Analysis of the typical fuzzy logic controller using cell concept

Fuzzy controllers are nonlinear controllers. Sources of the nonlinearity in a fuzzy logic controller include the fuzzification, the fuzzy inference and the defuzzification. As such, it is important to reveal analytical structure of fuzzy logic controllers so that the well-developed conventional control theory can be applied to effectively analyze and design fuzzy control systems. In this paper, we provide a mathematical analysis of the nonlinear characteristic of typical fuzzy logic controller by using the cell concept. The output of FLC is decomposed into two parts: a two-dimensional multi-level relay (interval effect) and a local nonlinear compensator (cell effect). With higher fuzzy resolution (i.e. by fine partitioning of fuzzy variables) a higher degree of linearity in the control surface can be attained. Based on this result, we compare the operational characteristic of fuzzy logic controller with that of the conventional PID controller.