Boundary function based Karnik-Mendel type reduction method for Interval Type-2 Fuzzy PID controllers

In this paper, we will present a Boundary Function (BF) based type reduction/ denazification method for Interval Type-2 Fuzzy PID (IT2-PID) controllers. Thus, we have presented a novel representation of the optimal Switching Points (SPs) of the Karnik Mendel (KM) method by first decomposing the IT2-FPID controller into SubControllers (SCs) and then derived Boundary Functions (BFs) to determine the optimal SPs of each SCs. Since the optimal SPs are calculated without an iterative algorithm, the explicit expressions of how the SPs are determined is represented in analytical structure via the proposed BFs. We have presented comparative studies where the computational time performance of the proposed BF-KM method is compared to the KM and the decomposition based KM methods. The presented results show that proposed method is superior in comparison to the other compared methods and feasible for especially real time control applications where there is a need of small sampling times.