Optimizing PI ^<i>λ</i> D ^<i>μ</i> controller parameters using tree seed optimization for enhanced control performance and stability

This research article exploits the tree seed optimization algorithm to optimize the parameters of the fractional-order proportional–integral–derivative (FOPID) controller. The study focuses on designing an FOPID controller by imposing constraints on both the performance metrics and closed-loop amplitude ratio to achieve enhanced control system performance. The tree seed algorithm is inspired by the growth and reproductive behavior of trees and demonstrates its efficacy in finding optimal solutions within constrained search spaces. The optimization process involves formulating an objective function subject to the constraints on performance metrics and closed-loop amplitude ratio, reflecting both tracking performance and stability. Besides, inverted decoupling is used to reduce the interaction between the control loops and enable individual tuning of each loop for improved performance. Besides, the smallest disc perturbation is employed to determine the system’s stability. The proposed approach is implemented in various industrial processes to demonstrate its effectiveness in achieving desirable performance. The tree seed algorithm efficiently navigates the parameter space, thereby converging to ideal FOPID controller configurations that meet the specified constraints. Comparative studies with other methods highlight the improved performance and robustness obtained by the tree seed–based FOPID controller.