(681c) Towards on-Line Development of Physically-Based Models for Model-Based Control Design

Many industrial model predictive controllers utilize linear empirical process models for making state predictions [1]. These have provided adequate state predictions around process steady-states; however, next-generation control designs like economic model predictive control (EMPC) [2] may not enforce steady-state operation, and therefore utilizing linear empirical models which may not be applicable in large regions of state-space may restrict the power of EMPC for optimizing profits. Furthermore, it may not be obvious how to design an EMPC without a more physically-meaningful process model, as a general economics-based objective function is required to be available and also important constraints (e.g., those related to safety when the process state is allowed to access broad regions of state-space) may be based on the process physics. Techniques for getting models from data (e.g., [3]) generally require some up-front guess of the types of terms which will appear in the model so that their coefficients can be selected and identified. Therefore, a critical step toward obtaining physically-based models for enabling practical development of next-generation model-based controllers is developing techniques for selecting the form of equations which describe the process physics so that the parameters can be fit in such equations utilizing available techniques.

Inspired by traditional experimentation techniques, which develop methods for obtaining very targeted data in an experimental setting, we seek to exploit the flexibility of the structure of EMPC and the closed-loop stability properties of EMPC designs with certain stability constraints (e.g., Lyapunov-based stability constraints [4]) to develop controllers with hard and soft constraints related to data which it is desired to gather from an on-line process for short periods of time. We explore formulations in which the controller objective function is augmented with terms that can be used in some sampling periods and not in others and which penalize the deviations of the closed-loop state from desired values to seek to obtain data with those desired values for short periods of time. We also explore formulations that enforce the data-gathering functionality through hard constraints on the state with and without feasibility guarantees and discuss some of the benefits and difficulties associated with utilizing such data-gathering EMPC’s in a distributed architecture. An implementation strategy is developed that allows an initial EMPC design with a quadratic objective function and linear empirical model to be used before a more physics-based process model is developed from the data obtained during operation under this initial EMPC augmented with the data-gathering functionality. A benchmark continuous stirred tank reactor chemical process example demonstrates the developments.

[1] J. Qin and T. Badgwell, “A survey of industrial model predictive control technology,” Control Engineering Practice, 11, 733-764, 2003.

[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] S. L. Brunton, J. L. Proctor and J. N. Kutz, “Discovering governing equations from data by sparse identification of nonlinear dynamical systems,” Proceedings of the National Academy of Sciences, 113, 3932-3937, 2016.

[4] 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.