Pareto Optimal Fractional PID for Position Control of Ultrasonic Motor

In this paper, optimal PID and optimal fractional PID controllers for position control of ultrasonic motor are proposed. To design these controllers both minimizing tracking error and control effort are considered. Since these objectives are contradictory the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is used as an evolutionary multi-objective method to derive the Pareto-optimal front consisting optimal solutions. The simulation results demonstrate the superiority of the optimal fractional PID controller in minimizing tracking error while utilizing less control effort. Besides, the robustness of the optimal controllers against parameter variations is investigated. The results ensure that the optimal fractional PID controller is more robust than the optimal PID controller.