Guaranteed dominant pole placement with PID controllers

Pole placement is a well-established design method in linear control systems. Note however that with an output feedback controller of low-order such as PID 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 assigned two 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.