Application of stability region centroids in robust PI stabilization of a class of second-order systems

Abstract

In this paper we offer a tuning method for the design of stabilizing PI controllers that utilizes the stability region centroid in the controller parameter space. To this end, analytical formulas are derived to describe the stability boundaries of a class of relative-degree-one linear time invariant second-order systems, the stability region of which has a closed convex shape. The so-called centroid stable point is then calculated analytically and the resultant set of algebraic formulas are utilized to tune the controller parameters. The freedom to choose the surface density function in the calculation of centroid stable point provides the designer with the possibility to incorporate optimal or robustness requirements in the controller design process. The proposed method uses the stability regions in the controller parameter space to ensure closed-loop stability, and, while offering robust stability properties, it does not rely on predetermined information with regard to the nature or range of parameter variations and coefficient uncertainty bounds. Being situated away from the boundaries of the stability region in the controller parameter space, controllers designed based on the centroid method are both robust and non-fragile.