Analytical Structure and Performance of Interval Type-2 Fuzzy Two-Term Controllers with Varying Footprint of Uncertainty

Abstract

Abstract While type-2 fuzzy control has gained a lot of attention in the recent years, several challenges still remain with respect to controller design. The footprint of uncertainty (FoU) plays a very important role in designing type-2 fuzzy controllers, since the performance of type-2 fuzzy controllers largely depends on the choice of FoU. In this paper, we propose a simplified model of interval type-2 (IT2) fuzzy two-term controllers of Takagi–Sugeno (TS) type with only two rules in the rule base. The controller model is derived with varying FoUs based on only two type-2 input fuzzy sets (the simplest case). An extension to multiple input fuzzy sets is also presented. We investigate the variation in control surface and computational aspects of the IT2 fuzzy two-term controller as the FoU is varied. The performance of the proposed IT2 fuzzy controller with respect to varying FoUs is evaluated in the simulation study.

Keywords

• Type-2 fuzzy control
• Takagi–Sugeno (TS) controller
• Variable gain controller
• PI/PD controller
• Mathematical model
• Footprint of uncertainty (FoU)