Optimal PID Controller based on Convex Optimisation and Particle Swarm Techniques

Abstract

This paper discusses the design and implementation of multiple optimisation algorithms for tuning a PID controller. A metaheuristic algorithm known as particle swarm optimisation (PSO) is used together with convex optimisation techniques, and the validity of the proposed algorithm is examined by comparing its performance with the performance of the classic PSO-PID and the well-known Ziegler–Nichols PID (ZN-PID). To obtain useful comparisons, a non-linear system, the air levitation system (AL), was utilised, controlled using a PID with three tuning strategies: the modified particle swarm technique (M-PSO-PID), the classic particle swarm (C-PSO-PID), and the Ziegler-Nichols method. The performance of the controllers was monitored through a cost function, the Integral Absolute Error (IAE). A disturbance was also imposed on the AL system to test the performance and the robustness of the algorithm under different conditions. The proposed algorithm is designed to determine and set the parameters for the M-PSO-PID controller utilising stabilising regions Kp, Ki, and Kd which form a convex problem. The PSO technique is then used to search for the optimal values inside the convex area. The simulation results for the control system show that the M-PSO-PID offered good closed-loop performance with advantages over other algorithms with regard to the system settling time and rise time. The results thus indicate the supremacy of the proposed algorithm.