Modelling of a Nonlinear Fuzzy Three-Input PID Controller and Its Simulation and Experimental Realization

Abstract

ABSTRACT Over the last three decades, finding the mathematical models of fuzzy controllers has become an interesting area of research in the control community. The mathematical model of a controller gives a clear insight into the analytical structure of a controller and helps to understand the control problem in the framework of well-defined control theory. Because of modelling and computational complexities, from the literature, it seems to the authors that modelling of three-input fuzzy PID controller has rarely been attempted using the Center of Gravity (CoG) defuzzification. The purpose of the present manuscript is to unveil the exact mathematical model of a nonlinear fuzzy three-input PID controller using CoG defuzzification and to investigate its properties. To justify the theoretical development made in this manuscript, the applicability of the proposed controller is shown through simulation and real-time studies. In the simulation, a nonlinear plant, an unstable plant with large time-delay, and a higher-order plant with dead-time and inverse response are controlled. Whereas in real-time an unstable nonlinear Magnetic levitation (Maglev) plant is controlled. As the proposed controller structure does not depend on plant dynamics, it can easily be implemented for other control applications also.