The derivation of the analytical structure of a class of Interval type-2 fuzzy PD and PI controllers

Abstract

Analytical structure of a fuzzy logic system (FLS) is to establish its mathematical input-output relationship. In this paper, the analytical structure of a class of Interval type-2 (IT2) fuzzy PD and PI controllers are derived by dividing the input space and identifying the input-output relationship for each region. Unlike the symmetric fuzzy PD and PI controller [12] which have three different consequent sets H 4 3 = H 2 1 , the IT2 fuzzy PD and PI controllers considered in this paper have four different consequent sets H 4 3 2 1 . Compared with the symmetric IT2 fuzzy controllers investigated in [12], the relatively large number of divisions of the input space indicates the potential of this class of IT2 fuzzy controllers in achieving better performance. The equations describing the input-output relationship for each region provide mathematical tools for further investigations of these IT2 fuzzy PD controllers.