(712g) Combining First-Principles and Empirical Modeling for Computation Time Reduction of Economic Model Predictive Control

Authors: 
Durand, H., University of California, Los Angeles
Christofides, P. D., University of California, Los Angeles
For large-scale nonlinear process systems, the computation time required to solve the optimization problem of an economic model predictive controller or EMPC [1] (a control design that computes control actions that optimize process economics), may be large due to the need to solve a nonlinear program with tens or hundreds of optimization variables. For processes requiring a sampling time shorter than the time to solve such a problem due to the time scale on which the process dynamics evolve, this significant computation time may prohibit the use of EMPC for a given process. One method of reducing the computation time of EMPC is by utilizing linear [2] or nonlinear [3] empirical models for making state predictions in the EMPC compared to using a first-principles model. These empirical models may have lower computation times than first-principles models because they may have less terms to evaluate during numerical integration of the model, they may be less stiff than the first-principles model, or, in the case of linear empirical models, they have an analytic solution that can be taken advantage of when computing state predictions within the EMPC. Prior works that have examined EMPC with empirical models [2,3,4] assume that the empirical model is used throughout the entire prediction horizon. However, due to the increased accuracy of a first-principles model, it may be more economically beneficial to utilize a first-principles model for making state predictions in EMPC, when such a model is available, rather than an empirical model.

Motivated by this, the present work investigates the trade-off between computation time and model accuracy for an EMPC design that utilizes a first-principles model for the first several sampling periods of the prediction horizon (including the first sampling period since the control actions computed for the first sampling period are implemented on the process according to the receding horizon implementation strategy of EMPC) and an empirical model for the remaining sampling periods (for computation time reduction). The number of sampling periods for which the first-principles model is used, the sampling period length, and the prediction horizon length are evaluated with respect to their impact on closed-loop economic performance and computation time. The use of the error-triggered on-line empirical model update strategy from [4] is investigated for updating the empirical model used within the EMPC with the combined first-principles/empirical model as the closed-loop state moves throughout state-space. Conditions that guarantee closed-loop stability and feasibility of the EMPC with the combined first-principles/empirical model are developed. In addition, the impact of changing the empirical model partway through a sampling period (i.e., allowing the EMPC to start using the empirical model after a non-integer multiple of a sampling period has passed) is investigated both from a closed-loop stability and feasibility standpoint and from a practical computation time and economic performance standpoint. A chemical process example compares the computation time and economic performance of a nonlinear process under the proposed combined first-principles/empirical EMPC design with the computation time and performance under both an EMPC utilizing only a first-principles model and an EMPC using only an empirical model.

[1] Ellis M, Durand H, Christofides PD. A tutorial review of economic model predictive control methods. Journal of Process Control. 2014;24:1156-1178.

[2] Alanqar A, Ellis M, Christofides PD. Economic model predictive control of nonlinear process systems using empirical models. AIChE Journal. 2015;61:816-830.

[3] Alanqar A, Durand H, Christofides PD. On identification of well-conditioned nonlinear systems: Application to economic model predictive control of nonlinear processes. AIChE Journal. 2015;61:3353-3373.

[4] Alanqar A, Durand H, Christofides PD. Error-triggered on-line model identification for model-based feedback control. AIChE Journal. 2016;63:949-966.