General structure of Interval Type-2 fuzzy PI/PD controller of Takagi–Sugeno type

Abstract In this paper, a new configuration of Interval Type-2 (IT2) fuzzy Proportional–Integral (PI) or fuzzy Proportional–Derivative (PD) controller of Takagi–Sugeno (TS) type is presented. An attempt is made to generalize the IT2 fuzzy PI/PD controller structure using multiple fuzzy sets. Fuzzification of the inputs is done with three or more fuzzy sets having triangular/trapezoidal membership functions. The rule base consists of only three rules to reduce the number of tuneable parameters of the controller. Minimum (Min) triangular norm and Bounded Sum (BS) triangular co-norm are used as conjunction and disjunction operators to reduce the number of rules. Karnik–Mendel (KM) type reducer and Weighted Average (WA) defuzzifier are considered to derive the analytical structure of the fuzzy controller. Properties and gain variations of the fuzzy controller are investigated. Simulation study is carried out on nonlinear dynamical systems to verify the applicability of the fuzzy controllers.