Modified PI controller for the stabilization of high-order unstable delayed systems with complex conjugate poles and a minimum phase zero

Abstract

This work deals with the stabilization problem of a particular class of high-order unstable linear systems with time delay. In particular, systems with one unstable pole, q — 1 complex conjugate stable poles and one minimum phase zero. To solve this problem a modified version for the traditional PI controller, called in this work the Proporcional Integral Filtered PIf, is proposed. This new scheme includes a low-pass first order filter and allows improving the existing results on controlling high-order systems with time delay. Necessary and sufficient conditions for the existence of the PIf controller are expressed in terms of the parameters of the system and the maximum allowable time-delay magnitude. The proposed control scheme is illustrated by a numerical example applied to the temperature control of an unstable Continuously Stirred Tank Reactor (CSTR) linear model focused on the production of propylene glycol.