퍼지제어기의 멤버쉽 함수의 퍼지변수 변화에 따른 안정도 고찰

Abstract

It is hard to design FLC because it has a nonlinear characteristic. For this reason, FLC design usually requires a quite amount of trial and error procedures based on computer simulation. This paper describes a simple method for designing FLC based on a describing function method and a circle criterion in frequency domain. Proposed method is simple and easy to understand, since it is based on the Nyquist stability criterion that is used to analyze absolute stability and relative stability, a phase margin and a gain margin, of linear system. To linearize in frequency domain, FLC is represented by a describing function using a piecewise linearization of the response plot of FLC. This describing function is represented as the function of magnitude of input sinusoid and nonlinear parameters and which change consequence fuzzy variables and nonlinearity of FLC. The describing function is redefined without the magnitude of sinusoid input because the maximum values of the describing function can explain the stability of system. This redefined describing function is used to get minimum stability characteristic, an absolute stability, phase margin and gain margin, of FLC. Using this function, we can explicitly figure out the various characteristic of FLC according to the width of consequence fuzzy variables in frequency domain. In this work, we suggest a minimum critical point(MCP), a minimum phase margin(MPM) and a minimum gain margin(MGM) for FLC which can be used to determine whether system is stable or not. For simplicity, we use one-input FLC with three, five and seven fuzzy variables. For various nonlinear response of FLC, changing fuzzy variables of a consequence membership function is used. Simulation results show that these parameters are effective in analyzing FLC.