Gradient Descent and Extended Kalman Filter based Self-Tuning Interval Type-2 Fuzzy PID Controllers

In this paper, we will present two novel self-tuning structure based on the Gradient Descent (GD) method and Extended Kalman Filter (EKF) estimation to improve the control performances of Interval Type-2 (IT2) Fuzzy PID (FPID) controllers. In this context, we will derive the analytical expressions of the output of the IT2-FPID controller as a function of the design parameter, namely the Footprint of the Uncertainty (FOU) parameters. We will present the proposed GD based Self-Tuning IT2 (STIT2) FPID controller and the EKF based STIT2-FPID controller structures. These self-tuning structures update the FOU design parameter so that the size of the FOU of the IT2 fuzzy sets is tuned in an online manner. The adjustment of the FOU parameter results with a hybrid controller behavior combining the aggressive nature of the Type-1 (T1) FPID and the robust nature of the IT2-FPID controllers. We will present simulation results where the proposed GD-STIT2-FPID and EKF-STIT2-FPID controllers are compared with their IT2 and STT1 counterparts. The results will show that the self-tuning IT2-FPID controller has ability to improve overall reference tracking and disturbance rejection performances in comparison with its T1, self-tuning T1, and IT2 counterparts.