Xian H. Li, Hai B. Yu, and Ming Z. Yuan
Optimal PID controller, dynamic performance items, AISE–HDPI performance index, Lyapunov theorems, dominant poles method, NLCO problem
A systematic tuning method is proposed to design the optimal proportional-integral-derivative (PID) controller with dynamic performances constraint for different processes. The proposed optimal PID controller can be acquired by minimizing an augmented integral squared error–hybrid dynamic performance items (AISE–HDPI) performance index. The AISE–HDPI performance index is constituted by error items and dynamic performance items which at least include one dynamic performance item. The optimal control problem is approximate equivalent transformed into a nonlinear constraint optimization (NLCO) problem through Lyapunov theorems and dominant poles method. Therefore, the proposed optimal PID controller can be obtained by solving the NLCO problem. The proposed method is utilized to design the optimal PID controller for different processes, and the optimal PID controllers under various control weight matrices are presented. The dynamic performances of different tuning methods are discussed. To deep study the proposed method, the robustness of different tuning methods is also investigated and a robustness evaluation function is proposed to assess the robust performances of different tuning methods. To further validate the proposed method, different tuning methods’ disturbance rejection ability is also investigated. The simulation results show effectiveness, usefulness, and robustness of the proposed method.
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