Modelling and simulation of an interval type-2 Mamdani fuzzy PID controllers

This paper presents mathematical models of three different Interval Type-2 (IT2) Fuzzy PID (FPID) controllers. The mathematical models of the controllers are obtained by considering triangular Membership Functions (MFs) for input and output Fuzzy Sets (FSs), Larsen Product (LP) inference, and three different types of defuzzification techniques, namely centroid defuzzification, average defuzzification, and Nie-Tan (NT) defuzzification. One-Dimensional (1D) input space is employed to reduce the computational complexity of the models of each controller. The properties of the mathematical models are thoroughly examined. A simulation study is conducted to justify the validity and usefulness of the proposed controllers.