Economic model predictive control (EMPC) has recently attracted substantial attention within the chemical process control and energy systems communities because of its unique ability to control nonlinear processes/systems while reconciling process economic optimization and process control (e.g., [1]-[4]; see, also, the recent review [5] for comprehensive reference list of recent papers on EMPC). Unlike tracking model predictive control which uses a quadratic stage cost, EMPC uses a general, user-defined stage cost that reflects the process economics. Owing to the generality of the stage cost, achieving recursive feasibility of the EMPC optimization problem, closed-loop stability, and certain guarantees on closed-loop economic performance properties do not generally follow by applying EMPC unless additional conditions are satisfied (e.g., additional constraints are imposed on the EMPC optimization problem and/or a sufficiently long prediction horizon be used).
A brief overview of EMPC methods is provided with a particular focus on the role of constraints imposed in the EMPC optimization problem to address recursive feasibility, closed-loop stability, and closed-loop performance. Three main types of constraints are considered including terminal equality constraints, terminal region constraints, and constraints designed via Lyapunov-based techniques. An explanation of the motivation behind each type of constraint is provided. Additionally, the conditions that must be satisfied to yield the three closed-loop properties (feasibility, stability, and performance) are presented and explained. A well-known chemical engineering example, a non-isothermal CSTR with a second-order reaction, is used to illustrate effectiveness and theoretical performance properties of time-varying operation to improve closed-loop economic performance compared to steady-state operation and to demonstrate the impact of economically motivated constraints on optimal operation.
[1] Angeli D, Amrit R, Rawlings JB. On average performance and stability of economic model predictive control. IEEE Transactions on Automatic Control. 2012;57:1615-1626.
[2] Amrit R, Rawlings JB, Angeli D. Economic optimization using model predictive control with a terminal cost. Annual Reviews in Control. 2011;35:178-186.
[3] Huang R, Harinath E, Biegler LT. Lyapunov stability of economically oriented NMPC for cyclic processes. Journal of Process Control. 2011;21:501-509.
[4] Heidarinejad M, Liu J, Christofides PD. Economic model predictive control of nonlinear process systems using Lyapunov techniques. AIChE Journal. 2012;58:855-870.
[5] Ellis M, Durand H, Christofides PD. A tutorial review of economic model predictive control methods. Journal of Process Control, 2014;24:1156--1178.
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