A synergistic approach to proportional‐integral controller design in linear time‐delay systems

Abstract This paper proposes a novel method for optimizing proportional–integral (PI) controllers to produce fast and energy‐efficient responses in linear time‐delay systems. The proposed methodology combines analytical‐geometric stability analysis with meta‐heuristic or numerical optimization techniques to systematically minimize a cost function based on quadratic regulator principles. This synergy effectively reduces the search space and ensures convergence to an optimal solution. The paper also compares the performance of the proposed synergistic method against a fully analytical tuning approach for PI controllers, focusing on achieving the highest rate of exponential decay in the system response. Results indicate that our method effectively mitigates the challenges associated with temporal delays in control systems while meeting multiple performance requirements. Furthermore, numerical simulations and experimental validations demonstrate significant improvements in closed‐loop performance, highlighting the practical advantages of the proposed approach.