Robust Stable Fuzzy Control via Fuzzy Modeling and Feedback Linearization with Its Applications to Controlling Uncertain Single-link Flexible Joint Manipulators

In this paper, a robust stable fuzzy control design based on feedback linearization is presented. Takagi–Sugeno fuzzy model is used as representing the nonlinear plant model and uncertainty is assumed to be included in the model structure with known bounds. For this structured uncertainty, the closed system can be analyzed by applying the perturbation system stability analysis to the fuzzy feedback linearization systems and a sufficient condition is derived to guarantee the stability of the closed-loop system with bounded parameter uncertainties. Based on the developed analysis method, we can design a robust fuzzy controller by choosing the control parameters satisfying the robust stability condition.

[1]  Hyung-Jin Kang,et al.  Numerical robust stability analysis of fuzzy feedback linearisation regulator based on linear matrix inequality approach , 2002 .

[2]  Kazuo Tanaka,et al.  Model construction, rule reduction, and robust compensation for generalized form of Takagi-Sugeno fuzzy systems , 2001, IEEE Trans. Fuzzy Syst..

[3]  Yeong-Chan Chang,et al.  Adaptive fuzzy-based tracking control for nonlinear SISO systems via VSS and H∞ approaches , 2001, IEEE Trans. Fuzzy Syst..

[4]  Kazuo Tanaka,et al.  Stability analysis and design of fuzzy control systems , 1992 .

[5]  J. H. Kim,et al.  Indirect model reference adaptive fuzzy control of dynamic fuzzy-state space model , 2001 .

[6]  Kurt Fischle,et al.  An improved stable adaptive fuzzy control method , 1999, IEEE Trans. Fuzzy Syst..

[7]  Li-Xin Wang,et al.  Adaptive fuzzy systems and control - design and stability analysis , 1994 .

[8]  Li-Xin Wang,et al.  Adaptive fuzzy systems and control , 1994 .

[9]  Andrzej Piegat,et al.  Fuzzy Modeling and Control , 2001 .

[10]  Suyong Kim,et al.  LMI-based quadratic stability analysis for hierarchical fuzzy systems , 2001 .

[11]  Stephen Yurkovich,et al.  Fuzzy Control , 1997 .

[12]  Youngwan Cho,et al.  A multirule-base controller using the robust property of a fuzzy controller and its design method , 1996, IEEE Trans. Fuzzy Syst..

[13]  Kiriakos Kiriakidis,et al.  Robust stabilization of the Takagi-Sugeno fuzzy model via bilinear matrix inequalities , 2001, IEEE Trans. Fuzzy Syst..

[14]  Jan Lunze.  Robust Multivariable Feedback Control , 1989 .

[15]  Mignon Park,et al.  Robust stability analysis and design method for the fuzzy feedback linearization regulator , 1998, IEEE Trans. Fuzzy Syst..

[16]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[17]  Jin Bae Park,et al.  Robust fuzzy control of nonlinear systems with parametric uncertainties , 2001, IEEE Trans. Fuzzy Syst..

[18]  Tor Arne Johansen,et al.  Fuzzy model based control: stability, robustness, and performance issues , 1994, IEEE Trans. Fuzzy Syst..

[19]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[20]  A. Isidori.  Nonlinear Control Systems , 1985 .