(231c) Economic Model Predictive Control With Time-Varying Objective Function: Handling Dynamic Energy Pricing and Demand Changes in Process Systems

Ellis, M., University of California, Los Angeles
Lao, L., University of California, Los Angeles
Christofides, P. D., University of California, Los Angeles

The traditional paradigm to economic optimization of chemical processes is typically infrequent steady-state optimization to compute optimal operating steady-states. As operating strategies of chemical processes migrate from the traditional paradigm to the smart manufacturing paradigm, advanced control structures must be able to optimize economic performance of chemical processes in real-time to address dynamic changes in demand, feedstock prices, feedstock quality, and energy cost. Economic model predictive control (EMPC) is one such control scheme that combines real-time dynamic economic process optimization with the feedback properties of model predictive control (MPC) by replacing the quadratic cost function of the conventional MPC with a general economic cost function. Recently, many EMPC formulations that address different aspects arising in chemical process control as well as many applications of EMPC schemes to chemical process examples have been presented in the chemical process control literature [1]-[6]. However, these EMPC schemes do not account directly for explicitly time-varying economic cost functions. The core of this issue is the requirement for an EMPC scheme to determine, in real-time, the optimal time-varying operating strategy while maintaining closed-loop stability and accounting for time-varying economic information.

In the present work, we focus on the development of an EMPC scheme that can accommodate for an explicitly time-varying economic cost function. First, we present the formulation of the EMPC scheme, designed via Lyapunov techniques [1]. With this formulation, process economic optimization and process control are handled in a one-layer control structure. Second, closed-loop stability, in the sense of boundedness of the closed-loop state, is proven through a theoretical treatment of the EMPC scheme. No restrictions on the type of economic cost function are required for provable closed-loop stability under the proposed EMPC scheme. Lastly, we demonstrate through extensive closed-loop simulations of chemical processes that the proposed EMPC can achieve stability with time-varying economic cost arising due to variable energy pricing and product demand changes.


  1. Heidarinejad M, Liu J, Christofides PD. Economic model predictive control of nonlinear process systems using Lyapunov techniques. AIChE Journal. 2012;58:855-870.
  2. Rawlings JB, Angeli D, Bates CN. Fundamentals of economic model predictive control. In: Proceedings of the 2012 IEEE 51st Annual Conference on Decision and Control. Maui, Hawaii, 2012:3851-3861.
  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. Muller MA, Allgower F. Robustness of steady-state optimality in economic model predictive control. In: Proceedings of the 2012 IEEE 51st Annual Conference on Decision and Control (CDC). Maui, Hawaii, 2012:1011-1016.
  5. Idris EAN, Engell S. Economics-based NMPC strategies for the operation and control of a continuous catalytic distillation process. Journal of Process Control. 2012;22:1832-1843.
  6. Kadam JV, Marquardt W, Schlegel M, Backx T, Bosgra OH, Brouwer P-J, Dunnebier G, van Hessem D, Tiagounov A, and de Wolf S. Towards integrated dynamic real-time optimization and control industrial processes. In:Proceedings of Foundations of Computer-Aided Process Operations. Coral Springs, Florida, 2003:593-596.