Analytical Structure of Three-Dimensional Fuzzy Controller

The analytical structures and properties of a general three-dimensional fuzzy controller, involving two triangular fuzzy sets for each of the three input variables, Zedeh AND T-norm, Zedeh OR T-co-norm, Mamdani inference method, four singleton fuzzy sets for output variable, eight nonlinear fuzzy control rules and the popular centroid defuzzification algorithm, are investigated in this paper. Especially, the division of three-dimensional input space, a divided cube, is first proposed and implemented. And we theoretically prove that this general three-dimensional fuzzy controller is a continuous and bounded combination of a nonlinear PID controller with dynamic proportional gain, dynamic integral gain and dynamic differential gain changing with the error of displacement, velocity of error and acceleration of error about the SP (set point), a nonlinear PI or PD controller with dynamic gains changing with one input and constant control offset, a one-dimensional linear controller, and saturation elements.