\(H_{\infty}\) control of a suspension with a magnetorheological damper. (English) Zbl 1282.93102
Summary: This research work presents an \(H_{\infty}\) controller based on a Takagi-Sugeno (T-S) fuzzy model for a two-degrees-of-freedom (2-DOF) one-quarter-vehicle semi-active suspension with a magnetorheological damper where the actuator dynamics are included in the control synthesis. These dynamics enclose nonlinear damper phenomena, avoided in many other studies, and that can improve the suspension system by means of a more accurate model. The objective is to obtain a semi-active suspension that considerably improves the passive suspension efficiency based on some frequency domain performance criteria. The advantage of having the T-S system as a reference is that each piecewise linear system can be exposed to the well-known control theory. Besides, the proposed solution is compared with the recent reported work to highlight its advantages. A case of study is included and simulation work supports the results. The methodology applied herein can be extended to a half-vehicle model, and to the four wheels to have a global chassis control in order to maximise passenger comfort and vehicle stability.
MSC:
| 93B36 | \(H^\infty\)-control |
| 93C42 | Fuzzy control/observation systems |
| 93B50 | Synthesis problems |
| 93C15 | Control/observation systems governed by ordinary differential equations |
Keywords:
semi-active suspension; magnetorheological dampers; \(H_\infty\) control; Takagi-Sugeno fuzzy model; frequency domain performance criteriaReferences:
| [1] | Abu-Ein, SQ, Fayyad, SM, Momani, W, Al-Alawin, A and Momani, M. 2010. Experimental Investigation of Using MR-fluids in Automobiles Suspension Systems. Research Journal of Applied Sciences, Engineering and Technology, 2: 159-163. |
| [2] | Assawinchaichote, W, Nguang, SK, Shi, P and Boukas, E. \(2008. H_∞\) Fuzzy State-feedback Control Design for Nonlinear Systems with D-stability Constraints: an LMI Approach. Mathematics and Computers in Simulation, 78: 514-531. · Zbl 1145.93026 · doi:10.1016/j.matcom.2007.07.002 |
| [3] | Beaven, R, Wright, M and Seaward, D. 1996. Weighting Function Selection in the \(H_∞\) Design Process. Control Engineering Practice, 4: 625-633. · doi:10.1016/0967-0661(96)00044-5 |
| [4] | Boyd, S, Ghaoui, L, Feron, E and Balakrishnan, V. 1994. Linear Matrix Inequalities in System and Control Theory, Philadelphia, , USA: SIAM. · Zbl 0816.93004 · doi:10.1137/1.9781611970777 |
| [5] | Cao, J, Li, P and Liu, H. 2010. An Interval Fuzzy Controller for Vehicle Active Suspension Systems. IEEE Transactions on Intelligent Transportation systems, 11: 885-895. · doi:10.1109/TITS.2010.2053358 |
| [6] | Cao, S, Rees, N and Feng, G. 1996. Stability Analysis and Design for a Class of Continuous-time Fuzzy Control Systems. International Journal of Control, 64: 1069-1087. · Zbl 0867.93053 |
| [7] | Chang, XH and Yang, GH. 2011. A Descriptor Representation Approach to Observer-based \(H_∞\) Control Synthesis for Discrete-time Fuzzy Systems. Fuzzy Sets and Systems, 185: 38-51. · Zbl 1237.93102 · doi:10.1016/j.fss.2011.06.010 |
| [8] | Do, A, Sename, O and Dugard, L. 2010. An LPV Control Approach for Semi-active Suspension Control with Actuator Constraints. American Control Conference. 2010. pp.4653-4658. Baltimore, , USA |
| [9] | Du, H and Zhang, N. 2009. Robust Controller Design for Vehicle Semi- Active Suspensions with Electrorheological Dampers. Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference. 2009. pp.7639-7644. Shanghai, , P.R. China |
| [10] | Félix-Herran, L, de Rodríguez-Ortiz, J, Soto, R and Ramírez-Mendoza, R. 2008. Modeling and Control for a Semi-active Suspension with a Magnetorheological Damper Including the Actuator Dynamics. IEEE Electronics, Robotics and Automotive Mechanics Conference (CERMA). 2008. pp.338-343. Mexico |
| [11] | Félix-Herran, L, Mehdi, D, de Rodríguez-Ortiz, J, Soto, R and Ramírez-Mendoza, R. 2009. Takagi-Sugeno Fuzzy Model of a Semi-active Suspension with a Magnetorheological Damper. European Control Conference. 2009. pp.4422-4427. Budapest Hungry |
| [12] | Félix-Herrán, L, Mehdi, D, Soto, R, de Journal Rodríguez-Ortiz, J and Ramírez-Mendoza, R. 2010. Control of a Semi-active Suspension with a Magnetorheological Damper Modelled via Takagi-Sugeno. IEEE Mediterranean Conference on Control and Automation. 2010. pp.1265-1270. |
| [13] | Gao, H, Sun, W and Shi, P. 2010. Robust Sampled-data \(H_∞\) Control for Vehicle Active Suspension Systems. IEEE Transactions on Control Systems Technology, 18: 238-245. · doi:10.1109/TCST.2009.2015653 |
| [14] | Gillespie, T. 1992. Fundamentals of Vehicle Dynamics, USA: SAE. · doi:10.4271/R-114 |
| [15] | Gysen, BLJ, Janssen, JLG and Lomonova, JJHP. 2009. Design Aspects of an Active Electromagnetic Suspension System for Automotive Applications. IEEE Transactions on Industry Applications, 45: 1589-1597. · doi:10.1109/TIA.2009.2027097 |
| [16] | Jager, AD. 1991. Comparison of Two Methods for the Design of Active Suspension Systems. Optimal Control Applications and Methods, 12: 173-188. · Zbl 0800.93014 · doi:10.1002/oca.4660120305 |
| [17] | Jun, Y. 2006. Robust \(H_∞\) Control Analysis and Synthesis for Takagi-Sugeno General Uncertain Fuzzy Systems. Fuzzy Sets and Systems, 157: 2205-2223. · Zbl 1106.93038 · doi:10.1016/j.fss.2006.03.020 |
| [18] | Kruczek, A, Stríbrský, A, Hyniová, K and Hlinovský, M. \(2008. H_∞\) Controlled Actuators in Automotive Active Suspension System. the 9th Biennial ASME Conference on Engineering Systems Design and Analysis. 2008. pp.1-6. Haifa, , Israel |
| [19] | Kruczek, A and Stribrsky, A. 2004. “\(H_∞\) Control of Automotive Active Suspension with Linear Motor”. In 3rd IFAC Symposium on Mechatronic Systems Sydney, Australia |
| [20] | Lam, HF, Lai, CY and Liao, WH. 2002. “Automobile Suspension Systems with MR Fluid Dampers”. In Technical Report, Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong. |
| [21] | Lee, K, Jeung, E and Park, H. 2001. Robust Fuzzy \(H_∞\) Control for Uncertain Nonlinear Systems via State Feedback: an LMI Approach. Fuzzy Sets and Systems, 120: 123-134. · Zbl 0988.93045 · doi:10.1016/S0165-0114(99)00072-X |
| [22] | Messoussi, WE, Pages, O and Hajjaji, AE. 2007. Four-wHeel Steering Vehicle Control using Takagi-Sugeno Fuzzy Models. IEEE International Fuzzy Systems Conference. 2007. pp.1-6. |
| [23] | Milliken, W and Milliken, D. 1995. Race Car Vehicle Dynamics, USA: Society of Automotive Engineers, Inc. |
| [24] | Nachidi, M, Tadeo, F and Benzaouia, A. 2011. Static Output-feedback for Takagi-Sugeno Systems with Delays. International Journal of Adaptive Control and Signal Processing, 25: 295-312. · Zbl 1233.93066 · doi:10.1002/acs.1196 |
| [25] | Ogata, K. 2000. Modern Control Engineering, USA: Pearson. |
| [26] | Pauwelussen, JP and Pacejka, HB. 1995. Smart Vehicles, The Netherlands: Sweets & Zeitlinger Publishers. |
| [27] | Peaucelle, D,AD. 2001. Robust Multi-objective Control for Real Uncertainties via Parameter-dependent Lyapunov Functions. European Control Conference. 2001. Porto Portugal · Zbl 1051.93078 |
| [28] | Poussot-Vassal, C, Sename, O, Dugard, L, Gáspár, P, Szabó, Z and Bokor, J. 2008. A New Semi-active Suspension Control Strategy Through LPV Technique. Control Engineering Practice, 16: 1519-1534. · doi:10.1016/j.conengprac.2008.05.002 |
| [29] | Sammier, D, Sename, O and Dugard, L. 2003. Skyhook and \(H_∞\) Control of Semi-active Suspensions: Some Practical Aspects. Vehicle System Dynamics, 39: 279-308. |
| [30] | Scherer, C and Weiland, S. 2005. Linear Matrix Inequalities in Control, The Netherlands: Delft University of Technology and Eindhoven University of Technology. |
| [31] | Sireteanu, T, Stancioiu, D and Stammers, CW. 2001. “Modelling of Magnetorheological Fluid Dampers”. In in Proceedings of the Romanian Academ : Series A 2 |
| [32] | Slotine, W and Li, J. 1991. Applied Nonlinear Control, USA: Prentice Hall. · Zbl 0753.93036 |
| [33] | Son, HY, Jeong, SG, Choi, JY, Kim, JK, Cheon, YS, Paek, YI, Kwon, S and Lee, MH. 2001. “A Robust Controller Design for Performance Improvement of a Semi-active Suspension Systems”. In ISIE, Vol. 3, 1458-1461. Pusan: Korea. |
| [34] | Spencer Jr, B, Dyke, S, Sain, M and Carlson, J. 1997. Phenomenological Model of a Magnetorheological Damper. ASCE Journal of Engineering Mechanics, 123: 230-238. · doi:10.1061/(ASCE)0733-9399(1997)123:3(230) |
| [35] | Stanway, R. 1996. “The Development of Force Actuators using ER and MR Fluid Technology”. In IEEE Colloquium on Actuator Technology: Current Practice and New Developments 1-5. London, , UK |
| [36] | Tanaka, K, Ikeda, T and Wang, HO. 1996. Robust Stabilization of a Class of Uncertain Nonlinear Systems via Fuzzy Control: Quadratic Stabilizability, \(H_∞\) Control Theory, and Linear Matrix Inequalities. IEEE Transactions on Fuzzy Systems, 4: 1-13. · doi:10.1109/91.481840 |
| [37] | Tanaka, K and Wang, H. 2001. Fuzzy Control Systems Design and Analysis, USA: John Wiley & Sons Inc. · doi:10.1002/0471224596 |
| [38] | Tyan, F, Tu, SH and Jeng, WS. 2008. A Lyapunov Based Multi-level Controller for a Semi-active Suspension System with an MRF Damper. American Control Conference. 2008. pp.3213-3218. Washington, , USA |
| [39] | VanAntwerp, J and Braatz, R. 2000. A Tutorial on Linear and Bilinear Matrix Inequalities. Journal of Process Control, 10: 363-385. · doi:10.1016/S0959-1524(99)00056-6 |
| [40] | Wang, HS, Yung, CF and Chang, FR. 1998. Bounded Real Lemma and \(H_∞\) Control for Descriptor Systems. IEE Proceedings On Control Theory & Applications, 145: 316-322. · doi:10.1049/ip-cta:19982048 |
| [41] | Wen, Y. 1976. Method for Random Vibration of Hysteretic Systems. Journal of the Engineering Mechanics Division, 102: 249-263. |
| [42] | Wong, JY. 2001. Theory of Ground Vehicles, USA: John Wiley and Sons, Inc. |
| [43] | Worden, GR and Tomlinson, K. 2001. Nonlinearity in Structural Dynamics, Detection, Identification and Modeling, Bristol, , UK: IoP Publishing. · Zbl 0990.93508 · doi:10.1887/0750303565 |
| [44] | Zhou, K, Doyle, J and Glover, K. 1996. Robust and Optimal Control, USA: Prentice Hall. · Zbl 0999.49500 |
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