Domain of pole placement with optimal modal control: analysis of a system represented by an uncertain model

The specific aim of this paper is to help the design of industrial process controls. Indeed, if an optimal control is chosen, a robust control is obtained. But on the other hand, the placement of the poles is not possible and thus, dynamics is not controlled. This is why in this paper an Optimal Modal Control, i.e. an Optimal Control (LQ criterion) with pole placement, is presented. The method is proposed to place the poles two by two and to obtain a positive-semidefinite resulting state-weighting matrix Q. So this method preserves the robustness of the Optimal Control and it enables to determine a domain of pole placement ("D-domain").A stability robustness analysis of this type of placement is carried out upon a system represented by an uncertain model. A 2-dimensional system is studied and a numerical example is developed. The matrix Q is obtained in a diagonal form, which is useful for the designer.