ABSTRACTSignificant improvement in fuel consumption, torque deliveryand emission could be achieved through flexible control ofthe valve timings, duration and lift. In most existing electro-hydraulic variable valve actuation systems, the desired valvelift within every engine cycle is achieved by accuratelycontrolling of the solenoid-valve opening interval; however,due to slow response time, precision control of these valves isdifficult particularly during higher engine speeds. In thispaper a new lift control strategy is proposed based on thehydraulic supply pressure and flow control. In this method, inorder to control the peak valve lift, the hydraulic pump speedis precisely controlled using a two-input gearbox mechanism.This eliminates the need for precision control of the solenoidvalves opening interval within every cycle. To achieve asmooth control signal, it is worthwhile to control themaximum valve lift within few engine cycles rather thanevery cycle; therefore, instead of using the governing non-linear differential equations of the mechanism, a novelaverage model of the system is developed based on energyconservation equations. A non-linear sliding mode controller(SMC) is also designed based on the developed averagemodel and the boundary layer method is used to eliminate thechattering problem. The performance of the proposedcontroller is then examined through some simulations.Moreover, the new lift control technique is implementedexperimentally by reconfiguration of the existing electro-

hydraulic valve system prototype and empirical results arethen compared with those obtained from the simulations.

INTRODUCTIONAlthough a significant numbers of engine valve-actuationsystems including cam-based and camless mechanisms havebeen already introduced by several researches and companies,only few types of these systems (mainly cam-based) havebeen employed on commercial vehicles due to the liability,durability and cost issues. Although cam-based valve systemsoffer more reliable and durable functionality, the camlessvalvetrains can vary valve lift and timings to a greater extentcomparing to the cam-based types [1]. Among variouscategories of camless mechanisms, the electro-hydraulicvalve actuation system is the most repeatable and durableone. This type of camless valvetrain was first developed byFord Motor Company in 1994 [2] and it was improved laterby Sturman (1997) [3] and Lotus (2004). The basic electro-hydraulic valve system, presented by Schechter and Levin[2], consists of two pressure sources, a spring-return single-acting actuator and two solenoid valves. The first solenoidactuated spool valve (HPSV) is located between the highpressure hydraulic source and the engine valve actuator and isresponsible for controlling the submission of the highpressure oil into the actuator during engine valve openinginterval. The second solenoid valve (LPSV) is locatedbetween the engine valve actuator and the low-pressurehydraulic source and is responsible for evacuating the

An Efficient Lift Control Technique in Electro-hydraulic Camless Valvetrain Using Variable SpeedHydraulic Pump

2011-01-0940Published

04/12/2011

Mohammad PournazeriUniversity of Waterloo

Amir KhajepourUniv of Waterloo

Amir FazeliUniversity of Waterloo

Copyright © 2011 SAE International

doi:10.4271/2011-01-0940

actuator during engine valve closing stage. In this type ofcamless valvetrain, the engine valve timings and duration canbe adjusted by controlling the opening and closing timings ofthe two hydraulic solenoid valves.

In addition to controlling the engine valve timings, the enginevalve lift can also be controlled using this type of valvetrain.Throttle-less engine control can be achieved through accuratecontrol of the valve lift during high engine speeds whereshort valve opening duration is not feasible due to the slowsolenoid valves response time [4]. Moreover, a precise liftcontrol is crucial in electro-hydraulic valve systems where theengine valve lift is highly influenced by the upstreamhydraulic pressure, valve operating speed and valve openinginterval.

In most of the current electro-hydraulic valvetrains, the valvedisplacement is controlled by precisely controlling the highpressure spool valve opening interval [5][6][7]. An adaptivepole-placement controller was designed by Anderson et al.based on the simplified model of the system to control themaximum lift [5]. They controlled the pulse-width of thesignal transmitted to the high pressure solenoid valve toadjust the hydraulic flow to the engine valve actuator, andconsequently, controlled the engine valve lift within eachcycle. A combination of adaptive feedforward and feedbackcontrollers were employed in [7] to control the engine valvedisplacement. A non-linear inverse model of the system wasdeveloped to design the feedforward controller. The valvedisplacement, hydraulic supply pressure and the spool-valveposition were measured precisely as feedback signals to thecontroller.

In this paper, a new technique is proposed to control theengine valve lift in the basic electro-hydraulic valvetrain. Inthis method, instead of precisely controlling the high pressuresolenoid valve opening interval, the hydraulic oil pressureand flowrate are controlled through adjusting the pumpspeed. This method is efficient where drastic changes in thereference engine valve lift is not necessary from engine cycleto cycle. Based on energy conservation law, an averagemodel of the system is developed [8] based on which a non-linear sliding mode controller is designed. The performanceof the designed lift controller is then studied through bothsimulations and experiment.

MECHANISM DYNAMICSSimilar to existing electro-hydraulic valve systems, theproposed mechanism consists of a hydraulic pressure unit anda valve actuation mechanism. The valve actuation mechanismhas the basic configuration which was proposed by [3]. Basedon this configuration, the actuation mechanism consists oftwo on/off solenoid valves (HPSV and LPSV) whichrepeatedly connect and disconnect the valve actuator cylinderto the high and low pressure sources, and consequently, open

and close the engine valve. The control signals to thesolenoid valves are determined based on the desired valvetimings and duration. The hydraulic pressure unit consists ofa positive displacement pump, an oil tank and an air-accumulator.

In contrast to existing lift control technology in electro-hydraulic valve systems in which the desired valve lift isachieved by precisely controlling the high pressure solenoidvalve (HPSV), in the proposed mechanism, the desired valvelift is achieved only by controlling the pump speed, and thesolenoid valves are only responsible for controlling theengine valves opening/closing timings. As shown in Figure 1,the hydraulic pump is driven by a gearbox mechanism withtwo inputs: one from the engine and one from the variablespeed electric motor. A transmission mechanism such as beltor chain is employed to transfer the power from the enginecrankshaft to the gearbox; thus, at zero electric motor speed,the pump to engine speed ratio (rpe) remains constant at alloperating conditions. This ratio is chosen such that themaximum required engine valve lift (liftmax≈10mm) can beobtained at every engine speed. In the positive displacementpump, the hydraulic pump flowrate (Qpump) is determined asfollows:

(1)

where, Npump and Vdisp are the pump speed and displacementvolume, respectively. Considering that the engine valveoperating speed is half of the engine speed, the requiredpump flowrate to achieve the maximum required lift (liftmax)can be determined as follows:

(2)

where, Ap and Nengine are engine valve actuator piston areaand engine speed, respectively. Therefore, equating theequations (1) and (2), the desired rpe at zero electric motorspeed is determined according to the following equation:

(3)

Using the proposed mechanism, at zero electric motor speed,the engine valve lift is as high as the maximum requiredvalve lift (liftmax); however, as the electric motor startsrotating, the pump speed will be a function of both crankshaftand electric motor speeds. As the pump speed deviates fromits original speed, the pump output flowrate is varied, whichconsequently, alters the engine valve lift. Hence, using thismechanism, the engine valve lift can be flexibly changed at

every operating condition. Moreover, in the case of havingleakage in the system (eg. pump internal leakage), the electricmotor can increase the pump speed to compensate for theleaked flow.

An air accumulator is used to reduce the supply pressurefluctuations and at the same time store the pump energy whilethe engine valve is standstill and there is no flow through thehigh pressure solenoid valve. The restored energy in the airaccumulator can be reused again during the subsequentengine cycle and this could reduce the system powerconsumption considerably.

SYSTEM MODELING IN AMESIMTo study the performance of the proposed lift controlmechanism for a conventional electro-hydraulic valvetrain,the system described in the previous section is modeled usingAMESim8.b© software. As shown in Figure 2, the modelconsists of several sub-models: engine, positive displacementpump, engine valve actuator, air accumulator, HP and LPsolenoid valves, valve timing controller and lift controller.

Figure 2. AMESim model of the electro-hydraulic valvesystem with the proposed lift controller

In this model, it is assumed that the electric motor is fastenough and the pump can easily follows the pump speedsignal commanded by the lift controller. Therefore, for thesake of model simplification, the dynamics of the electricmotor and gearbox is neglected. The HPSV and LPSV aremodeled with two solenoid operated two-position, two-porthydraulic valves. A second order lag is also employed asfollows to model the solenoid valve dynamics:

(4)where, ω, ζ and Asv,max are solenoid valve bandwidth,damping ratio and maximum port area respectively. uHPSVand uLPSV are control signals from timing controller to HPSVand LPSV.

Figure 1. The schematic drawing of the proposed valve lift control mechanism

The timing controller is a simple digital controller whichswitches the HP and LP solenoid valves based on thecrankshaft angular position and desired engine valve openingand closing timings.

(5)

where, θ, θopening and θclosing are crankshaft angular position,desired engine valve opening and closing respectively.

The valve actuator is also modeled with a single-actingspring-assistance hydraulic actuator. For the sake ofsimplicity, the engine valve and hydraulic piston masses arelumped into a single linear mass. Due to the large heattransfer from the accumulator casing to the ambient, the aircompression and expansion processes in the accumulator areconsidered as isothermal processes (PV=P0V0). The liftcontroller will be discussed later in this paper. The modelparameters are set based on the existing experimental setupspecifications and are given in Table 1.

Table 1. Simulation parameters

SYSTEM AVERAGE MODELIn controlling the valve lift in variable valve systems, the aimis to achieve the desired maximum valve lift at each cyclerather than tracking a desired valve trajectory within eachcycle. Therefore, it is more valuable if an average model ofthe system correlating the maximum valve lift to the controlinputs is developed. To this end, an average model of thesystem is proposed based on the system energy conservation.Assuming a steady-state steady-flow condition, the powerproduced by the hydraulic pump is either reserved in the air

accumulator or used to power the valve-system. Therefore,the energy conservation equation for the studied system couldbe written as below:

(6)

Assuming that the hydraulic energy transferred to the valvesystem is dedicated to compress the returning spring and alsoovercome the friction forces, the total energy consumed bythe valve system within each cycle could be determined asfollows:

(7)

In the four-stroke internal combustion engine with the enginespeed of Nengine, the engine cycle duration is (120/Nengine).Thus, the average power consumption of the engine valvesystem can be approximated as follows:

(8)

In the above equation, the effects of stiction and viscousfriction are neglected and it is assumed that the dominantfriction in the hydraulic cylinder is of Coulomb type and isconstant. The pump power consumption can be determinedbased on the following equation:

(9)

where,

(10)

Assuming isothermal air compression and expansionprocesses (PVair=constant) in the accumulator, the rate ofenergy storing in the air accumulator could be approximatedas follows:

(11)

Substituting Eq. (8), (9), (10), (11) in Eq.(6):

(12)

The average oil flowrate into the engine valve actuatorcylinder can be approximated as follows:

(13)

Also,

(14)

Therefore, the average engine valve lift can be determined byequating (13) and (14):

(15)

Although the valve lift can be estimated based on the aboveequation, the rate of engine valve lift variation is still neededfor the lift controller design. Substituting (15) in (12) andarranging the final equation for V̇air, following differentialequation is obtained for the rate of change of air-accumulatorgas volume with respect to time:

(16)

Moreover, by substituting (13) in (14), following dynamics isalso achieved for the air-accumulator gas volume:

(17)

Differentiating (16) and (17), and equating them, thefollowing first order differential equation is obtained for theengine valve lift:

(18)

Considering Qpump as the control input u, the system modelcan be written in the following controllable form:

(19)

where,

(20)

(21)

LIFT CONTROLLER DESIGNThe objective of the lift controller is to control the pumpspeed such that the desired valve lift is achieved at differentoperating conditions. Figure 3 illustrates the operation of theproposed control strategy. As shown in this figure, the enginevalve displacement and hydraulic supply pressure aremeasured by displacement and pressure transducer. The valvelift at each engine cycle is then determined using themeasured valve displacement within each cycle. Since thedesigned controller is based on the mean-value-model of thesystem, the average supply pressure should be used as thefeedback signal to the controller. Therefore, a low-pass filteris employed to reject the high frequency components of thesignal coming from the pressure transducer. The determinedengine valve lift along with average upstream pressure andengine speed are then employed by the controller at everycycle to calculate the required hydraulic pump speed.

Figure 3. The proposed control strategy flowchart

Several control techniques could be applied for the abovemechanism; however due to severe non-linearities whichexist in the discussed mechanism, the non-linear sliding modecontrol could be best fitted model among different controltechniques. The sliding mode control (SMC) is one of themost powerful and robust tools in controlling systems withsevere non-linearities [9],[10]. Here in this paper, the slidingmode controller is designed based on the average model ofthe system derived in the previous section. The slidingsurface is defined as follows::

(22)

Where,

(23)

Therefore, the control problem is equivalent to that ofreaching and remaining on the surface

. In fact, at S≡0 the equation (22)becomes a linear differential equation whose unique solutionis e=0 [11][10]. The next step is to find a control law suchthat it not only guarantees that the system convergences to thesliding surface but also it keeps the system on the slidingsurface after reaching condition is satisfied. Based on theFilippov's equivalent dynamics [11], the following controllaw avoids the system diverging from the sliding surface:

(24)

However, the equivalent control law does not guarantee theconvergence to the sliding surface when the system is faraway from the surface. Hence, a feedback control term ufb =−ksign(S) is introduced to assure the Lyapunov stability.Thus, the final control law consists of both equivalent andfeedback terms and can be written as follows:

(25)

In the above control law k and λ are the controller gains andmust be tuned to optimize the system response. The stabilityof the above controller was already studied by severalresearchers [10],[11]. In the conventional SMC control law,the signum function results in severe chattering problem. Tosolve this problem, a sliding mode control with boundarylayer formulation can be employed. In this method, thesliding surface is replaced with the boundary layer with thethickness of ε [11]:

(26)

The signum function is also replaced with the saturationfunction as below:

(27)

Therefore, the required hydraulic pump flowrate for thedesired valve lift is determined as follows:

(28)

Substituting equation (10) in equation(28), the required pumpspeed is calculated as follows:

(29)

It is also possible to include the hydraulic power unit (pump,driver and gearbox) response characteristics in the controllerdesign. To this end, the relation between the actual pumpspeed (Npump) and the commanded signal (Npump Commanded)is shown using a first order transfer function as follows:

(30)

Where, τ is the response time of the hydraulic power unit.Therefore, based on the required pump speed, thecommanded pump signal is determined as follows:

(31)

Substituting equation (29) in the above equation, thecommanded pump speed must be calculated as follows:

(32)

In this paper, to reduce the computational cost, it is assumedthat the hydraulic unit is fast enough to follow thecommanded pump speed signal without any delay (τ ≈ 0).

As shown in Figure 4, the designed controller is modeled inSimulink7.2© and is coupled with the hydraulic model inAMESim8.b©. Using the AMESim/Simulink interface shownin Figure 2, both numerical models are synchronized and runsimultaneously.

Figure 4. AMESim/Simulink interface

EXPERIMENTAL SETUPThe experimental setup consists of a hydraulic pressure unitand a valve actuation system. The valve actuation systemconsists of two spool valves (HPSV and LPSV), a hydrauliccylinder acting as engine valve actuator and a displacementtransducer. When the HPSV opens, the high pressure oilflows into the hydraulic cylinder pushing the hydraulic pistondownward and it opens the engine valve. The engine valveremains open until the LPSV opens. At this time, the trappedoil in the hydraulic cylinder is discharged through the LPSVport and it drains to the tank. A separate controller isresponsible for spool valves ports opening and closing. Thiscontroller is programmed such that the engine valve isopened at 0 CA° and it is closed at 200 CA°. To this end, theHPSV is opened at 0 CA° and it is closed at 100 CA° and theLPSV is opened at 100 CA° and it is closed at 200 CA°. Theengine valve actuator is a single-acting hydraulic cylinder(Mack Corporation) equipped with a return spring. Theengine valve actuator shaft is connected to a displacementtransducer (Novo Technik) with 0-10 Vdc output signal forlift measurement. The transducer is an analoguepotentiometer with accuracy of 50µm and bandwidth of 10kHz.

The hydraulic pressure unit consists of a positivedisplacement pump (gear pump), an oil tank, an air-

accumulator and a pressure transducer. In this experiment,instead of a two-input gearbox, the pump is connected to asynchronous electric motor. Because the speed of thesynchronous motor is a determined by the number of polesand line frequency, therefore its speed can be varied bychanging the line frequency. To this end, a variable frequencydrive (AC Tech, MC series) is employed to precisely controlthe line frequency.

A modular control system with embedded PC (Beckhoff CPUmodule) is used to communicate and control the system. TheTwinCAT PLC run-time programmed in Structured-Textlanguage is used as the control software.

Figure 5. Experimental Setup

RESULTS AND DISCUSSIONa) Single-Valve Mechanism ControllabilityAs discussed in the previous section, regardless of the valvelift, the input signal to the valve actuation system iscontrolled such that the engine valve opening (VO) andclosing (VC) timings of 0 and 120 CA° are achieved at alloperating conditions. Figure 6 shows the measured valvedisplacement for 75 engine cycles and varying referencevalve lift. As shown in this figure, there are deviations ofabout ±10% between the engine valve timings and thecommanded signal (VO≈0 CA°, VC≈120 CA°). Thecontroller's processor speed, spool valves response time andsampling limitation are the major factors for these errors. Inthis paper, because the focus is on the lift controller, therewas a little attention to the precise timing controller.

The valve speed plot is also depicted in Figure 6. As shownin this figure, the average valve sitting velocity is less than0.1m/s in majority of the cycles. In the proposed lift controlstrategy, because the solenoid valves are only responsible forcontrolling the valve opening and closing timings, there willbe no control on the engine valve landing velocity; however,the valve sitting velocity can be controlled using othermechanisms such as hydraulic cushioning. Controlling thevalve sitting speed is not in the scope of this paper.

The lift control law achieved in the previous section is firstsimulated in Simulink and its performance is evaluatednumerically using Simulink/AMESim interface. Thecontroller parameters (κ, λ, ε) are tuned based on the systemresponse and are given in Table 2. The Beckhoff PLCcontroller is then programmed with the obtained law and theexperimental setup is run while the reference engine valve liftis changed arbitrary between 5 and 9mm.

Table 2. Controller parameters

The measured engine valve lift and the commanded pumpspeed signal are recorded for almost 55 seconds. Figure 7 andFigure 8 depict the performance of the designed lift controllerthrough simulation and the empirical results. As shown inthese figures, using the designed lift control system, it ispossible to follow the desired trajectory mostly with 1 mmtracking error. Moreover, the experimental results show muchbetter tracking performance than the simulation results. Thelarge tracking error between the 0s and 2s is due to the lowaccumulator pressure during the system start-up (Figure 9).However in the real situation, this problem can be solved bypressurizing the accumulator to a certain pressure just beforethe engine start-up. Besides, there are some other error spikes

during abrupt changes in the reference engine valve lift whichare due to system response time. In this mechanism, the gasdynamics in the air-accumulator is the major cause of thesystem delay.

Figure 7. Controlled engine valve lift (simulation andexperiment) at constant engine speed (1000 rpm) and

varying reference lift

Figure 6. Measured engine valve displacement and velocity at 1000 rpm engine speed for 75 engine cycles and differentcommanded valve lifts (experiment)

Figure 8. Lift controller tracking errors for simulationand experiment (Engine Speed: 1000 rpm)

Figure 9. System upstream pressure during constantengine speed (1000rpm) and different engine valve lift

Figure 10. Commanded pump speed signal and internalleakage flowrate at constant engine speed (1000 rpm)

and varying reference valve lift

Figure 10 (left axis) presents the commanded pump speedsignals in both simulation and experiment. As shown in thisfigure, for similar reference valve lift signals and mechanismspecifications, the commanded pump speed in the experimentis more than twice that in the simulation. This is due to theinternal pump leakage resulted from the clearances that existbetween the pump gears. As shown in Figure 10 (right axis),the amount of leaked flow is proportional to the pumppressure and therefore it can be modeled as the orifice with aconstant opening area of about 0.32mm2 with dischargecoefficient of 0.7. This in fact reduces the model uncertaintiesand increases the controller robustness.

As mentioned before, one of the significances of the valve liftcontroller in electro-hydraulic valvetrain is to keep a constantengine valve lift during varying engine speeds. As shown inFigure 11, the designed controller can maintain the desiredvalve lift with almost 1mm error while the engine speedvaries between 1000-3000rpm.

Figure 11. Controlled engine valve lift and commandedpump signal at varying engine speed and constant

reference lift

b) Mechanism Sensitivity and Robustnessin Multi-Cylinder EngineBeside the controllability of the proposed mechanism, itsrobustness should be also studied when the mechanism isextended for multi-cylinder engine. In fact, when the systemis used for several engine valves, a specific upstream pressurewhich leads to a certain amount of lift in one engine valvemay lead to a different lift in another one due to unavoidabledifferences exist between two set of valves. Thedissimilarities in the valves return spring rates (due tomanufacturing repeatability errors) and engine cylinderspressures are the two major sources of these differences.Because, the engine cylinder pressure is much higher duringthe exhaust process compared with the intake process, it isnecessary to use two separate hydraulic lines for the intakeand exhaust valves. This eliminates the lift variations caused

by different cylinder pressures during intake and exhaustprocesses to some extent; however the problem still remainsdue to slight variation in the amount gas forces acted on eachexhaust valve in different cylinders and also cycle-to-cyclevariations in the exhaust gas pressure at every enginecylinder. To study these effects, a sensitivity analysis isperformed for different cases. For each engine valveincluding intake or exhaust valve, the following system ofequations can be written:

(33)

Where, x, β, Pact, Fcyl, Vact,0, ρ, Cd and Q are valvedisplacement, hydraulic fluid bulk modulus, hydrauliccylinder pressure, engine cylinder gas force, hydrauliccylinder dead volume, oil density, spool valve dischargecoefficient and HPSV discharge coefficient respectively.Assuming a certain amount of accumulator pressure (P=53.5bar) and a constant HPSV opening duration (≈ 6ms), 10mmvalve lift (xmax= 10mm) is achieved for the valve with thespecification listed in Table 1 and engine cylinder gas forceof 200N. However, with the same amount of accumulatorpressure, different values of engine valve lift (xmax) may beachieved as the valve spring rate (and consequently springpreload) or the engine cylinder pressure varies. Figure 12shows the sensitivity of the proposed mechanism to 10%variability in the valves spring stiffness and also 10%inconsistency in the engine cylinders gas pressures during gasexchange process. The results show the maximum deviationof ±9% in the final valve lift. This variation could be furtherminimized by increasing the spring preload or actuator pistonarea.

Figure 12. Effects of variation in valve spring rate andcylinder gas force on the final valve lift

SUMMARY/CONCLUSIONSA new lift control technique for electro-hydraulic valvetrainswas proposed in this paper. Based on this method, the enginevalve lift is controlled by adjusting the hydraulic pump speedusing a two-input gearbox. An average model of the systemwas developed based on the energy conservation equation ofthe complete system. This model was then used to design anon-linear sliding mode control law and a boundary layerapproach was also employed to reduce the control signalchattering. The complete hydraulic model of the system andthe designed controller were simulated in AMESim andSimulink respectively. Using AMESim/Simulink interface,both models were coupled and run simultaneously fordifferent operating conditions to examine the performance ofthe proposed lift control technique. The designed controllerwas also implemented experimentally and the empiricalresults were compared with those obtained from thesimulation. The results showed that by using the proposedstrategy, tracking error of less than 1 mm is achievable atmost times. Finally, the sensitivity of the proposedmechanism in the multi-cylinders engine application wasstudied. By direct comparison between the proposed liftcontrol technique and the existing technologies, followingconclusion can be made:

• In contrast to the exiting lift control approach, the proposedtechnique is not efficient when the desired valve lift variessignificantly from one engine cycle to another (modetransition operation e.g. SI to HCCI and throttle tip-in).However, in the normal engine operation, the optimum valvelift is determined based on the parameters such as actual anddesired output torque, exhaust gas emission and fuelconsumption. These parameters are usually measured withinfew engine cycles (not every engine cycle) and their averagevalues are used for reference valve trajectory generation.This, in fact, reduces the rate of the change in the desiredengine valve lift from one cycle to another. Moreover, thesystem sensitivity to cycle-to-cycle variation in the cylindergas force (especially during exhaust stage), could bediminished by increasing the mechanism stiffness (e.g.increasing hydraulic cylinder diameter and spring stiffnessand preload).

• By using the proposed method, the solenoid valves are onlyresponsible for engine valve timing control. Thisconsequently reduces the solenoids controller complexity andreduces the cost considerably.

• The developed technique allows the valvetrain to producemaximum lift even during higher engine speeds when theHPSV opening interval is so limited.

• In the proposed mechanism, because the lifts of all theintake or exhaust valves are controlled directly by the HPSVupstream pressure, any inconsistency between the enginevalves (e.g. hydraulic cylinder size, spring rate, springpreload or cylinder gas force) can lead to unequal valve lifts

at different cylinders (about 9% variability for 10%dissimilarity in the valves spring rates and cylinders gasforces).

• The mechanism sensitivity to external disturbances such ascycle-to-cycle variation in cylinder gas forces could bereduced by increasing the mechanism stiffness (i.e. increasingthe spring stiffness, hydraulic piston area and spring preload).However, this leads to higher energy consumption whichconsequently deteriorates the mechanism performance. In thefuture, a regenerative method is introduced in which themechanism stiffness could be increased without affecting theoverall performance of the system.

• The proposed lift control method may be also useful inproviding an efficient power supply system for a hydrauliccam-based valvetrain.

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CONTACT INFORMATIONMohammad Pournazeri (PhD Candidate)University of Waterloo200 University Ave WestWaterloo, N2L 3G1, OntarioCanadampournaz@uwaterloo.ca

Amir Fazeli (PhD Candidate)University of Waterloo200 University Ave WestWaterloo, N2L 3G1, OntarioCanadaamfazeli@uwaterloo.ca

Amir khajepour (Professor)University of Waterloo200 University Ave WestWaterloo, N2L 3G1, OntarioCanadaa.khajepour@uwaterloo.ca

DEFINITIONS/ABBREVIATIONSAp

Hydraulic piston area [m3]

AsvSpool valve port opening area [m2]

Asv,maxMaximum spool valve port opening area [m2]

CA°Crank angle degree

CdSpool valve discharge coefficient

eValve lift tracking error [m]

EaccumulatorHydraulic energy stored in the accumulator [J]

EpumpPump hydraulic energy [J]

EsystemValve system energy consumption [J]

FcylEngine cylinder gas force [N]

FfrictionHydraulic piston friction [N]

FpreloadSpring preload at zero valve displacement [N]

HPSVHigh pressure spool valve

kSMC controller gain

KspringSpring stiffness [N/m]

LPSVLow pressure spool valve

NengineEngine speed [rpm]

NPumpHydraulic pump speed [rpm]

PHydraulic supply pressure [Pa]

PatmAtmospheric pressure [Pa]

PactHydraulic cylinder pressure [Pa]

P0Initial accumulator pressure [Pa]

QpumpPump flowrate [m3/s]

rpepump to crankshaft speed ratio

SSliding Surface

SMCSliding Mode Controller

uControl signal to the pump

uHPSVControl signal to high pressure spool valve

uLPSVControl signal to low pressure spool valve

Vact,0Hydraulic cylinder dead volume [m3]

VairAir volume in the accumulator [m3]

VdispHydraulic pump displacement volume [m3/rev]

V0Initial accumulator gas volume [m3]

xEngine valve displacement [m]

xmaxEngine valve lift [m]

xmax,dReference engine valve lift [m]

εBoundary layer thickness [m]

ζSpool valve actuator damping ratio

θCrankshaft angular position [0-720°]

θopeningEngine valve opening angle [CA°]

θclosingEngine valve closing angle [CA°]

βHydraulic fluid bulk modulus [Pa]

λSliding surface slope

ρHydraulic fluid density [kg/m3]

ωSpool valve actuator bandwidth

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