Comparison of Stabilization with P/I-Delayed Controllers for Second-Order Systems Using Built-In MATLAB Heuristic Optimization Methods

In control theory, optimization is a process that makes some system behavior as likelihood, functional, or practical as possible (depending on the design requirements). From a mathematical point of view, optimization is a way to find the minimum or maximum of the mathematical function by which the system is described. 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 necessary to optimize the system transient response. This paper will compare selected heuristic methods of optimization of linear-time invariant (LTI) systems with time delay in an integral part of the P/I-delayed controller. Some examples are chosen as benchmarks to verify the effectiveness of the 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.