Modeling and simulation of a general three-input Mamdani fuzzy proportional-integral-derivative controller using non-uniformly distributed fuzzy sets

It appeared from the literature that Non-Uniformly Distributed (NUD) Fuzzy Sets (FSs) play a critical role in the control of nonlinear dynamical systems. Hence, fuzzy controllers developed with NUD FSs have more potential to provide better control performance whenever the systems under control are nonlinear. It seems from the literature that there is no relevant work related to the modeling of a general Three-Input (3-I) Fuzzy PID (FPID) controller using NUD FSs and Centre of Area (CoA) defuzzification. So far, most of the developments have dealt with Uniformly Distributed (UD) FSs and Center of Sums (CoS) defuzzification only. Hence, this paper attempts to model and design a general 3-I FPID controller considering NUD FSs for fuzzification of input and output variables, and CoA defuzzification. To derive the mathematical models of the controller, Algebraic Product (AP) AND operator, Maximum (Max) OR operator, Larsen Product (LP) inference, and Max aggregation operator are taken into consideration. Guidelines for the design of the controller are provided. The applicability and usefulness of the proposed controller are depicted with a simulation study on the Single Link Manipulator (SLM) system and a real-time study on the Magnetic Levitation (Maglev) system.