Approximate Pole Placement with Dominance for Continuous Delay Systems by PID Controllers

It is well known that a continuous‐time feedback system with time delay has infinite spectrum and it is not possible to assign such infinite spectrum with a finite‐dimensional controller. In such a case, only the partial pole placement may be feasible and hopefully some of the assigned poles are dominant. But there is no easy way to guarantee dominance of the desired poles. In this paper, an analytical PID design method is proposed for continuous‐time delay systems to achieve approximate pole placement with dominance. Its idea is to bypass continuous infinite spectrum problem by converting a delay process to a rational discrete model and getting back continuous PID controller from its discrete form designed for the model with pole placement. Simulation results are included to illustrate the effectiveness of this method.