Guaranteed dominant pole placement with PID controllers

Pole placement is a well-established design method for linear control systems. Note however that with an output feedback controller of low-order such as the PID controller one cannot achieve arbitrary pole placement for a high-order or delay system, and then partially or hopefully, dominant pole placement becomes the only choice. To the best of the authors' knowledge, no method is available in the literature to guarantee dominance of the assigned poles in the above case. This paper proposes two simple and easy methods which can guarantee the dominance of the two assigned poles for PID control systems. They are based on root locus and Nyquist plot respectively. If a solution exists, the parametrization of all the solutions is explicitly given. Examples are provided for illustration.