Modelling and analysis of an interval type-2 Mamdani fuzzy PID controller

Abstract

From the last decade, modelling of Interval Type-2 (IT2) fuzzy controllers has become an exciting area of research in the field of control systems engineering. The input-output relationship of the fuzzy controller gives insights into the exact structure of the controller. From the literature, it is observed that IT2 fuzzy controllers handle plant uncertainty in a better way than their Type 1 (T1) counterparts due to the presence of additional Degree of Freedom (DoF) provided by the Footprint of Uncertainty (FoU) present in the membership functions of Interval Type-2 Fuzzy Sets (IT2FSs). Further, it is also noticed that controllers obtained with non-uniformly distributed fuzzy sets control the uncertain and nonlinear plants in a better way than their uniformly distributed counterparts. To take advantage of these two, in this study, the authors have made an attempt to unveil the exact input-output relationship of an Interval Type-2 Fuzzy PID (IT2FPID) controller, where the modelling is done using a particular type of FoU and non-uniformly distributed fuzzy sets. Apart from modelling, the properties of the newly derived controller are analysed. Moreover, to justify the theoretical development made in this manuscript, the applicability of the controller is shown through simulation, where an unstable chemical reactor plant with a large time delay is controlled. Finally, the effectiveness of the proposed controller is delineated by comparing its performance with that of some recently developed controllers.