Optimal tuning of multi-PID controller using improved CMOCSO algorithm

To mitigate synchronization errors within a multi-PID controller system and enhance its resistance to interference, an improved competitive and cooperative swarm optimizer for constrained multi-objective optimization (CMOCSO) algorithm is employed to optimize the parameters of the multi-PID controller. Initially, a mathematical model representing the constrained multi-objective problem associated with the multi-PID controller is formulated. In this model, the parameters are designated as decision variables, the performance index serves as the objective function, and the stability constraints of the system are incorporated. Subsequently, an improved CMOCSO algorithm is introduced, which bifurcates the evolutionary process into two distinct stages using a central point-moving strategy; each stage employs different evolutionary techniques to accelerate convergence rates, and a novel grouping strategy is implemented to increase the learning efficiency of the population. The efficacy of the algorithm is evaluated through testing on 16 standard functions, demonstrating its effectiveness in addressing constrained multi-objective problems. Ultimately, the algorithm is applied to optimize the parameters of the multi-PID controller. The simulation results indicate that the proposed method yields superior control performance, reduced synchronization errors, and notable interference resistance capacity.