(295g) Self-Stabilizing Economic Nonlinear Model Predictive Control

Economic Nonlinear Model Predictive Control (eNMPC) has been recognized as a viable alternative to advanced distributed control systems because it provides the most economical transient operations. However, the closed-loop controlled process may exhibit periodic behavior when eNMPC is implemented in a stable process[1]. This behavior is caused by the existence of a more cost-effective transient path around the steady-state optimal solution, and eNMPC prioritizes the solution path with a lower operating cost. While operating a process unsteadily may have its economic advantages, it may also have undesirable consequences, including higher equipment degradation rates, increased operational risks, and higher downstream operating costs. In this work, a novel eNMPC formulation is proposed, in which a pre-calculated steady-state condition is not required to effectively bring the system toward a feasible steady-state optimal operation.

In eNMPC literature, a Lyapunov function is typically used as the stabilizing constraint to guarantee asymptotic stability, and the available formulations of the Lyapunov constraints require a pre-calculated steady state by an upper layer of a distributed control system[2,3]. As the upper control layers are typically solved less frequently than the eNMPC at a regulatory level, the provided optimal steady state may become suboptimal when process disturbances alter the process operating conditions. Motivated by this challenge, a self-stabilizing eNMPC approach that is independent of an external steady-state optimization is proposed. In this approach, the Lyapunov functions are reformulated to achieve closed-loop asymptotic stability using a norm of the KKT conditions of the respective steady-state economic optimization as the stage cost and the terminal constraint.

The proposed eNMPC is demonstrated with a case study of an intensified process, which can be more challenging to operate because of the potential loss in the control degrees of freedom due to process integration and optimization[4,5]. Closed-loop simulation results will be shown to illustrate the eNMPC effectiveness and the stability properties. Also, implementation guidelines will be discussed to address high-dimensional dynamic processes of industrial interest.

[1] D. Angeli, R. Amrit, J.B. Rawlings, On Average Performance and Stability of Economic Model Predictive Control, IEEE Trans. Automat. Contr. 57 (2012) 1615–1626. https://doi.org/10.1109/TAC.2011.2179349.

[2] J.B. Rawlings, D. Angeli, C.N. Bates, Fundamentals of economic model predictive control, in: 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), IEEE, Maui, HI, USA, 2012: pp. 3851–3861. https://doi.org/10.1109/CDC.2012.6425822.

[3] D.W. Griffith, V.M. Zavala, L.T. Biegler, Robustly Stable Economic NMPC for Non-Dissipative Stage Costs, Journal of Process Control. 57 (2017) 116–126.

[4] B.A. Bishop, F.V. Lima, Novel Module-Based Membrane Reactor Design Approach for Improved Operability Performance, Membranes. 11 (2021) 157. https://doi.org/10.3390/membranes11020157.

[5] S. Dinh, F.V. Lima, Dynamic Operability Analysis for Process Design and Control of Modular Natural Gas Utilization Systems, Ind. Eng. Chem. Res. 62 (2023) 2052–2066. https://doi.org/10.1021/acs.iecr.2c03543.