2021 Annual Meeting

(346v) Sparse-Identification-Based Predictive Control of Nonlinear Multiple Time-Scale Processes

Chemical processes are often governed by nonlinear process dynamics with the process states evolving at disparate time-scales due to the physics of such processes. This phenomenon is seen in catalytic crackers [1], distillation columns, and large-scale process networks, amongst others [1,2]. Neglecting the time-scale-multiplicity in the design of controllers for such systems can lead to controller ill-conditioning, closed-loop performance deterioration and even instability due to the stiffness introduced in the process model by the fast dynamical phenomena [3]. Hence, traditionally, the mathematical framework of singular perturbation theory has been applied to such systems for modeling and designing well-conditioned controllers [4,5]. However, this requires knowledge of the complex first-principles models that characterize the nonlinear system. In contrast, recent advances in the intersection of engineering and data science have demonstrate the possibility of using machine learning methods for nonlinear dynamic modeling and, hence, designing controllers [6]. Machine learning is a modern technique of data analysis that has been successfully implemented in classical engineering problems for nonlinear regression and modeling when a comprehensive set of data encompassing all or most process outcomes is available. Currently, the incorporation of machine learning methods in advanced process control systems such as model predictive control for multiple-time-scale systems has not been studied.

This work proposes an approach to the design of model predictive controllers for nonlinear multiple-time-scale systems using only process measurement data. By first identifying and isolating the slow and fast variables in a multiple-time-scale system using process data only, the controller is designed based on the reduced slow subsystem consisting of only the slow variables. In this work, the reduced slow subsystem is constructed from only data using sparse identification, which identifies nonlinear dynamical systems as nonlinear first-order ordinary differential equation models using an efficient, convex algorithm that is highly optimized and scalable. Results from the mathematical framework of singularly perturbed systems are combined with appropriate stability assumptions to derive sufficient conditions for closed-loop stability of the full singularly perturbed closed-loop system. The applicability and effectiveness of the proposed controller design is illustrated via its application to a non-isothermal reactor with the concentration and temperature profiles evolving in different time-scales, where it is found that the controller based on the sparse identified slow subsystem can achieve superior closed-loop performance compared to available controller design approaches.

References:

[1] Chang, H.-C., Aluko, M., 1984. Multi-scale analysis of exotic dynamics in surface catalyzed reactions-I: justification and preliminary model discriminations. Chem. Eng. Sci. 39 (1), 37–50.

[2] Lévine, J., Rouchon, P., 1991. Quality control of binary distillation columns via nonlinear aggregated models. Automatica. 27 (3), 463–480.

[3] Kokotović, P., Khalil, H.K., O’Reilly, J., 1999. Singular Perturbation Methods in Control: Analysis and Design. Society for Industrial and Applied Mathematics.

[4] Christofides, P.D., Daoutidis, P., 1996. Feedback control of two-time-scale nonlinear systems. Int. J. Control. 63 (5), 965–994.

[5] Christofides, P.D., Teel, A.R., Daoutidis, P., 1996. Robust semi-global output tracking for nonlinear singularly perturbed systems. Int. J. Control. 65 (4), 639–666.

[6] Wu, Z., Tran, A., Rincon, D., Christofides, P.D., 2019. Machine-learning-based predictive control of nonlinear processes. Part II: Computational implementation. AIChE Journal. 65:e16734.