Design of the GPPI controller for stability and performance of unstable plant models with long dead times

In this paper we consider the control of plant models described by first order unstable linear systems with long dead times (UFOPD) in discrete time. Such types of models may arise when linearizing nonlinear systems at unstable operating points or due to fault conditions. We demonstrate that a Generalized Predictive Proportional Integral (GPPI) controller, designed with either a coprime factorization approach or a model predictive control (MPC) strategy, is well-equipped to handle arbitrarily long dead time unstable plant systems. We provide illustrative examples that showcase our main findings and offer deeper insights into the advantages of using the GPPI controller in these control scenarios, when compared with the widely used Proportional Integral (PI) controller, or the alternative Predictive Proportional Integral (PPI) controller available in the literature.