Modelling and Force Tracking Control of Hydraulic Actuator for an Active Suspension System

Transcription

1 Modelling and Force Tracking Control of Hydraulic Actuator for an Active Supenion Sytem Y. M. Sam and K. Hudha Faculty of Electrical Engineering, Malayia Univerity of Technology, Skudai, Johor - Malayia yahaya@fke.utm.my Abtract Thi paper preent modelling and force tracking control of a non-linear hydraulic actuator applied in a quarter-car active upenion ytem. The controller tructure of the active upenion ytem wa decompoed into two loop namely outer loop and inner loop controller. Outer loop controller i ued to calculate the optimum target force to reject the effect of road diturbance, while, the inner loop controller i ued to keep the actual force cloe to thi deired force. The reult of the tudy how that the inner loop controller i able to track well the target force ranging from inuoidal to random. The performance of outer loop controller alo how ignificant improvement in term of body acceleration, body diplacement and upenion diplacement a compared to the paive upenion ytem. 1 Introduction Active Supenion ytem have been widely tudied over the lat 30 year, with hundred of paper publihed [1]. Mot of the publihed work focu on the outer-loop controller in computation of the deired control force a a function of vehicle tate and the road diturbance [2]. It i commonly aumed that the hydraulic actuator i an ideal force generator and able to carry out the commanded force accurately. Simulation of thee outer-loop controller were frequently done without conidering actuator dynamic, or with highly implified hydraulic actuator dynamic. In real implementation, actuator dynamic can be quite complicated, and the interaction between the actuator and the vehicle upenion cannot be ignored. It i alo difficult to produce the actuator force cloe to the target force without implementing inner-loop or force tracking controller. Thi i due to the fact that hydraulic actuator exhibit non-linear behavior reulted from ervo-valve dynamic, reidual tructural damping, and the unwanted effect of back-preure due to the interaction between the hydraulic actuator and vehicle upenion ytem. A few previou work on the force tracking controller of hydraulic actuator can be found on [2], [3], [4] and [5]. Thi tudy focue on the development of a nonlinear hydraulic actuator model including it force tracking controller for an active upenion ytem. The non-linear hydraulic actuator model conit of ervovalve dynamic and the interaction of piton-cylinder. Force tracking control of the hydraulic actuator model i then performed uing Proportional Integral (PI) controller for a variety of the namely tep, inuoidal, aw-tooth, quare and random function. Once the inner loop controller of hydraulic actuator i able to track well the target force with acceptable error, the hydraulic actuator model and the inner loop controller are then integrated with the outer loop of active upenion control. In thi configuration, the inner loop controller mut be able to track the optimum target force of hydraulic actuator calculated by the outer loop controller. The actual force of hydraulic actuator i inerted to the vehicle model to reject the effect of road diturbance to the vehicle dynamic performance. For outer loop controller, modified hybrid kyhook groundhook controller i conidered [6], [7],[8]. Thi paper i organized a follow: the firt ection contain introduction, the econd ection decribe the equation of motion of the hydraulic actuator model, the third ection preent force tracking control of the hydraulic actuator model, the fourth ection elaborate the diturbance rejection control of the active upenion ytem and the lat ection preent ome concluion. 2 Hydraulic Actuator Model A complete et of a hydraulic actuator conit of five main component namely electro hydraulic powered pool valve, piton-cylinder, hydraulic pump, reervoir and piping ytem a hown in Figure 1. Power upply i needed to drive the hydraulic pump through AC motor and to control the pool valve poition. The hydraulic pump will keep the upply preure at the optimum level of about 20,684 kn/m 2. The pool valve poition will control the fluid to come-in or come-out to the piton-cylinder which determine the amount of force produced by the hydraulic actuator. The hydraulic actuator are governed by electro hydraulic ervo valve allowing for the generation of force between the prung and unprung mae. The electro hydraulic ytem conit of an actuator, a primary power pool valve and a econdary bypa valve. A een in Figure 2, the hydraulic actuator X/06/$ IEEE ICIEA 2006

2 cylinder lie in a follower configuration to a critically centered electro hydraulic power pool valve with matched and ymmetric orifice. Poitioning of the pool u 1 direct high preure fluid flow to either one of the cylinder chamber and connect the other chamber to the pump reervoir. Thi flow create a preure difference P L acro the piton. Thi preure difference multiplied by the piton area A p i what provide the active force F A for the upenion ytem. Figure 1: Diagram of a complete et of hydraulic actuator. i et to zero, the bypa valve and actuator will behave imilar to a variable orifice damper. Spool valve poition u 1 and u 2 are controlled by a current-poition feedback loop. The eential dynamic of the pool have been hown to reemble a firt order ytem a the following τ u + u = kv (2) 3 Force Tracking Control of Hydraulic Actuator Model The tructure of force tracking control of hydraulic actuator i hown in Figure 3. The hydraulic actuator model take two input namely pool valve poition and real time piton peed. Proportional Integral control i implemented which take force tracking error a the input and deliver control current to drive the pool valve. The target force i repreented by inuoidal, quare, aw-tooth and random function. The parameter of hydraulic actuator model are taken from [9] a the following: A p = m 2, α = 2.273e9 N/m 5, C d1 = 0.7, C d2 = 0.7, w = m, P = kn/m 2, ρ =3500, C tm = 15e-12, τ = ec -1. Figure 3: Force tracking control of hydraulic actuator Figure 2: Phyical chematic and variable for the hydraulic actuator. Dynamic for the hydraulic actuator valve are given a the following: the change in force i proportional to the poition of the pool with repect to center, the relative velocity of the piton, and the leakage through the piton eal. A econd input u 2 may be ued to bypa the piton component by connecting the piton chamber. F A = A P gn( u1) PL Cd1wu1 ρ 2PL α C gn( ) d 2u 2 PL (1) ρ Ctm PL Ap ( x x u ) p The bypa valve u 2 could be ued to reduce the energy conumed by the ytem. If the pool poition u 1 The force tracking error of the hydraulic actuator model uing Proportional Integral controller for inuoidal, quare, aw-tooth and random function of the target force are hown in Figure 4, 5, 6 and 7 repectively. Thi i to check the controllability of the force tracking controller for a cla of continuou dicontinuou function. In thi imulation tudy, the parameter of proportional gain P i et to 1.25 and for Integral gain I i et to From thee figure, it can bee een clearly that the hydraulic actuator model track the deired force well. Figure 4: Force tracking performance for inuoidal

3 4 Diturbance Rejection Control of an Active Supenion Sytem Figure 5: Force tracking performance for quare 4.1 Quarter Vehicle Model The vehicle model conidered in thi tudy i a quarter car model. The quarter car model for paive upenion ytem conit of one-fourth of the body ma, upenion component and one wheel a hown in Figure 8 (a). The quarter car model for active upenion ytem, where the hydraulic actuator i intalled in parallel with the pring, i hown in Figure 8 (b). Figure 8: Paive and active quarter car model. Figure 6: Force tracking performance for aw-tooth The aumption of a quarter car modelling are a follow: the tyre i modelled a a linear pring without damping, there i no rotational motion in wheel and body, the behaviour of pring and damper are linear, the tyre i alway in contact with the road urface and effect of friction i neglected o that the reidual tructural damping i not conidered into vehicle modelling. The equation of motion for the prung and unprung mae of the paive quarter car model are given by ( Z Z ) + C ( Z Z ) = 0 M Z + K u u (3) M uz u + Kt ( Zu Zr ) + K( Zu Z ) + C Z Z = ( ) 0 u Figure 7: Force tracking performance for random It i alo noted that due to the rapid change of force magnitude in the cae of dicontinuou function of target force uch a aw-tooth and quare function, the performance of force tracking controller i lightly wore than that of continuou. Thi i caued by the repone of the pool valve that fail to follow the target force without time delay particularly when the rapid change of force magnitude i occurred. Wherea, the equation of motion for the prung and unprung mae of the emi-active quarter-car model are given by where, M ( Zu Zr ) + K( Zu Z ) F = 0 ( Z Z ) + F = 0 (4) uzu + Kt a M Z M K M u C Z r + K u a = prung ma = pring tiffne = unprung ma = damping contant = road profile

4 K t Z u Z F a = tyre tiffne = unprung ma diplacement = prung ma diplacement = actuator force Due to the tyre tiffne, vertical force acting on the contact point between tyre and the road will be created when the tyre hit a certain road profile. Then, the vertical force i tranferred to the wheel reulting in vertical acceleration of the wheel. Part of the vertical force i damped out by the upenion element, wherea, the ret i tranferred to the vehicle body via the upenion element. The vehicle body will move vertically in repone to the vertical force of the upenion element. The performance criteria of the upenion ytem to be invetigated in thi tudy are body acceleration ( Z ), body diplacement (Z ), upenion working pace (Z u Z ) and wheel diplacement ( Z u ). Performance of the upenion ytem i characterized by the ability of the upenion ytem in reducing thoe four performance criteria effectively. 4.2 Controller Structure Baically, the controller tructure of an electronically controlled upenion ytem utilize two controller loop namely outer loop and inner loop controller which correpond to vehicle controller and actuator controller. The imilar term, which i often ued for outer and inner loop controller, are global and local controller. The controller tructure wa ued for an active upenion ytem in [4] and [5]. The imilar controller tructure wa ued for emi-active upenion control by Sim et al. (1999), Lai and Liao (2002a; 2002b). The controller tructure adopted in thi tudy i hown in Figure 9. The outer loop controller i ued for diturbance rejection control to reduce unwanted vehicle motion. The input of the outer loop controller are vehicle tate namely body velocity and wheel velocity, wherea the output of the outer loop controller i the target force that mut be tracked by the hydraulic actuator. On the other hand, the inner loop controller i ued for force tracking control of the hydraulic actuator in uch a way that the force produced by the hydraulic actuator i a cloe a poible with the target force produced by the diturbance rejection control. The diturbance rejection control adopted in thi tudy i a limited tate feed back controller in which the optimum target force i calculated a the um of vehicle tate multiplied by certain feed back gain. Since only three vehicle tate namely body vertical velocity, wheel vertical velocity and relative velocity between body and wheel are choen in thi tudy, thi control cheme i known a limited tate feed back controller. The optimum value of the real time target force for the hydraulic actuator i given by F a = Z Z u (5) Z u Z [ K K K ] Figure 9: The controller tructure of an active upenion ytem 4.3 Simulation Reult In thi imulation tudy, the typical road diturbance i hown in Figure 10 and et in the form of Z r = 0.50 ( 1 co(8πt )) a if 2 t 0.75 and 3.00 t otherwie (6) where, a denote bump amplitude which i et to be ± 8 cm. Thi type of road diturbance ha been ued by D Amato and Viaalo [15] and Sam et al. [16]. Figure 10: Bump configuration The numerical value of quarter car model parameter are a the following: M = 282 kg M u = 45 kg K = N/m C = 1500 Nec/m K t = N/m

5 The imulation wa performed for a period of 5 econd uing Heun olver with a tep ize of econd. The tate feed back gain i et to K = [ ]. The body acceleration and body diplacement performance of active ytem compared with paive ytem are hown in Figure 11 and 12. From the figure, it i clear that the active ytem i able to ignificantly reduce both amplitude and the ettling time of unwanted body motion in the form of body acceleration and body diplacement a compared with the paive ytem. Figure 13: Supenion deflection Figure 11: Body acceleration Figure 14: Wheel diplacement The force tracking performance of the inner loop controller i hown in Figure 15. It i clear that the hydraulic actuator i able to provide the actual force cloe to the optimum target force for the pecified bump configuration. From the figure, it can be een that when the tyre hit the bump with poitive magnitude a hown in Figure 10, the hydraulic actuator produce negative force to prevent the vehicle body in moving upward and to lift up the wheel in following the bump profile. Figure 12: Body diplacement The imilar trend wa found on the upenion deflection performance a hown in Figure 13, in which the active ytem how ignificant performance in reducing both amplitude and the ettling time compared with the paive ytem. It i alo noted that the active ytem i able to improve the rattle-pace dynamic of the upenion ytem. In term of the wheel diplacement, it can be een that the magnitude of the wheel diplacement for the active ytem i lightly wore than the paive ytem a hown in Figure 14. Roughly, the magnitude of wheel diplacement of the active ytem i about 1% larger than the paive ytem. But, it can be een that the ettling time of wheel-hop for the active ytem i better than paive ytem. Figure 15: Force tracking performance 5 Concluion The paper preent modelling and force tracking control of hydraulic actuator to be ued for an active upenion ytem. Proportional Integral control wa implemented for force tracking control of the hydraulic actuator. The reult of the tudy how that the hydraulic actuator i able to provide the actual force cloe to the target force with acceptable force tracking error.

6 A limited tate feed back controller wa ued to reject the effect of road diturbance to the vehicle dynamic performance. From the imulation reult, it can be een that the limited tate feed back controller how ignificant improvement in reducing both magnitude and ettling time of the body acceleration, body diplacement and upenion diplacement. In term of the wheel diplacement, it i noted that even though the magnitude of the wheel diplacement for the active ytem i lightly wore than paive ytem, the ettling time of wheel-hop for the active ytem i better than paive ytem. Acknowledgement Thi reearch i upported by the Minitry of Science, Technology and Innovation (MOSTI) Malayia through the IRPA Grant of Robut Control for Active Supenion Sytem reearch project lead by Aoc. Prof. Dr. Yahaya Md. Sam. The author are grateful to the Minitry for upporting the preent work. Reference [1] D. Hrovat, Survey of Advanced Supenion Development and Related Optimal Control Application,. Automatica. vol. 33, no. 10, pp , [2] X. Shen, and H. Peng, Analyi of Active Supenion Sytem with Hydraulic Actuator, in Proceeding of the 2003 IAVSD Conference, Atugi, Japan, Augut [3] Y. Zhang, and A. Alleyne, A Practical and Effective Approach to Active Supenion Control, in Proceeding of the 6th International Sympoium on Advanced Vehicle Control, Hirohima, Japan September [4] S. Chantranuwathana, Adaptive Robut Force Control for Vehicle Active Supenion. Univerity of Michigan: Ph.D. Diertation, Active Damper, in Proceeding of the International Mechanical Engineer Conference.. Wahington, DC, Paper No , November 16 21, [8] S. Ikenaga, Development of a Real Time Digital Controller: Application to Active Supenion Control. Univerity of Michigan: PhD. Diertation, [9] M.D. Donahue, Implementation of an Active Supenion and Preview Controller for Improved Ride Comfort. Univerity of California at Berkeley: MSc. Thee, [10] N. D. Sim, R. Stanway, D. J. Peel, W. A. Bullough, and A. R. Johnon, Controllable Vicou Damping: An Experimental Study of an Electrorheological Long-Stroke Damper Under Proportional Feedback Control, Journal of Smart Material and Structure, vol. 8, pp [11] C. W. Lai, and W. H. Liao, Vibration Control of a Supenion Sytem Via a Magnetorheological Fluid Damper, Journal of Sound and Vibration, vol. 8, pp , 2002a. [12] C. W. Lai, and W. H. Liao, Harmonic Analyi of a Magnetorheological Damper for Vibration Control, Journal of Smart Material and Structure, vol. 11, pp , 2002b. [13] F. J. D Amato, and D. E. Viaalo, Fuzzy Control for Active Supenion, Journal of Mechatronic, vol. 10, pp , [14] Y. M. Sam, J. H. S. Oman, and M. R. A. Ghani, A Cla of Proportional-Integral Sliding Mode Control with Application to Active Supenion. Sytem, Sytem & Control Letter, vol. 51, pp , [5] S. Chantranuwathana, and H. Peng, Practical Adaptive Robut controller for Active Supenion. in Proceeding of the 2000 ASME International Congre and Expoition. Orlando, Florida, [6] M. Ahmadian, A Hybrid Semiactive Control for Secondary Supenion Application, in Proceeding of the Sixth ASME Sympoium on Advanced Automotive Technologie. November. Dalla, Texa, November [7] M. Ahmadian, and N. Vahdati, An analytical Evaluation of the Tranient Dynamic of Semi