Abstract :
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.
Keywords :
fuzzy control; fuzzy set theory; inference mechanisms; nonlinear control systems; three-term control; Mamdani inference method; Zedeh AND T-norm variable; Zedeh OR T-co-norm variable; centroid defuzzification algorithm; dynamic integral gain; dynamic proportional gain; nonlinear PID controller; three-dimensional nonlinear fuzzy controller; triangular fuzzy sets; Algorithm design and analysis; Displacement control; Error correction; Fuzzy control; Fuzzy sets; Inference algorithms; Input variables; Pi control; Proportional control; Velocity control; Mamdani inference method; PID controller; analytical structure; fuzzy controller; input space division;
