Exploring Delay-Based Controllers. A Comparative Study for Stabilizing Angular Positioning

This study aims to perform a comparison of different control schemes, which are characterized by their delay-based nature, where the time delay is considered as a parameter of the control law. To facilitate this research, we look at a second-order linear time-invariant (LTI) single-input single-output (SISO) system as our test bench. Moreover, we propose a simple but efficient methodology to compute the delay margin for these control schemes, which exploits the continuity of the characteristic roots with respect to the parameters of the characteristic function of the closed-loop system. Furthermore, we evaluate the performance and robustness of the closed-loop system by numerical simulations and physical experiments. By conducting this in-depth analysis, we gain valuable insight into the strengths and limitations of each control scheme, providing a clearer understanding of their real-world applicability.