Interval Type-2 Fuzzy PI Controllers: Why They are More Robust

Many experiments have shown that interval type-2 (IT2) fuzzy PI controllers are generally more robust than their type-1 (T1) counterparts, as they are better able to cope with disturbances and uncertainties and eliminate oscillations. This paper aims at providing theoretical explanations to these experimental observations. Analysis has shown that the additional degrees of freedom provided by the footprint of uncertainty enable an IT2 fuzzy PI controller to emulate a variable gain PI controller around the origin, and these PI gains are smaller than those of the baseline type-1 fuzzy PI controller, consequently, the same amount of disturbance will cause a smaller control signal change for an IT2 fuzzy PI controller, and hence reduces the risk of oscillation. The results in this paper enable us to connect traditional PI controllers with IT2 fuzzy PI controllers. Based on the closed-form equivalent PI gains, controller design rules in one domain may be transferred to the other domain, and it is possible to develop new control laws by combining the merits of both traditional PI controllers and IT2 fuzzy PI controllers.