×

A robust predictive control design for nonlinear active suspension systems. (English) Zbl 1338.93147

Summary: This paper proposes a novel method for designing robust nonlinear multivariable predictive control for nonlinear active suspension systems via the Takagi-Sugeno fuzzy approach. The controller design is converted to a convex optimization problem with linear matrix inequality constraints. The stability of the control system is achieved by the use of terminal constraints, in particular the Constrained Receding-Horizon Predictive Control algorithm to maintain a robust performance of vehicle systems. A quarter-car model with active suspension system is considered in this paper and a numerical example is employed to illustrate the effectiveness of the proposed approach. The obtained results are compared with those achieved with model predictive control in terms of robustness and stability.

MSC:

93B40 Computational methods in systems theory (MSC2010)
93B35 Sensitivity (robustness)
93C95 Application models in control theory
93C15 Control/observation systems governed by ordinary differential equations

References:

[1] Göhrle, C., A.Schindler, A.Wagner, and O.Sawodny, “Design and vehicle implementation of preview active suspension controllers,” IEEE Trans. Control Syst. Technol., Vol. 22, No. 3, pp. 1135-1142 (2014).
[2] Crews, J. H., M. G.Mattson, and G. D.Buckner, “Multi‐objective control optimization for semi‐active vehicle suspensions,” J. Sound Vibr., Vol. 330, No. 23, pp. 5502-5516 (2011).
[3] Han, S. Y., G. Y.Tang, Y. H.Chen, X. X.Yang, and X.Yang, “Optimal vibration control for vehicle active suspension discrete‐time systems with actuator time delay,” Asian J. Control, Vol. 15, No. 6, pp. 1579-1588 (2013). · Zbl 1283.49046
[4] Wu, J.‐L., “A simulations mixed LQR/H∞ control approach to the design of reliable active suspension controllers,” Asian J. Control, (2015). DOI: 10.1002/asjc.1058.
[5] Jahromi, A. F. and A.Zabihollah, “Linear quadratic regulator and fuzzy controller application in full‐car model of suspension system with magnetor‐heological shock absorber,” in Proceedings of IEEE/ASME International Conference on Mechatronics and Embedded Systems and Applications, pp. 522-528 (2010).
[6] Wong, P.‐K., H.Shaojia, X.Tao, W. H.Cheong, and X.Zhengchao, “Design of a new suspension system controlled by fuzzy‐PID with wheelbase preview,” Adv. Mech. Eng. II, Adv. Mech. Mater., Vol. 192, pp. 106-110 (2012).
[7] Kim, C. and P. I.Ro, “A sliding mode controller for vehicle active suspension systems with non‐linearities,” Proc. Inst. Mech. Eng. Part D J. Automob. Eng., Vol. 212, No. 2, pp. 79-92 (1998).
[8] Al‐Holou, N., T.Lahdhiri, D. S.Joo, J.Weaver, and F.Al‐Abbas, “Sliding mode neural network inference fuzzy logic control for active suspension systems,” IEEE Trans. Fuzzy Syst., Vol. 10, No. 2, pp. 234-246 (2002).
[9] Fialhm, I. and G. J.Balas, “Road adaptive active suspension design using linear parameter‐varying gain‐scheduling,” IEEE Trans. Control Syst. Technol., Vol. 10, No. 1, pp. 43-54 (2002).
[10] Demir, O., I.Keskin, and S.Cetin, “Modeling and control of a nonlinear half‐vehicle suspension system: A hybrid fuzzy logic approach,” Nonlinear Dyn., Vol. 67, pp. 2139-2151 (2012).
[11] Anwar, S. “Generalized predictive control of yaw dynamics of a hybrid brake‐by‐wire equipped vehicle,” Mechatronics, Vol. 15, pp. 1089-1108 (2005).
[12] Shoukry, Y., M. W.El‐Kharashi, and S.Hammad, “An embedded implementation of the Generalized Predictive Control algorithm applied to automotive active suspension systems,” Comput. Electr. Eng., Vol. 39, No. 2, pp. 512-529 (2013).
[13] Constantin, F., M. L.Caruntu, R. H.Gielen, P. P. J.van denBosch, and S.Di Cairano, “Lyapunov based predictive control of vehicle drivetrains over CAN,” Control Eng. Practice, Vol. 21, No. 12, pp. 1884-1898 ( 2013).
[14] Bououden, S., M.Chadli, et al., “A new approach for fuzzy predictive adaptive controller design using particle swarm optimization algorithm,” Int. J. Innovative Comput., Inf. Control, Vol. 9, No. 9, pp. 3741-3758 (2013).
[15] Li, H., J.Yu, C.Hilton, and H.Liu, “Adaptive sliding mode control for nonlinear active suspension vehicle systems,” IEEE Trans. Ind. Electron., Vol. 60, No. 8, pp. 3328-3338 (2013).
[16] Li, H., X.Jing, H. K.Lam, and P.Shi, “Fuzzy sampled‐data control for uncertain vehicle suspension systems,” IEEE T. Cybern., Vol. 44, No. 7, pp. 1111-1126 (2014).
[17] Orukpe, P. E., X.Zheng, I. M.Jaimoukha, A. C.Zolotas, and R. M.Goodall, “Model predictive control based on mixed H2/H∞ control approach for active vibration control of railway vehicles,” Veh. Syst. Dyn., Vol. 46, pp. 151-160 (2008).
[18] Canale, M., M.Milanese, and C.Novara, “Semi‐active suspension control using ‘fast’ model‐predictive techniques,” IEEE Trans. Control Syst. Technol., Vol. 14, No. 6, pp. 1034-1046 (2006).
[19] Takagi, T., and M.Sugeno, “Fuzzy identification of systems and its application to modeling and control,” IEEE Trans. Syst. Man. Cybern., Vol. 15, No. 1, pp. 116-132 (1985). · Zbl 0576.93021
[20] Ohtake, H., K.Tanaka, and H. O.Wang, “Fuzzy model‐based servo and model following control for nonlinear systems,” IEEE Trans. Syst. Man. Cybern. Part B‐ Cybern., Vol. 39, No. 6, pp. 1634-1639 (2009).
[21] Chadli, M., and M.Darouach, “Robust admissibility of uncertain switched singular systems,” Int. J. Control, Vol. 84, No. 10, pp. 1587-1600 (2011). · Zbl 1236.93107
[22] Aouaouda, S., M.Chadli, V.Cocquempot, and M. T.Khadir, “Multi‐objective H−∕H∞ faults detection observer design for Takagi-Sugeno fuzzy systems with unmeasurable premise variables: descriptor approach,” Int. J. Adapt. Control Signal Process., Vol. 27, No. 12, pp. 1031-1047 (2013). · Zbl 1282.93153
[23] Espinosa, J., Vandewalle, J., and Wertz, V., Fuzzy Logic, Identification and Predictive Control, Springer, Berlin (2005). · Zbl 1061.93001
[24] Maciejowski, J., Predictive Control with Constraints, Prentice Hall, London (2002).
[25] Bououden, B., M.Chadli, S.Filali, and A.El Hajjaji, “Fuzzy model based multivariable predictive control of a variable speed wind turbine: LMI approach,” Renew. Energy, Vol. 37, No. 1. pp. 434-439 (2012).
[26] Rawlings, J. B., and Mayne, D. Q., Model Predictive Control: Theory and Design, Nob Hill, Madison, WI (2009).
[27] Saifia, D., M.Chadli, S.Labiod, and T. M.Guerra, “Robust H∞ static output feedback stabilization of T‐S fuzzy systems subject to actuator saturation,” Int. J. Control Autom. Syst., Vol. 10, No. 3, pp. 613-622 (2012).
[28] Bazaraa, M. S., Sherali, H. D., and Shetty, C. M., Nonlinear Programming. Theory and Algorithms, 3rd edn., John Wiley & Sons, Hoboken (2006). · Zbl 1140.90040
[29] Fletcher, R. “Minimizing general functions subject to linear constraints, Numerical methods for non‐linear optimization,” F. A.Lootsma (ed.) (ed.), pp. 279-296, Academic Press, London (1972). · Zbl 0268.90061
[30] Fletcher, R., Practical Methods of Optimization, 2nd edn., John Wiley & Sons, New York (2000).
[31] Gill, P. E., and W.Murray, “Linearly constrained problems including linear and quadratic programming,” in D.Jacobs (ed.) (ed.), The State of the Art in Numerical Analysis, Academic Press, London and New York, pp. 313-363 (1977).
[32] Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V., Linear Matrix Inequalities In System and Control Theory, SIAM, Philadelphia, USA (1994). · Zbl 0816.93004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.