Guide for Stabilization and Heuristic Optimization of Second-order Systems Controlled by P/I-delayed Controllers

The present paper shows the procedure for the stabilization and subsequent optimization of second-order systems using a proportional plus integral delayed controller. Stabilizing closed-loop control systems using a controller comprehends several techniques to increase the control circuit's stability. Even in some simple second-order plants, the classical proportional integral controller cannot be applied to pursue closed-loop stability. However, the design requires constant reference tracking capability, for example. Moreover, if there is a time delay in the feedback loops inside a controlled system, the system has an infinite spectrum – infinitely many roots (poles); this degrades the control's quality, especially in terms of stability, robustness, and oscillation response. For these reasons, it is also necessary to optimize the transient response of the system. The main objective of this paper is to provide a guide for optimal control of second-order systems controlled by a proportional integral-delayed controller. Some examples are chosen as benchmarks to verify the effectiveness of the stabilization and subsequent heuristic optimization. In future research, we would like to focus on implementing selected modern optimization algorithms for solving non-smooth, non-convex, and non-Lipschitz optimization problems.