(106h) Data-Driven Predictive Control of Two-Timescale Dynamics: Application to a Battery System

Many chemical and biological processes operate in continuous cycles, wherein important process variables evolve in two distinct timescales [1-5]. In particular, the evolution of process variables can be characterized by slow dynamics at the end of every operating cycle (inter-cyclic) and fast dynamics within each operating cycle (intra-cyclic). Several modeling methods proposed in the literature describe only the inter-cyclic behavior considering the slow timescale [6]. However, it is necessary to understand the intra-cyclic behavior to better contemplate the overall process behavior. In this context, it becomes imperative to develop process models that represent both fast and slow dynamics under continuous cycling operation. Developing such models based on first principles is infeasible as it requires deeper understanding of process behavior at both timescales, which is especially difficult for complex processes. Hence, we develop a data-driven modeling framework that captures both intra-cyclic and inter-cyclic process dynamics in a unified manner.

In the developed method, we employ a sparse regression-based modeling technique to determine a sparse model as sparsity enhances the simplicity, interpretability, and generalizability of a process model. Specifically, we utilize sparse identification of nonlinear dynamics (SINDy) to model the two-timescale dynamics from input-output data of a process [7]. Firstly, we identify two different process models for intra-cyclic (intra-SINDy) and inter-cyclic (inter-SINDy) dynamics by using SINDy offline. Next, the identified intra-SINDy and inter-SINDy models are applied online to predict the evolution of process dynamics within each operating cycle and at the end of every operating cycle, respectively. In particular, the intra-SINDy model predicts the intra-cyclic dynamics based on the inter-SINDy model’s prediction in the long term. This integration of both the SINDy models improves the prediction accuracy of intra-SINDy. The main advantages of the developed method are three-fold: 1) simultaneously describing the two-timescale process dynamics; 2) predicting accurately by accounting for the interdependence among fast and slow dynamics; 3) providing an insight into the governing dynamics because of sparsity in the model structure. The implementation of the developed framework is demonstrated using a battery. Because of operating the battery under repeated charging and discharging cycles, its performance degrades with time due to various factors such as dendrite formation, mechanical stress, and electrolytic decomposition. By predicting the battery degradation, we enhance its durability through model predictive control of the battery operation. First, the developed method is deployed to predict the evolution of state of charge (SoC) and voltage within each operating cycle and forecast future capacity degradation at the end of every operating cycle. Next, we design a controller with the objective of maximizing the battery’s lifetime and minimizing its charging time. Prediction of SoC and voltage reflects charging time, and prediction of capacity degradation assists in estimating the battery’s lifetime. Based on these predictions, the controller provides an optimal charging profile to enhance the battery’s performance.

Literature cited:

1. Yan, L., Deneke, T.L., Heljanko, K., Harjunkoski, I., Edgar, T.F. and Baldea, M., 2021. Dynamic Process Intensification via Data-Driven Dynamic Optimization: Concept and Application to Ternary Distillation. Industrial & Engineering Chemistry Research, 60(28), pp.10265-10275.
2. De, R., 2018. A general model of focal adhesion orientation dynamics in response to static and cyclic stretch. Communications biology, 1(1), pp.1-7.
3. Severson, K.A., Attia, P.M., Jin, N., Perkins, N., Jiang, B., Yang, Z., Chen, M.H., Aykol, M., Herring, P.K., Fraggedakis, D. and Bazant, M.Z., 2019. Data-driven prediction of battery cycle life before capacity degradation. Nature Energy, 4(5), pp.383-391.
4. Iyer, S.S., Bajaj, I., Balasubramanian, P. and Hasan, M.F., 2017. Integrated carbon capture and conversion to produce syngas: novel process design, intensification, and optimization. Industrial & Engineering Chemistry Research, 56(30), pp.8622-8648.
5. Arora, A., Bajaj, I., Iyer, S.S. and Hasan, M.F., 2018. Optimal synthesis of periodic sorption enhanced reaction processes with application to hydrogen production. Computers & Chemical Engineering, 115, pp.89-111.
6. Kevrekidis, I.G. and Samaey, G., 2009. Equation-free multiscale computation: Algorithms and applications. Annual review of physical chemistry, 60, pp.321-344.
7. Brunton, S.L., Proctor, J.L. and Kutz, J.N., 2016. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the national academy of sciences, 113(15), pp.3932-3937.