CONTROL OF AN ELECTROMECHANICAL CAMLESS VALVE ACTUATOR

Transcription

1 Proceeding of the American Control Conference Anchorage, AK May 8-, CONROL OF AN ELECROMECHANICAL CAMLESS VALVE ACUAOR Chun ai, u-chin ao Department of Mechanical and Aeropace Engineering Univerity of California at Lo Angele Lo Angele, CA 995 ABSRAC hi paper addree modeling analyi and the oft eating control of an electromagnetic actuator ued in electromechanical camle valvetrain. Our mathematical modeling analyi reveal the intability of the actuator dynamic linearized around the eating poition and zero velocity. hi implie that open loop pule haping alone cannot render repeatable valve cloing and eating motion. Cloed loop feedback control i neceary to generate repeatable motion that i inenitive to diturbance. A linear model i contructed baed on gray-bo approach that combine mathematical modeling and ytem identification. Notch filtering and linear quadratic optimal control i deigned and eperimentally teted. Control performance i evaluated in term of cloing time, valve eating velocity and eating taillength, armature croing velocity and armature eating velocity.. INRODUCION In recent year camle engine ha caught much attention in the automotive indutry. Camle valvetrain offer programmable valve motion control capability. However, it alo introduce valvetrain control iue. here are mainly two type of camle actuator, electrohydraulic valve (EHV) [4][7] and electromechanical valve (EMV) [][][][6][8][9][] actuator. hi paper deal with the EMV type of actuator. he EMV ytem dicued in thi paper i lightly different from the previou eperimental ytem that the author had worked on [8][9]. Firt of all, tronger pring are ued in current ytem etup in order to get fater cloing. Secondly, there i no phyical lah pring between the engine valve and armature in the new ytem. he engine valve tem i directly in contact with the armature of the electromagnet. A lah, the clearance between the valve tep and the armature when each i eated to it own mechanical top (valve eat and electromagnet) repectively, of.5-.5 mm i maintained to allow for the valve tem thermal epanion. hirdly, the poition meaurement of armature i ued for feedback control. he engine valve poition i till being monitored, but only for the purpoe of modeling and performance evaluation. For an EMV ytem, the control of engine valve eating velocity ha been identified to be a critical problem. he motion of an engine valve on a conventional engine i driven by a camhaft and contrained by a pring to follow the cam profile. herefore, mall eating velocity i not difficult to achieve. For a camle valvetrain, however, a control ytem i required to maintain the eating velocity below a given level. In addition to the reult from uing the new ytem and intrumentation decribed above, in thi paper we will preent new modeling analye that hed light to the adequate control ytem deign approach. he objective i to find out what kind of control trategy i uitable for thi particular ytem. Open-loop feedforward control will be the firt choice if it i feaible. Cycleto-cycle iteration upon the open-loop feedforward control could be conidered given the cyclic nature of engine operation and the fact that the ytem dynamic may change lowly with temperature and aging effect. However, mathematical analyi reveal that an EMV actuator become open loop untable a the engine valve move cloe to the eating poition. Although tability of the ytem i not a concern for the finite duration valve cloing control problem, intability doe indicate large enitivity and poor repeatability. herefore open-loop control alone i unlikely to give u acceptable reult. Feedback control mut be applied for to render conitent oft-eating motion control performance.. MODELING ANALYSIS An EMV ytem conit of two oppoing electromagnet, an armature, two pring and an engine valve. he armature move between the two magnet. When neither magnet i energized, the armature i held at the mid-point of the two magnet by the two pring located on either ide of the armature. hi ytem i ued to control the motion of the engine valve. he engine valve i then in turn ued to control the flow of air into and out of a combution engine cylinder. Figure how the eperimental ytem. wo pule width modulated (PWM) amplifier with two DC power upplie are ued to drive the two electromagnetic coil of the EMV. wo laer encoder enor with reolution of.68 m meaure the armature and valve poition. Real-time control program i eecuted by a ea Intrument MSC digital ignal proceor at KHz ampling rate, implying a velocity reolution of.658 m/ec from the encoder meaurement. A PC i ued to download program into DSP and upload meaured data. Armature Poition Senor EMV actuator Valve Poition Senor Figure. EMV Eperimental Sytem he eperimental ytem dicued in thi paper ha a natural frequency of 5 Hz, which i higher than the ytem dicued in the author previou paper. Figure how the free repone of both ytem. Neither magnet i energized in thee tet when the Correponding author ttao@ea.ucla.edu //$7. AACC 6

2 engine valve i releaed from the fully opened poition. Higher natural frequency i neceary for fater valve opening and cloing peed in order to operate at high engine peed. Figure 4. Eperimental Frequency Repone, voltage to current Figure. EMV Free Repone with No Current.. Electromagnetic Coil he current-force relationhip i governed by the following equation before magnetic aturation occur... Power Amplifier For valve cloing, we need to energize the upper olenoid coil hown in Figure. It wa decided that the power amplifier wa et at voltage model intead of current mode, which mean that the control variable i the voltage applied on the coil intead of the current. For the upper coil, the voltage and current relationhip i governed by the following equation. Spring Solenoid Solenoid Spring L di L V ir i g g g d dt dt Armature b b b m m Figure. Coordinate for Modeling of EMV Actuator k k k (.) Previou identification tet how that if the engine valve i fied at eating poition, the tep repone from voltage to current eem to fit in a firt-order prototype, and the time contant i about - m. [6] However, when the engine valve i free to move under a certain current, the back-emf effect ha to be taken into account. A frequency repone from voltage to current i hown in figure 4. No ignificant phae lag actually appear before khz, and the magnitude variation cro decade i only db. Hence the relationhip from voltage to current i modeled a a tatic gain and the control ytem deign i deired to have at leat db gain margin. F F ( g ) (.) Small ignal linearization around ome operating poition and current give where df GdG di (.) G G ( g ) ( g ) (.4) (.5).. Spring-Ma Sytem he mechanical part of the ytem dicued in thi paper i imilar a the one dicued in [8] ecept without having an apparent lah pring. However, it i till neceary to model the connection between the armature and the engine valve a a tiff pring ince they are not rigidly connected. he mall-ignal tranfer function from the current to poition are: d Gm ( b b) ( k k) di ( m ( bb) ( kk G))( m ( b b) ( k k)) ( bk) (.6) d G( bk) di ( m ( bb) ( kk G))( m ( b b) ( k k)) ( bk) (.7) Intereted reader could refer to the author previou paper [8] for detailed derivation..4. Stability Analyi A mentioned, a table ytem i not neceary for valve cloing becaue an engine valve can be dragged and held on it eating poition by large enough electromagnetic in finite time duration. However the enitivity of the tranient motion to diturbance relie much on the ytem tability. In [8], eperimental data of the valve motion under certain open loop control pule ha hown poor repeatability. We may eamine the pole location of the tranfer function given in the linearized model in equation (.)~(.6) to analyze the ytem tability. For tability analyi, we may implify without lo of generality 6

3 the characteritic equation by auming b and b to be zero. hi give u: ( m ( k k G))( m ( k k )) k (.8) After reformulating thi equation, we have: (( m m ) ( k k G )) k ( ( ))( ) m kg m k (.9) k i known to be large, therefore the pole of the tranfer function are cloe to kk G m m. he ytem i table only if (.) G ( k k ) Since the electromagnetic force i balanced by the pring force a the valve i held at certain poition and the lah pring contant i much greater than the other pring contant, the difference between and can be neglected. herefore the pring force can be epreed a F ( k k )( ) (.) he intability of the open-loop control i demontrated by the following open-loop repeatability tet. In thi tet the control ignal i tuned uch that the engine valve barely touch the valve eat. hen the tuned control ignal i applied to the actuator conecutively for i cycle. he reult i hown in Figure 5. Unlike the cae of free repone when the engine valve conitently ettle down at the middle table equilibrium poition, thi open-loop feedforward control may or may not cloe the valve. If we increae the control ignal to make ure that the engine valve cloe every time, then the eating velocity will be inevitably large. where i the valve equilibrium poition under zero Figure 5. EMV Repeatability et under Open-loop Control electromagnetic force. he combination of equation (.) and (.) give u.5. Sytem Identification ( g) ( kk)( ) (.) Baed on the previou derivation, we parameterize the plant model a following: Plug equation (.) into (.4), and G can be olved a ( ) K G ( k k) (.) g Gp() (.7) o atify the tability condition, it i neceary to have or ( ) g g (.4) (.5) he air-gap g can be neglected due to the fact that g (ee [6]). herefore, the neceary condition for the ytem to be table i (.6) Equation (.6) reveal the intability nature of the electromagnetic type of actuator regardle of the actuator parameter. It tell u that no matter how we chooe the pring contant, the valve cannot be held tably at the poition of within one-third of the total lift by open-loop control current. hi i important in that neither open-loop control nor cycle-tocycle iteration only i poible to give u acceptable quiet-eating performance, becaue the ytem intability over the one-third point toward the valve eat implie poor repeatability and conitency. Feedback control mut be applied to tabilize the ytem and reduce the enitivity of the ytem to diturbance. Sytem identification tet were conducted on the eperimental ytem to etract the unknown parameter in the model. Since the open-loop plant i untable, the ytem ha to be tabilized with a tuned PD controller before the ytem identification tet could be conducted. Chirp ignal wa ued a the ecitation input. he ditance of the regulated poition to the eating poition of thee tet are.,.5 and.7 mm, repectively (Figure 6). hen the parameter of the tranfer function were obtained by curve-fitting the frequency repone manually. he difference of the dynamic repone between the armature poition and valve poition are illutrated in Figure 7. he thin line are eperimental frequency repone, and the thick line are matching model. he agreement of thee frequency repone of different enor location validate the model tructure we propoed.. CONROL DESIGN When the valve-cloing event tart, the lower olenoid coil in Figure i deactivated, and the valve move up toward it eating poition by the mechanical pring force. An EMV actuator work according to the pring-ma pendulum principle, which mean that the ytem follow it own natural ocillation frequency, and eternal electromagnetic force i only needed for overcoming the friction lo. he electromagnetic actuator i only effective in a relatively hort range cloing to the eating poition, and o it i not efficient in the ene of energy conumption to apply cloed-loop control when the valve i till far away from the 64

4 eating poition. However, previou analyi in ection.4 how that the ytem goe untable a the engine valve move to the region within one-third of the total lift. herefore, the cloed-loop control hould tart at leat before thi critical point. Gn() (.) Ideally, hould be equal to the reonant model for perfect cancellation. However, in real implementation, hould be et to be a little bit maller than for the robutne of deign. he neceity of having thi notch filter ha been demontrated by eperiment in the author previou paper. [9] Figure 6. Eperimental Frequency Repone, Voltage to Armature Poition Figure 7. Difference of the Dynamic Repone between the Armature poition and Valve Poition he relatively large gain variation hown in the modeling proce tell u that the deigned control ytem hould have relative large gain margin. near-quadratic optimal control deign i choen for thi purpoe. he control tructure i hown in Figure 8. Gp i the plant model. Gn i a notch filter, which will be eplained in ection.. Gc i a tabilizing controller, which will be deigned in ection.. he feedforward ignal u ff will be dicued in ection.. ref + - Gc Figure 8. Control Structure uff ufb + + u + y Gn + Gp.. Notch filter he plant ha been identified to be fourth order model. It i noticed that the lightly-damped econd-order pole-zero pair hould be canceled out before the optimal control deign i applied. d.. LQ Optimal Control Deign he augmented plant, i.e. the plant cacaded with the notch filter, i converted into tate-pace form. (.) () t A() t Bu() t yt () Ct () (.) hi model ha two tate, the armature poition and velocity. he poition can be directly meaured, and the velocity can be etimated with the differentiation of poition meaurement. An LQ optimal controller i deigned for tabilizing the augmented plant. he cot function that need to be minimized i () () () dt (.4) J t Q t Ru t where Q and R need to be choen baed on the given ytem. he final control law i given by (.5) ut () R BPt () where P i the olution to the Riccati algebraic equation A P PA PBR B P Q (.6).. Feedforward Control Sequence and rajectory Deign A natural way to control the valve eating proce i that we firt tune an open-loop control ignal equence uch that the provided energy barely matche the friction lo. By applying thi control equence, ometime the valve cloe with very mall eating velocity, but ometime it doe not cloe at all due to the intability nature of the ytem. Now we pick the cae when the valve land moothly with acceptable eating velocity, record the armature motion trajectory and ue it a the reference trajectory for the cloed-loop ytem to track. Meanwhile the tuned openloop control ignal equence erve a the feedforward control ignal. he objective of the feedback controller i to reduce the enitivity of the ytem to diturbance and maintain valve motion along the given reference trajectory. 4. EXPERIMENAL RESULS he deign proce in ection i conducted in continuou-time domain. When it come to digital implementation, bilinear tranformation i ued to digitalize the deigned controller. he ampling frequency i khz. Since the frequency range of interet i le than khz, the frequency warping effect during the tranformation proce i neglected. 65

5 4.. Performance Indice he cloing and eating performance of the cloed-loop controlled EMV ytem can be quantified by uing the following three indice: Cloing ime t c, Seating ail-length t, Valve Seating Velocity v, Armature Croing Velocity v c and Armature Seating Velocity v a. Definition, Cloing ime, t c : he time it take for the valve to move from 9% of the maimum lift to % of the maimum lift. Definition, Seating ail-length, t : Run a free-repone tet for the EMV ytem and record the moment that the engine valve reache the lowet poition (cloet to it eat) a time t. hen for each quieting-eating control tet, record the moment of the firt time the engine valve get to the eating poition a t f. he "eating tail-length" i defined a t f - t. Definition, Valve Seating Velocity, v : he intant velocity of engine valve at the firt time it get to it eating poition. Definition 4, Armature Croing Velocity, v c : he average velocity of the armature moving from.5 mm above the valve eating poition to.5 mm below the valve eating poition. Definition 5, Armature Seating Velocity, v a : he intant velocity of armature at the firt time it get to it own mechanical boundary. he method of finding the eating poition in eperiment i decribed in the author previou paper [9]. he reaon why we have different indice for the valve eating velocity and armature croing velocity i due to the fact that the armature and valve are not rigidly connected, and their velocitie are not necearily the ame. he difference between the armature motion and valve motion i illutrated in Figure Cloed-Loop Repeatability et In thi tet we implemented the controller deigned in Section to the EMV ytem, and conducted 5 weep of engine cycle. It doe not mean much by jut having one good (quiet) repone becaue the eential problem we had at the beginning wa that the ytem wa enitive to unknown diturbance. (Indeed, even open-loop control could occaionally render u quiet-eating performance.) herefore when we tet our cloedloop control ytem, the mot important iue i to ee if we can have good and conitent ytem repone. he 5 weep of engine valve motion trajectorie are hown in Figure. Figure. Cloed-Loop Repeatability et Figure how the ditribution of Valve Seating Velocity, v. Figure how the ditribution of Armature Seating Velocity, v a. he mean value and tandard deviation for all the performance indice are ummarized in able. Figure. Ditribution of Valve Seating Velocity, v, over 5 Sweep Figure 9. he Difference between Armature Motion and Valve Motion Figure. Ditribution of Armature Seating Velocity, v a, over 5 Sweep able. Summary of Cloed-Loop Seating Control Reult Mean Standard Deviation Cloing ime, t c, (m).76. Seating ail-length, t, (m).68. Valve Seating Velocity, v, (m/).9.4 Armature Croing Velocity, v, (m/).9.5 Armature Seating Velocity, v, (m/)

6 4.. Compromie of Supply Voltage and Power Conumption he upply voltage ha to be higher than ome minimum required value, V min, in order for providing enough energy to overcome the ytem friction lo. A the upply voltage i higher than V min, oft-eating may be realized, but depending on how cloe the upply voltage i to V min, the power conumption might be high. A we dicued at the beginning of ection, the electromagnetic actuator i only effective in a relatively hort range. herefore, the energy-efficient way to control the valve i that there i zero current when the valve i far away from the eating poition, and high enough current when the valve i cloe. However, it take time for the current to build up to the level that i neceary for the valve cloing due to the eitence of coil inductance, and the time for building up the required current depend on the given upply voltage. Baically, the higher the upply voltage i, the horter time it take for the current to build up, and the le energy i wated during the current tranient time. Seating control wa teted with two different upply voltage, 5V and 8V repectively, to demontrate the trade-off between upply voltage and power conumption. Figure how the voltage, current and valve motion in both cae. able lit the energy conumed during the valve cloing proce in both cae. he cae with higher upply voltage conume le energy. Figure. rade-off between Supply Voltage and Power Conumption able. Energy Conumption during Valve Cloing Supply Voltage (V) 5 8 Energy Conumption (J).9.9 CONCLUSIONS Our mathematical modeling analyi reveal that a camle electromechanical valve actuator become untable, a the ditance of the engine valve to it eating poition i le than roughly one third of the total lift, regardle of pring rate or electromagnetic coil turn. A linear model wa obtained baed on the derived model tructure and ytem identification tet reult for control ytem deign. An LQ optimal control i deigned and implemented on the hardware ytem. he eperimental reult have hown conitent cloed-loop ytem repone. he average valve eating velocity i.9 m/ with tandard deviation of.4 m/ and the armature average eating velocity i.48 m/ with tandard deviation of.9 m/. he cloing time i.76m and eating tail-length i.68 m. Both of them indicate improvement from the author previou work with weaker mechanical pring. he compromiing relationhip between upply voltage and power conumption i dicued and demontrated by eperiment. Preent and future reearch effort i directed toward further improving the valve motion control performance and energy conumption under upply voltage contraint. ACKNOWLEDGMEN he author gratefully thank Ford Reearch Lab for lending the electromagnetic actuator and Viteon for providing the mechanical pring ued in thi work. REFERENCES [] Butzmann, S., Melbert, J., and Koch, A., Senorle Control of Electromagnetic Actuator for Variable Valve rain, SAE Paper --5 [] Hoffmann, W., and Stefanopoulou, A., "Valve Poition racking for Soft Land of Electromechanical Camle Valvetrain," rd IFAC Conference Advance in Automotive Control, [] Hoffmann, W., and Stefanopoulou, A., "Iterative Learning Control of Electromechanical Camle Valve Actuator," Proceeding of the American Control Conference, Arlington, VA, June [4] Schechter, M., and Levin, M., Camle Engine, SAE Paper 9658, 996. [5] Skogetad, S. and Potlethwaite, I., Multivariable Feedback Control Analyi and Deign, Hohn Wiley & Son, 996 [6] Stubb, A., Modeling And Controller Deign Of An Electromagnetic Engine Valve, M.S. hei, Univerity of Illinoi at Urbana-Champaign, [7] ai, C., ao, -C. and Levin, M., Nonlinear Adaptive Feedforward Control of an Electrohydraulic Camle Valvetrain, Proc. American Control Conference, - 5, Chicago, IL, June. [8] ai, C., Stubb, A. and ao, -C., Modeling and Controller Deign of an Electromagnetic Engine Valve, Proc. American Control Conference, , Arlington, VA, June [9] ai, C. and ao, -C., Quiet Seating Control Deign of an Electromagnetic Engine Valve Actuator, ASME International Mechanical Engineering Congre and Epoition, New York, NY, November -6,. [] omizuka, M., ao, -C., and Chew, K-K., Analyi and Synthei of Dicrete-ime Repetitive Controller, Journal of Dynamic Sytem, Meaurement, and Control, 989 [] ao, -C., and omizuka, M., Robut Adaptive and Repetitive Digital racking Control and Application to a Hydraulic Servo for Noncircular Machining, ranaction of ASME, 994 [] Wang, Y., Stefanopoulou, A., Haghgooie, M., Kolmanovky, I., and Hammoud, M. Modelling of an Electromechanical Valve Actuator for a Camle Engine, 5th International Sympoium on Advanced Vehicle Control, Ann Arbor, Michigan USA, 67