(184z) Smart Constrained Model Predictive Control

Process control of chemical plants needs to address a number of objectives including safety, environmental regulations, product quality, energy efficiency, profitability, etc. In the control system design, these objectives are usually translated into three types of control objectives: setpoint tracking, constraint control or zone control and economic optimization. The different control objectives are either handled separately at different levels of a hierarchical framework or altogether in an integrated framework. An important yet challenging task in practice is to obtain desired closed-loop performance via controller parameter tuning, which can be overwhelmingly difficult due to lack of transparency in the tuning process.

Model predictive control (MPC) has been the ideal platform for integrated control system design due to its ability to handle constraints and incorporate economic considerations. The literature is rich with theories for conventional setpoint tracking MPC [1]. The past decade has seen an increasing academic interest in economic model predictive control (EMPC) [2] which integrates economic objectives into regulatory setpoint tracking control. On the contrary, zone control has received less attention. In the MPC framework, zone control is usually dealt with by the so-called soft constraint technique [3-5]. As its name suggests, soft constraint is often dismissed as a trick to avoid feasibility issue with hard constraint, and is addressed separately from the stability analysis of setpoint tracking MPC or economic MPC. To the best of our knowledge, only a few MPC frameworks explicitly handle zone tracking objectives [6-8] with guaranteed stability.

In this work, we propose a smart constrained MPC framework which addresses setpoint tracking, zone control and economic optimization in a unified framework. A zone tracking stage cost which penalizes weighted l1 norm and squared l2 norm distance to the target zone is incorporated into the existing EMPC framework to form a multi-objective optimization problem. We provide sufficient conditions for asymptotic stability of the optimal steady state and characterize exact penalty for the zone tracking cost which prioritizes the zone tracking objective over the economic objective. Moreover, we propose an algorithm to modify the target zone based on the economic performance and reachability of the optimal steady state in the target zone. The modified target zone is constructed as an invariant subset of the original target zone in which closed-loop transient economic performance is guaranteed. EMPC with modified target zone effectively decouples the zone tracking and economic objectives and enjoys a simplified and more transparent parameter tuning procedure. Finally, two numerical examples are investigated which reveal the intrinsic difficulties in parameter tuning for EMPC with zone tracking and demonstrate the efficacy of the proposed approach.

References

[1] Mayne, D.Q.; Rawlings, J.B.; Rao, C.V.; Scokaert, P.O.M. Constrained model predictive control: stability and optimality. Automatica 2000, 36, 789–814.

[2] Ellis, M.; Durand, H.; Christofides, P.D. A tutorial review of economic model predictive control methods. Journal of Process Control 2014.

[3] Scokaert, P.; Rawlings, J.B. Feasibility issues in linear model predictive control. AIChE Journal 1999, 45, 1649–1659.

[4] Kerrigan, E.C.; Maciejowski, J.M. Soft constraints and exact penalty functions in model predictive control. Proc. UKACC International Conference Control, 2000.

[5] De Oliveira, N.M.C.; Biegler, L.T. Constraint handing and stability properties of model-predictive control. AIChE journal 1994, 40, 1138–1155.

[6] Ferramosca, A.; Limon, D.; González, A.H.; Odloak, D.; Camacho, E. MPC for tracking zone regions. Journal of Process Control 2010, 20, 506–516.

[7] Lez, A.H.G.; Marchetti, J.L.; Odloak, D. Robust model predictive control with zone control. IET Control Theory & Applications 2009, 3, 121–135.

[8] González, A.H.; Odloak, D. A stable MPC with zone control. Journal of Process Control 2009, 19, 110–122.