Derivation of the analytical structure of symmetrical IT2 fuzzy PD and PI controllers

Abstract

This paper introduces the analytical structure of a class of interval type-2 (IT2) fuzzy PD and PI controllers that have symmetrical rule base. Two assumptions are made: (1) Zadeh AND operator is employed as the t-norm operator; (2) the centroid type-reduction method is used. The main contribution of this paper is the analytical relationship between the inputs and output of this IT2 fuzzy controller. Comparing with its T1 counterpart, the addition of two FOU parameters generated 31 extra local regions that each provides a unique relationship between the inputs and output signals. The relatively large number of local regions that results, at the cost of two extra design parameters, means that an IT2 fuzzy controller has the potential to provide better performance. Another outcome is the analysis of the centroid type-reduction algorithm yielded closed form expressions for each partition. This result may provide a platform for further theoretical study.