Application of IHMPC to an unstable reactor system: study of feasibility and performance

Almost all the theoretical aspects of Model Predictive Control (MPC), such as stability, recursive feasibility and even the optimality are now well established for both, the nominal and the robust case. The stability and recursive feasibility are usually guaranteed by means of additional terminal constraints, while the optimality is achieved considering closed-loop predictions. However, these significant improvements are not always applicable to real processes. An interesting case is the control of open-loop unstable reactor systems. There, the traditional infinite horizon MPC (IHMPC), which constitutes the simplest strategy ensuring stability, needs to include an additional terminal constraint to cancel the unstable modes, producing in this way feasibility problems. The terminal constraint could be an equality or an inclusion constraint, depending on the local controller assumed for predictions. In both cases, however, a prohibitive length of the control horizon is necessary to produce a reasonable domain of attraction for real applications. In this work, we propose an IHMPC formulation that has maximal domain of attraction (i.e. the domain of attraction is determined by the system and the constraints, and not by the controller) and is suitable for real applications in the sense that it accounts for the case of output tracking, it is offset free if the output target is reachable, and minimizes the offset if some of the constraints become active at steady-state.