Design of a Takagi-Sugeno Fuzzy Regulator for a Set of Operation Points

The paper proposes a new design method based on linear matrix inequalities (LMIs) for tracking constant signals (regulation) considering nonlinear plants described by the Takagi-Sugeno fuzzy models. The procedure consists in designing a single controller that stabilizes the system at operation points belonging to a certain range or region, without the need of remaking the design of the controller gains at each new chosen equilibrium point. The control system design of a magnetic levitator illustrates the proposed methodology.

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

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

[3]  Valter J. S. Leite,et al.  A Dynamic Compensator for Parameter Varying Systems Subject to Actuator Limitations applied to a T-S Fuzzy System , 2011 .

[4]  Junwei Gao,et al.  Adaptive Fuzzy Tracking Control for a Permanent Magnet Synchronous Motor via Backstepping Approach , 2010 .

[5]  Antonio Sala,et al.  Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem , 2007, Fuzzy Sets Syst..

[6]  Fernando de Oliveira Souza,et al.  Reducing conservativeness in recent stability conditions of TS fuzzy systems , 2009, Autom..

[7]  Marcelo C. M. Teixeira,et al.  Stabilizability and Disturbance Rejection with State-Derivative Feedback , 2010 .

[8]  Cheng-Wu Chen,et al.  GA-based modified adaptive fuzzy sliding mode controller for nonlinear systems , 2009, Expert Syst. Appl..

[9]  Cheng-Wu Chen,et al.  Stability analysis of an oceanic structure using the Lyapunov method , 2010 .

[10]  Bor-Sen Chen,et al.  A Fuzzy Approach for Robust Reference-Tracking-Control Design of Nonlinear Distributed Parameter Time-Delayed Systems and Its Application , 2010, IEEE Transactions on Fuzzy Systems.

[11]  Ricardo C. L. F. Oliveira,et al.  LMI approach for H linear parameter-varying state feedback control , 2005 .

[12]  R. Cardim.  Projeto de controladores baseados em LMIs: realimentação derivativa e sistemas chaveados utilizando estrutura variável , 2009 .

[13]  Thierry-Marie Guerra,et al.  LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form , 2004, Autom..

[14]  Cheng-Wu Chen,et al.  Robustness design of time-delay fuzzy systems using fuzzy Lyapunov method , 2008, Appl. Math. Comput..

[15]  Cheng-Wu Chen,et al.  Stability analysis and robustness design of nonlinear systems: An NN-based approach , 2011, Appl. Soft Comput..

[16]  Kazuo Tanaka,et al.  Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs , 1998, IEEE Trans. Fuzzy Syst..

[17]  H. Marquez.  Nonlinear Control Systems: Analysis and Design , 2003, IEEE Transactions on Automatic Control.

[18]  Marcelo C. M. Teixeira,et al.  Stabilizing controller design for uncertain nonlinear systems using fuzzy models , 1999, IEEE Trans. Fuzzy Syst..

[19]  Kuang-Yow Lian,et al.  Output Tracking Control for Fuzzy Systems Via Output Feedback Design , 2006, IEEE Transactions on Fuzzy Systems.

[20]  Luigi Galotto Junior,et al.  Controle ótimo H∞ de sistemas não-lineares com modelos fuzzy takagi-sugeno , 2008 .

[21]  Cheng-Wu Chen,et al.  Application of Fuzzy-model-based Control to Nonlinear Structural Systems with Time Delay: an LMI Method , 2010 .

[22]  Cheng-Wu Chen,et al.  Modeling and Fuzzy PDC Control and Its Application to an Oscillatory TLP Structure , 2010 .

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

[24]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[25]  Tzuu-Hseng S. Li,et al.  New Nonlinear Controller for a Class of Chaotic Systems Based on Adaptive Backstepping Fuzzy-Immune Control , 2011 .

[26]  W. Chiang,et al.  GA-Based Fuzzy Sliding Mode Controller for Nonlinear Systems , 2008 .

[27]  D. Siljak,et al.  Robust stabilization of nonlinear systems: The LMI approach , 2000 .

[28]  H. C. Pietrobom,et al.  On relaxed LMI-based designs for fuzzy regulators and fuzzy observers , 2001, ECC.

[29]  Ricardo C. L. F. Oliveira,et al.  Convergent LMI Relaxations for Quadratic Stabilizability and ${{\mathscr H}}_{\infty}$ Control of Takagi–Sugeno Fuzzy Systems , 2009, IEEE Transactions on Fuzzy Systems.

[30]  Cheng-Wu Chen,et al.  Fuzzy Control for an Oceanic Structure: A Case Study in Time-delay TLP System , 2010 .

[31]  G. Feng,et al.  A Survey on Analysis and Design of Model-Based Fuzzy Control Systems , 2006, IEEE Transactions on Fuzzy Systems.