On Gain Stabilizing Regions of PID Controller for Time Delay Systems

A new method based on the inverse Nyquist curve is given to ascertain the stabilizing gain regions of time delay systems using PID controller. According to the characteristics of the inverse Nyquist curve of time delay systems and the generalized Hermite-Biehler theorem, the required frequency range for estimating the system stability can be acquired, and the abscissas of two kinds of key points can be obtained in this range. These key points divides the PID gain into several regions. Using an inference and two theorems derived in this paper, the stabilizing PID gain regions are acquired by the number of intersections of the inverse Nyquist curve and the vertical line in the required frequency range. This method can effectively solve the problem of getting the stabilizing gain regions in PID control for time delay systems using PID controller.