(324h) Model Predictive Control-Assisted Online Data Collection

For decades, system identification methods (e.g., step response identification) have been used to develop linear and empirical, but not necessarily physical, models from data for advanced model-based control designs such as model predictive control (MPC) [1]. From an operational standpoint, the identification of such process models results in reasonably accurate state predictions for an MPC designed to force the process to track a steady-state. However, economic model predictive control (EMPC) [2, 3], which is an optimization-based control design that incorporates an economics-based objective function, may dictate a time-varying operating policy for superior economic performance compared to steady-state operation. The chemistry and physics of the process become more important to capture in process models when state predictions are needed away from the steady-state, and they may also be important to understand for properly formulating objective functions that reflect process profit or safety-critical constraints. Nevertheless, while first-principles models may capture this behavior, developing these models can be a time-consuming task that would be unattractive to industry. Methods for seeking to obtain physically-meaningful process dynamic models from process data have been suggested (e.g., [4, 5]). Building on the concept that the structure of first-principles models is postulated based on experimental data that has a certain form (e.g., when finding the temperature-dependence of a rate law, other variables that might impact the rate such as concentration should be kept constant), [6] suggested that the flexibility of EMPC could be exploited to use control to guide the process state through time-series data which has a desired form and can thereby provide online operating data that aids in proposing physically-relevant structures for empirical models. However, [6] did not provide techniques for guaranteeing that the operating conditions with a desired form could be reached when the process was operated under EMPC.

To address this gap, this work develops and compares EMPC formulations for guiding the process state through operating conditions that cause the on-line process data to have a form desired for postulating physics-based model structures, along with analysis of the conditions under which the desired operating conditions are guaranteed to be reached or reached within a given tolerance. Not only must these formulations enable the desired information to be collected, but they must also account for when that information should be obtained (to avoid forcing the process to operate in a data-gathering mode that is disconnected from the operating goal of profitability). EMPC formulations which enforce the data collection through hard constraints on the states reached within the prediction horizon will be explored, as will sets of EMPC formulations with Lyapunov-based stability constraints which can maintain closed-loop stability and recursive feasibility at each sampling time as the data-gathering progresses through an implementation strategy that trades off between the different formulations over time. The impacts on model identification of the sample-and-hold implementation of MPC (i.e., when it can only be guaranteed that the closed-loop state can closely approach a desired value rather than attain that value exactly) will be clarified. Various triggering mechanisms for preventing the data-gathering from significantly impacting economic optimization will be proposed, such as those which only collect desired information when the optimal solution to the optimization problem is close to the information which it is desired to obtain. The proposed schemes are demonstrated with a chemical process example and compared in terms of economic performance and speed with which a desired set of data is gathered under each triggering method.

References:

[1] J. M. Maciejowski. Predictive Control: With Constraints. Pearson Education, 2002.

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

[3] J. B. Rawlings, D. Angeli, and C. N. Bates. Fundamentals of economic model predictive control. In Proceedings of the IEEE Conference on Decision and Control, pp. 3851-3861, Maui, Hawaii, 2012.

[4] M. Schmidt and L. Hod. Distilling free-form natural laws from experimental data. Science, 324:81-85, 2009.

[5] S. L. Brunton, J. L. Proctor and J. N. Kutz. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. PNAS, 113:3932-3937, 2016.

[6] L. Giuliani and H. Durand. Data-based nonlinear model identification in economic model predictive control. Smart and Sustainable Manufacturing Systems 2, 2: 61-109, 2018.