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The fractional-order PID controller provides more adjustable parameters in the controller optimization than conventional PID controller. Therefore, FOPID is designed to achieve more goals, and multi-objective optimization based genetic algorithm is adopted. To solve this problem, a multi-objective optimization design method is proposed in this paper. Not only the robust performance, but also frequency angle margin, overshoot and rise time are all taken as the objectives to optimize. Then a variant of NSGA-II reach the optimal solution. This method can obtain uniformly distributed Pareto-optimal solutions and have good convergence and excellent robustness. The satisfactory solution is selected in Pareto optimum solution set according to the system requirement, which provides an effective tool for trade-off among the performance of quickness, stability and robustness. Simulation results support the superiority and effectiveness of the proposed method.
Li et al. (Mon,) studied this question.