Online Footprint of Uncertainty Tuning Mechanism for Single-Input Interval Type-2 Fuzzy PID Controllers

Abstract

Single-input interval type-2 fuzzy PID (SI-IT2-FPID) control approach is a simple and effective way of adding nonlinear characteristics to linear PID controllers to increase the control performance and the capability of handling system nonlinearities. In the SI-IT2-FPID approach, the nonlinear characteristic of the PID controller is provided by a single-input-single-output interval type-2 fuzzy controller (IT2-FC) positioned before the PID controller. In the literature, a constant footprint of uncertainty (C-FOU) structure is used in SI-IT2-FPID controller design procedures in almost all studies. However, the C-FOU structure limits the performance of the SI-IT2-FPID controller. In this study, an online footprint of uncertainty (FOU) tuning mechanism is proposed for SI-IT2-FPID controllers in order to increase their control performances. Online tuning of FOUs of interval type-2 membership functions (IT2-MFs) enhances the capability of SI-IT2-FPID controllers to handle system nonlinearities since FOU levels of IT2-MFs have a dominant effect on the control and robustness performance of SI-IT2-FPID controllers. In the proposed method, FOUs of IT2-MFs of an IT2-FC are adjusted by an analytical function based on the system error and the change of the error. In this way, the simple structure of the SI-IT2-FPID controller is preserved. In order to illustrate the control and robustness performance of the proposed controller, simulation studies are carried out on three benchmark systems, namely a second-order nonlinear system, a ball and beam system, and a first-order plus dead time system. Additionally, the performance of the proposed controller is compared to a SI-IT2-FPID controller with C-FOU and a classical PID controller. The simulation results show that the proposed controller exhibits better control and robustness performance than the other controllers.