Fuzzy Fractional-Order PID Tuned via Relative Rate Observer for the Egyptian Load Frequency Regulation

Abstract

This paper deals with the design of a Fractional-Order Fuzzy PID (FOFPID) controller tuned by the Relative Rate Observer (RRO) that eliminates the steady-state error and improves the performance of the Load-Frequency Control system. The first step is to design a Fuzzy PID (FPID) controller by assembling the Proportional-P and Integral-I to make the PI part and assembling the Proportional-P and Derivative-D to make the PD part with Fuzzy Inference Engine. The Fractional-Order Fuzzy PID (FOFPID) is then obtained from the Fuzzy PID controller by substituting the Integral (I) and Derivative (D) parts by their fractional counterparts. Further, Derivative and Integral scaling factors are adjusted online using the Relative Rate Observer (RRO) to obtain both RRO-based Fuzzy PID(RRO-FPID) and RRO-based FOFPID (RRO-FOFPID). For effectiveness analysis, a comparison between the named three controllers is carried out. The controllers were used to operate, separately, the Egyptian Load-Frequency Control (ELFC) which represents a major part of the system is used for such an application. The carried numerical simulations show better results which motivate for more investigations.