Limitations on dominant pole pair selection with continuous PI and PID controllers

In the dominant pole placement approach, it is important non-dominant poles to be located far away from the dominant pole pair. Otherwise, predicting the closed-loop system transient response is difficult and satisfying the performance criteria becomes very challenging. It is known that PI and PID controllers are well-known and commonly used controllers in industrial applications. However, it is not possible to assign all of the closed-loop poles for higher order systems using such controllers because of the small number of controller parameters to be tuned. Therefore, the remaining poles may be located in the dominant region for a chosen dominant pole pair. In this study, it is aimed to find the limitations on dominant pole pair selection such that the unassigned poles can be located "m" times away from the design poles with PI and PID controllers. The success of the method is demonstrated on numerical examples.