Stability conditions of fuzzy systems and its application to structural and mechanical systems

This paper provided the stability conditions and controller design for a class of structural and mechanical systems represented by Takagi-Sugeno (T-S) fuzzy models. In the design procedure of controller, parallel-distributed compensation (PDC) scheme was utilized to construct a global fuzzy logic controller by blending all local state feedback controllers. A stability analysis was carried out not only for the fuzzy model but also for a real mechanical system. Furthermore, this control problem can be reduced to linear matrix inequalities (LMI) problems by the Schur complements and efficient interior-point algorithms are now available in Matlab toolbox to solve this problem. A simulation example was given to show the feasibility of the proposed fuzzy controller design method.

[1]  Cheng-Wu Chen,et al.  Stability Analysis Of Nonlinear Interconnected Systems Via T-S Fuzzy Models , 2004, Int. J. Comput. Intell. Appl..

[2]  Lotfi A. Zadeh,et al.  On Fuzzy Mapping and Control , 1996, IEEE Trans. Syst. Man Cybern..

[3]  Kazuo Tanaka,et al.  Design of a stable fuzzy controller for an articulated vehicle , 1997, IEEE Trans. Syst. Man Cybern. Part B.

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

[5]  Jin Bae Park,et al.  Robust fuzzy-model-based controller for uncertain systems , 1999, FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315).

[6]  Kazuo Tanaka,et al.  A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer , 1994, IEEE Trans. Fuzzy Syst..

[7]  Wei-Ling Chiang,et al.  Application of Fuzzy H Infinity Control via T-S Fuzzy Models for Nonlinear Time-Delay Systems , 2003, Int. J. Artif. Intell. Tools.

[8]  Kazuo Tanaka,et al.  Fuzzy control systems design and analysis , 2001 .

[9]  Bor-Sen Chen,et al.  Robustness design of nonlinear dynamic systems via fuzzy linear control , 1999, IEEE Trans. Fuzzy Syst..

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

[11]  M. Braae,et al.  Theoretical and linguistic aspects of the fuzzy logic controller , 1979, Autom..

[12]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .

[13]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[14]  Gang Feng,et al.  Analysis and design for a class of complex control systems part II: Fuzzy controller design , 1997, Autom..

[15]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[16]  Fabio Casciati,et al.  Checking the Stability of a Fuzzy Controller for Nonlinear Structures , 1997 .

[17]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[18]  W.J.M. Kickert ANALYSIS OF A FUZZY LOGIC CONTROLLER , 1993 .

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

[20]  Fabio Casciati,et al.  Control of nonlinear structures using the fuzzy control approach , 1996 .

[21]  Cheng-Wu Chen,et al.  Active control for a benchmark building under wind excitations , 2003 .

[22]  An-Pei Wang,et al.  Fuzzy sliding mode control for a building structure based on genetic algorithms , 2002 .

[23]  Wjm Walter Kickert,et al.  ANALYSIS OF A FUZZY LOGIC CONTROLLER , 1978 .

[24]  W. Chiang,et al.  LQG/LTR Control Methodology in Active Structural Control , 1998 .

[25]  E. Yaz Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.