Modeling of some simplest Mamdani interval type-2 fuzzy PID controllers using Larsen product inference

Interval Type-2 (IT2) Fuzzy Logic Controllers (FLCs) have emerged in the past several years due to their ability to handle high levels of uncertainties and disturbances in real-world applications. They are most widely used due to their superior control performance compared to their Type-1 (T1) counterparts. This paper presents nine different mathematical models of the simplest IT2 Fuzzy PID (FPID) controllers of Mamdani-type by considering IT2 Fuzzy Sets (FSs) with triangular Membership Functions (MFs) on both input and output linguistic variables, Larsen Product (LP) inference, and three different defuzzification methods, 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. The properties of the models are thoroughly examined. Guidelines for the synthesis of controllers are presented. Simulation and real-time studies are conducted to justify the validity and usefulness of the proposed controller models. The robustness property of the proposed controllers is also investigated via simulation studies and real-time experiments by considering input and output disturbances and plant parameter variations.