A new methodology for fuzzy model based robust control for nonlinear systems

This paper proposes a robust fuzzy model based control methodology from the gain and phase margins robust specifications for nonlinear systems. The nonlinear plant is decomposed into several input-output spaces by Gustafson-Kessel clustering algorithm. These input-output spaces are used to compute several linear submodels by least squares algorithm. The input-output spaces and the linear submodels are grouped in a Takagi-Sugeno (TS) fuzzy inference system to model the nonlinear plant. According to Paralel and Distributed Compensation (PDC) strategy and definitions of the gain and phase margins in the frequency domain, analytical formulas are derived for TS fuzzy model based robust PID control design of the closed-loop fuzzy control system. Results for the necessary and sufficient conditions, with the proposal of one axiom and two theorems are presented. Simulation results for the control of a single link robotic manipulator are shown and compared to others control methods widely cited in the literature, illustrating the efficiency of the proposed method.