Design of Robust Fuzzy Sliding-Mode Controller for a Class of Uncertain Takagi-Sugeno Nonlinear Systems

Authors

  • X.Z. Zhang 1. School of Electrical and Information Engineering Hunan University China, 410082 Changsha, Yuelushan 2. Cooperative Innovative Center of Wind Power Hunan Institute of Engineering China, 411104 Xiangtan, Fuxing Road 88
  • Y.N. Wang School of Electrical and Information Engineering Hunan University China, 410082 Changsha, Yuelushan

Keywords:

uncertain T-S nonlinear system, sliding mode control, linear matrix

Abstract

This paper presents the fuzzy design of sliding mode control (SMC) for nonlinear systems with uncertainties, which can be represented by a Takagi-Sugeno (T-S) model. There exist the parameter uncertainties in both state and input matrices, as well as the matched external disturbance. The key feature of this work is the great ability of the controller to deal with systems without assuming that the control matrices of each local T-S model to be same and knowing the priori information of the upper norm-bounds of uncertainties. A sufficient condition for the existence of the desired fuzzy SMC is obtained by solving a set of linear matrix inequalities (LMIs). The reachability of the specified sliding surface is proven. A numerical example is illustrated in order to show the validity of the proposed scheme.

References

Takagi, T.; Sugeno, M. (1985); Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst., Man, Cybern., ISSN 0018-9472, 15(1): 116-132.

Feng, G. (2006); A survey on analysis and design of model-based fuzzy control systems, IEEE Trans. Fuzzy Syst., ISSN 1063-6706, 14(5): 676-697.

Tanaka, K.; Ikeda, T.; Wang, H.O. (1998); Fuzzy regulators and fuzzy observers: Relaxed stability conditions and LMI-based designs, IEEE Trans. Fuzzy Syst., ISSN 1063-6706, 6(2): 250-265.

Zhang, X. Z.; Wang, Y. N. (2009); Fuzzy variable structure control based on a Takagi- Sugeno model for permanent magnet synchronous motors, Journal of Systems and Control Engineering, ISSN 0959-6518, 223(6): 773-783.

Besheera, A. H.; Emarab, H. M.; Azizb, M. M. A.(2009); Wind energy conversion system regulation via LMI fuzzy pole cluster approach, Electric Power System Research, ISSN 0378- 7796, 79(6): 531-538.

Aouaouda, S.; Chadli, M.et.al.(2012); Robust fault tolerant tracking controller design for unknown inputs TS models with un-measurable premise variables, Journal of Process Control, I 0959-1524, 22(5): 861-872.

Liang, Y. W.; Xu, S. D.; Liaw, D. C.et.al.(2008); A study of T-S model-based SMC scheme with application to robot control, IEEE Trans. Ind.Electron., ISSN 0278-0046, 55(11): 3964- 3971.

Tian, E. G.; Peng, C.(2006); Delay dependent stability analysis and synthesis of uncertain TS fuzzy systems with time-varying delay, Fuzzy Sets and Systems, ISSN 0165-0114, 157(4): 544-559.

Wu, H. N.(2007); Robust H2 fuzzy output feedback control for discrete-time nonlinear systems with parametric uncertainties, International Journal of Approximate Reasoning, ISSN 0888- 613X, 46(1): 151-165.

Lin, Y.C.; Lo, J.C.(2005); Robust mixed H2/H∞ filtering for discrete-time delay fuzzy systems, International Journal of System Science, ISSN 1841-9836, 36(15): 993-1006.

Wang Y.N.; Zhang X.Z.et.al.(2011); Position-sensorless hybrid sliding mode control of electric vehicles with brushless DC motor, IEEE Trans. Veh. Technol., ISSN 0018-9545, 60(2): 421-432.

Zheng, F.; Wang, Q. G. et.al.(2002); Output tracking control of MIMO fuzzy nonlinear systems using variable structure control approach, IEEE Trans. Fuzzy Syst., ISSN 1063-6706, 10(3): 686-697.

Cao, W. J.; Xu, J. X.(2004); Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems, IEEE Trans. Automat. Contr., ISSN 0018-9286, 49(8): 1355- 1360.

Choi, H. H.(2008); Robust stabilization of uncertain fuzzy systems using variable structure system approach, IEEE Trans. Fuzzy Syst., ISSN 1063-6706, 16(3): 715-724.

Zhang, X.Z.; Wang, Y.N.et.al.(2010); H∞ robust T-S fuzzy design for uncertain nonlinear systems with state delays based on sliding-mode control, International Journal of Computers Communications & Control, ISSN 1841-9836, 5(4): 592-602.

Wu, T.Z.; Juang, Y.T.(2008); Design of variable structure control for fuzzy nonlinear systems, Expert Systems with Applications, ISSN 0957-4174, 35(3): 1496-1503.03.

Published

2014-11-17

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