A Gradient Descent based online tuning Mechanism for PI Type Single input Interval Type-2 fuzzy logic controllers

Abstract

In this paper, we will present design methods for Single input IT2-FLCs (SIT2-FLCs) and we will introduce an online tuning mechanism to enhance their control system performance. The most important feature of the SIT2-FLC is the closed form output presentation which is defined in a two dimensional domain. Based on this structural information, we will present design methods for SIT2-FLCs composed of 3 rules to produce a Smooth SIT2-FLC (S-SIT2-FLC) and an Aggressive SIT2-FLC (A-SIT2-FLC) by only tuning a single parameter. It will be shown that the S-SIT2-FLC will result in a potentially more robust control performance in comparison A-SIT2-FLC. However, the transient state and disturbance rejection performance of the S-SIT2-FLC might degrade in comparison to the A-SIT2-FLC. This drawback will be solved by tuning the FOU size of the SIT2-FLCs to provide a trade-off between the robust control performance of the S-SIT2-FLC and the acceptable transient and disturbance rejection performance of the A-SIT2-FLC structure. Thus, we will present a Gradient- Descent (GD) based online tuning mechanism to enhance both the transient state and disturbance rejection performances of the SIT2-FLCs while preserving a certain degree of the robustness against nonlinearities and disturbances. We will present simulation results where the GD based SIT2-FLC (GD-SIT2- FLC) is compared with the S-SIT2-FLC and the A-SIT2-FLC structures. Moreover, we will compare the performance GD-SIT2-FLC with a robust self-tuning Type-1 (T1) FLC which has a fuzzy based tuning mechanism. The results will show that the GD-SIT2-FLC enhances both the transient state and disturbance rejection performances when compared to the IT2 and robust self-tuning T1 counterparts.