Development, experimental validation, and comparison of interval type-2 Mamdani fuzzy PID controllers with different footprints of uncertainty

Abstract

Interval Type-2 Fuzzy PID (IT2FPID) controllers use Interval Type-2 Fuzzy Sets (IT2FSs). The difference between Type-1 Fuzzy PID (T1FPID) controllers and IT2FPID controllers is the Footprint of Uncertainty (FOU) which occurs due to the use of IT2FSs. FOU gives an extra degree of freedom to the controller structure, which is capable of handling uncertainty in the plant. However, the effect of FOU on the analytical structures of the IT2FPID controllers is not yet explored when uniformly/non-uniformly distributed multiple IT2FSs are used on the input side and uniformly/non-uniformly distributed multiple singleton fuzzy sets are considered on the output side of the controller. In this paper, controllers with three different types of FOUs and two different defuzzification methods are considered, and their analytical structures are derived. The suitability of the controllers is examined, and the properties of the suitable controllers are explored. Effects of FOU on the nonlinearity, gain, and computational aspects of the suitable controllers are studied. The applicability of proposed IT2FPID controllers is shown through simulation and real-time studies. The effectiveness of the proposed controllers is depicted by comparing their performances with that of the recently developed Integer Order Fuzzy PID (IOFPID) and Fractional Order Fuzzy PID (FOFPID) controllers.