Analytical Structures of Takagi-Sugeno Fuzzy Two-Input Two-Output Proportional-Integral/Proportional-Derivative Controllers With Multiple Fuzzy Sets

Abstract

In this paper, an attempt is made to generalize the analytical structures of Takagi-Sugeno (TS) fuzzy two-input two-output (TITO) proportional-integral (PI)/proportional-derivative (PD) controllers using multiple input fuzzy sets. Two models of fuzzy TITO PI/PD controllers are proposed based on two distinct control strategies. The inputs are fuzzified by multiple fuzzy sets with trapezoidal/triangular membership functions. The generalized rule base consists of nine control rules imbibing the complete control strategy and is closer in spirit to the original TS rule base. Algebraic product (AP) triangular norm, bounded sum (BS) triangular conorm, and center of gravity (CoG) defuzzifier are applied to derive the models. The models of the fuzzy TITO PI/PD controllers with multiple input fuzzy sets are (nonlinear) variable gain/structure controllers. Also, each output of the fuzzy controller is the sum of two nonlinear PI/PD controllers with variable gains. The gain variation and properties of the proposed controllers are studied. Two examples of nonlinear dynamic processes are considered to demonstrate the applicability of the proposed controllers.