(769g) Economic Model Predictive Control Base on a Data-Driven Input-Output Model

In this work, an economic model predictive control (EMPC) based on the autoregressive moving average with exogenous inputs (ARMAX) model is proposed to optimize operations of processes. The primary innovation is that the dynamic lower and upper bounds on the process variables (PV) are identified based on the experimental data, to address the stability issue of the EMPC.

The task of EMPC applied in the process industry is similar with the real-time optimization (RTO), to minimize the energy consumptions or maximize certain products [1]. Its objective function does not contain the term of setpoint tracking and thus may incur the closed-loop stability issue. Moreover, conventional EMPC in literature requires a first-principle dynamic model, which may not be sufficiently accurate in practice [2]. The MPC in the industry usually relies on a linear input-output model [3], such as ARX or ARMAX, but also suffers from the model mismatch or disturbances. Given this fact, we use the low-order ARMAX models to characterize the lower and upper bounds on the PV, such that the true value of the process output is bounded within a tube. Different from the well-known tube-based MPC [1, 4], our method does not need to find a robust control invariant (RCI) set for the error term. Instead, two pseudo-states: lower and upper bounds with their dynamics are built, respectively. Then, the EMPC only needs to ensure that these two pseudo-states satisfy the constraints for the closed-loop stability.

To successfully guarantee the stability while maximizing the economic performance, we develop an algorithm to generate tight bounds on PV with long prediction horizon. Within a low-order model structure, the relation between dynamic response and ARMAX parameters can be explicitly derived. Then, we can enforce the resulting model prediction error between output data and dynamic response to be always positive, and a prediction error minimization (PEM) framework can be employed to obtain model parameters. The feature of the proposed method is that the number of resulting bilinear terms in PEM is only proportional to the number of model parameters and prediction horizon, not the experimental data. Therefore, the computational demand for modeling work can be reduced substantially. The proposed EMPC and modeling work are evaluated by a fermenter and a reaction-storage-separation network to show its effectiveness.

Reference

[1] F. A. Bayer, M. A. Müller, and F. Allgöwer, Tube-based robust economic model predictive control, Journal of Process Control, 24, 2014, 1237-1246.

[2] M. Ellis, H. Durand, and P. D. Christofides, A tutorial review of economic model predictive control methods, Journal of Process Control, 24, 2014, 1156-1178.

[3] J. Zhao, Y. C. Zhu, and R. Patwardhan, Identification of k-step-ahead prediction error model and MPC control, Journal of Process Control, 24, 2014, 48-56.

[4] S. V. Rakovic, B. Kouvaritakis, M. Cannon, C. Panos, and R. Findeisen, Parameterized tube model predictive control, IEEE Transactions on Automatic Control, 57, 2746-2761, 2012.