Data-Based Nonlinear Model Identification in Economic Model Predictive Control

Many chemical/petrochemical processes in industry are not completely modeled from a first-principles perspective because of the complexity of the underlying physico-chemical phenomena and the cost of obtaining more accurate, physically relevant models. System identification methods have been utilized successfully for developing empirical, though not necessarily physical, models for advanced model-based control designs such as model predictive control (MPC) for decades. However, a fairly recent development in MPC is economic model predictive control (EMPC), which is an MPC formulated with an economics-based objective function that may operate a process in a dynamic (i.e., off steady-state) fashion, in which case the details of the process model become important for obtaining sufficiently accurate state predictions away from the steady-state, and the physics and chemistry of the process become important for developing meaningful profit-based objective functions and safety-critical constraints. Therefore, methods must be developed for obtaining physically relevant models from data for EMPC design. While the literature regarding developing models from data has rapidly expanded in recent years, many new techniques require a model structure to be assumed a priori, to which the data is then fit. However, from the perspective of developing a physically meaningful model for a chemical process, it is often not obvious what structure to assume for the model, especially considering the often complex nonlinearities characteristic of chemical processes (e.g., in reaction rate laws). In this work, we suggest that the controller itself may facilitate the identification of physically relevant models online from process operating data by forcing the process state to nonroutine operating conditions for short periods of time to obtain data that can aid in selecting model structures believed to have physical significance for the process and, subsequently, identifying their parameters. Specifically, we develop EMPC designs for which the objective function and constraints can be changed for short periods of time to obtain data to aid in model structure selection. For one of the developed designs, we incorporate Lyapunov-based stability constraints that allow closed-loop stability and recursive feasibility to be proven even as the online "experiments" are performed. This new design is applied to a chemical process example to demonstrate its potential to facilitate physics-based model identification without loss of closed-loop stability. This work therefore reverses a question that has been of interest to the control community (i.e., how new techniques for developing models from data can be useful for control of chemical processes) to ask how control may be utilized to impact the use of these techniques for the identification of physically relevant process dynamic models that can aid in improving process operation and control for economic and safety purposes.