A study on the robustness of time delay control systems

In this paper, a recently proposed measure of the robustness margin of SISO control systems with plant parametric uncertainty is applied to a control loop composed of a PI controller and a FOPTD plant. A comparison with the widely used frequency gain and phase margins shows that the robustness margin index (RMI) has the advantage of explicitly considering the magnitude of errors in the plant parameters. When applied to control systems with plants having a dependent uncertainty structure, the RMI leads to conservative results. Such conservatism is strongly influenced by the degree of dependency between the coefficients of the plant model.