Fuzzy Optimal State Observers For Takagi-Sugeno Fuzzy State Feedback Control

In this work, a comparative study is developed among different methods for state observers design, analyzing their advantages and drawbacks. Three optimal design methods are considered. First, an observer based on the duality theorem and the Linear Quadratic Regulator (LQR) controller design method. Second, a new optimal observer for noiseless described systems. Third, a Kalman filter. The fuzzy observers are obtained by the linearized Takagi-Sugeno (TS) function at each fuzzy rule, so the optimal observers become suboptimal among the fuzzy interpolation of the rules. Two examples are proposed to evaluate the performance of the observers. The first one is an example of linear discrete system, and the second one is a thermal mixing tank, which is a multivariable, delayed and nonlinear system. The results show that for noiseless described systems, the best and easiest method is the new optimal observer, but the Kalman filter is the best choice for reducing noise.