Stabilization of an arbitrary order transfer function with time delay using PI and PD controllers

This paper is concerned with developing a procedure for stabilizing a linear time-invariant plant of any order with time delay utilizing proportional-integral (PI) and proportional-derivative (PD) controllers. The method presented here is based on computing the stability boundary in terms of the proportional and integral gain for the PI case, and similarly, proportional and derivative gain for the PD case. The two variables are then plotted on the same coordinate system, thus obtaining the stability region for each controller used. The advantage of this procedure is the fact that it does not require the knowledge of the plant transfer function parameters, but only its frequency response. In addition, if the plant function is known, the procedure may also be used to analytically obtain the stabilizing controllers. We also present the tuning rules for user specified gain and phase margins