Achievable Robustness for Time-Varying Delay Systems

This work proposes a closed-loop stability analysis of unstable open-loop systems represented by first-order and second-order plus time-delay (FOPTD and SOPTD) models. This analysis considers a proportional (P) controller and a predictor-based controller for FOPTD models, while a P and a phase-lead controller are considered for SOPTD models. In all cases, the achievable robustness has been computed considering time-varying delays. Several simulations were performed, and based on the integrated absolute error, it is shown that using a predictor is a better solution for large time-delay systems. Otherwise, the results are equivalent. In addition, the effect of the left half-plane pole of the SOPTD system is analysed. Finally, a comparison is made with recently published results that employ more complex and iterative algorithms.