Modified root locus plots for SISO systems with time delay

The use of modified root locus plots in the assessment of the robustness of closed-loop systems with respect to phase lag is examined. It is suggested that the use of a pure time delay in series with the nominal open-loop transfer function provides a natural model of an important way in which modeling error arises. A modified root locus plot depicting the variation of closed-loop pole magnitudes and damping factors explicitly as a function of the time delay then provides a transparent means of assessing the effects of such modeling error.<>