Design Of Fuzzy Controler Based On T-S Model

The design of controllers for fuzzy control systems have been an active question for a long time. It is very difficult of the design of controllers for fuzzy control because of the systems' nonlinear. Now there have existed a lot of measures to ensure the stability of fuzzy control. However, more perfect methods are required eagerly. It is necessary to resolve theoretical problems of control more deeply.In recently years, Linear Matrix Inequality (LMI) has been used widely in control fields. As a convex method, with the method of interior point put forward, LMI becomes more and more important. Many problems of control can be transform feasible problems of linear matrix inequalities or convex problems with constraint of linear matrix inequalities. During solving problems of matrix inequalities, LMI is more useful than the equation of Lyapunov and Riccati. Moreover, The problems about matrix inequalities can be solved more easily due to the appearance of toolbox in MATLAB.In practice, the states of the nonlinear systems are usually unobservable, so it is necessary to design a fuzzy observer in order to estimate the state variable. The paper is studied fuzzy controllers and fuzzy observers based on linear matrix inequality (LMI) for T-S fuzzy models. A method of designing fuzzy controllers and fuzzy state observers with pole placement constraints for nonlinear systems approximately expressed by Takagi-Sugeno (T-S) fuzzy dynamic model was proposed. Firstly, the parallel distributed compensation (PDC) is to design fuzzy controllers and fuzzy observers for T-S fuzzy models. Methods that design fuzzy controllers are through state feedback, and except introducing some former methods ,an novel method that with respect to pole placement constraints is derived and utilized in the design procedures for it can improved system's dynamic quality. Then, the method combines Stability conditions of closed-loop T-S fuzzy systems, desired control performance based fuzzy controllers and fuzzy observers are into a framework of linear matrix inequalities (LMI). So parameters for controllers and observers are derived by solve LMIs. The simulated models choose inverted pendulum, the result of simulation demonstrates these methods are effective and convenient.