The pole placement problem via PI feedback controllers

Abstract

In this paper we study the pole placement problem using generalized PI controllers of a fixed lag k as compensators. We derive a new strong sufficiency condition which guarantees the arbitrary pole assignability of a given system having m inputs p outputs and McMillan degree n. This sufficiency condition misses the theoretical best possible necessary condition by one degree of freedom. The proof of the main result can be used to derive a numerical procedure. This numerical procedure is however very sensitive in the parameters and further research is required to investigate the conditions under which sensitivity occurs and whether the solution can be made more robust in this regard.