Analysis of FLC with Changing Fuzzy Variables in Frequency Domain

This paper discusses a simple method for analyzing FLC in frequency domain based on describing function. Since nonlinear characteristics of FLC make it difficult FLC analysis, it usually requires a big deal of trial-and-error procedures based on computer simulation. The proposed method is simple and easy to understand, because it is based on the Nyquist stability criterion used to analyze absolute and relative stability, phase and gain margin of a linear system. To linearize in frequency domain, a describing function for FLC is derived by using a piecewise linearization of the FLC response plot. This describing function is represented as a function of magnitude of input sinusoid and nonlinear parameters x 1 and x 2 which change consequence fuzzy variables and nonlinearity of FLC. The describing function is redefined without the magnitude of sinusoid input because maximum values of the describing function can explain the stability of the 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 various characteristic of FLC according to x 1 and x 2 in frequency domain. In this work, we suggest a minimum phase margin (MPM) and a minimum gain margin (MGM) for FLC which can be used to determine whether the system is stable or not and how stable it is. For simplicity, we use one-input FLC with three rules. 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.