Limit-cycle prediction of a fuzzy control system based on describing function method

A limit-cycle is the phenomenon that can be observed in systems composed of nonlinear elements. The phenomenon is of fundamental importance in nonlinear systems and, as far as the design of a nonlinear system is concerned, it should be considered along with the stability analysis. In the paper, the limit-cycle of a system controlled by a fuzzy logic controller (FLC) is addressed via some of the classical control techniques used to analyze nonlinear systems in the frequency domain. First, reasonable assumptions are made on the structure of the FLC by using fuzzy basis functions (FBFs) and the describing function of the FLC is derived to analyze and predict the existence of the limit-cycle of the closed-loop system including the FLC. Finally computer simulation is performed to show how the analysis given in the paper is used to predict the existence of the limit-cycle of the fuzzy control system.