Development method for a robust PID fuzzy controller of LPV systems

This paper proposes the analysis and design of robust fuzzy control to nonlinear systems with time delay. 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 of second order with time delay, 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.