New Results on PID Stabilization of Integral Process with Time Delay

摘要

This paper considers the problem of stabilizing an integral process with time delay by a PID controller. As the proportional gain reaches the extreme value, the closed-loop system contains a double pole on the non-negative imaginary axis. Using this property, the admissible range of the proportional gain is derived, also the corresponding integral gain and derivative gain are obtained. For a fixed value of the proportional gain, the stability region in the plane of the integral and derivative gains is determined analytically. Moreover, the admissible ranges of the integral and derivative gains are computed and found to be non-convex. A numerical example illustrates the method presented.