Explicit structure of the typical two-input fuzzy controllers

Fuzzy controllers are nonlinear controllers. As such, it is important to reveal analytical structure of fuzzy controllers relative to classical nonlinear controllers so that the well-developed conventional nonlinear control theory can be applied to effectively analyze and design fuzzy control systems. In this paper, we derive the analytical structure of the general and typical fuzzy controllers: the ones that employ trapezoidal input fuzzy sets and arbitrary nonlinear control rules. We show that the structure of the fuzzy controllers is the sum of a global nonlinear controller and a local nonlinear PI-like or PD-like controller with variable proportional-gain and integral-gain (or derivative-gain). This result generalizes our previously published results