PID Controller Autotuning Design by a Deterministic Q-SLP Algorithm

The proportional integral and derivative (PID) controller is extensively applied in many applications. However, three parameters must be properly adjusted to ensure effective performance of the control system: the proportional gain (
$K_{P}$
), integral gain (
$K_{I}$
) and derivative gain (
$K_{D}$
). Therefore, the aim of this paper is to optimize and improve the stability, convergence and performance in autotuning the PID parameter by using a deterministic Q-SLP algorithm. The proposed method is a combination of the swarm learning process (SLP) algorithm and Q-learning algorithm. The Q-learning algorithm is applied to optimize the weight updating of the SLP algorithm based on the new deterministic rule and closed-loop stabilization of the learning rate. To validate the global optimization of the deterministic rule, it is proven based on the Bellman equation, and the stability of the learning process is proven with respect to the Lyapunov stability theorem. Additionally, to demonstrate the superiority of the performance and convergence in autotuning the PID parameter, simulation results of the proposed method are compared with those based on the central position control (CPC) system using the traditional SLP algorithm, the whale optimization algorithm (WOA) and improved particle swarm optimization (IPSO). The comparison shows that the proposed method can provide results superior to those of the other algorithms with respect to both performance indices and convergence.