A design methodology and analysis for interval type-2 fuzzy PI/PD controllers

In this paper, a systematical methodology is introduced to construct the rule base of an interval type-2 fuzzy logic controller based on an existing linear PI/PD controller. An easy and rapid generation of the fuzzy rules can be achieved through this technique. In addition, analytical structure of this controller is derived. A closed-fonn of the fuzzy controller output is achieved under the circumstances that the input type-2 membership functions a,re diamond-shaped and a closed-form inference engine is used. Consequently, a linear control law is transformed to a nonlinear structure and certain elaborations can be done on the parameters of the evolved closed output structure. Moreover, the designer can benefit from the nonlinear structure of the proposed controller and the extra degree of freedom of type-2 fuzzy sets. It can be concluded from the results that the proposed controller can be more robust to the parameter uncertainties and eliminate the oscillations much better than type-1 fuzzy logic and linear conventional controllers.