Electro-Pneumatic Exhaust Valve Modeling and Control for an Internal Combustion Engine

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Proceedings of ICES 2008 Proceedings of the ASMEASME Internal 2008 Combustion International Engine Combustion Division Engine 2008 Spring Technical ConferenceConference April 27-30, 2008, Chicago,ICES2008 IL, USA April 27-30, 2008, Chicago, Illinois, USA

ICES2008-1653

ELECTRO-PNEUMATIC EXHAUST VALVE MODELING AND CONTROL FOR AN INTERNAL COMBUSTION ENGINE

Jia Ma, Guoming Zhu, Tom Stuecken, Andrew Hartsig, Harold Schock Department of Mechanical Engineering Michigan State University

ABSTRACT and control flame speed by manipulating in-cylinder turbulence. Variable valve actuation of Internal Combustion (IC) en- Exhaust valve timing and lift control makes it possible to vary the gines is capable of significantly improving their performance. amount of Residual Gas Recirculation (RGR) and control valve It can be divided into two main categories: variable valve tim- overlap when combined with intake valve control. Variable valve ing with cam shaft(s) and camless valve actuation. For camless timing and lift control is also a key technology for HCCI (Ho- valve actuation, research has been centered in electro-magnetic, mogenous Charge Compression Ignition) combustion control. electro-hydraulic, and electro-pneumatic valve actuators. This Variable valve actuation can be achieved with mechani- research studies the control of the electro-pneumatic valve actu- cal (cam-based), electro-magnetic (electric mechanical), electro- ator. The modeling and control of intake valves for the Electro- hydraulic, and electro-pneumatic valvetrain mechanisms. The Pneumatic Valve Actuators (EPVA) was shown in early publi- cam based variable valve actuation is able to provide either a cations and this paper extends the EPVA modeling and control multiple stepping or a continuously changing valve timing phase development to exhaust valves for the lift control which is the shift (see [1], [2] and [3]). Infinitely variable valvetrain, of- key to the exhaust valve control since an accurate and repeatable ten referred to as camless valvetrain, includes electro-magnetic lift control guarantees a satisfactory valve closing timing control. ([4], [5], [6], [7], and [8]), electro-hydraulic ([9], [10] and [11]), Note that exhaust valve closing timing is a key parameter for con- and electro-pneumatic actuation ([12]). The electro-pneumatic trolling engine residual gas recirculation. The exhaust valve lift valve actuator (EPVA) utilizes the supplied air pressure to actu- control challenge is the disturbance from the randomly varying ate either the intake or exhaust valve by electronically control- in-cylinder pressure against which the exhaust valve opens. The ling solenoids that regulate the motion of the actuator’s piston. developed strategy utilizes model based predictive techniques to For both electro-hydraulic and electro-pneumatic valves, there is overcome this disturbance. This exhaust valve lift control al- a potential issue of having a repeatable valve lift over the life of gorithm was validated on a 5.4 Liter 3 valve V8 engine head an engine. with a pressurized chamber to imitate the in-cylinder pressure. Valve lift control for electro-hydraulic valvetrain actuation The experimental results demonstrated that the exhaust valve lift ([22]) has been investigated by a number of researchers. Adap- tracked the step reference in one cycle with the lift error under tive peak lift control was presented in [16], and digital valve tech- 1mm and the steady state lift error was kept below 1mm. 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]. 1 INTRODUCTION Model-based control scheme has been used to regulate the cylin- Variable intake valve timing and lift can be used to optimize der air charge of a camless multi-cylinder engine for throttleless engine performance over a wide operating range, for instance, operations (see [19]). to reduce engine pumping losses, deactivate selected cylinder(s), Unlike the intake valve, the exhaust valve opens against an

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Downloaded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use in-cylinder pressure that varies as a function of the engine opera- cycle variations. This in-cylinder pressure produces a force on tional conditions with cycle-to-cycle combustion variations. This the face of the exhaust valve that affects the valve dynamics. This pressure disturbance slows down the valve actuator response and in-cylinder pressure is modeled and integrated with the exhaust as a result, it increases the variation of valve opening delay. In valve actuator model to capture the exhaust valve dynamics. fact, this disturbance makes it difficult to maintain repeatable valve opening timing and lift. As a result, unrepeatable valve I II III lift affects the closing timing control which is critical for RGR opendwell close control. Therefore, this work addresses exhaust valve lift con- x 4 (X(t p)=Xmax, X(t p)=0) 0: solenoid #1 activated 5 6 Peak Displacement 1: air pressure force on trol. and valve opens Calculation 3 A mathematical in-cylinder pressure model during exhaust (X(t d)=X 0 , X(t d)=v 0) 2: solenoid #2 activated Initial Fa 3: air pressure force off valve opening period was developed and integrated with the Condition 4: valve peak displacement Prediction 5: solenoid #1 and #2 deactivated 2 7 exhaust valve dynamic model for control development. The (X=X , X=X) 6: valve returns without resistance TM 7: valve returns against thermodynamics data was obtained using WAVE simulations cmpressed residual air TM Kalman Filter 8: hydraulic damper activation (www.ricardo.com). The WAVE model was calibrated and 8 9: valve closes 9 validated using experimental in-cylinder pressure data. The 0 1 (X=0 , X=0) d1 d2 time mathematical in-cylinder pressure model is then used to develop tp S : solenoid #1 td 1 S : solenoid #2 the model based predictive control scheme for exhaust valve lift d 2 1 Dt1: solenoid #1 turn-on delay control. In this paper, the model-based predictive control scheme 12 v Dt2: solenoid #2 turn-on delay D is used to predict the control required to reach desired valve lift S1 S2 t3: solenoid #1 and #2 turn-off delay Dt Dt Dt time under varying exhaust pressure. This is the key to achieve accu- 1 2 3 rate valve lift control since the valve control signal needs to be Figure 1. Valve lift profile with the solenoid command chart sent to actuator solenoid before the valve reaches its desired lift due to solenoid electro-magnetic delay. The controller consists of two parts: feedforward and closed loop controls. The feedfor- The system dynamics illustrated here focuses on the rela- ward control is used to provide a nominal lift control based upon tionship between the solenoid control commands and the exhaust the predicted valve opening trajectory, while the closed loop con- valve displacement. It follows the same analysis as that of the troller is used to minimize the mean control error. The closed- level two model. As shown in Figure 1, the valve response can loop control strategy was developed and verified in simulation be divided into three stages. They are the opening stage (I), dwell using the combined mathematical model of exhaust valve and in- stage (II), and closing stage (III). Solenoid #1 is activated at point cylinder pressure, and then, demonstrated on a 5.4 Liter 3 valve 0 first. It induces a high air pressure force to push the valve open V8 engine head with a pressurized chamber. at point 1 after ∆t1. Solenoid #2 is then activated (point 2) with ˆ The paper is organized as follows. First, an exhaust valve a time lag δ1. It removes this air pressure force ∆t2 time after dynamic model is presented in Section 2. Next, the feedforward solenoid #2 is activated (point #3). Note that the interplay be- and closed loop control strategies are described in Section 3. tween two solenoids results in a pulse force input to the actuator Third, the experimental validation results are shown in Section valve piston with pulse width δ1. Note that this pulse width is 4, and finally, conclusions are drawn. proportional to the valve lift. Now, with zero input, the valve movement continues until it reaches its peak lift at point #4, the valve equilibrium. This ends the open stage. Next, the valve en- 2 EXHAUST VALVE DYNAMIC MODEL ters the dwell stage where it is held open by a hydraulic latch A physics based nonlinear model, called a level one model, mechanism. At the end of the dwell stage, solenoid #1 is de- was built component-by-component based upon the flow and activated at point #5. After ∆t3 time, the valve starts to return fluid dynamics. The details of the level one model and its ver- (point #6). The close stage starts at point #6 and ends at point #9 ification can be found in [12]. This model provides an insight to where the valve is considered closed. The returning duration is the operation of the pneumatic/hydraulic mechanical actuation δ2 between these two points. system. A piecewise linearized level two model was then cre- The two solenoids have electro-mechanical delays after their ated based on the level one model to reduce the computational activation and de-activation (see Figure 1). ∆t1 is defined as the throughput for control system development purpose. The details delays for solenoid #1 at activation. ∆t2 is defined as solenoid of the level two model are described in [13]. The level two model #2 delay at activation. The de-activation delay for both solenoids was used as the actuator model for the intake valve in the pre- are ∆t3. The solenoid commands direct the valve motion after vious studies (see [13] and [14]). In this study, it is used for the delays. The time lag applied between the activation of two ˆ the exhaust valve actuator modeling. The exhaust valve opens solenoids is denoted as δ1. This differs from the time lag between against an in-cylinder combustion pressure with certain cycle-to- two delayed solenoid activations which is denoted as δ1 since two

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Downloaded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use control formulation process are gauge pressure in this article. solenoid delays, ∆t1 and ∆t2, are not equal. The exhaust valve lift control algorithm is to determine when to activate solenoid Mx¨+C x˙+ K (x + δ ) = F (t) − F (x) (1) #2 during exhaust valve opening for each engine cycle with the f p p a ½ b varying in-cylinder pressure at the surface of the valve and its 0, t < 0 Fa(t) = F(t) − F(t − δ1),F(t) = (2) activation delay in presence. It is impossible to remove the input ApPp, t ≥ 0 force Fa instantly upon the activation of solenoid #2 due to its activation delay. An model based predictive lift control algorithm where, Pp is supply air pressure; Fb(x) is the in-cylinder pres- is developed to make this possible. The details are described in sure force applied at the exhaust valve surface; M is the sum of the control strategy section. equivalent mass of actuator piston, effective valve spring mass, The exhaust valve closing timing control requires knowl- exhaust valve and cap; Ap is the sum of actuator piston and oil edge of δ , the amount of time that the valve takes to close. To 2 passage areas; Cf is the damping ratio approximating energy dis- guarantee the exhaust valve closing at the desired time requires sipation due to ﬂow loss and frictional loss; Kp and δp are the de-activating solenoid #1 by time δ2 before exhaust valve clos- stiffness and preload displacement of the valve spring respec- ing. δ can be predetermined from the different valve lift set 2 tively; δ1 is the lag between the activation of solenoids #1 and #2 points. In other words, the closing timing control relies on a re- after solenoid delays as shown in Figure 1. peatable valve lift control. Developing a lift control system is the primary emphasis of work described in this paper. The opening stage exhaust valve actuator model and the in- 2.2 In-cylinder Pressure Model cylinder pressure model are employed to formulate the model The in-cylinder pressure force Fb(x) needs to be modeled based predictive lift control scheme. In order to validate the ex- and evaluated in Equation (1). Figure 3 illustrates the dynamics haust valve lift control algorithm, the level two model integrated in the combustion chamber with an exhaust valve. A control vol- with the in-cylinder pressure model is used as a plant model in ume is drawn above the piston, where mcyl, Tcyl and Pcyl are the simulation. The opening stage exhaust valve actuator model and mass, temperature and pressure inside the combustion cylinder. the in-cylinder pressure model are introduced in the following Acyl is the engine piston area. m˙ ex is the mass ﬂow rate at the exit two subsections. when the exhaust valve opens. Tatm and Patm are the atmospheric temperature and pressure. x and y are the exhaust valve displacement and cylinder piston displacement respectively. The mass 2.1 Actuator Model The opening stage exhaust actuator model with the in- cylinder pressure as external disturbance is studied in this sub- x Tatm section. This model is expanded based on the level two model Patm [13] to include the in-cylinder pressure dynamics. Figure 2 mex

y valve C.V. oil Poil

Psupply Ain outlet port inlet port Aout mcyl Tcyl Pcyl Acyl Fa x

piston cylinder piston

Mspring p Cf Kp

Mvalve Figure 3. In-cylinder pressure model

Fb(x) Figure 2. Actuator piston model ﬂow rate equations at the exit are written for both choked and unchoked ﬂow cases through Equations (3) to (5) following their derivation in [16]. shows the schematic diagram of a single actuating piston for this system. At the opening stage, the valve actuator is modeled as s a second order mass-spring-damper system with zero initial con- k m˙ ex = Cdex γPcylAex(x) , Aex = 2πrvalvex, (3) ditions, see Equation (1). All pressures used in modeling and RTcyl

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Downloaded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use where, Aex is the flow area with rvalve being the valve radius; Cdex Therefore, Fb(x) can be expressed in Equation (9) below. 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 Fb(x) = PcylAvalve, (9) pressure and constant volume respectively; and k = Cp . When Cv k P ≥ ( k+1 ) k−1 P , the flow is choked at the exit. In this case, cyl 2 atm where P is defined in Equation (7). γ is shown in Equation (4) cyl

r 2.3 In-cylinder Pressure Model Validation 2 k+1 γ = ( ) k−1 . (4) The in-cylinder pressure force Fb is a function of the exhaust k + 1 valve displacement since the ﬂow out area Aex is a function of the exhaust valve displacement. k k+1 k−1 When Pcyl ≤ ( 2 ) Patm, the ﬂow is unchoked and γ is expressed in Equation (5). Measured and modeled cylinder pressure with cam profile at 1500RPM 6 x 10 3 window r model pressure k+1 1−k 2 Patm Patm (Pa) measured pressure 2k k 2 γ = ( ) [( ) − 1]. (5) cyl k − 1 Pcyl Pcyl

and and P 1 cam P The mass of the residual gas inside the combustion cylinder in 0 Equation (6) can be obtained by integrating the calculated mass Cam profile ﬂow rate. The initial mass m0 is derived using ideal gas law, 0.01 where P0, V0, R0 and Tcyl0 are the initial in-cylinder gas pressure, volume, gas constant and temperature at the exhaust valve opening. 0.005 cam profile (m) camprofile

0 Z t 1 2 3 P0V0 cycle mcyl = − m˙ exdt + m0, m0 = . (6) 0 RTcyl0 Figure 4. In-cylinder pressure model validation by simulation

Using the ideal gas law again with the obtained mcyl results in an expression of in-cylinder pressure as shown in Equation (7). In order to validate the in-cylinder pressure model, combustion experiments were conducted using a 5.4L 3 valve V8 engine with in-cylinder pressure measurement and a conventional mcylRTcyl cam shaft at 1500RPM. The pressure model was simulated us- Pcyl = , Vcyl = Acyly, (7) Vcyl ing the conventional cam profile as the valve displacement input. The modeled in-cylinder pressure was then compared with the measured in-cylinder pressure as shown in Figure 4. The top where, k, R and T are variables acquired from the WAVETM cyl diagram of this figure shows the modeled pressure (solid line) simulation with the same engine configuration and parameters; in the rectangular windows and measured in-cylinder pressure and y is the piston displacement derived from the engine geome- (dash line). The bottom diagram shows the exhaust cam profile try in Equation (8). used in the simulation and experiments. The in-cylinder pres- r sure model is then integrated into the pneumatic exhaust valve L L model and the responses are shown in Figure 5. Here, the pres- y = r[1 + − cos(θ) − − sin2(θ)], (8) r r sure model uses the EPVA valve lift profile to calculate the corresponding in-cylinder pressure. The modeled pressure (solid line in top diagram) and the associated EPVA valve lift profile (solid where line in bottom diagram) are compared with the experiment pres- 1 2 2 sure (dash line) and the cam profile (dash line). The simulation - Acyl = π( 2 × bore) = 0.0401m (bore = 90.2mm), - L is the connecting rod length (L = 169.2mm), results demonstrated that the in-cylinder pressure reduces rather 1 quickly with the EPVA exhaust valve actuation since the EPVA - r is the crank shaft radius (r = 2 stroke = 52.9mm), - θ is the engine crank angle. valve opens much faster than the conventional cam based valve.

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Downloaded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use This simulated in-cylinder pressure is used to construct the con- 4 reaches the reference maximum valve lift, point 3 is found to trol signals. The exhaust valve model is used as a plant model be the right time to remove force Fa. If activating solenoid #2 and it is integrated with the in-cylinder pressure model in simula- could turn off the input force Fa immediately, we would only tions to validate the control algorithm. The modeled in-cylinder need to activate it whenever the calculated displacement of point pressure is one of the two inputs to the plant (exhaust valve) and 4 reaches the reference lift. But the solenoid delay requires the the actuation force Fa commanded by the two solenoid control activation to take place at point 2 with ∆t2 amount of time before signals is the other input. point 3. This means that if point 3 is the time to eliminate input force, point 2 is the time to activate solenoid #2. However, the initial conditions at point 3, where the peak displacement of the Measured cylinder pressure with cam profile valve is calculated, are not yet available at point 2. Therefore, and model cylinder pressure with EPVA lift profile at 1500RPM 6 x 10 an algorithm is derived to predict initial conditions of point 3 at 3 Pcam point 2. This strategy of initial condition prediction can be im- (Pa)

yl 2 Pcyl c plemented as long as the delay ∆t2 of solenoid #2 is less than the ˆ lag δ1 between the activation of two solenoids. The predictive and and P 1 algorithm needs to know both states, valve displacement and ve- cam P 0 locity, at point 2. A Kalman state estimator was used to estimate CAM profile and EPVA lift profile them with minimized effect of measurement noise. Now we can x determine the time to activate solenoid #2 (point 2), which is 0.01 x cam served as a feedforward control of the valve actuator. A proportional and integral (PI) scheme is used as a closed-loop feedback and x (m) x and 0.005 lift control system to reduce the steady state lift tracking error. cam x The flow chart of the feedforward control scheme is shown 0 0.05 0.06 0.07 0.080.09 0.10 0.11 0.12 0.13 0.14 in Figure 6. First, solenoid #1 is activated. Secondly, the Kalman time (sec) state estimator provides the current states (valve displacement Figure 5. In-cylinder pressure model integrated into exhaust valve model and its velocity). Finally, a model based prediction algorithm uses the estimated states to calculate the states after solenoid #2 delay ∆t2, which is then used to calculate the peak valve displacement. If the calculated peak displacement is greater than or equal to the reference valve lift, solenoid #2 is activated, otherwise, the 3 CONTROL STRATEGY process repeats until the condition is satisfied. The details of the Since the in-cylinder pressure on the face of the exhaust derivations are discussed in the following four subsections. valve varies significantly from cycle-to-cycle, the valve lift control needs to be adjusted as a function of the current in-cylinder 3.1 Peak Displacement Calculation (PDC) pressure for each individual cycle. As explained in the actuator This section describes the solution for the peak displace- dynamics section, the exhaust actuator is modeled as a second ment at point 4 based on the initial conditions at point 3. Recall order mass-spring-damper system at the opening stage. Activat- that the governing equation of the exhaust valve at the opening ing solenoid #1 applies the force Fa on the valve and moves the stage is presented in Equation (1). The back pressure force Fb(x) exhaust valve. Activating solenoid #2 removes the force and the equals the product of the exhaust valve area and the modeled in- valve continues to open until it reaches the maximum displace- cylinder pressure. The in-cylinder pressure used in the control ment. Solenoid #2 activation timing determines the maximum algorithm development here is piece-wisely linearized according valve lift. Therefore, the key for valve lift control is to find when to the simulated in-cylinder pressure against EPVA exhaust valve to activate solenoid #2. Figure 1 illustrates the idea of the ex- profile, where F (x) = px + q (p ≤ 0 and q ≥ 0) with haust valve lift control strategy. Solenoid #1 is activated at time b 0. After the delay of ∆t1, the input force Fa acts on the system  and the exhaust valve starts to open at point 1. Solenoid #2 is  p = p1, q = q1, x ≤ 0.002m p = p2, q = q2, 0.002m < x ≤ 0.008m . then activated at point 2, after ∆t2 delay, force Fa is removed at  point 3. The valve moves further until its velocity decreases to 0 p = p3, q = q3, x > 0.008m at point 4. The second order valve system response from points 3 to 4 can be calculated with zero input and nonzero initial con- Substituting Fb(x) with its linearized expression into Equa- ditions at point 3. In other words, the valve peak displacement at tion (1) results in Equation (10) below. point 4 can be calculated if the initial displacement and velocity at point 3 are known. Once the calculated displacement at point Mx¨+Cf x˙+ Kpx = Fa − (px + q) − Kpδp. (10)

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Downloaded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use Feed forward exhaust valve lift control scheme in one engine cycle 3.2 Model Based Initial Condition Prediction (ICP) Start The previous section solves for the peak displacement x(tp) using the displacement and velocity at point 3 as initial condi- Activate solenoid #1 tions (Figure 1). This section derives the formulas to predict the displacement x(td) and velocity x˙(td) at point 3, given the dis- Current state estimation placement and velocity at point 2. The displacement and velocity using Kalman filter at point 2 are initial conditions denoted as x(0) = x0 and x˙(0) = v0 in this subsection. Their values are estimated by the Kalman state Model based state prediction for the delay of solenoid #2 estimator described in the next subsection. Solenoid #2 delay, ∆t2, is the time input and Fa is a constant force input between

Peak exhaust valve displacement points 2 and 3. Consider the governing equation again in Equa- xmax calculation tion (1). Given Fb(x) = px + q, Equation (1) becomes

no xmax > xref ? Mx¨+Cf x˙+ Kpx = Fa − (px + q) − Kpδp. (14)

yes

Activate solenoid #2 Rearrange the equation above to obtain

End Mx¨+Cf x˙+ (Kp + p)x = Fa − q − Kpδp. (15) Figure 6. Feedforward exhaust valve lift control strategy

Let K = Kp + p and W = q + Kpδp − Fa, Equation (15) becomes Move term px to the left resulting in Equation (11): Equation (16).

Mx¨+Cf x˙+ (Kp + p)x = Fa − q − Kpδp. (11) Mx¨+Cf x˙+ Kx = −W. (16)

Let K = Kp + p and Fa = 0, since it is assumed that input force Fa is turned off, to obtain Equation (12) in a general format given It is clear that Equations (12) and (16) have the same form. the initial condition x(0) = x0, x˙(0) = v0. Previously, Equation (12) was evaluated for the maximum displacement given initial conditions. Now, Equation (16) is evalu-

Mx¨+Cf x˙+ Kx = −Q, Q = Kpδp + q. (12) ated for the displacement and velocity in td amount of time with given initial conditions, where td = ∆t2 (see Figure 1). Equa- tion (16) can be solved in a similar way to Equation (12) by re- Recall that p takes three different values, p1, p2 and p3 in three valve displacement regions. K could be either negative, zero or placing Q with W, and the solutions are omitted in this paper. positive depending on the value of p. When K is positive, Equa- The techniques of solving analytical solutions for a second order tion (12) can be rewritten into Equation (13) as below: mass-spring-damper system can be found in [21].

2 Q 3.3 Kalman Filter State Estimation (KFE) x¨+ 2ζωnx˙+ ωnx = − , (13) M The displacement and velocity at point 2 (see Figure 1) are q q needed as initial conditions in the previous section. The system K Cf 1 is equipped with a displacement sensor which measures the ex- where ωn = M and ζ = 2 MK . In this case, the solution can be categorized into under damped, critically damped and haust valve displacement. The velocity obtained through taking a over damped scenarios depending on the value damping ratio ζ, time derivative of the measured displacement is unreliable due to the measurement noise. The observer formulated in this section damping coefﬁcient Cf , mass M and equivalent stiffness K in Equation (13). Based upon the system dynamic equations shown performs the optimal estimations of both the displacement and in (13), the peak displacement solution can be derived for four velocity at point 2 in the presence of noise using Kalman state cases (see [15] for details). They are K > 0 with 0 < ζ < 1 (case estimator (see [20]). The estimated displacement and velocity ˙ #1), K > 0 with ζ = 1 (case #2), K > 0 with ζ > 1 (case #3) and are denoted as xb and xb respectively. The state space notation of the system is expressed below: K ≤ 0 (case #4). The initial condition denoted as x(0) = x0 and x˙(0) = v0 in this section are derived in the next section of model x˙ = Ax + Bu + Gw(t) based initial condition prediction. y = Cx + v(t)

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Downloaded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use · ¸ · ¸ · ¸ · ¸ 0 1 0 1 x pressure model as the plant model (see [14]), where the three- where A = , B = , CT = , x = 1 , and −K −Cf 1 0 x segment feedforward control strategy and the closed-loop control M M M 2 G is an identity matrix; w(t) and v(t) represent the process noise scheme are evaluated in sequence. In this section, the closed- and measurement noise. Note that u = −W is the input to the loop lift control strategy was implemented in a prototype con- system, x1 = x and x2 = x˙ are the states representing the valve troller and evaluated by experiments. The feedforward lift con- displacement and velocity. The Kalman state estimator takes the trol signals were precalculated and implementation in a form following forms: of lookup tables to reduce the real-time calculation throughput. Note that both ICP and PDC calculations require only system xb˙ = Axb+ Bu + L(y − cxb) initial states, and they can be precalculated to reduce realtime yb= Cxb, xb(0) = 0, processing throughput. where L is the observer gain acquired through solving the algebraic Riccati Equation (17); and xb is the estimated displacement 4.1 Experiment Setup x1 and velocity x2. 4.1.1 Mechanical system conﬁguration Experi- ments were conducted on a 5.4L 3 valve (2 intake valves and T T T −1 1 exhaust valve) V8 engine head. As displayed in Figure 8, the AP + PA + GWpG − PC V CP = 0, (17) cam and cam shaft were removed from the engine head. Three T −1 L = PC V ,where W ≥ 0 and V > 0, (18) electro-pneumatic actuators were installed on the top of each valve to manage both intake and exhaust valve events. Micro- EpsilonTM point range sensors were mounted under each valve where Wp and V are covariance matrices of w and v, respectively. If (C,A) is observable, the algebraic Riccati equation has to measure the valve displacements (see Figure 9). a unique positive deﬁnite solution P, and the estimated state xb asymptotically approaches true state x.

3.4 Closed-Loop Control Scheme The feedforward solution of solenoid #2 activation timing is obtained by implementing the formulas from the peak displacement calculation, model based initial condition prediction and Kalman ﬁlter state estimation subsections. This solution combined with the displacement error compensation from the proportional and integrator (PI) feedback scheme forms a closed-loop control signal of solenoid #2 as illustrated in Figure 7.

Closed-loop exhaust valve lift control scheme

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

To test the exhaust valve control system, a pressurized cham- xref + Plant xmax + PI + - model ber was build and installed under the cylinder head, which imitates the in-cylinder pressure acting at the back of the exhaust valve. The pressure chamber is shown in Figure 9. It was pressurized with the supplied compressed air at 4.48 × 105Pa Figure 7. Closed-loop exhaust valve lift control scheme (65psi). The pressure inside chamber drops quickly when the exhaust valve opens and builds up when it closes. The exhaust lift control experiments were performed at 600RPM that is lower enough to ensure that the chamber pressure can recover close to 4.14×105Pa (60psi) at every cycle. An optical window was built 4 EXPERIMENTAL IMPLEMENTATION underneath the exhaust valve on the bottom of the chamber. The The developed control algorithms was validated in simu- exhaust valve laser sensor sends and receives laser beam through lation using the combined valve actuator and the in-cylinder this optical window to measure the exhaust valve displacement

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Downloaded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use (see Figure 9). A pressure transducer was mounted on the cylin- CPU #1 is configured to be updated every 1ms and to execute the der head close to the exhaust valve. engine control strategy every combustion cycle. This means that this CPU updates input and updates analog outputs every 1ms, but calculates the engine control parameters every engine combustion event. The digital inputs and outputs of CPU #1 are synchronized with the engine crank angle with one-third crank degree resolution. The crank angle calculation is completed within the digital I/O card of CPU #1 utilizing digital inputs from cam sensor, gate and crank signals from an encoder. The CPU #1 digital outputs are spark pulse, fuel injection pulse, charge motion control, and intake and exhaust valve timing pulses, espe- cially the pulses De f A and De f B that synchronize the valve control between the engine and valve control system. The inputs of the 16 channel analog I/O board include ionization signal, pressure signal, throttle position, mass air flow rate, coolant temperature, manifold pressure and temperature, and air-to-fuel ratio from universal exhaust gas oxygen (UEGO) sensor. The valve control CPU #2 is configured to operate at 40µs Figure 9. Pressure chamber under the valves sample 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 16 channel A/D board reads crank synchronized De f A and De f B 4.1.2 Control system hardware configuration A pulse signals from CPU #1, valve lift signal from valve lift point realtime Opal-RTTM prototype control system was employed for range position sensors, solenoid current signals from their drive the EPVA exhaust valve bench tests. The system consists of: circuits, and supply air pressure signal. The solenoid control pulses and the exhaust valve pressure (which is needed to cal- - Two 3.2GHz CPU’s culate the feedforward lift control inputs in simulation) are the - An IEEE 1934 fire wire serial bus with the data transfer rate output from a 16 channel D/A board. at 400MHz per bit The solenoid driving circuit for the exhaust valve used the - Two 16 channel A/D and D/A boards with less than 1 µs peak and hold scheme to minimize the solenoid electro-magnetic conversion rate delays. The total solenoid delay including the electro-magnetic - One 16 channel digital I/O board at 50 ns sampling rate and mechanical delays was kept below 2ms.

Engine Control Valve Control 4.2 Feedforward Lift Control Input Calculation (Visteon) (ARES) 1 ms 40 us The damping ratio of the exhaust valve model at the open-

16 ch 16 ch 16 D CPU#1 CPU#2 16 ch 16 ch ing stage is needed in constructing the feedforward lift control D/A A/D I/O A/D D/A 3.2GHz 3.2GHz 2 us 1 us 50 ns IEEE 1934 firewire 1 us 2 us signal using the developed model based predictive lift control engine 400MHz/bit valve control control strategy. To identify this model parameter, open loop lift control

solenoids tests were conducted on the exhaust valve test bench at 600RPM. throttle position cam position ignition timing valve displacement The maximum pressure at the back of exhaust valve was set to mass air flow crank angle fuel control solenoid currents 5 injector be 4.14 × 10 Pa (60psi), the supply air and oil pressure was at manifold pressure gate signal chamber pressure and temperature (syn) cam phaser 5 air fuel ratio 8.28 × 10 Pa (120psi) and the target lift was 10mm. The valve charge motion control coolant back pressure varies randomly from cycle to cycle with the vari- temperature Def B UEGO 5 Def A ation as large as 10 Pa (14.5psi). The measured valve back pres- Figure 10. Modular control system configuration sure was used in the exhaust valve model simulation. The lag between the activation of two solenoids remained unchanged in both simulations and tests for parameter identification purpose. Figure (10) displays the hardware configuration of the system. The experiment and simulation valve responses are displayed in CPU #1 is used for engine controls and CPU #2 is dedicated to Figure 11. The bottom diagram shows the model (dot line) and the valve actuator (EPVA) control. An IEEE 1934 fire wire serial the measured (solid line) valve lift profiles in five cycles. The top bus is used for communication between CPU #1 and CPU #2. diagram shows the corresponding pressure against with the ex-

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Downloaded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use haust valve opens. The damping ratio was chosen in such a way strategy is based upon a mean pressure model, the control strat- that the model valve responses agree with the experimental valve egy is demonstrated under certain cycle-to-cycle pressure varia- responses as demonstrated in this ﬁgure. The developed model tions. Evaluation of this controller against cycle-to-cycle variation is going to be part of our future study.

Simulations were performed to determine the lags between

¢£ ¨ © © ¨ © © ©

¥ ¤ ¥ ¦ ¤¥ § § § ¥ ¥¤ E ¡ Mo I u p ch

5 the activation of two solenoids according to the given reference x 0 4 lifts. The exhaust valve model was identiﬁed earlier and used as the plant in the simulations. The measured back pressure during 2 exhaust valve opening was used to make the simulation consis- 0 Chamber pressure (Pa) tent with experimental results. The Riccati equation was solved off-line with three different stiffness coefﬁcient K. The results 0.014

mo are displayed in Figure 13. The diagrams in the left column are

0.012 expe 0.01 the valve lift output from the exhaust valve model. Those in the 0.008 right column are the calculated feedforward lift control inputs 0.006 which are the calculated lags between the activation of the ﬁrst 0.004 and second solenoids. The lag was found to be about 3.8ms (top Valve displacement (m) 0.002 right), 4.1ms (middle right) and 4.8ms (bottom right) to achieve 0 1 2 3 4 5 the target lift of 6mm (top left), 8mm (middle left) and 10mm

cycl ¥ (bottom left).

Figure 11. Exhaust valve model identiﬁcation Piecewise linearization of the pressure force at the back of the exhaust valve in 20 cycles

500

based predictive control strategy can be used to determine the 450 activating timing of the second solenoid and use this timing as a F1=p1x+q1 400 F2=p2x+q2

feedforward lift control input in realtime. In order to reduce real- ) N

350

time computational throughput, the developed strategy was used e c

300

to calculate the lag between the activation of the ﬁrst and the sec- f F3=p3x+q3 e ond solenoids for different lift set points in off-line simulations to 250

200 precalculate for all possible initial conditions. In realtime appli- e

cations, this lag was the feedforward lift control input, combined P 150

with the feed back PI compensation, to form a closed-loop lift 100

control input. The measured valve back pressure in the pressur- 50

ized chamber was piecewisely linearized and used in the feed- 0

forward control input calculation. The measured pressure was 0 0.002 0.004 0.006 0.008 0.01

¡ ¦ §¡ ¨

£ ©£ © multiplied by the area of the exhaust valve to obtain the pressure V ¢ £ ¤ ¥ force applied at the exhaust valve surface. This force was plot- Figure 12. Piecewise linearized valve back pressure force ted in Figure 12 (grey curves) against the valve displacement for 20 cycles. As shown in this figure, they were linearized in three segments (solid lines) during the exhaust valve opening to ap- proximate the averaged forces. The coefficients, p1,q1, p2,q2, p3 4.3 Experimental Results of Closed-Loop Exhaust and q3, were used to construct the feedforward lift control input Valve Lift Tracking through the model based predictive control algorithm. Finally, Figures 14 to 17 present the closed-loop lift track- ¿From Figure 12 we can observe that the pressure force ap- ing control results with the feedforward control. 150 cycles of plied to the face of exhaust valve varies between 260N and 410N. valve responses were recorded with sequences assembled at three This is equivalent to that the exhaust back pressure varies be- reference lift set points in Figure 14. The reference valve lift tween 2.28 × 105Pa (33.1psi) and 3.57 × 105Pa (51.7psi). The varies every 50 engine cycles from 8mm to 6mm, 6mm to 10mm, control strategy was developed based upon the averaged exhaust and 10mm to 8mm. The complete sequences of lift tracking re- pressure profile, but the experimental validation using the pres- sponses are presented in Figures (14). The responses at every surized chamber simulates a variable in-cylinder pressure, that set point were enlarged through Figures 15 to 17 to illustrate the exhaust valve opens against, between 2.28×105Pa (33.1psi) their transient and steady state performance. On the top dia- and 3.57 × 105Pa (51.7psi). Therefore, even though the control gram of every figure, the black line is the reference valve lift,

9 Copyright °c 2008 by ASME

Downloaded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use 5 Exhaust valve lift tracking against 4.14 x10 Pa ( 60psi) back pressure Calculation of nominal Target valve lift (m) with cycle to cycle variation at 600RPM lift control input (sec) 3 x 10 -3 x 10 measured reference 0.01 10 4 0.005

Lift (m) 5

6mm target 0 3.5 -3 x 10 0 0.01 3 4.5 x 10 0.005 4 5

8mm target 0 3.5 -3 x 10 5.5 0 0.01 5 Lift error (m) 5 0.005

0 4.5 50 75 100 125 150 175 200 10mm target 0 5 10 15 0 5 10 15 cycle cycle cycle Figure 14. Experimental responses: three set points Figure 13. Feedforward exhaust valve lift control calculation

and the grey line is the actual valve lift. The bottom diagram shows the lift error between the reference and the actual valve lifts. Figure 15 shows that the exhaust valve follows the refer- Exhaust valve lift tracking from 8mm to 6mm 3 ence lift of 6mm in two engine cycles with the lift error less than x 10 0.7mm. Figures 16 and 17 show that the exhaust valve tracks measured 9 referenence the reference lift of 10mm and 8mm in one engine cycle with 8

the lift error less than 0.7mm. It can also be observed from Fig- Lift (m) 7 6

ures 16 and 17 that steady state errors were not converged to 5 3 x 10 zero. This is mainly due to small integration gain used for this 5 set of the tests. The enlarged responses display that the absolute

steady state lift tracking errors of all three set points are below 0

1mm. Here, an accurate feedforward controlled input ensures a Lift error (m)

fast transient responses. The valve responses at low lift is more 5 50 55 60 65 70 75 sensitive to the error in the calculated feedforward controlled in- cycle put, which has relatively greater fraction in the entire input (the Figure 15. Experimental responses: transient from 8mm to 6mm lag between the activation of solenoid #1 and #2). A slight error in the feedforward input calculation due to the model uncertainty, measurement inaccuracy or numerical error leads to a signiﬁcant satisfactory modeling accuracy. deviation of the actual valve lift from its desired lift in transi- A model based predictive control strategy was developed tion. Therefore, the valve at low reference lift exhibits a slower for feedforward control. This strategy contains three segments: transient response than that at high reference lift. peak displacement calculation, model based initial condition prediction and Kalman state estimation. The acquired feedforward input combined with the closed loop proportional and integral 5 CONCLUSIONS control forms the closed-loop lift control signal to accomplish A mathematical exhaust valve actuator model and an in- the exhaust valve lift tracking. The exhaust valve model was cylinder pressure model have been developed for a model based calibrated using the measured exhaust valve back pressure sig- predictive lift control of an exhaust valve. The exhaust valve nal to obtain piecewisely linearized parameters required for the model was approximated by a piece-wisely linearized second or- feedforward input calculation. Experiments were conducted on a der spring-mass-damper system. The in-cylinder pressure was 5.4L 3 valve V8 engine head at 600RPM to evaluate the closed- modeled during the exhaust valve opening stage. This model loop lift control system. A pressurized chamber was installed un- was integrated with the exhaust valve actuator model for control der the cylinder head which imitates the in-cylinder pressure act- development. The thermodynamics data used in this model was ing at the back of the exhaust valve. The actual chamber pressure obtained using WAVETM simulation which was calibrated using that the exhaust valve opens against varies between 2.28×105Pa experimental in-cylinder pressure data. The in-cylinder pressure (33.1psi) and 3.57 × 105Pa (51.7psi). Therefore, even though model was validated using experimental data and demonstrated the control strategy is based upon a mean pressure model, the

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Downloaded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use Exhaust valve lift tracking from 6mm to 10mm 3 REFERENCES x 10 12 [1] K. Inoue et al., “A High Power Wide Torque Range Efﬁ- 10 cient Engine with a Newly Developed Variable Valve Lift 8 and Timing Mechanism,” SAE 890675, 1989. Lift (m) measured 6 referenence [2] Y. Moriya et al., “A Newly Developed Intelligent Variable 4 Valve Timing System Continuously Controlled Cam Phas- !3 x 10 ing as Applied to a New 3 Liter Inline 6 Engine,” SAE 2 960579, 1996.

0 [3] R. Flierl and M. Kluting, “The Third Generation of New

Lift error (m) Fully Variable Valvetrain for Throttle Free Load Control,” !2 SAE 2000-01-1227, 2000. 100 105 110 115 120 125 cycle [4] M. Theobald, B. Lequesns, and R. Henry, ”Control of Figure 16. Experimental responses: transient from 6mm to 10mm Engine Load via Electromagnetic Valve Actuators,” SAE 940816, 1994. [5] C. Boie et al., “Method for Controlling a Electromag- netic Actuator for Achieving a Gas Exchange Valve On a Reciprocating Internal Combustion Engine,” US Patent Exhaust valve lift tracking from 10mm to 8mm 3 x 10 12 6,340,008, 2000. measured 10 reference [6] L. Schneider, “Electromagnetic Valve Actuator with Me-

8 chanical End Position Clamp or Latch,” US Patent Lift (m) 6 6,267,351, 2001.

4 [7] I. Haskara, L. Mianzo, and V. Kokotovic, “Method of Con- !3 x 10 trolling an Electromagenatic Valve Actuator,” US Patent

2 6,644,253, 2003. [8] Y. Wang, A. Stefanopoulou, K. Peterson, T. Megli, M. 0 Haghgooie, “Modeling and Control of Electromechanical Lift error (m) !2 Valve Actuator,” SAE 2002-01-1106, 2002. 30 32 34 36 38 40 cycle [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. Figure 17. Experimental responses: transient from 10mm to 8mm [11] Z. Sun and D. Cleary, ”Dynamics and Control of an Electro-Hydraulic Fully Flexible Valve Actuation System,” Proceedings of American Control Conference, Denver, Col- orado, June, 2003. control strategy is demonstrated with certain cycle-to-cycle pres- [12] Jia Ma et al., “Analysis and Modeling of an Electronically sure variations. The experimental results with three lift reference Controlled Pneumatic Hydraulic Valve for an Automotive points showed that the steady state valve lift error is below 1mm. Engine,” SAE 2006-01-0042, 2006. The exhaust valve tracks the reference lift in a single engine cycle [13] Jia Ma et al., “Model reference adaptive control of a pneu- at high reference lift (greater than 8mm) and two engine cycles matic valve actuator for inﬁnitely variable valve timing and at low reference lift (6mm) with a lift error less than 0.7mm. lift,” 2007 SAE World Congress (SAE 2007-01-1297), De- troit, MI, April, 2007. [14] Jia Ma et al., “Adaptive control of a pneumatic valve actuator for an internal combustion engine,” 2007 American Control Conference, New York, NY, July, 2007 ACKNOWLEDGMENT [15] Jia Ma et al., “Model Based Predictive Control of an The authors gratefully acknowledge the support for this Electro-Pneumatic Valve Actuator for Internal Combustion work from the U.S. Department of Energy, National Energy Engines,” Submitted to 2008 American Control Conference, Technology Laboratory, Energy Efﬁciency and Renewable En- Seattle, WA, June, 2008. ergy Division, Samuel Taylor, Project Manager. [16] M. Anderson, T. C. Tsao, M. Levin, “Adaptive Lift Control

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Downloaded From: http://asmedigitalcollection.asme.org/ on 05/16/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use for a Camless Electrohydraulic Valvetrain,” SAE 981029, 1998. [17] J. M. Tressler et al., “Dynamic Behavior of Pneumatic Sys- tems for Lower Extremity Extenders,” Proceedings of the 2002 IEEE International Conference on Robotics & Au- tomation, Washington, D.C., May 2002. [18] K. Misovec et al., “Digital Valve Technology Applied to the Control of an Hydraulic Valve Actuator,” SAE 1999-01- 0825, 1999. [19] M.-S. S. Ashhab, A. G. Stefanopoulou, J. A. Cook, and M. 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, “Design and Control of a Two-Stage, Electro-Hydraulic Valve Ac- tuation System,” SAE 2004-01-1265, 2004.

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