(187b) Enhancing Tractability of Model Predictive Control-Assisted Online Data Collection

A goal of next-generation manufacturing is to utilize control to enhance efficiency and improve profits [1]. To integrate economic optimization and process control, an optimization-based control design termed economic model predictive control (EMPC) has been studied [2, 3], which uses a stage cost that is not required to have its minimum at a process steady-state. This type of control design is of interest, for example, for potentially enabling next-generation manufacturing systems to account for the impacts of time-varying costs on profitability. More accurate process models may aid in the development of this model-based control design, which raises the question of whether it is possible to obtain physics-based models automatically from process data. Though techniques have been developed which seek to fit potentially more physics-based models to data using techniques such as symbolic [4] or sparse [5] regression, there is still a need for additional techniques which can postulate model structures based on the trends in process data, so that parameters can be subsequently fit to such models. One idea for achieving this is to utilize EMPC to guide the process state over time to take values which correspond to information that is meaningful for discriminating between various model structures that might be postulated [6]. However, control designs which have these capabilities also must be examined for tractability in design and computation time.

Motivated by the above, this work focuses on methods for enhancing the tractability of EMPC-assisted online data collection by exploring a variety of techniques which can increase practicality of the methods. For example, we explore a distributed control framework for driving the process state between operating conditions in state-space when multiple Lyapunov-based EMPC (LEMPC) [7] designs are available that can be selected between at a given sampling time, which guide the process state toward different desired data. We also explore methods for reducing the computation time required for mechanisms which trigger a decision to gather desired data rather than operate the process in a standard fashion and suggest techniques for developing stability region estimates for LEMPC on-line. A chemical process example is used to demonstrate the proposed methods in terms of closed-loop stability, feasibility, and computation time reduction.

References:

[1] J. Davis, T. Edgar, J. Porter, J. Bernaden and M. Sarli. Smart manufacturing, manufacturing intelligence and demand-dynamic performance. Computers & Chemical Engineering, 47:145-156, 2012.

[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] D. Angeli, R. Amrit and J. B. Rawlings. On average performance and stability of economic model predictive control. IEEE Transactions on Automatic Control, 57:1615-1626, 2012.

[4] M. Schmidt and H. Lipson. 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, 2:61-109, 2018.

[7] M. Heidarinejad, J. Liu and P. D. Christofides. Economic model predictive control of nonlinear process systems using Lyapunov techniques, AIChE Journal, 58:855-870, 2012.