On the difference in control performance of interval type-2 fuzzy PI control system with different FOU shapes

Abstract

Interval type-2 fuzzy logic controllers (IT2-FLCs) have been attracting a lot of attention. However, challenges in designing IT2-FLCs still remain. One of the main challenges is to choose the appropriate FOU shape for interval type-2 fuzzy sets (IT2-FSs). This paper aims to analyse the differences in control performance between three IT2 fuzzy PI controllers (IT2-F-PICs) with different FOU shapes as antecedent sets, namely the triangular top wide IT2 fuzzy set, the triangular bottom wide IT2 fuzzy set and the trapezoidal (also called parallel) IT2 fuzzy set. First, the analytical structures of these IT2-FLCs are derived and the mathematical input–output equations are obtained. Three interesting differences between the analytical structures and input–output relationship of the IT2-F-PICs are then presented. From the differences in the analytical structures of the three IT2-F-PICs and numerical simulation results, it is demonstrated that IT2-F-PICs with trapezoidal (IT2-F-PI-P) and triangular bottom wide (IT2-F-PI-BW) antecedent sets with the potential to provide faster transient response and faster settling time than the IT2-F-PICs with triangular top wide (IT2-F-PI-TW). In addition, IT2-F-PI-P is better able to handle plant uncertainties and disturbances than IT2-F-PI-BW and IT2-F-PI-TW. The contribution of this paper is to provide insights into the performance differences between different FOU shaped controllers, which in turns allowing control designers to select the appropriate FOU shape in order to meet design requirements.