Takagi-Sugeno fuzzy control method for nonlinear systems

This paper proposes a new methodology for analysis and design of robust fuzzy Takagi-Sugeno (TS) control, with PID structure, for nonlinear systems, based on gain and phase margins specifications. The nonlinear system to be controlled, is studied in the context of Linear Parameters Varying (LPV) systems, it is partitioned into several linear sub-models in terms of transfer function, forming a convex polytope. Once defined the linear sub-models of the plant, these are organized into fuzzy Takagi-Sugeno (TS) structure. From the Parallel Distributed Compensation (PDC) strategy, a mathematical formulation is defined in the frequency domain, based on the gain and phase margins specifications, to obtain robust PID sub-controllers in accordance to the Takagi-Sugeno fuzzy model of the plant. Results for the robust stability conditions with the proposal of one Axiom and two Theorems are also presented.