Modeling, analysis and real-time implementation of five new simplest fuzzy nonlinear PI/PD controllers

In spite of accuracy, but due to computational complexity, Center of Gravity (CoG) defuzzification remained dormant for the mathematical modeling of fuzzy controllers for a long time in the past. Recently, Arun and Mohan (ISA Trans 70:16–29, 2017) obtained the mathematical models of two simplest fuzzy PI/PD controllers using CoG defuzzification. In this study, the mathematical models of another five simplest fuzzy PI/PD controllers are obtained, and their properties and computational aspects are investigated. Sufficient conditions for Bounded-Input-Bounded-Output stability of a closed-loop system containing one of these controllers in the loop are also established using the Small-Gain theorem. To justify the theoretical developments made in this manuscript, the applicability of the controllers is shown in simulation and real-time.