Multi-objective robust PID controller tuning using state transition algorithm

In many control systems, achieving high accuracy, rapid response, and robustness depends on the precise configuration of controller parameters. This is particularly true for Proportional-Integral-Derivative (PID) controllers, widely used in various applications for their efficiency and adaptability. However, the tuning of these parameters becomes challenging due to conflicting control performance requirements, particularly in uncertain multi-input multi-output (MIMO) systems. In this paper, the PID controller design problem is formulated as a multi-objective optimization problem (MOP) by minimizing balanced robust performance criteria and integral squared error (ISE). The multi-objective state transition algorithm (MOSTA) is applied to solve the MOP and obtain Pareto optimal solutions, representing the optimal trade-offs among conflicting objectives. Then, the parameters of a robust PID controller are determined for a MIMO system by using a visualizing multi-attribute decision-making (V-MADA) approach, achieving a more comprehensive evaluation and a better understanding of the decision-making process. The efficacy of this multi-objective robust PID controller design is demonstrated through its application to the supper maneuverable F18/HARV fighter aircraft. The results show that the PID controller designed by MOSTA and V-MADM exhibits superior robustness. The proposed method offers valuable insights for various engineering applications that require the design of robust PID controllers with multiple performance objectives.