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

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 H₄ <; H₃ = H₂ <; H₁, the IT2 fuzzy PD and PI controllers considered in this paper have four different consequent sets H₄ <; H₃ <; H₂ <; H₁. 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.