Mathematical model of a Takagi-Sugeno PI/PD controller

In this paper, we introduce a simple linear Takagi - Sugeno (T-S) fuzzy rules, and derive a mathematical model of Takagi-Sugeno PI/PD controller using at least three trapezoidal fuzzy sets on each scaled input variable, minimum AND operator, bounded sum OR operator, and centre of gravity defuzzification method. We show the superiority of this model over the existing model in the literature. We reveal that this controller is inherently a nonlinear PI / PD controller with its gains (proportional, integral / derivative) changing with respect to the scaled input variables. The gains either continuously change or remain constant in different regions of input plane. Moreover, the gains switch continuously between adjacent regions of input plane. Geometrical shape and bounds of gain variation are investigated.