Optimal Takagi-Sugeno Fuzzy Gain-Scheduler Design Using Taguchi-MHGA Method.

Abstract

The fuzzy gain scheduling (FGS) control scheme based on TS (Takagi-Sugeno) fuzzy model is an effective approach to control nonlinear systems whose dynamics change with different operating condition. However, when the TS-model-based FGS control scheme is adopted to the stabilization/tracking control problem, a considerable amount of approximation errors between the nonlinear system and fuzzy approximation system apparently affect the control performance. Besides, when the LQR (linear quadratic regulator) method is employed to design local linear controllers, it is necessary to adjust the weighting matrices in performance index of the LQR for getting minimum performance index. Hence, in order to reduce the aforementioned approximation errors and enhance the dynamic performance of the TS-model-based FGS control scheme, a systematic and optimal reasoning method, named as Taguchi-MHGA (Taguchi-modified-hierarchical-genetic-algorithm) approach, is proposed in this paper to search for the optimal fuzzy centers (the linearization points) of the fuzzy regions, the optimal set of membership functions, and the weighting matrices of the LQR method. Furthermore, for ensuring that the closed-loop FGS system at any arbitrary operating point is asymptotically stable, two new sufficient conditions are presented. Finally, computer simulations are performed to demonstrate the effectiveness of the TS-model-based FGS control scheme designed by Taguchi-MHGA method. It is shown that the satisfactory performances have been achieved by such designed optimal TS-model-based FGS control scheme.