Robust PID TS fuzzy control methodology based on gain and phase margins specifications

Abstract

This paper proposes the analysis and design of TS fuzzy robust PID control based on gain and phase margins specifications for uncertain nonlinear dynamic systems with time delay. The input-output data set of the uncertain nonlinear time delay dynamic system is decomposed into several input-output spaces by Gustafson-Kessel GK clustering algorithm, which are used to compute several linear submodels by least squares algorithm, and grouped in a Takagi-Sugeno TS fuzzy inference system. From the gain and phase margins specifications, in the frequency domain, analytical formulas are derived for fuzzy model based robust PID control design via Paralel and Distributed Compensation PDC strategy, considering the influence of the time delay. The main contribution of the paper is the proposal of two theorems related to necessary and sufficient conditions for fuzzy robust control design. The first theorem shows that the robust PID controller in the i-th rule of the fuzzy robust PID controller guarantees the gain and phase margins specifications for the corresponding linear model. The second theorem shows that the robust PID controller in the i-th rule of the fuzzy robust PID controller guarantees the stability for all linear models. A simulation example illustrates the efficiency of the fuzzy controller for control of a single link robotic manipulator when compared to others control methods. The experimental results for real-time fuzzy robust PID control of a termic process are obtained to demonstrate the effectiveness and practical viability of the proposed strategy.