Stability Analysis of Time-Delayed Linear and Interval Systems: Application to DC Servo System

In frequency domain analysis, gain margin, and phase margin plays a vital role in the relative stability analysis of the system. It is observed that for some classes of systems, gain margin and phase margin can be the same for two different types of systems, but the closed-loop poles of the system can be different. Because of this, in this paper, it is shown that for a simplified model of position control of the DC servo motor, even though there is a change in the parameters of the model, there will be no change in the gain margin and phase margin of the system. Therefore, it is shown that an additional performance measure, i.e., delay margin, is an essential criterion for the stability analysis of the system. Further, it is shown that the practical approach belongs to the interval type; therefore, a method is presented to determine the delay margin of an interval system using Kharitonov's theorem.