(106f) Deep Learning Aided Koopman Predictive Control for Post-Combustion CO2 Capture Process

Man-made carbon dioxide emissions have led to climate change and global warming. CO₂ reduction strategies, including carbon capture and storage (CCS) [1], are needed to curb this trend. There are three main methods for CCS: pre-combustion capture, post-combustion capture, and oxyfuel process. Among the three means, post-combustion CO₂ capture (PCCC) is considered to be the most mature solution. In addition, PCCC does not require significant modifications to the existing combustion technologies and facilities. Therefore, PCCC is expected to play an increasingly important role in achieving environmental sustainability. To ensure the operating safety and efficiency, and to reduce the operating cost, it is critical to develop and implement advanced control schemes to appropriately regulate the process operation. Model predictive control (MPC) is considered to be a promising solution, and some representative methods based on first-principles models have been proposed [2-5]. Meanwhile, a PCCC process is typically complex and highly nonlinear, which can lead to difficulties in designing and implementing optimization-based control strategies. In addition, building an accurate first-principle model for the process is a time-consuming and challenging task. Therefore, it is favorable to propose an alternative solution that can bypass first-principles modeling and the utilization of nonlinear MPC. Based on the above observations, we aim to propose a data-driven modeling and linear MPC framework for PCCC processes.

Koopman theory can be used to find a linear representation of nonlinear systems to predict the future evolution of the system state, based on which linear control theories can be applied [6,7,8]. For example, Koopman-based identification has been adopted for developing MPC schemes for hydraulic fraction operation [8] and chemical processes [9]. Extended dynamic mode decomposition has been a commonly used technique to identify a Koopman linear model [10]. The main idea is to lift the original state space into a higher dimensional linear state space through a nonlinear mapping. However, manual selection of this nonlinear mapping is challenging and may lead to unsatisfactory results. To address such limitations, machine learning has been conducted to describe this nonlinear mapping instead of leaving this task to users [11,12].

In this work, we address data-driven dynamic modeling and linear MPC design for PCCC processes within an integrated framework by leveraging Koopman theory and deep learning. Specifically, we propose a two-level deep learning-based hierarchical structure to account for the nonlinear mapping associated with Koopman identification, where each level of the hierarchical structure is established as a long short-term memory neural network (LSTM) [13]. As is different from the existing learning-based Koopman identification methods (e.g., [12]), our method concatenates the original state variables and comparatively low-dimensional neural networks feature to account for the nonlinear mapping. The Koopman operator and the parameters of the two LSTMs are estimated simultaneously in the offline training phase. Then, a linear predictive control scheme is developed based on the data-driven linear model to regulate the operation of the PCCC process in the presence of constraints. Extensive simulations are conducted to verify the effectiveness of the proposed modeling and control method. The superiority of the proposed two-level hierarchical-LSTMs-based Koopman identification is also demonstrated.

References

[1] E. Rubin, H. De Coninck. IPCC special report on carbon dioxide capture and storage. UK: Cambridge University Press. TNO (2004): Cost Curves for CO2 Storage, Part, 2, 14, 2005

[2] G. D. Patrón L. Ricardez-Sandoval. An integrated real-time optimization, control, and estimation scheme for post-combustion CO₂ capture. Applied Energy, 308:118302, 2022.

[3] Z.He, M. H. Sahraei, L. A. Ricardez-Sandoval. Flexible operation and simultaneous

scheduling and control of a CO₂ capture plant using model predictive control. International

Journal of Greenhouse Gas Control, 48:300-311, 2016.

[4] T. Bankole, D. Jones, D. Bhattacharyya, R. Turton, and S. E. Zitney. Optimal scheduling and its Lyapunov stability for advanced load-following energy plants with CO₂ capture. Computers & Chemical Engineering, 109:30-47, 2018

[5] B. Decardi-Nelson, S. Liu, and J. Liu. Improving flexibility and energy efficiency of post-combustion CO₂ capture plants using economic model predictive control. Processes, 6:135, 2018.

[6] B. O. Koopman. Hamiltonian systems and transformation in Hilbert space. Proceedings of the National Academy of Sciences of the United States of America, 17(5):315, 1931.

[7] J. N. Kaiser, E. Kutz, S. L. Brunton. Data-driven discovery of Koopman eigenfunctions for control. Machine Learning: Science and Technology, 2021.

[8] A. Narasingam, J. S.-I. Kwon. Application of Koopman operator for model-based control of fracture propagation and proppant transport in hydraulic fracturing operation. Journal of Process Control, 91:25-36, 2020.

[9] A. Narasingam, J. S.-I. Kwon. Koopman Lyapunov‐based model predictive control of nonlinear chemical process systems. AIChE Journal, 65(11):e16743, 2019.

[10] M. O. Williams, I. G. Kevrekidis, C. W. Rowley. A data-driven approximation of the Koopman operator: Extending dynamic mode decomposition. Journal of Nonlinear Science, 25(6):1307-1346, 2015.

[11] B. Lusch, J. N. Kutz, S. L. Brunton. Deep learning for universal linear embeddings of nonlinear dynamics. Nature communications, 9(1):1-10, 2018.

[12] E. Yeung, S. Kundu, N. Hodas. Learning deep neural network representations for Koopman operators of nonlinear dynamical systems. American Control Conference, 4832-4839, 2019.

[13] A. Graves. Long short-term memory. Supervised sequence labelling with recurrent neural networks, 37-45, 2012.