Parameter plane analysis of fuzzy control systems for limit cycle prediction

The main purpose of this paper is to predict the limit cycles of fuzzy control system by combining the approaches of stability equation, describing function and parameter plane. The fuzzy controller is first linearized by using the describing function method. The stability of equivalent linearized system is then analyzed by using stability equations and the parameter plane method. According to this procedure, the amplitude and frequency of limit cycles generated by the fuzzy controller can be figured out clearly in the parameter plane. In addition, both the continuous and sampled-data systems are considered. Finally, a fuzzy control system with multiple nonlinearities is also illustrated to verify its validity.