Further Results on Dominant Pole Placement via Stability Mapping Approach

Abstract

Dominant roots of the closed loop characteristic equation play a crucial role in terms of the performance of Linear Time Invariant (LTI) systems. Within the scope of this study, a dominant pole placement approach which has two main phases is proposed for PI/PID type controllers. In the first phase, characteristic equation is partitioned into its dominant and non-dominant polynomial pairs and dominant poles are placed to predetermined locations. In the second phase, it is required to determine how far the non-dominant poles can be placed. In the current study, this requirement is transformed into a stability problem and Lyapunov Equation-based stability mapping approach is used. This combined approach creates a more flexible design environment compared to the currently existing approaches in literature. In order to demonstrate this flexibility, two benchmark case studies are included with different definitions of dominant pole placement problem.