High Order Approximation of Fractional PID Controller based on Grey Wolf Optimization for DC Motor

The purpose of this study is to make a high fractional PID (FPID) controller for managing the speed of a direct current (DC) motor using Grey Wolf Optimization (GWO). The GWO/FPID controller approximation, characterized by a lengthy memory (or high order approximation (HOA)), by an integer order transfer function, necessitates the employment of a large number of parameters. This new controller, named the HOA-GWO/FPID is used to regulate the DC motor system. With regard to percentage overshoot, settling time, rising time, and disturbance rejection, it demonstrates remarkable robustness and superior control performance. The effectiveness of the proposed controller was examined using transient and frequency responses.