Modeling, simulation and experimental realization of a new nonlinear fuzzy PID controller using Center of Gravity defuzzification

Abstract

Though Center of Gravity (CoG) defuzzification is a well-known and long-standing method in the history of fuzzy systems, because of its computational complexity, its use in the field of modeling of fuzzy controllers is almost nil. From literature, it appears that modeling of fuzzy Proportional Integral Derivative (FPID) controllers is rarely attempted using CoG defuzzification. In fact, none of the FPID controller models are obtained using both two-dimensional input space and CoG defuzzification. The available mathematical models of fuzzy Proportional Integral (FPI) and fuzzy Proportional Derivative (FPD) controllers using two-dimensional input space and CoG defuzzification were due to Arun and Mohan (2017). In this paper, the authors make an attempt to model and design an FPID controller using two-dimensional input space and CoG defuzzification. The incremental control effort produced by the newly developed FPID controller is found by combining the individual control efforts produced by incremental FPI and incremental FPD controllers. The incremental FPI and incremental FPD controller structures are unveiled using two-dimensional input space, CoG defuzzification, Min t-norm, Max t-conorm, and Larsen Product (LP) inference. The applicability and usefulness of the newly obtained FPID controller are depicted with simulation and real-time experimentation.