electro-pneumatic exhaust valve modeling and control for ... · hydraulic, and electro-pneumatic...

Proceedings of ICES 2008ASME 2008 International Combustion Engine Spring Technical Conference

April 27-30, 2008, Chicago, IL, USA

ABSTRAVaria

gines is c

.

Proceedings of the ASME Internal Combustion Engine Division 2008 Spring Technical Conference ICES2008

April 27-30, 2008, Chicago, Illinois, USA

Downloaded From

ICES2008-1653

ELECTRO-PNEUMATIC EXHAUST VALVE MODELING AND CONTROL FOR ANINTERNAL COMBUSTION ENGINE

Jia Ma, Guoming Zhu, Tom Stuecken, Andrew Hartsig, Harold SchockDepartment of Mechanical Engineering

Michigan State University

CT and control flame speed by manipulating in-cylinder turbulence
ble valve actuation of Internal Combustion (IC) en-apable of significantly improving their performance.
Exhaust valve timing and lift control makes it possible to vary theamount of Residual Gas Recirculation (RGR) and control valveoverlap when combined with intake valve control. Variable valve

1

It can be divided into two main categories: variable valve tim-ing with cam shaft(s) and camless valve actuation. For camlessvalve actuation, research has been centered in electro-magnetic,electro-hydraulic, and electro-pneumatic valve actuators. Thisresearch studies the control of the electro-pneumatic valve actu-ator. The modeling and control of intake valves for the Electro-Pneumatic Valve Actuators (EPVA) was shown in early publi-cations and this paper extends the EPVA modeling and controldevelopment to exhaust valves for the lift control which is thekey to the exhaust valve control since an accurate and repeatablelift control guarantees a satisfactory valve closing timing control.Note that exhaust valve closing timing is a key parameter for con-trolling engine residual gas recirculation. The exhaust valve liftcontrol challenge is the disturbance from the randomly varyingin-cylinder pressure against which the exhaust valve opens. Thedeveloped strategy utilizes model based predictive techniques toovercome this disturbance. This exhaust valve lift control al-gorithm was validated on a 5.4 Liter 3 valve V8 engine headwith a pressurized chamber to imitate the in-cylinder pressure.The experimental results demonstrated that the exhaust valve lifttracked the step reference in one cycle with the lift error under1mm and the steady state lift error was kept below 1mm.

1 INTRODUCTIONVariable intake valve timing and lift can be used to optimize

engine performance over a wide operating range, for instance,to reduce engine pumping losses, deactivate selected cylinder(s),

: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: ht

timing and lift control is also a key technology for HCCI (Ho-mogenous Charge Compression Ignition) combustion control.

Variable valve actuation can be achieved with mechani-cal (cam-based), electro-magnetic (electric mechanical), electro-hydraulic, and electro-pneumatic valvetrain mechanisms. Thecam based variable valve actuation is able to provide either amultiple stepping or a continuously changing valve timing phaseshift (see [1], [2] and [3]). Infinitely variable valvetrain, of-ten referred to as camless valvetrain, includes electro-magnetic([4], [5], [6], [7], and [8]), electro-hydraulic ([9], [10] and [11]),and electro-pneumatic actuation ([12]). The electro-pneumaticvalve actuator (EPVA) utilizes the supplied air pressure to actu-ate either the intake or exhaust valve by electronically control-ling solenoids that regulate the motion of the actuator’s piston.For both electro-hydraulic and electro-pneumatic valves, there isa potential issue of having a repeatable valve lift over the life ofan engine.

Valve lift control for electro-hydraulic valvetrain actuation([22]) has been investigated by a number of researchers. Adap-tive peak lift control was presented in [16], and digital valve tech-nology was applied to control of an hydraulic valve actuator in[18]. The modeling and control of intake valves for the electro-pneumatic valve actuators were shown in [12], [13] and [14].Model-based control scheme has been used to regulate the cylin-der air charge of a camless multi-cylinder engine for throttlelessoperations (see [19]).

Unlike the intake valve, the exhaust valve opens against an

Copyright c© 2008 by ASME

tp://www.asme.org/about-asme/terms-of-use

in-cylinder pressure that varies as a function of the engine opera-tional conditions with cycle-to-cycle combustion variations. Thispressure disturbance slows down the valve actuator response andas a result, it increases the variation of valve opening delay. In

cycle variations. This in-cylinder pressure produces a force onthe face of the exhaust valve that affects the valve dynamics. Thisin-cylinder pressure is modeled and integrated with the exhaust

2

Down

fact, this disturbance makes it difficult to maintain repeatablevalve opening timing and lift. As a result, unrepeatable valvelift affects the closing timing control which is critical for RGRcontrol. Therefore, this work addresses exhaust valve lift con-trol.

A mathematical in-cylinder pressure model during exhaustvalve opening period was developed and integrated with theexhaust valve dynamic model for control development. Thethermodynamics data was obtained using WAVET M simulations(www.ricardo.com). The WAVET M model was calibrated andvalidated using experimental in-cylinder pressure data. Themathematical in-cylinder pressure model is then used to developthe model based predictive control scheme for exhaust valve liftcontrol. In this paper, the model-based predictive control schemeis used to predict the control required to reach desired valve liftunder varying exhaust pressure. This is the key to achieve accu-rate valve lift control since the valve control signal needs to besent to actuator solenoid before the valve reaches its desired liftdue to solenoid electro-magnetic delay. The controller consistsof two parts: feedforward and closed loop controls. The feedfor-ward control is used to provide a nominal lift control based uponthe predicted valve opening trajectory, while the closed loop con-troller is used to minimize the mean control error. The closed-loop control strategy was developed and verified in simulationusing the combined mathematical model of exhaust valve and in-cylinder pressure, and then, demonstrated on a 5.4 Liter 3 valveV8 engine head with a pressurized chamber.

The paper is organized as follows. First, an exhaust valvedynamic model is presented in Section 2. Next, the feedforwardand closed loop control strategies are described in Section 3.Third, the experimental validation results are shown in Section4, and finally, conclusions are drawn.

2 EXHAUST VALVE DYNAMIC MODELA physics based nonlinear model, called a level one model,

was built component-by-component based upon the flow andfluid dynamics. The details of the level one model and its ver-ification can be found in [12]. This model provides an insight tothe operation of the pneumatic/hydraulic mechanical actuationsystem. A piecewise linearized level two model was then cre-ated based on the level one model to reduce the computationalthroughput for control system development purpose. The detailsof the level two model are described in [13]. The level two modelwas used as the actuator model for the intake valve in the pre-vious studies (see [13] and [14]). In this study, it is used forthe exhaust valve actuator modeling. The exhaust valve opensagainst an in-cylinder combustion pressure with certain cycle-to-

loaded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: h

valve actuator model to capture the exhaust valve dynamics.

(X(tp)=Xmax, X(tp)=0)

(X=X , X=X)

Dt1 Dt2

Fa

x

time

S1: solenoid #1

S2: solenoid #2

Dt1: solenoid #1 turn-on delay

Dt2: solenoid #2 turn-on delay

Dt3: solenoid #1 and #2 turn-off delay

time

S1 S2

1

2

3

45

td

tp

Kalman Filter

Initial

Condition

Prediction

Peak Displacement

Calculation

(X=0 , X=0)

12 v

0

6

Dt3

(X(td)=X0 , X(td)=v0)

89

7

d1 d2

d1

0: solenoid #1 activated

1: air pressure force on

and valve opens

2: solenoid #2 activated

3: air pressure force off

4: valve peak displacement

5: solenoid #1 and #2 deactivated

6: valve returns without resistance

7: valve returns against

cmpressed residual air

8: hydraulic damper activation

9: valve closes

open closedwellI II III

Figure 1. Valve lift profile with the solenoid command chart

The system dynamics illustrated here focuses on the rela-tionship between the solenoid control commands and the exhaustvalve displacement. It follows the same analysis as that of thelevel two model. As shown in Figure 1, the valve response canbe divided into three stages. They are the opening stage (I), dwellstage (II), and closing stage (III). Solenoid #1 is activated at point0 first. It induces a high air pressure force to push the valve openat point 1 after ∆t1. Solenoid #2 is then activated (point 2) witha time lag δ1. It removes this air pressure force ∆t2 time aftersolenoid #2 is activated (point #3). Note that the interplay be-tween two solenoids results in a pulse force input to the actuatorvalve piston with pulse width δ1. Note that this pulse width isproportional to the valve lift. Now, with zero input, the valvemovement continues until it reaches its peak lift at point #4, thevalve equilibrium. This ends the open stage. Next, the valve en-ters the dwell stage where it is held open by a hydraulic latchmechanism. At the end of the dwell stage, solenoid #1 is de-activated at point #5. After ∆t3 time, the valve starts to return(point #6). The close stage starts at point #6 and ends at point #9where the valve is considered closed. The returning duration isδ2 between these two points.

The two solenoids have electro-mechanical delays after theiractivation and de-activation (see Figure 1). ∆t1 is defined as thedelays for solenoid #1 at activation. ∆t2 is defined as solenoid#2 delay at activation. The de-activation delay for both solenoidsare ∆t3. The solenoid commands direct the valve motion afterthe delays. The time lag applied between the activation of twosolenoids is denoted as δ1. This differs from the time lag betweentwo delayed solenoid activations which is denoted as δ1 since two


ttp://www.asme.org/about-asme/terms-of-use

solenoid delays, ∆t1 and ∆t2, are not equal. The exhaust valvelift control algorithm is to determine when to activate solenoid#2 during exhaust valve opening for each engine cycle with the

control formulation process are gauge pressure in this article.

Mx+C f x+Kp(x+δp) = Fa(t)−Fb(x) (1){

Down

varying in-cylinder pressure at the surface of the valve and itsactivation delay in presence. It is impossible to remove the inputforce Fa instantly upon the activation of solenoid #2 due to itsactivation delay. An model based predictive lift control algorithmis developed to make this possible. The details are described inthe control strategy section.

The exhaust valve closing timing control requires knowl-edge of δ2, the amount of time that the valve takes to close. Toguarantee the exhaust valve closing at the desired time requiresde-activating solenoid #1 by time δ2 before exhaust valve clos-ing. δ2 can be predetermined from the different valve lift setpoints. In other words, the closing timing control relies on a re-peatable valve lift control. Developing a lift control system is theprimary emphasis of work described in this paper.

The opening stage exhaust valve actuator model and the in-cylinder pressure model are employed to formulate the modelbased predictive lift control scheme. In order to validate the ex-haust valve lift control algorithm, the level two model integratedwith the in-cylinder pressure model is used as a plant model insimulation. The opening stage exhaust valve actuator model andthe in-cylinder pressure model are introduced in the followingtwo subsections.

2.1 Actuator ModelThe opening stage exhaust actuator model with the in-

cylinder pressure as external disturbance is studied in this sub-section. This model is expanded based on the level two model[13] to include the in-cylinder pressure dynamics. Figure 2

piston

oil

outlet port inlet port

CfKp

pMspring

Mvalve

Psupply

Ain

Aout

x

Fa

Poil

Fb(x)

Figure 2. Actuator piston model

shows the schematic diagram of a single actuating piston for thissystem. At the opening stage, the valve actuator is modeled asa second order mass-spring-damper system with zero initial con-ditions, see Equation (1). All pressures used in modeling and

3

loaded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: htt

Fa(t) = F(t)−F(t−δ1),F(t) = 0, t < 0ApPp, t ≥ 0 (2)

where, Pp is supply air pressure; Fb(x) is the in-cylinder pres-sure force applied at the exhaust valve surface; M is the sum ofequivalent mass of actuator piston, effective valve spring mass,exhaust valve and cap; Ap is the sum of actuator piston and oilpassage areas; C f is the damping ratio approximating energy dis-sipation due to flow loss and frictional loss; Kp and δp are thestiffness and preload displacement of the valve spring respec-tively; δ1 is the lag between the activation of solenoids #1 and #2after solenoid delays as shown in Figure 1.

2.2 In-cylinder Pressure ModelThe in-cylinder pressure force Fb(x) needs to be modeled

and evaluated in Equation (1). Figure 3 illustrates the dynamicsin the combustion chamber with an exhaust valve. A control vol-ume is drawn above the piston, where mcyl , Tcyl and Pcyl are themass, temperature and pressure inside the combustion cylinder.Acyl is the engine piston area. mex is the mass flow rate at the exitwhen the exhaust valve opens. Tatm and Patm are the atmospherictemperature and pressure. x and y are the exhaust valve displace-ment and cylinder piston displacement respectively. The mass

y

x

valve

cylinder piston

Tcyl Pcyl Acyl

Tatm

Patmmex

C.V.

mcyl

Figure 3. In-cylinder pressure model

flow rate equations at the exit are written for both choked andunchoked flow cases through Equations (3) to (5) following theirderivation in [16].

mex = Cdex γPcylAex(x)

√k

RTcyl, Aex = 2πrvalvex, (3)


p://www.asme.org/about-asme/terms-of-use

where, Aex is the flow area with rvalve being the valve radius; Cdex

is the flow coefficient at the exit; R is the residual gas constant.Cp and Cv are the specific heat of the residual gas at constant

Cp

Therefore, Fb(x) can be expressed in Equation (9) below.

F (x) = P A , (9)

Down

pressure and constant volume respectively; and k = Cv. When

Pcyl ≥ ( k+12 )

kk−1 Patm, the flow is choked at the exit. In this case,

γ is shown in Equation (4)

γ =

√(

2k +1

)k+1k−1 . (4)

When Pcyl ≤ ( k+12 )

kk−1 Patm, the flow is unchoked and γ is ex-

pressed in Equation (5).

γ =

√2

k−1(

Patm

Pcyl)

k+12k [(

Patm

Pcyl)

1−kk −1]. (5)

The mass of the residual gas inside the combustion cylinder inEquation (6) can be obtained by integrating the calculated massflow rate. The initial mass m0 is derived using ideal gas law,where P0, V0, R0 and Tcyl0 are the initial in-cylinder gas pres-sure, volume, gas constant and temperature at the exhaust valveopening.

mcyl =−∫ t

0mexdt +m0, m0 =

P0V0

RTcyl0. (6)

Using the ideal gas law again with the obtained mcyl results in anexpression of in-cylinder pressure as shown in Equation (7).

Pcyl =mcylRTcyl

Vcyl, Vcyl = Acyly, (7)

where, k, R and Tcyl are variables acquired from the WAVET M

simulation with the same engine configuration and parameters;and y is the piston displacement derived from the engine geome-try in Equation (8).

y = r[1+Lr− cos(θ)−

√Lr− sin2(θ)], (8)

where

- Acyl = π( 12 ×bore)2 = 0.0401m2 (bore = 90.2mm) ,

- L is the connecting rod length (L = 169.2mm),- r is the crank shaft radius (r = 1

2 stroke = 52.9mm),- θ is the engine crank angle.

4


b cyl valve

where Pcyl is defined in Equation (7).

2.3 In-cylinder Pressure Model ValidationThe in-cylinder pressure force Fb is a function of the exhaust

valve displacement since the flow out area Aex is a function of theexhaust valve displacement.

0

1

2

3x 10

6

Measured and modeled cylinder pressure with cam profile at 1500RPM

Pcam

an

d P

cyl (

Pa

)

1 2 30

0.005

0.01

cycle

ca

m p

rofi

le (

m)

Cam profile

windowmodel pressuremeasured pressure

Figure 4. In-cylinder pressure model validation by simulation

In order to validate the in-cylinder pressure model, combus-tion experiments were conducted using a 5.4L 3 valve V8 en-gine with in-cylinder pressure measurement and a conventionalcam shaft at 1500RPM. The pressure model was simulated us-ing the conventional cam profile as the valve displacement input.The modeled in-cylinder pressure was then compared with themeasured in-cylinder pressure as shown in Figure 4. The topdiagram of this figure shows the modeled pressure (solid line)in the rectangular windows and measured in-cylinder pressure(dash line). The bottom diagram shows the exhaust cam profileused in the simulation and experiments. The in-cylinder pres-sure model is then integrated into the pneumatic exhaust valvemodel and the responses are shown in Figure 5. Here, the pres-sure model uses the EPVA valve lift profile to calculate the corre-sponding in-cylinder pressure. The modeled pressure (solid linein top diagram) and the associated EPVA valve lift profile (solidline in bottom diagram) are compared with the experiment pres-sure (dash line) and the cam profile (dash line). The simulationresults demonstrated that the in-cylinder pressure reduces ratherquickly with the EPVA exhaust valve actuation since the EPVAvalve opens much faster than the conventional cam based valve.



This simulated in-cylinder pressure is used to construct the con-trol signals. The exhaust valve model is used as a plant modeland it is integrated with the in-cylinder pressure model in simula-

4 reaches the reference maximum valve lift, point 3 is found tobe the right time to remove force Fa. If activating solenoid #2could turn off the input force Fa immediately, we would onlyneed to activate it whenever the calculated displacement of point

Downl

tions to validate the control algorithm. The modeled in-cylinderpressure is one of the two inputs to the plant (exhaust valve) andthe actuation force Fa commanded by the two solenoid controlsignals is the other input.

0

1

2

3x 10

6

Pcam a

nd

Pcyl (

Pa

)

0

0.005

0.01

xcam

CAM profile and EPVA lift profile

Pcam

Pcyl

x

xcam

an

d x

(m

)

0.05 0.07 0.140.100.06 0.08 0.110.09 0.12 0.13

time (sec)

Measured cylinder pressure with cam profile

and model cylinder pressure with EPVA lift profile at 1500RPM

Figure 5. In-cylinder pressure model integrated into exhaust valve model

3 CONTROL STRATEGYSince the in-cylinder pressure on the face of the exhaust

valve varies significantly from cycle-to-cycle, the valve lift con-trol needs to be adjusted as a function of the current in-cylinderpressure for each individual cycle. As explained in the actuatordynamics section, the exhaust actuator is modeled as a secondorder mass-spring-damper system at the opening stage. Activat-ing solenoid #1 applies the force Fa on the valve and moves theexhaust valve. Activating solenoid #2 removes the force and thevalve continues to open until it reaches the maximum displace-ment. Solenoid #2 activation timing determines the maximumvalve lift. Therefore, the key for valve lift control is to find whento activate solenoid #2. Figure 1 illustrates the idea of the ex-haust valve lift control strategy. Solenoid #1 is activated at time0. After the delay of ∆t1, the input force Fa acts on the systemand the exhaust valve starts to open at point 1. Solenoid #2 isthen activated at point 2, after ∆t2 delay, force Fa is removed atpoint 3. The valve moves further until its velocity decreases to 0at point 4. The second order valve system response from points3 to 4 can be calculated with zero input and nonzero initial con-ditions at point 3. In other words, the valve peak displacement atpoint 4 can be calculated if the initial displacement and velocityat point 3 are known. Once the calculated displacement at point

5

oaded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: h

4 reaches the reference lift. But the solenoid delay requires theactivation to take place at point 2 with ∆t2 amount of time beforepoint 3. This means that if point 3 is the time to eliminate inputforce, point 2 is the time to activate solenoid #2. However, theinitial conditions at point 3, where the peak displacement of thevalve is calculated, are not yet available at point 2. Therefore,an algorithm is derived to predict initial conditions of point 3 atpoint 2. This strategy of initial condition prediction can be im-plemented as long as the delay ∆t2 of solenoid #2 is less than thelag δ1 between the activation of two solenoids. The predictivealgorithm needs to know both states, valve displacement and ve-locity, at point 2. A Kalman state estimator was used to estimatethem with minimized effect of measurement noise. Now we candetermine the time to activate solenoid #2 (point 2), which isserved as a feedforward control of the valve actuator. A propor-tional and integral (PI) scheme is used as a closed-loop feedbacklift control system to reduce the steady state lift tracking error.

The flow chart of the feedforward control scheme is shownin Figure 6. First, solenoid #1 is activated. Secondly, the Kalmanstate estimator provides the current states (valve displacementand its velocity). Finally, a model based prediction algorithmuses the estimated states to calculate the states after solenoid #2delay ∆t2, which is then used to calculate the peak valve displace-ment. If the calculated peak displacement is greater than or equalto the reference valve lift, solenoid #2 is activated, otherwise, theprocess repeats until the condition is satisfied. The details of thederivations are discussed in the following four subsections.

3.1 Peak Displacement Calculation (PDC)This section describes the solution for the peak displace-

ment at point 4 based on the initial conditions at point 3. Recallthat the governing equation of the exhaust valve at the openingstage is presented in Equation (1). The back pressure force Fb(x)equals the product of the exhaust valve area and the modeled in-cylinder pressure. The in-cylinder pressure used in the controlalgorithm development here is piece-wisely linearized accordingto the simulated in-cylinder pressure against EPVA exhaust valveprofile, where Fb(x) = px+q (p≤ 0 and q≥ 0) with

p = p1, q = q1, x≤ 0.002mp = p2, q = q2, 0.002m < x≤ 0.008m .p = p3, q = q3, x > 0.008m

Substituting Fb(x) with its linearized expression into Equa-tion (1) results in Equation (10) below.

Mx+C f x+Kpx = Fa− (px+q)−Kpδp. (10)



Feed forward exhaust valve lift control scheme in one engine cycle

Start

3.2 Model Based Initial Condition Prediction (ICP)The previous section solves for the peak displacement x(tp)

using the displacement and velocity at point 3 as initial condi-

Downlo

Activate solenoid #1

Current state estimation

using Kalman filter

Model based state prediction

for the delay of solenoid #2

Peak exhaust valve displacement

xmax calculation

xmax > xref ?

Activate solenoid #2

yes

no

End

Figure 6. Feedforward exhaust valve lift control strategy

Move term px to the left resulting in Equation (11):

Mx+C f x+(Kp + p)x = Fa−q−Kpδp. (11)

Let K = Kp + p and Fa = 0, since it is assumed that input forceFa is turned off, to obtain Equation (12) in a general format giventhe initial condition x(0) = x0, x(0) = v0.

Mx+C f x+Kx =−Q, Q = Kpδp +q. (12)

Recall that p takes three different values, p1, p2 and p3 in threevalve displacement regions. K could be either negative, zero orpositive depending on the value of p. When K is positive, Equa-tion (12) can be rewritten into Equation (13) as below:

x+2ζωnx+ω2nx =−Q

M, (13)

where ωn =√

KM and ζ = C f

2

√1

MK . In this case, the solutioncan be categorized into under damped, critically damped andover damped scenarios depending on the value damping ratio ζ,damping coefficient C f , mass M and equivalent stiffness K inEquation (13). Based upon the system dynamic equations shownin (13), the peak displacement solution can be derived for fourcases (see [15] for details). They are K > 0 with 0 < ζ < 1 (case#1), K > 0 with ζ = 1 (case #2), K > 0 with ζ > 1 (case #3) andK ≤ 0 (case #4). The initial condition denoted as x(0) = x0 andx(0) = v0 in this section are derived in the next section of modelbased initial condition prediction.

6

aded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use:

tions (Figure 1). This section derives the formulas to predict thedisplacement x(td) and velocity x(td) at point 3, given the dis-placement and velocity at point 2. The displacement and velocityat point 2 are initial conditions denoted as x(0)= x0 and x(0)= v0in this subsection. Their values are estimated by the Kalman stateestimator described in the next subsection. Solenoid #2 delay,∆t2, is the time input and Fa is a constant force input betweenpoints 2 and 3. Consider the governing equation again in Equa-tion (1). Given Fb(x) = px+q, Equation (1) becomes

Mx+C f x+Kpx = Fa− (px+q)−Kpδp. (14)

Rearrange the equation above to obtain

Mx+C f x+(Kp + p)x = Fa−q−Kpδp. (15)

Let K = Kp + p and W = q+Kpδp−Fa, Equation (15) becomesEquation (16).

Mx+C f x+Kx =−W. (16)

It is clear that Equations (12) and (16) have the same form.Previously, Equation (12) was evaluated for the maximum dis-placement given initial conditions. Now, Equation (16) is evalu-ated for the displacement and velocity in td amount of time withgiven initial conditions, where td = ∆t2 (see Figure 1). Equa-tion (16) can be solved in a similar way to Equation (12) by re-placing Q with W , and the solutions are omitted in this paper.The techniques of solving analytical solutions for a second ordermass-spring-damper system can be found in [21].

3.3 Kalman Filter State Estimation (KFE)The displacement and velocity at point 2 (see Figure 1) are

needed as initial conditions in the previous section. The systemis equipped with a displacement sensor which measures the ex-haust valve displacement. The velocity obtained through taking atime derivative of the measured displacement is unreliable due tothe measurement noise. The observer formulated in this sectionperforms the optimal estimations of both the displacement andvelocity at point 2 in the presence of noise using Kalman stateestimator (see [20]). The estimated displacement and velocityare denoted as x and ˙x respectively. The state space notation ofthe system is expressed below:

x = Ax+Bu+Gw(t)y = Cx+ v(t)


http://www.asme.org/about-asme/terms-of-use

where A =[

0 1−KM

−C fM

], B =

[01M

], CT =

[10

], x =

[x1x2

], and

G is an identity matrix; w(t) and v(t) represent the process noise

pressure model as the plant model (see [14]), where the three-segment feedforward control strategy and the closed-loop controlscheme are evaluated in sequence. In this section, the closed-

7

Down

and measurement noise. Note that u = −W is the input to thesystem, x1 = x and x2 = x are the states representing the valvedisplacement and velocity. The Kalman state estimator takes thefollowing forms:

˙x = Ax+Bu+L(y− cx)y = Cx, x(0) = 0,

where L is the observer gain acquired through solving the alge-braic Riccati Equation (17); and x is the estimated displacementx1 and velocity x2.

AP+PAT +GWpGT −PCTV−1CP = 0, (17)

L = PCTV−1,where W ≥ 0 and V > 0, (18)

where Wp and V are covariance matrices of w and v, respec-tively. If (C,A) is observable, the algebraic Riccati equation hasa unique positive definite solution P, and the estimated state xasymptotically approaches true state x.

3.4 Closed-Loop Control SchemeThe feedforward solution of solenoid #2 activation timing is

obtained by implementing the formulas from the peak displace-ment calculation, model based initial condition prediction andKalman filter state estimation subsections. This solution com-bined with the displacement error compensation from the propor-tional and integrator (PI) feedback scheme forms a closed-loopcontrol signal of solenoid #2 as illustrated in Figure 7.

Feed forward

control signal

PIPlant

model+

+-+xref xmax

Closed-loop exhaust valve lift control scheme

Figure 7. Closed-loop exhaust valve lift control scheme

4 EXPERIMENTAL IMPLEMENTATIONThe developed control algorithms was validated in simu-

lation using the combined valve actuator and the in-cylinder


loop lift control strategy was implemented in a prototype con-troller and evaluated by experiments. The feedforward lift con-trol signals were precalculated and implementation in a formof lookup tables to reduce the real-time calculation throughput.Note that both ICP and PDC calculations require only systeminitial states, and they can be precalculated to reduce realtimeprocessing throughput.

4.1 Experiment Setup4.1.1 Mechanical system configuration Experi-

ments were conducted on a 5.4L 3 valve (2 intake valves and1 exhaust valve) V8 engine head. As displayed in Figure 8, thecam and cam shaft were removed from the engine head. Threeelectro-pneumatic actuators were installed on the top of eachvalve to manage both intake and exhaust valve events. Micro-EpsilonT M point range sensors were mounted under each valveto measure the valve displacements (see Figure 9).

Figure 8. Top view of EPVA installed on the 5.4L 3V V8 engine head

To test the exhaust valve control system, a pressurized cham-ber was build and installed under the cylinder head, which imi-tates the in-cylinder pressure acting at the back of the exhaustvalve. The pressure chamber is shown in Figure 9. It waspressurized with the supplied compressed air at 4.48× 105Pa(65psi). The pressure inside chamber drops quickly when theexhaust valve opens and builds up when it closes. The exhaustlift control experiments were performed at 600RPM that is lowerenough to ensure that the chamber pressure can recover close to4.14×105Pa (60psi) at every cycle. An optical window was builtunderneath the exhaust valve on the bottom of the chamber. Theexhaust valve laser sensor sends and receives laser beam throughthis optical window to measure the exhaust valve displacement



(see Figure 9). A pressure transducer was mounted on the cylin-der head close to the exhaust valve.

CPU #1 is configured to be updated every 1ms and to execute theengine control strategy every combustion cycle. This means thatthis CPU updates input and updates analog outputs every 1ms,

Down

Figure 9. Pressure chamber under the valves

4.1.2 Control system hardware configuration Arealtime Opal-RTT M prototype control system was employed forthe EPVA exhaust valve bench tests. The system consists of:

- Two 3.2GHz CPU’s- An IEEE 1934 fire wire serial bus with the data transfer rate

at 400MHz per bit- Two 16 channel A/D and D/A boards with less than 1 µs

conversion rate- One 16 channel digital I/O board at 50 ns sampling rate

CPU#1 CPU#2

3.2GHz

engine

control

valve

control

3.2GHz

16 D

I/O

50 ns

16 ch

A/D

1 us

16 ch

D/A

2 us

16 ch

A/D

1 us

16 ch

D/A

2 us

1 ms 40 us

IEEE 1934 firewire400MHz/bit

ignition timing

fuel control

cam phaser

charge motion control

injector

Def A

Def B

valve displacement

solenoids

chamber pressure

cam position

crank angle

gate signal

(syn)

throttle position

mass air flow

manifold pressure

and temperature

coolant

temperature

air fuel ratio

UEGO

Engine Control

(Visteon)

Valve Control

(ARES)

solenoid currents

Figure 10. Modular control system configuration

Figure (10) displays the hardware configuration of the system.CPU #1 is used for engine controls and CPU #2 is dedicated tothe valve actuator (EPVA) control. An IEEE 1934 fire wire serialbus is used for communication between CPU #1 and CPU #2.

8


but calculates the engine control parameters every engine com-bustion event. The digital inputs and outputs of CPU #1 are syn-chronized with the engine crank angle with one-third crank de-gree resolution. The crank angle calculation is completed withinthe digital I/O card of CPU #1 utilizing digital inputs from camsensor, gate and crank signals from an encoder. The CPU #1digital outputs are spark pulse, fuel injection pulse, charge mo-tion control, and intake and exhaust valve timing pulses, espe-cially the pulses De f A and De f B that synchronize the valve con-trol between the engine and valve control system. The inputs ofthe 16 channel analog I/O board include ionization signal, pres-sure signal, throttle position, mass air flow rate, coolant temper-ature, manifold pressure and temperature, and air-to-fuel ratiofrom universal exhaust gas oxygen (UEGO) sensor.

The valve control CPU #2 is configured to operate at 40µssample rate, which is close to one-sixth crank degree at 600RPM.CPU #2 executes most of the valve control algorithms and gen-erates the control signals for the pneumatic valve actuators. A 16channel A/D board reads crank synchronized De f A and De f Bpulse signals from CPU #1, valve lift signal from valve lift pointrange position sensors, solenoid current signals from their drivecircuits, and supply air pressure signal. The solenoid controlpulses and the exhaust valve pressure (which is needed to cal-culate the feedforward lift control inputs in simulation) are theoutput from a 16 channel D/A board.

The solenoid driving circuit for the exhaust valve used thepeak and hold scheme to minimize the solenoid electro-magneticdelays. The total solenoid delay including the electro-magneticand mechanical delays was kept below 2ms.

4.2 Feedforward Lift Control Input CalculationThe damping ratio of the exhaust valve model at the open-

ing stage is needed in constructing the feedforward lift controlsignal using the developed model based predictive lift controlstrategy. To identify this model parameter, open loop lift controltests were conducted on the exhaust valve test bench at 600RPM.The maximum pressure at the back of exhaust valve was set tobe 4.14× 105Pa (60psi), the supply air and oil pressure was at8.28× 105Pa (120psi) and the target lift was 10mm. The valveback pressure varies randomly from cycle to cycle with the vari-ation as large as 105Pa (14.5psi). The measured valve back pres-sure was used in the exhaust valve model simulation. The lagbetween the activation of two solenoids remained unchanged inboth simulations and tests for parameter identification purpose.The experiment and simulation valve responses are displayed inFigure 11. The bottom diagram shows the model (dot line) andthe measured (solid line) valve lift profiles in five cycles. The topdiagram shows the corresponding pressure against with the ex-



haust valve opens. The damping ratio was chosen in such a waythat the model valve responses agree with the experimental valveresponses as demonstrated in this figure. The developed model

strategy is based upon a mean pressure model, the control strat-egy is demonstrated under certain cycle-to-cycle pressure varia-tions. Evaluation of this controller against cycle-to-cycle varia-

Down

0

2

4

x�05

E�� Mo�� I�� u�� p�� ch��1 2 3 4 5

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

cycl�mo��expe��C

ham

ber

pre

ssu

re (

Pa)

Va

lve

dis

pla

cem

en

t (m

)

Figure 11. Exhaust valve model identification

based predictive control strategy can be used to determine theactivating timing of the second solenoid and use this timing as afeedforward lift control input in realtime. In order to reduce real-time computational throughput, the developed strategy was usedto calculate the lag between the activation of the first and the sec-ond solenoids for different lift set points in off-line simulations toprecalculate for all possible initial conditions. In realtime appli-cations, this lag was the feedforward lift control input, combinedwith the feed back PI compensation, to form a closed-loop liftcontrol input. The measured valve back pressure in the pressur-ized chamber was piecewisely linearized and used in the feed-forward control input calculation. The measured pressure wasmultiplied by the area of the exhaust valve to obtain the pressureforce applied at the exhaust valve surface. This force was plot-ted in Figure 12 (grey curves) against the valve displacement for20 cycles. As shown in this figure, they were linearized in threesegments (solid lines) during the exhaust valve opening to ap-proximate the averaged forces. The coefficients, p1,q1, p2,q2, p3and q3, were used to construct the feedforward lift control inputthrough the model based predictive control algorithm.

¿From Figure 12 we can observe that the pressure force ap-plied to the face of exhaust valve varies between 260N and 410N.This is equivalent to that the exhaust back pressure varies be-tween 2.28× 105Pa (33.1psi) and 3.57× 105Pa (51.7psi). Thecontrol strategy was developed based upon the averaged exhaustpressure profile, but the experimental validation using the pres-surized chamber simulates a variable in-cylinder pressure, thatthe exhaust valve opens against, between 2.28×105Pa (33.1psi)and 3.57× 105Pa (51.7psi). Therefore, even though the control

9

loaded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: ht

tion is going to be part of our future study.Simulations were performed to determine the lags between

the activation of two solenoids according to the given referencelifts. The exhaust valve model was identified earlier and used asthe plant in the simulations. The measured back pressure duringexhaust valve opening was used to make the simulation consis-tent with experimental results. The Riccati equation was solvedoff-line with three different stiffness coefficient K. The resultsare displayed in Figure 13. The diagrams in the left column arethe valve lift output from the exhaust valve model. Those in theright column are the calculated feedforward lift control inputswhich are the calculated lags between the activation of the firstand second solenoids. The lag was found to be about 3.8ms (topright), 4.1ms (middle right) and 4.8ms (bottom right) to achievethe target lift of 6mm (top left), 8mm (middle left) and 10mm(bottom left).

0 0.002 0.004 0.006 0.008 0.010

50

100

150

200

250

300

350

400

450

500

V�� P

� e�� u� ef� � ce� N)F1=p1x+q1

F2=p2x+q2

F3=p3x+q3

Piecewise linearization of the pressure force

at the back of the exhaust valve in 20 cycles

Figure 12. Piecewise linearized valve back pressure force

4.3 Experimental Results of Closed-Loop ExhaustValve Lift Tracking

Finally, Figures 14 to 17 present the closed-loop lift track-ing control results with the feedforward control. 150 cycles ofvalve responses were recorded with sequences assembled at threereference lift set points in Figure 14. The reference valve liftvaries every 50 engine cycles from 8mm to 6mm, 6mm to 10mm,and 10mm to 8mm. The complete sequences of lift tracking re-sponses are presented in Figures (14). The responses at everyset point were enlarged through Figures 15 to 17 to illustratetheir transient and steady state performance. On the top dia-gram of every figure, the black line is the reference valve lift,


tp://www.asme.org/about-asme/terms-of-use

Target valve lift (m)

t

x 10-3

Calculation of nominal

lift control input (sec)x 10

3

measured

Exhaust valve lift tracking against 4.14x10 Pa (60psi) back pressure

with cycle to cycle variation at 600RPM

5

Downlo

0

0.005

0.01

6m

m t

arg

e

3.5

4

0

0.005

0.01

8m

m t

arg

et

3.5

4

4.5

x 10-3

0 5 10 150

0.005

0.01

cycle

10

mm

ta

rge

t

0 5 10 154.5

5

5.5x 10

-3

cycle

Figure 13. Feedforward exhaust valve lift control calculation

and the grey line is the actual valve lift. The bottom diagramshows the lift error between the reference and the actual valvelifts. Figure 15 shows that the exhaust valve follows the refer-ence lift of 6mm in two engine cycles with the lift error less than0.7mm. Figures 16 and 17 show that the exhaust valve tracksthe reference lift of 10mm and 8mm in one engine cycle withthe lift error less than 0.7mm. It can also be observed from Fig-ures 16 and 17 that steady state errors were not converged tozero. This is mainly due to small integration gain used for thisset of the tests. The enlarged responses display that the absolutesteady state lift tracking errors of all three set points are below1mm. Here, an accurate feedforward controlled input ensures afast transient responses. The valve responses at low lift is moresensitive to the error in the calculated feedforward controlled in-put, which has relatively greater fraction in the entire input (thelag between the activation of solenoid #1 and #2). A slight errorin the feedforward input calculation due to the model uncertainty,measurement inaccuracy or numerical error leads to a significantdeviation of the actual valve lift from its desired lift in transi-tion. Therefore, the valve at low reference lift exhibits a slowertransient response than that at high reference lift.

5 CONCLUSIONSA mathematical exhaust valve actuator model and an in-

cylinder pressure model have been developed for a model basedpredictive lift control of an exhaust valve. The exhaust valvemodel was approximated by a piece-wisely linearized second or-der spring-mass-damper system. The in-cylinder pressure wasmodeled during the exhaust valve opening stage. This modelwas integrated with the exhaust valve actuator model for controldevelopment. The thermodynamics data used in this model wasobtained using WAVET M simulation which was calibrated usingexperimental in-cylinder pressure data. The in-cylinder pressuremodel was validated using experimental data and demonstrated

10

aded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: h

0

5

10

Lif

t (m

)

50 75 100 125 150 175 200

�5

0

5

x 10�3

Lif

t err

or

(m)

cycle

reference

Figure 14. Experimental responses: three set points

5

6

7

8

9

x 103

Lif

t (m

)

Exhaust valve lift tracking from 8mm to 6mm

50 55 60 65 70 75�5

0

5x 10

�3

Lif

t err

or

(m)

cycle

measured

referenence

Figure 15. Experimental responses: transient from 8mm to 6mm

satisfactory modeling accuracy.A model based predictive control strategy was developed

for feedforward control. This strategy contains three segments:peak displacement calculation, model based initial condition pre-diction and Kalman state estimation. The acquired feedforwardinput combined with the closed loop proportional and integralcontrol forms the closed-loop lift control signal to accomplishthe exhaust valve lift tracking. The exhaust valve model wascalibrated using the measured exhaust valve back pressure sig-nal to obtain piecewisely linearized parameters required for thefeedforward input calculation. Experiments were conducted on a5.4L 3 valve V8 engine head at 600RPM to evaluate the closed-loop lift control system. A pressurized chamber was installed un-der the cylinder head which imitates the in-cylinder pressure act-ing at the back of the exhaust valve. The actual chamber pressurethat the exhaust valve opens against varies between 2.28×105Pa(33.1psi) and 3.57× 105Pa (51.7psi). Therefore, even thoughthe control strategy is based upon a mean pressure model, the



12x 10

3Exhaust valve lift tracking from 6mm to 10mm REFERENCES

[1] K. Inoue et al., “A High Power Wide Torque Range Effi-cient Engine with a Newly Developed Variable Valve Lift

1

Down

4

6

8

10

Lif

t (m

)

100 105 110 115 120 125

!2

0

2

x 10!3

Lif

t err

or

(m)

cycle

measured

referenence


4

6

8

10

12x 10

3

Lif

t (m

)

Exhaust valve lift tracking from 10mm to 8mm

30 32 34 36 38 40

!2

0

2

x 10!3

Lif

t e

rro

r (m

)

cycle

measured

reference


control strategy is demonstrated with certain cycle-to-cycle pres-sure variations. The experimental results with three lift referencepoints showed that the steady state valve lift error is below 1mm.The exhaust valve tracks the reference lift in a single engine cycleat high reference lift (greater than 8mm) and two engine cyclesat low reference lift (6mm) with a lift error less than 0.7mm.

ACKNOWLEDGMENT

The authors gratefully acknowledge the support for thiswork from the U.S. Department of Energy, National EnergyTechnology Laboratory, Energy Efficiency and Renewable En-ergy Division, Samuel Taylor, Project Manager.

1


and Timing Mechanism,” SAE 890675, 1989.[2] Y. Moriya et al., “A Newly Developed Intelligent Variable

Valve Timing System Continuously Controlled Cam Phas-ing as Applied to a New 3 Liter Inline 6 Engine,” SAE960579, 1996.

[3] R. Flierl and M. Kluting, “The Third Generation of NewFully Variable Valvetrain for Throttle Free Load Control,”SAE 2000-01-1227, 2000.

[4] M. Theobald, B. Lequesns, and R. Henry, ”Control ofEngine Load via Electromagnetic Valve Actuators,” SAE940816, 1994.

[5] C. Boie et al., “Method for Controlling a Electromag-netic Actuator for Achieving a Gas Exchange Valve Ona Reciprocating Internal Combustion Engine,” US Patent6,340,008, 2000.

[6] L. Schneider, “Electromagnetic Valve Actuator with Me-chanical End Position Clamp or Latch,” US Patent6,267,351, 2001.

[7] I. Haskara, L. Mianzo, and V. Kokotovic, “Method of Con-trolling an Electromagenatic Valve Actuator,” US Patent6,644,253, 2003.

[8] Y. Wang, A. Stefanopoulou, K. Peterson, T. Megli, M.Haghgooie, “Modeling and Control of ElectromechanicalValve Actuator,” SAE 2002-01-1106, 2002.

[9] G. Wright, N. Schecter, and M. Levin, ”Integrated Hy-draulic System for Electrohydraulic Valvetrain and Hy-draulicly Assisted Turbocharger,” US Patent 5,375,419,1994.

[10] O. Sturman, “Hydraulic Actuator for an Internal Combus-tion Engine,” US Patent 5,638,781, 1994.

[11] Z. Sun and D. Cleary, ”Dynamics and Control of anElectro-Hydraulic Fully Flexible Valve Actuation System,”Proceedings of American Control Conference, Denver, Col-orado, June, 2003.

[12] Jia Ma et al., “Analysis and Modeling of an ElectronicallyControlled Pneumatic Hydraulic Valve for an AutomotiveEngine,” SAE 2006-01-0042, 2006.

[13] Jia Ma et al., “Model reference adaptive control of a pneu-matic valve actuator for infinitely variable valve timing andlift,” 2007 SAE World Congress (SAE 2007-01-1297), De-troit, MI, April, 2007.

[14] Jia Ma et al., “Adaptive control of a pneumatic valve ac-tuator for an internal combustion engine,” 2007 AmericanControl Conference, New York, NY, July, 2007

[15] Jia Ma et al., “Model Based Predictive Control of anElectro-Pneumatic Valve Actuator for Internal CombustionEngines,” Submitted to 2008 American Control Conference,Seattle, WA, June, 2008.

[16] M. Anderson, T. C. Tsao, M. Levin, “Adaptive Lift Control



for a Camless Electrohydraulic Valvetrain,” SAE 981029,1998.

[17] J. M. Tressler et al., “Dynamic Behavior of Pneumatic Sys-

Dow

tems for Lower Extremity Extenders,” Proceedings of the2002 IEEE International Conference on Robotics & Au-tomation, Washington, D.C., May 2002.

[18] K. Misovec et al., “Digital Valve Technology Applied tothe Control of an Hydraulic Valve Actuator,” SAE 1999-01-0825, 1999.

[19] M.-S. S. Ashhab, A. G. Stefanopoulou, J. A. Cook, andM. B. Levin, “Control of Camless Intake ProcessPart II,”Journal of Dynamic Systems, Measurement, and Control,Vol. 122, Issue 1, pp. 131-139, 2000.

[20] D. S. Naidu, “Optimal Control Systems,” Electrical Engi-neering Textbook Series CRC Press, Boca Raton, FL, USA,2003

[21] W. T. Thomson, “Theory of vibration with applications,”(5th edition), Prentice Hall, Upper Saddle River, New Jer-sey, 1998.

[22] C. Turner, G. Babbitt, C. Balton, and M. Raimao, “Designand Control of a Two-Stage, Electro-Hydraulic Valve Ac-tuation System,” SAE 2004-01-1265, 2004.

12 Copyright c© 2008 by ASME

nloaded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use

electro-pneumatic exhaust valve modeling and control for ... · hydraulic, and electro-pneumatic...

Documents