Type-2 Fuzzy Controller for Stability of a System

Abstract

Type-2 Fuzzy sets (T2FSs) handle a greater modeling and uncertainties which exist in the real world applications especially control systems. To avoid mathematical complexity, interval T2FSs (IT2FSs) have been pertained in majority of the fields. One of the important components which influence the fuzzy controller is the t-norm. For obtaining the stability of a control system, t-norm operator can be preferred for better results and in this paper the minimum and maximum operations have been used to simplify the work of the system with Gaussian interval type-2 membership function (GIT2MF). Also proposed Gaussian interval type-2 weighted geometric (GIT2WG) operator and mathematical properties of aggregation operator have been proved using the proposed operator. The goal of this work is to analyze the stability of an inverted pendulum using interval type-2 fuzzy logic controller (IT2FLC) and the results are compared with Proportional Integrated Derivative (PID) Controller. It is observed that IT2FL controller gives the better stability.