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

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 PI _f, 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 PI _f 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.