Mechanical Systems and Signal Processing

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1 Mechanical Sytem and Signal Proceing 5 () 9 9 Content lit available at ScienceDirect Mechanical Sytem and Signal Proceing journal homepage: Simulation and control of an electro-hydraulic actuated clutch Andreea-Elena Balau n, Contantin-Florin Caruntu, Corneliu Lazar Department of Automatic Control and Applied Informatic, Gheorghe Aachi Technical Univerity of Iai, Str. Prof. dr. docent Dimitrie Mangeron, Number 7, Iai 75, Romania article info Article hitory: Received 4 February Received in revied form December Accepted 3 January Available online January Keyword: Simulation Dynamic modelling Hydraulic actuator Wet clutch control Networked predictive control trategy Time-varying delay abtract The baic function of any type of automotive tranmiion i to tranfer the engine torque to the vehicle with the deired ratio moothly and efficiently and the mot common control device inide the tranmiion are clutche and hydraulic piton. The automatic control of the clutch engagement play a crucial role in Automatic Manual Tranmiion (AMT) vehicle, being een a an increaingly important enabling technology for the automotive indutry. It ha a major role in automatic gear hifting and traction control for improved afety, drivability and comfort and, at the ame time, for fuel economy. In thi paper, a model for a wet clutch actuated by an electrohydraulic valve ued by Volkwagen for automatic tranmiion i preented. Starting from the developed model, a imulator wa implemented in Matlab/Simulink and the model wa validated againt data obtained from a tet-bench provided by Continental Automotive Romania, which include the Volkwagen wet clutch actuated by the electro-hydraulic valve. Then, a predictive control trategy i applied to the model of the electro-hydraulic actuated clutch with the aim of controlling the clutch piton diplacement and decreaing the influence of the network-induced delay on the control performance. The imulation reult obtained with the propoed method are compared with the one obtained with different networked controller and it i hown that the trategy propoed in thi paper can indeed improve the performance of the control ytem. & Elevier Ltd. All right reerved.. Introduction Nowaday, clutch pedal a well a automatic tranmiion, double-clutch tranmiion, hybrid drive concept and chai control ytem increaingly require open-loop and cloed-loop controlled actuator. The introduction of a new actuator open up new opportunitie for controlling the engine and drive-line, and new trategie that can improve the drive-line performance are predictable. In the lat decade, the ue of control ytem for automated clutch and tranmiion actuation ha been contantly increaing; a clear trend i that automatic clutch ytem will be introduced and ued in a wider variety of application, which would benefit from advanced clutch control. For example, tart and top trategie can be employed and in addition the clutch control can be utilied in automated manual tranmiion to reduce the time for gear change. Furthermore, clutch control i alo a factor in look-ahead control. Recent attention ha focued on modelling different valve type ued a actuator in automotive control ytem: phyic-baed nonlinear model for an exhauting valve [], nonlinear tate-pace model decription of the actuator that i derived baed on phyical principle and parameter identification [,3], nonlinear phyical model for programmable n Correponding author. addree: abalau@ac.tuiai.ro, andreea984@yahoo.com (A.-E. Balau), caruntuc@ac.tuiai.ro (C.-F. Caruntu), clazar@ac.tuiai.ro (C. Lazar) /$ - ee front matter & Elevier Ltd. All right reerved. doi:.6/j.ymp...9 Downloaded From

2 9 A.-E. Balau et al. / Mechanical Sytem and Signal Proceing 5 () 9 9 valve [4], nonlinear model of an electro-magnetic actuator ued in brake ytem baed on ytem identification [5], mathematical model obtained uing identification method for a valve actuation ytem of an electro-hydraulic engine [6], linear model contructed baed on a grey-box approach which combine mathematical modelling and ytem identification for an electro-magnetic control valve [7], input output implified mathematical model and tate-pace mathematical model for an electro-hydraulic valve actuator, both baed on parameter identification and phyical law [8]. Alo, during the lat year, the automated clutch actuator have been actively reearched and different model and control trategie have been developed: a model for an electro-hydraulic valve ued a actuator for a wet clutch [9], dynamic modelling and control of electro-hydraulic wet clutche [], PID control for a wet plate clutch actuated by a preure reducing valve [], predictive and piecewie LQ control of a dry clutch engagement [], witched control of an electro-pneumatic clutch actuator [3], Model Predictive Control of a two tage actuation ytem uing piezoelectric actuator for controllable indutrial and automotive brake and clutche [4], explicit Model Predictive Control of an electro-pneumatic clutch actuator [5]. All of the above control olution aume that the enor, controller and actuator are directly connected, which i not realitic. Rather, in modern vehicle, the control ignal from the controller and the meaurement from the enor are exchanged uing a communication network, e.g., Controller Area Network (CAN) or Flexray, among control ytem component, yielding a o called Networked Control Sytem (NCS). Although thee NCS brought many attractive advantage, which include: low cot, imple intallation and maintenance, increaed ytem agility, higher reliability and greater flexibility, thi alo bring up a new challenge on how to deal with the effect of the network-induced delay and packet loe in the control loop. The delay may be unknown and time-varying and may degrade the performance of control ytem deigned without conidering them and can even detabilie the cloed-loop ytem. The predictive control technique were introduced mainly in order to deal with plant that have complex dynamic (untable invere ytem, time-varying delay, etc.) and plant model mimatch. Thee trategie are of a particular interet from the point of view of both broad applicability and implementation implicity, being applied on large cale in indutry procee, having good performance and being robut at the ame time. They were initially utilied for low procee: oil refinerie, petrochemical, pulp and paper, primary metal indutrie, ga plant [6], but tarting with the evolution of hardware component and algorithm, the poibility to implement thee type of control algorithm to fat procee, which have reduced ampling period, appeared: vehicle engine and traction control, aero-patial application, autonomou vehicle, power generation and ditribution [7]. Some predictive control algorithm were already propoed for different vehicle ubytem: Anti-lock Braking Sytem (ABS) control [8], Vehicle Dynamic Control (VDC) [9], vehicle magnetic actuator [], middle-layer control [], but without taking into account the delay that can appear in a networked environment. A uch, in thi paper, an input output model for a wet clutch actuated by an electro-hydraulic valve ued by Volkwagen for automatic tranmiion i developed. The electro-hydraulic valve ued to control the wet clutch i not a typical one, being epecially deigned for Volkwagen vehicle. Thi type of valve wa not modelled in literature and a proper model wa needed in order to control the wet clutch with the aim of lowering emiion, reducing fuel conumption and increaing comfort. The deigned electro-hydraulic clutch actuator model ha a input the upply voltage and a output the clutch preure and the clutch piton diplacement. Starting from the developed model, a imulator wa implemented in Matlab/Simulink and the model wa validated againt data obtained from a tet-bench provided by Continental Automotive Romania, which include the Volkwagen DQ5 wet clutch actuated by the electrohydraulic valve DQ5. The imulation are very imilar to the experimental data proving that the modelling approach i uitable to thi kind of clutch actuated by an electro-hydraulic valve. Uing the developed input output model for the valve clutch ytem, an appropriate networked controller baed on a predictive trategy i propoed in order to control the clutch piton diplacement, while decreaing the influence of the variable time delay induced in the CAN-baed NCS on the control performance. The plant i a ubytem of the automatic tranmiion of a Volkwagen vehicle and the main control goal i to make the clutch plate poition track a given external reference, while taking into account the delay that appear in the NCS. The reult obtained with the propoed method are compared with the one obtained with different networked controller and it i hown that the trategy preented in thi paper can indeed improve the performance of the control ytem.. Modelling of the actuator clutch ytem In thi ection an input output mathematical model baed on phyical principle for flow and fluid dynamic for the electro-hydraulic actuated clutch i preented... Structure and functional operation Schematic of the electro-hydraulic valve actuator and wet multi-plate clutch layout are given in Fig.. A pump produce the line preure P S ued a input for the electro-hydraulic actuator repreented by a preure reducing valve. Thi valve realie a preure P R on the clutch ide, depending on the current i in the olenoid, which will have a conequence the magnetic force F mag exerted on the valve plunger, which move linearly within a bounded region under the effect of thi force. Such a force i generated by a olenoid placed at one boundary of the region. The magnetic force i a

3 A.-E. Balau et al. / Mechanical Sytem and Signal Proceing 5 () Fig.. Actuator and clutch ytem: (a) charging phae and (b) dicharging phae. function of the olenoid current i and the diplacement x, defined by k a i F mag ¼ f ðiþ¼ ðk b þxþ ; L di þri ¼ u, dt where k a and k b are contant, L i the olenoid induction, R the reitance and u i the upply voltage. The preure to be controlled P R i ened on the plunger end area C and D and compared with the magnetic force F mag. The two force F C and F D from the two ened preure chamber generate the feedback force F feed ¼ F C F D. Depending on the valve plunger poition, there are two phae: the charging phae, when the magnetic force i greater than the feedback force and the valve plunger i moved to the left, connecting the ource with the hydraulic actuated clutch (Fig. a), and the dicharging phae, when the magnetic force i witched off or ha a lower value than the feedback force o that the valve plunger i moved to the right, connecting the hydraulic actuated clutch to the tank (Fig. b). The wet clutch i a chamber with a piton a repreented in Fig.. In the charging phae when the valve plunger i moved to the left and the diplacement x i conidered poitive, the oil flow from the ource through the valve to the clutch and the piton in the clutch move toward the clutch plate compreing them. In the dicharging phae, when the valve plunger i moved to the right and the diplacement x i negative, the clutch piton move to the left and the oil flow from the clutch chamber through the valve to the tank... Input output model of the actuator clutch ytem In [8] two model for an electro-hydraulic actuator were developed: an input output model, where implification were made in order to obtain a uitable tranfer function to be implemented in Matlab Simulink, and a tate-pace model. Starting from the equation that decribe the actuator input output model, an input output model for a wet clutch actuated by an electrohydraulic valve ued by Volkwagen for automatic tranmiion wa developed in [] and it i preented in thi ubection. Comparing the magnetic force and the feedback force it reult a force balance, which decribe the plunger motion and the output preure. Thi equation of force balance i the ame for both poitive and negative diplacement of the plunger F mag CP C þdp D ¼ M v xþk e x, ðþ where P C repreent the preure of the left ened chamber, P D the preure of the right ened chamber, M v i the plunger ma, K e ¼ :43wðP S P R Þ repreent the flow force pring rate, P S i the upply preure, P R i the reduced preure, P S,P R are the nominal value of the preure, w repreent the area gradient of main orifice (from the ource to the wet clutch), x i the plunger diplacement and repreent the Laplace operator. In order to capture the dynamical behaviour of the ytem, phyical law were applied for the charging phae of the preure reducing valve, illutrated in Fig. a. The linearied continuity equation which decribe the dynamic from the ened preure chamber are Q C ¼ K ðp R P C Þ¼ V C b e P C Cx, ðþ Q D ¼ K ðp R P D Þ¼ V D b e P D þdx, ð3þ

4 94 A.-E. Balau et al. / Mechanical Sytem and Signal Proceing 5 () 9 9 where K, K are the flow-preure coefficient of retrictor, V C, V D are the ened chamber volume and b e repreent the effective bulk modulu. Uing the flow through the left and right ened chamber, the flow through the main orifice from the ource to the wet clutch and the clutch flow, the linearied continuity equation at the chamber of the preure being controlled i K C ðp S P R Þ Q L K l P R K ðp R P C Þ K ðp R P D ÞþK q x ¼ V t b e P R, ð4þ where Q L i the clutch flow, K C i the flow-preure coefficient of main orifice, K q i the flow gain of main orifice, K l i the leakage coefficient and V t repreent the total volume where the preure i being controlled. Thee equation define the actuator dynamic and combining them into a more ueful form, olving () and (3) with repect to P C and P D and ubtituting into (4) yield after ome manipulation ðk C P S Q L Þ þ þ þk o o q x þ þ þ C D o o K q K q þ þ C D o o K q o K q o ¼ P R K ce þ þ þ, ð5þ o o o 3 where o ¼ b e K =V C, o ¼ b e K =V D are the break frequencie of the left and right ened chamber, repectively, o 3 ¼ b e K ce =V t i the break frequency of the main volume and K ce ¼ K C þk l repreent the equivalent flow-preure coefficient. The model (5) wa obtained conidering that V C =V t 5, V D =V t 5. In the dicharging phae of the preure reducing valve, illutrated in Fig. b, the dynamical behaviour of the ytem i obtained by applying phyical law to the oil flow. The linearied continuity equation at the ened preure chamber are imilar with () and (3), but having changed ign. Uing the flow through the left and right ened chamber, the flow through the main orifice from the wet clutch to the tank and the clutch flow, the linearied continuity equation obtained for the chamber of the preure being controlled i Q L þk ðp C P R ÞþK ðp D P R Þ K D ðp R P T Þ K l P R þk q x ¼ V t b e P R, ð6þ where K D i the flow-preure coefficient of main orifice and P T repreent the tank preure. In an entire analogue manner like demontrated for the charging phae, again making the aumption that V C =V t 5, V D =V t 5 and conidering that the flow-preure coefficient of the main orifice are equal, K D ¼ K C, the final form for the reducing valve model in the dicharging phae wa obtained h i ðk D P T þq L Þ o þ o þ þk q x þ o þ o þ C D þ Kq Kq o o þ Kqo C Kqo D ¼ P R K ce o þ o þ o 3 þ, ð7þ In order to obtain the actuator model the preure P C and P D from () and (3) are replaced in () reulting after ome manipulation þ F x C þ D þ ¼ xk K o K o e þ, o m p whereo m ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi K e =M v note the mechanical natural frequency of the actuator plunger and P R P F ¼ F mag C þd R, ð=o Þþ ð=o Þþ For the clutch model, the firt equation arie by applying Newton econd law to the force on the piton, reulting A L P L ¼ M p x p þb f x p þkx p, ð8þ where A L i the area of piton, P L the preure from the piton chamber, x p the piton diplacement, M p the total ma of the piton, K the load pring gradient and B f i the vicou damping coefficient of the piton. Applying the continuity equation to the piton chamber yield Q L ¼ K 3 ðp R P L Þ¼ V L b e P L þa L x p, ð9þ where K 3 i the flow-preure coefficient of the pipe from valve actuator to the clutch and V L i the piton chamber volume. Eq. () and (5), for the charging phae of the actuator, and () and (7) for the dicharging phae of the actuator together with the piton dynamic given by (8) and (9), define the actuator clutch ytem dynamic model. Starting from thee equation, a chematic diagram of the tranfer function for the actuator clutch ytem wa created and repreented in Fig.. It can be een that a witch block wa ued in order to commutate between the two phae that decribe the functionality of the actuator, the charging and the dicharging phae. The ign of the diplacement of the plunger wa ued a the witch parameter, with the threhold a, thu electing different perturbation for poitive or negative diplacement of the plunger.

5 A.-E. Balau et al. / Mechanical Sytem and Signal Proceing 5 () Fig.. Tranfer function block diagram of valve clutch ytem. 3. Networked predictive control trategy The actuator clutch ytem, which i a ubytem of the automatic tranmiion from a Volkwagen vehicle, i controlled over a communication network (i.e., CAN), o the control ignal from the controller, which i implemented in an Electronic Control Unit (ECU), have to be ent to the actuator (valve) through a communication network; alo, the value of the meaurement from the enor have to be ent to the controller through the ame network, reulting a NCS. Thi NCS introduce a variable time delay in the control loop, which can degrade the performance of the control ytem; that i the reaon why the delay have to be conidered in the controller deign, in order to be compenated. To thi end, in thi ection, firtly, an equivalent ARX actuator clutch model i identified, econdly, the predictive control problem i olved for a given time delay and, thirdly, three method on how to deal with the time-varying network-induced delay are propoed. Alo, at the end of thi ection, the control architecture i decribed. 3.. CARIMA model of the actuator clutch ytem In order to apply the predictive control trategy that will be decribed in Section 3., a CARIMA model for the valve clutch ytem wa developed Aðz ÞyðkÞ¼z d Bðz Þuðk Þþ eðkþcðz Þ, ðþ Dðz Þ conidering a input the upply voltage and a output the clutch piton diplacement. In () d i the delay of the plant, eðkþ i white noie with zero mean value, Aðz Þ, Bðz Þ are the ytem polynomial with the degree n A and n B and Cðz Þ, Dz are the diturbance polynomial. The ytem wa identified with an ARX equivalent model employing the imulation model, utiliing a input a PeudoRandom Binary Sequence (PRBS) ignal. Thee equence are ucceion of quared pule, width modulated, that approximate adicretewhitenoieandtheir richne in frequencie help capturing the dynamical behaviour of the ytem. The ARX model i given by the following ytem polynomial: Aðz Þ¼ :78z þ:839z Bðz Þ¼:33z þ:z, ðþ For diturbance model, the polynomial C i conidered to equal one and Dðz Þ¼ z for obtaining a zero teadytate error. 3.. Control trategy In the predictive control trategie, the control action i obtained by olving a minimiation problem at each ampling period. Uually, a equence of future predicted control action are calculated, but only the firt i, in fact, ent to the

6 96 A.-E. Balau et al. / Mechanical Sytem and Signal Proceing 5 () 9 9 actuator. At the next ampling period, the optimiation problem i olved again with the new meaurement coming from the enor and the control action i recalculated. Conidering the plant decribed by the Controlled AutoRegreive Integrated Moving Average (CARIMA) model (), the prediction model i given by ^yðkþj9kþ¼g j d ðz ÞDðz Þz d uðkþjþþ H j dðz ÞDðz Þ uðk Þþ F jðz Þ Cðz Þ Cðz Þ yðkþ, with j ¼ hi,hp, where hi i the minimum prediction horizon and hp i the prediction horizon. uðkþj kþ, j ¼,hc i the future control, computed at time k and ^yðkþj kþ are the predicted value of the output, hc being the control horizon. The two Diophantine equation preented in [3] are ued to determine the polynomial F j z, Gj z and Hj z. Now, conidering a input Dz uk ð Þ and collecting the j-tep predictor in a matrix notation, the prediction model can be written a ^y ¼ Gu d þ ^y, where ^y repreent the free repone and the matrix G i given in [3]. The objective function i baed on the minimiation of the tracking error and on the minimiation of the controller output, the control weighting factor l being introduced in order to make a trade-off between thee objective J ¼ðGu d þ ^y wþ T ðgu d þ ^y wþþlu T d u d, ubject to Dðz ÞuðkþiÞ¼ for i hc,hp d, where w i the reference trajectory vector with the component wðkþj kþ, j ¼ hi,hp. Minimiing the objective function (@J=@u d ¼ ), the optimal control equence yield a u d ¼ðGT GþlI hc Þ G T ½w ^y Š,: Uing the G receding horizon principle and conidering that g j,j ¼ hi,hp are the element of the firt row of the matrix G T GþlI T hc, the following control algorithm reult: Dðz ÞuðkÞ¼ Xhp j ¼ hi g j ½wðkþj9kÞ ^y ðkþj9kþš, 3.3. Time-varying delay In order to deal with the variable-time network-induced delay, firtly, a method to determine the upper bound of the delay i preented, and, econdly, three method of conidering the delay by the predictive control algorithm are propoed. The equation developed in [6] i ued to determine the upper bound of the communication delay that appear on Controller Area Network (CAN) in automotive application d j r ðjþþul R P j i ¼ ðl=c iþ, ðþ where l=36 bit denote the maximum frame length including the 6 bit CS time, R=5 kbp i the rate of a high-peed CAN, c i i the cycle length of the ith priority meage and j i the priority of the node for which the upper bound i being calculated. Uing typical value for the parameter, it yield that the um of the delay from enor-to-controller and from controller-to-actuator i randomly ditributed in the interval, T, where T= m i the ampling period of the ytem. Knowing the upper bound of the time-varying communication delay, in thi paper, three method of conidering the communication delaypropoedtobeuedbythepredictive algorithm are dicued tarting from the reult preented in [4,5]: (i) average delay value method: the delay conidered by the prediction model i calculated uing d ¼ d m þd M, where d m i the minimum delay and d M i the maximum delay that can appear in the communication network; (ii) identification method: the delay i conidered equal to the minimum delay that can appear in the communication network d ¼ d m, and intead of the polynomial B, another polynomial B, ~ identified in order to model the ytem including the delay between d m and d M wa introduced ~Bðz Þ¼ b ~ þ b ~ z þþ b ~ n ~B z n B ~,

7 A.-E. Balau et al. / Mechanical Sytem and Signal Proceing 5 () Reference generator ECU r(k) r(kt) Predictive controller ca u(k) (ukt) (ukt τ k ) c y(kt τ k ) C A N Valve actuator (yk) y(kt) Wet clutch Fig. 3. Schematic diagram of the NCS. with n ~B ¼ n B þd M d m ~b ¼ b ~ ¼¼ b ~ n ~B ¼ b þb þþb nb ; BðÞ¼ BðÞ, n ~B þ ~ (iii) gain-cheduling method: thi method i applied in order to adapt the control algorithm to the variable time delay that appear in the communication network. The adaptation algorithm i derived with aumption that the average communication delay from enor-to-controller and from controller-to-actuator are equal, both being variable. So, for every delay between d m and d M, the coefficient of the previou control action, of the previou output and thoe of the future reference were a priori explicitly calculated and then a look-up table wa created with thee coefficient. At each ampling time new coefficient are elected uing a election variable P N i ¼ t c i d ¼, ð3þ N where t c i i the communication delay from enor-to-controller in ith tep. Therefore, the average value of N previou delay i calculated in thi way. Unlike for the other two predictive method (average delay value method and identification method), in the cae of thi method the upper bound of the delay can be unknown and only an etimation of it can be ued in order to apply the trategy Control architecture After applying the control trategy decribed in Section 3. to the CARIMA model decribed by (), the tructure wa implemented in Matlab/Simulink and a chematic diagram of the NCS i repreented in Fig. 3. The reference generator block compute and end the reference trajectory vector to the predictive controller, which ha the main control goal of making the clutch plate poition track the given external reference. The valve actuator and the wet clutch block are illutrated in detail in Fig.. The valve actuator ha a input the control ignal end by the predictive controller through the network, the voltage u, and a output the reduced preure P R, which i the input of the wet clutch block. The output of the lat block are the clutch preure P L and the clutch piton diplacement x p, whoe value i ent a a meaurement ignal back through the network to the predictive controller. The predictive controller block implement the control algorithm decribed in Section 3.. The delay that are induced by the communication network from enor-to-controller t c and from controller-to-actuator t ca can alo be een in Fig Simulation and experimental reult Baed on the mathematical model preented in Section, in thi ection a imulator wa implemented for the actuator clutch ytem and the imulation reult are dicued. Alo, a networked predictive controller i deigned for the ytem while taking into account the delay that appear in the NCS. 4.. Model validation In order to validate the model obtained for the electro-hydraulic actuated clutch, a imulator wa deigned in Matlab/ Simulink tarting from the mathematical model decribed in Section and the reult obtained with the imulator were compared with the one obtained on a real tet-bench. The tet-bench STAH 5., which include the Volkwagen DQ5 wet clutch actuated by the electro-hydraulic valve DQ5, wa provided by Continental Automotive Romania. The tet-bench can be ued to tet the hydraulic command, ditribution and control device. In order to imulate more preciely the real work condition from the plant (equipment), where the device will be intalled, the tet-bench ha the option to tune the three functional parameter (preure, flow and temperature) to the real value. The tuned value can be predefined and they are hold into pecific limit by a programmable logic controller (PLC).

8 98 A.-E. Balau et al. / Mechanical Sytem and Signal Proceing 5 () 9 9 The parameter ued in imulation for the electro-hydraulic actuator, which are ummaried in Table : the volume of the actuator chamber, the left and right area of the valve plunger, the flow-preure coefficient, were obtained by meaurement made on the tet-bench. The tet-bench alo provide meaurement for the output of the ytem, repreented by the valve plunger diplacement and the clutch preure which are ued in order to validate the implemented imulator. Following experiment made on the tet-bench from Continental Automotive Romania, uing a input the upply voltage, the real-time clutch preure repone P L from Fig. 4b wa obtained. Although the input of the plant i the upply voltage, only the olenoid current i, repectively, the magnetic force F mag, which are repreented in Fig. 4a, were meaured Table Parameter value. Symbol Value Unit Symbol Value Unit K e (N/m) V C 7.53e-8 (m 3 ) M v 5e-3 (kg) V D.4e-7 (m 3 ) b e.6e+9 (N/m ) V t 3.e-4 (m 3 ) o.7e+6 (rad/) C 3.66e-5 (m ) o 5.4e+7 (rad/) D.94e-5 (m ) o 3.4e+6 (rad/) a e-5 (m) K C =K D 7.58e- ((m 3 /)/(N/m )) M p.5 (kg) K 5.5e- ((m 3 /)/(N/m )) V L.5e-5 (m 3 ) K 3.5e-9 ((m 3 /)/(N/m )) A l 7.75e-4 (m ) K q ((m 3 /)/(N/m )) K 9 (N/m) w 3e-3 (m) B f (N /m) P S e+6 (N/m ) k a.5 (N m /A ) P T (N/m ) k b. (m) K l e-9 ((m 3 /)/(N/m )) L. (H) K 3.6e-8 ((m 3 /)/(N/m )) R. (O) Current [A], Fmag [N] Fmag Current (i) Preure [bar] 4 3 imulated PR imulated PL meaured PL Fig. 4. Model validation: (a) input ignal and (b) preure behaviour.

9 A.-E. Balau et al. / Mechanical Sytem and Signal Proceing 5 () Plunger diplacement [mm] Clutch flow [m 3 /] 4 x Piton diplacement [mm] Fig. 5. Simulation reult: (a) valve plunger diplacement; (b) clutch flow and (c) clutch piton diplacement. Communication delay [] x Average comunication delay [] Fig. 6. Time delay: (a) ditribution of communication delay under interval ½,6TŠ and (b) average communication delay for N=.

10 9 A.-E. Balau et al. / Mechanical Sytem and Signal Proceing 5 () 9 9 on the tet-bench. The imulation reult are validated due to imilar behaviour obtained for the preure in the clutch chamber. Uing a input ignal the ame electric current i from the experiment made on the tet-bench, Fig. 4b how the comparion between meaurement and imulation for the preure obtained in the clutch chamber, along with the imulation reult of the reduced preure. Good agreement between the real-time and imulation reult prove that the model capture the eential dynamic of the ytem. The behaviour of the imulated preure from the piton chamber follow the meaured preure behaviour, having the ame teady-tate value, but with a difference in the high frequency due to the approximation of the very mall time contant. Thee approximation reult in a tranient behaviour of the model a little bit different than that of the real repone in the two phae. Thu, in the charging phae thi difference appear a a time delay and in the dicharging phae a a low repone. Thee modelling error demand the ue of an advanced control technique a the predictive approach, which i capable of compenating them. The behaviour obtained for the valve diplacement repreented in Fig. 5a, i imilar with the behaviour obtained in [8] where a linearied input output model and a tate-pace model were developed for the electro-hydraulic preure reducing valve ued a actuator for the wet clutch. In the imulator of the actuator clutch ytem, the clutch flow, which i illutrated in Fig. 5b, wa obtained a a difference between the preure from thevalveandtheclutchpreure.theimulationreult obtained for the clutch piton diplacement are illutrated in Fig. 5c, reult obtained with the ame input ignal from Fig. 4a. It can be een that for a poitive clutch flow, there are poitive diplacement both for the valve plunger and the clutch piton, illutrating the charging phae of the valve when the clutch chamber i filled with oil, while for a negative clutch flow, there are negative diplacement, illutrating the dicharging phae of the valve and the oil going from the clutch chamber through the valve to the tank. The value obtained for the valve piton diplacement i in the range of [,+] mm, like it i uppoed to be, becaue the actuator i a cloed loop ytem and the plunger diplacement i retricted by the balance in force. On the other hand, the clutch i an open loop ytem, with no feedback, o it reult a high value of the piton diplacement which can be further limited by applying a proper control trategy for the electro-hydraulic actuated wet clutch. 4.. Controller performance Thi ection preent the validation of the propoed predictive control trategie invetigated on the valve clutch ytem model uing the Matlab/Simulink programme. 6 x 3 Clutch Diplacement [m] 4 reference PI without delay PI with delay Smith predictor with delay x 3 Clutch Diplacement [m] 4 reference average delay identification gain cheduling Fig. 7. Clutch diplacement: (a) PI and Smith controller and (b) predictive controller.

11 A.-E. Balau et al. / Mechanical Sytem and Signal Proceing 5 () Being component of the ame powertrain ubytem it can be conidered that the communication delay from enorto-controller and from controller-to-actuator have the ame value and they are uniform ditributed. In Fig. 6a, a time ditribution of the communication delay (enor-to-controller) under interval, 6T, generated uing a Matlab/Simulink model, i hown. Chooing N=, in Fig. 6b the average value of N previou delay (3), ued for the gain-cheduling method, i repreented for the delay illutrated in Fig. 6a. It wa conidered that d m = and d M = from () and the predictive control trategy with the three method wa applied uing the following tuning parameter: hc ¼ naþ ¼ 3, hi ¼ dþ and hp ¼ hcþd. The control action obtained uing the identified ARX model () wa then applied to the model of the valve clutch ytem. The reult obtained are compared with two different controller: a PI controller and a Smith-like predictive controller with adaptation to communication delay developed in [7]. A tep ignal wa applied a reference for the clutch piton diplacement and it wa deired that the ytem track the reference ignal a fat a poible, the following figure howing the controlled output and the reference ignal. In Fig. 7a, four ignal were repreented: the reference clutch diplacement value, the repone of the ytem uing the PI controller without communication delay and with communication delay, the repone of the ytem with delay when the Smith-like predictive controller i applied. Fig. 7b illutrate the reference clutch diplacement value and the repone of the ytem with communication delay when the predictive average value method, the predictive identification method and the predictive gain-cheduling method are applied. The repone are clearly different from thoe obtained with the PI controller and the Smith predictor. The et-point repone for the PI and the Smith-like predictive controller have an obviou overhoot, while the et-point curve for the predictive method are imilar except that the rie time for the gain-cheduling method i much maller than thoe for the other method and all the repone have almot no overhoot. In Fig. 8a, the control ignal for the PI controller and for the Smith predictor were repreented and in Fig. 8b, the control ignal for the predictive method were repreented. The reult illutrate that the variation of the control ignal are much maller for the propoed identification method, while the variation are much bigger for the gain-cheduling method. It can be concluded that the performance of the predictive control method are better than the performance of the Smith predictor developed in [7]..8 Voltage [V].6.4 PI without delay. PI with delay Smith predictor with delay Voltage [V].6.4 average delay. identification gain cheduling Fig. 8. Control ignal: (a) PI and Smith controller and (b) predictive controller.

12 9 A.-E. Balau et al. / Mechanical Sytem and Signal Proceing 5 () Concluion In thi paper a linearied input output model for an electro-hydraulic actuated clutch i developed. Simplification were made in order to obtain a uitable tranfer function to be implemented in Matlab/Simulink and to achieve an appropriate behaviour for the output. The model wa validated by comparing the reult with data obtained on a real tet-bench provided by Continental Automotive Romania. Baed on the validated input output model, a networked predictive controller ha been deigned for the wet clutch actuated by an electro-hydraulic valve with the aim of controlling the clutch piton diplacement, while decreaing the influence of the variable-time delay on the cloed-loop control performance over the communication network. Simulation a well a the experimental reult are preented to how the applicability of the modelling and control approache. Acknowledgement The work wa upported by The National Centre for Program Management from Romania under the reearch grant SICONA /8. Reference [] J. Ma, G. Zhu, A. Hartig, H. Schock, Model-baed predictive control of an electro-pneumatic exhaut valve for internal combution engine, in: Proceeding of American Control Conference, Seattle, USA, June 8, pp [] Y. Wang, T. Megli, M. Haghgooie, K.S. Peteron, A.G. Stefanopoulou, Modeling and control of electromechanical valve actuator, SAE, Tranaction Journal of Engine, SAE --6 (). [3] K.S. Peteron, A.G. Stefanopoulou, Y. Wang, T. Megli, Virtual lah adjuter for an electromechanical valve actuator through iterative learning control, in: Proceeding of International Mechanical Engineering Congre, Wahington, USA, November 3. [4] S. Liu, B. Yao, Coordinative control of energy aving programmable valve, IEEE Tranaction on Control Sytem Technology 6 (8) [5] A. Forrai, T. Ueda, T. Yumura, A imple approach to electromagnetic actuator control baed on aymptotically exact linearization, Archive of Applied Mechanic 74 (5) [6] H.-H. Liao, M.J. Roelle, J.C. Gerde, Repetitive control of an electro-hydraulic engine valve actuation ytem, in: Proceeding of American Control Conference, Seattle, USA, June 8, pp [7] C. Tai, T.-C. Tao, Control of an electromechanical camle valve actuator, in: Proceeding of American Control Conference, Anchorage, USA, May, pp [8] A.E. Balau, C.F. Caruntu, D.I. Patracu, C. Lazar, M.H. Matcovchi, O. Patravanu, Modeling of a preure reducing valve actuator for automotive application, in: Proceeding of the 8th IEEE International Conference on Control Application, Saint Peterburg, Ruia, July 9, pp [9] R. Morelli, R. Zanai, Modeling of automotive control ytem uing power oriented graph, in: Proceeding of 3nd Annual Conference on Indutrial Electronic (IECON), Pari, France, November 6, pp [] R. Morelli, R. Zanai, R. Cirone, R. Sereni, R. Bedogni, E. Sedoni, Dynamic modeling and control of electro-hydraulic wet clutche, in: Proceeding of IEEE Intelligent Tranportation Sytem, October 3, pp [] M.J.W.H. Edelaar, Model and control of a wet plate clutch, Ph.D Thei, Eindhoven, Holland, 997. [] A.C. Van der Heijden, A.F.A. Serraren, M.H. Camlibel, H. Nijmeijer, Hybrid optimal control of dry clutch engagement, Int. J. Control 8 (7) [3] H. Langjord, T.A. Johanen, J.P. Hepanha, Switched control of an electropneumatic clutch actuator uing on/off valve, in: Proceeding of American Control Conference, Seattle, USA, July 7, pp [4] V.A. Neelakantan, Model predictive control of a two tage actuation ytem uing piezoelectric actuator for controllable indutrial and automotive brake and clutche, Journal of Intelligent Material Sytem and Structure 9 (8) [5] A. Grancharova, T.A. Johanen, Explicit model predictive control of an electropneumatic clutch actuator uing on/off valve and pule-width modulation, in: Proceeding of European Control Conference (ECC 9), Budapet, Hungary, Augut 9. [6] T. Tran, L. Vlacic, Practical proce control technique training, in: Proceeding of Seventh IFAC Sympoium on Advance in Control Education, Madrid, Spain, June 6. [7] R. Gu, S.S. Bhattacharyya, W.S. Levine, Dataflow-baed implementation of model predictive control, in: Proceeding of American Control Conference, St. Loui, USA, June 9. [8] D.K. Yoo, L. Wang, Model baed wheel lip control via contrained optimal algorithm, in: Proceeding of IEEE Multi-conference on Sytem and Control, Singapore, October 7. [9] S. Anwar, Predictive yaw tability control of a brake-by-wire equipped vehicle via eddy current braking, in: Proceeding of American Control Conference, New York, USA, July 7. [] S. Di Cairano, A. Bemporad, I.V. Kolmanovky, D. Hrovat, Model predictive control of magnetically actuated ma pring damper for automotive application, Int. J. Control 8 (7) [] C. Sehyun, A flexible hierarchical model-baed control methodology for vehicle active afety ytem, Ph.D Thei, Michigan, USA, 7. [] C. Lazar, C.F. Caruntu, A.E. Balau, Modelling and predictive control of an electro-hydraulic actuated wet clutch for automatic tranmiion, in: Proceeding of IEEE International Sympoium on Indutrial Electronic (ISIE ), Bari, Italy, July. [3] E.F. Camacho, C. Bordon, Model Predictive Control, Springer-Verlag, London, 4. [4] C.F. Caruntu, C. Lazar, Predictive control for time-varying delay in networked control ytem, in: Proceeding of the Eighth IFAC Workhop on Time Delay Sytem (IFAC-TDS 9), Sinaia, Romania, September 9. [5] C.F. Caruntu, A.E. Balau, C. Lazar, Networked predictive control trategy for an electro-hydraulic actuated wet clutch, in: Proceeding of IFAC Sympoium Advance in Automotive Control (AAC ), Munich, Germany, July. [6] U. Klehmet, T. Herpel, K.-S. Hielcher, R. German, Delay bound for CAN communication in automotive application, in: Proceeding of the 4th GI/ITG Conference Meaurement, Modelling and Evaluation of Computer and Communication Sytem, Dortmund, Germany, March April 8. [7] J. Velagic, Deign of Smith-like predictive controller with communication delay adaptation, in: Proceeding of World Congre on Science, Engineering and Technology, Fifth International Conference on Control and Automation (ICCA 8), Pari, France, July 8, pp