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

Limb-cycle is the phenomenon that can be observed in the systems composed o f nonlinear elements, The phenomenon is of fundamental importance in nonlin ear systems and, as far as the design of a nonlinear system is concerned, i t should be considered along with the stability analysis. In this paper, th e limit-cycle of a system controlled by a fuzzy logic controller (FLC) is a ddressed via some of the classical control techniques used to analyze non-l inear systems in the frequency domain. First, reasonable assumptions are ma de on the structure of the FLC by using fuzzy basis functions (FBP's) and t he describing function of the FLC is derived to analyze and predict the exi stence of the limit-cycle of the closed-loop system including the FLC, Fina lly, 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 con trol system.