftand integral area were reduced by about 45%. This indicates thatthe closed-loop valve lift control reduces the valve lift variation,and hence, improves its lift repeatability.


Fig. 16. Steady state and transient responses (valve lifts: 10 to 7 and 7 to 9 mm).

The feedforward control portion of remains relativelysteady since the parameter identification convergence is pre-served during the closed-loop lift control. It takes about one en-gine cycle for the valve to reach the reference valve lift with lessthan 0.5 mm of lift error. This is critical for transient air chargecontrol. The closed-loop control (combining both feedforwardand PI control) is close to feedforward control portion of

which is sufficiently accurate to bring the valve lift closeto the reference valve lift in the first cycle. In all four cases, theactual valve lift is within 0.5 mm lift error region of the refer-ence lift in one cycle.

B. Experimental Results at High Speed

The high speed closed-loop valve lift tracking results are pre-sented and discussed in this subsection. Similar to the low speedcase, 2500 cycles of valve responses were collected with mul-tiple reference valve lifts at 9.3, 6.0, 10, 7.0, and 9.0 mm. Thevalve lift responses of all five lift levels were close to the lowspeed and therefore the corresponding time response plots areomitted in this paper.

Similar to the low speed case, the maximum absolute steady-state errors at the four reference levels are listed in Table VII.The steady-state lift errors are less than 0.8 mm at high valvelift (9 to 10 mm) and less than 1.1 mm at low lift (6 to 7 mm),which is compatible with the low lift case shown in Table V.

The same statistical analysis was performed for the closed-loop lift control at 5000 r/min. Five 200 cycle steady-state valvelift responses were collected with 9 mm reference lift and usedto calculate the means and standard deviations of the valve lift

TABLE VIIMAX SS ABSOLUTE LIFT ERROR (5000 r/min)

and its integral area. The open-loop statistical study results ofboth valve lift and its integral at 5000 r/min engine speed areshown in both Fig. 13 (top row) and Table III. They show thatthe open-loop worst lift value is 0.63 mm at 5000 r/min, com-paring with 0.86 mm at 1200 r/min (see Table II), and the worstopen-loop integral value is 11.7% at 5000 r/min, comparingwith 10.9% at 1200 r/min (see Table II), for the target lift at 9mm using the worst case data set among five test data groups.

The open and closed-loop valve lift results were also com-pared. The diagrams displayed in Fig. 13 depict the histogramsof the valve lift and integral area with the largest variations (datagroup #1 in Table VIII). For easy comparison, the axes rangesand the bin width of the valve lift (left) and integral area (right)histograms in Fig. 13 are the same for both open and closed-loopdata. The five sets of means and values of valve lift and inte-gral area were summarized in Table VIII. The worst value ofthe valve lift reduced from the open-loop 0.63 mm (see Table III)to the closed-loop 0.45 mm, which is a reduction of about 29%.The worst integral area value reduced from 11.7% to 9.45%,which was reduced by about 19% (see both Tables VIII andIII). The low engine speed closed-loop lift control data showeda reduction of about 45% on both the values of the valvelift and integral area in their worst case. The reduction on thecycle-to-cycle lift variation at 5000 r/min seems to be less than


TABLE VIIISTATISTICAL STUDY OF CL VALVE TEST AT 5000 r/min

that at 1200 r/min. We believe that moderate improvement athigh engine speed could be due to the fixed control sample pe-riod at 40 s that reduces the valve lift control resolution at highengine speed and reduced lift variation at 5000 r/min (0.63 mm)from 1200 r/min (0.86 mm).

VI. CONCLUSION

In this paper, a control oriented model of an electro-pneu-matic valve actuator was established based upon the physicsbased nonlinear model for model reference parameter identifi-cation. The control oriented model reduces computational ef-fort and enables real-time implementation. A model referenceadaptive scheme was developed to identify two key nonlinearsystem parameters on line. The identified parameters are thenused to construct the feedforward control as part of the closed-loop valve lift PI controller. The closed-loop valve lift tracking,valve opening and closing timing control strategies were devel-oped and validated on an electro-pneumatic valve actuator testbench. The test data, mainly for the value lift control, cover mul-tiple reference lift levels at both 1200 and 5000 r/min enginespeeds for both steady state and transient operations. The ex-perimental results show that the actual valve lift reaches the ref-erence lift within 0.5 mm lift error in one cycle with the helpof the model reference adaptive feedforward control. The max-imum steady state lift errors are less than 0.7 mm at high valvelift and less than 1.3 mm at low valve lift. Furthermore, theclosed-loop valve lift control improved valve lift repeatabilitywith more than 30% reduction of standard deviation over theopen-loop control results.

ACKNOWLEDGMENT

The authors would like to thank the U.S. Department ofEnergy, National Energy Technology Laboratory, Energy Ef-ficiency and Renewable Energy Division, S. Taylor, ProjectManager.

REFERENCES

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[23] J. Ma, G. Zhu, H. Schock, and J. Winkelman, “Adaptive control of apneumatic valve actuator for an internal combustion engine,” presentedat the Amer. Control Conf., New York, Jun. 2007.

[24] J. Ma, G. Zhu, T. Stuecken, A. Hartsig, and H. Schock, “Electro-pneu-matic exhaust valve modeling and control for internal combustion en-gines,” presented at the ASME ICE Spring Techn. Conf., Chicago, IL,Apr. 2008.

Jia Ma received the M.S. degree in mechanical engi-neering from Ohio University, Athens, in 2002, andthe M.S. degree in electrical engineering and Ph.D.degree in mechanical engineering from MichiganState University, East Lansing, in 2006 and 2007,respectively.

She is currently a Senior Systems Engineer withDelphi Powertrain Systems, Auburn Hill, MI, whereshe specializes in the engine management algorithmdevelopment. Her research interests include analysis,modeling and design of dynamic systems, implemen-

tation of control theories, system modeling, testing, identification and valida-tion, and automotive powertrain controls design.


Guoming (George) Zhu received the B.S. and M.S.degrees from Beijing University of Aeronautics andAstronautics, Beijing, China, in 1982 and 1984, re-spectively, and the Ph.D. degree in aerospace engi-neering from Purdue University, West Lafayette, IN,in 1992.

He is an Associate Professor with the Departmentof Mechanical Engineering (ME), Michigan StateUniversity, East Lansing. Prior to joining the MEdepartment, he was a Technical Fellow in advancedpowertrain systems of the Visteon Corporation. He

also worked for Cummins Engine Co. His teaching interests focus on controlclasses at both undergraduate and graduate levels; and his current researchinterests include closed-loop combustion control of internal combustion (IC)engines, engine system modeling and identification, hybrid powertrain controland optimization, etc. Dr. Zhu has over 24 years of experience related tocontrol theory, engine diagnostics, and combustion control. He has authored orcoauthored over 90 refereed technical papers and received 36 U.S. patents.

Dr. Zhu is an Associate Editor for ASME Journal of Dynamic Systems, Mea-surement, and Control.

Harold Schock received the Ph.D. degree in mechan-ical engineering from Michigan Technological Uni-versity, Houghton, in 1979.

He is a Professor with the Department of Mechan-ical Engineering, Michigan State University (MSU),East Lansing. He joined MSU in 1987 and from thattime until he joined MSU, worked as a Research En-gineer and an IC Engine Section Supervisor with theNASA Lewis Research Center, Cleveland, OH. Hisprimary research interests have been in-cylinder com-bustion and flow diagnostics for advanced engine sys-

tems, cylinder-kit tribology, thermoelectrics, and powertrain research. He hasover 180 publications related to engines technology. He currently leads a groupof graduate students and staff working at the Energy and Automotive ResearchLaboratory, MSU.

Dr. Schock is a Fellow of the Society of Automotive Engineers.

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