Gain-phase margin analysis of fuzzy control systems

Abstract

In this paper, we extend some effective methods, including the gain-phase margin tester method, the describing function method and the parameter plane method, to predict the limit cycles of fuzzy control systems. In general, fuzzy control systems are nonlinear. By use of the classical method of describing functions, a fizzy controller may be linearized first. The stability of the equivalent linearized system with adjustable parameters is then analyzed due to the stability equations and parameter plane methods. For the robust design, a novel way is proposed to determine the gain margin and phase margin which limit cycles can occur. Two examples are offered to illustrate the design procedure. First, the fuzzy control system with a third-order linear plant is considered. In addition, this approach is also extended to the fuzzy control system with nonlinearity. The results of computer simulation can verify its validity.