(610b) Development of Koopman-Based Model Predictive Control with Multimodel Approach to Handle Local Dynamics of Chemical Processes in Presence of Feed Fluctuation | AIChE

(610b) Development of Koopman-Based Model Predictive Control with Multimodel Approach to Handle Local Dynamics of Chemical Processes in Presence of Feed Fluctuation


Son, S. H. - Presenter, Texas A&M University
Choi, H. K., Texas A&M University
Moon, J., Inha University
Kwon, J., Texas A&M University
Koopman operator is an infinite-dimensional linear operator proposed by Koopman and Neumann to describe the nonlinear system dynamics using an alternative operator theoretic perspective [1,2]. Herein, the original dynamics is lifted to a higher-dimensional observable (function of original state) space where an infinite-dimensional linear operator (i.e., Koopman operator) governs the evolution of observable functions. However, due to its infinite-dimensional characteristic, the direct implementation of the Koopman operator to practical systems has been avoided. Hence, data-driven algorithms have been suggested as alternatives to derive a finite-dimensional approximation of the Koopman operator [3,4].

Recently, owing to the possibility of exploiting the established linear control methods, the Koopman-based model identification methods have gained extensive attention in the realm of model-based control. Hence, the Koopman-based model predictive control (KMPC) schemes have been developed [5,6] and successfully implemented in the chemical process control systems [7,8]. Although the Koopman-based model generates a reliable global linear predictor of a nonlinear system, it is challenging to accurately capture the local dynamics of the process, which has highly complex nonlinear dynamics with a broad operation range by only a single Koopman-based model [9].

Hence, in this study, a KMPC framework with the multimodel approach was developed to manage the local dynamics of the complex chemical processes. First, time-series data collected from the process operation is partitioned into several clusters. Subsequently, a local linear predictor for each cluster is derived by the Koopman-based model identification method. A local Koopman-based model predictive controller is then designed for each cluster based on the previously derived (Koopman-based) local models. Thereafter, the constructed local controllers are implemented in the closed-loop operation with a model switching framework that selects and employs one local controller associated with the cluster exhibiting the process dynamic behavior most similar to the current process state. To validate the efficacy of the KMPC with a multimodel approach, a batch digester where the pulp products are produced from wood chips via delignification reaction was adopted as a case study to control the multiscale variables such as Kappa number and cell wall thickness (CWT) of fibers inside the wood chips. In the closed-loop operation, a high-fidelity multiscale model developed in [10,11] was utilized as a virtual batch pulping process in the presence of feed fluctuation. During the operation, the designed KMPC system with a multimodel approach accurately predicted the local behavior of the pulping process and successfully allowed the controlled variables to reach the set-point value, whereas the KMPC system with a single Koopman-based model could not accurately achieve the desired values.


[1] Koopman, B. O. (1931). Hamiltonian systems and transformation in Hilbert space. Proceedings of the national academy of sciences of the united states of America, 17(5), 315.

[2] Koopman, B. O., & Neumann, J. V. (1932). Dynamical systems of continuous spectra. Proceedings of the National Academy of Sciences of the United States of America, 18(3), 255.

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

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

[7] Narasingam, A., & Kwon, J. S. I. (2020). 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.

[8] Sootla, A., Mauroy, A., & Ernst, D. (2018). Optimal control formulation of pulse-based control using Koopman operator. Automatica, 91, 217-224.

[9] Bangi, M. S. F., Narasingam, A., Siddhamshetty, P., & Kwon, J. S. I. (2019). Enlarging the domain of attraction of the local dynamic mode decomposition with control technique: Application to hydraulic fracturing. Industrial & Engineering Chemistry Research, 58(14), 5588-5601.

[10] Choi, H. K., & Kwon, J. S. I. (2019). Modeling and control of cell wall thickness in batch delignification. Computers & Chemical Engineering, 128, 512-523.

[11] Choi, H. K., & Kwon, J. S. I. (2020). Multiscale modeling and multiobjective control of wood fiber morphology in batch pulp digester. AIChE Journal, 66(7), e16972.