Steady-state analysis of a three-term fuzzy controller

The steady-state response of a fuzzy logic controller that uses fuzzy addition as the basis for its decision making process is analyzed mathematically. The nature of the look-up table constructed from fuzzy addition enables the decomposition of the fuzzy controller into three one-dimensional-multilevel relays. Unlike the sinusoidal-input describing function technique, the steady-state response of the closed-loop system is analyzed. The sufficient conditions derived depend on the parameters of the controller and can be used as guidelines to achieve a good step response at steady-state, one that does not lend itself to sustained oscillations or limit cycles