(575f) Machine Learning-Based Modeling and Predictive Control of Crystallization Processes Under Batch-to-Batch Parametric Drift

Batch crystallization is typically regarded as one of the crucial unit operations in pharmaceutical manufacturing as more than 90% of the active pharmaceutical ingredients are synthesized in the form of crystals [1]. The selection of the optimal operating and control strategies is of great interest to pharmaceutical manufacturers in achieving a more effective and eco-friendlier attainment of the crystalline product specification targets (e.g., crystal size distribution (CSD), purity, shape), which in turn dictate the performance of downstream operations, and are hence the pivotal enablers for enhanced productivity, smoother downstream processing, and superior drug bioavailability. While model predictive control (MPC) has emerged as the state-of-the-art optimal control strategy for chemical processes, several limitations (e.g., high computational costs for first-principles model-based MPC, low modeling accuracy and deteriorating control performance with respect to batch-to-batch (B2B) parametric drift [2, 3]) have to be addressed for its practical implementation.

Motivated by the above considerations, this work proposes a general framework for constructing computationally efficient machine learning models as substitutions for the mechanistic models in MPC and developing machine learning (ML)-based MPC schemes equipped with error-triggered online model update mechanisms for implementation to batch crystallization processes under the influence of B2B parameter drift. Specifically, we consider a seeded fesoterodine fumarate cooling crystallization and dissolution in a batch crystallizer ([6]) and present the methodology for designing a ML-based MPC controller to optimize product yield, crystal size, and energy consumption while accounting for the physical constraints on cooling jacket temperature. The ML model is constructed via the integration of recurrent neural network (RNN) with autoencoder (AE), where the RNN is developed to model the process dynamics and the AE is incorporated as a dimensionality reduction technique to further enhance the computational efficiency [4, 5]. Deviations in the crystallization kinetic parameters are considered in the closed-loop simulations to account for B2B parametric drift, and error-triggered online update mechanisms are incorporated into the MPC to improve its control performance by taking the availability of real-time system measurements into account. The results demonstrate that the proposed AERNN-MPC with online update, irrespective of the accessibility to real-time measurement data, achieves a desired closed-loop performance as compared with the MPC without online update.

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[2] Q. Su, M. Chiu, and R. Braatz. Integrated b2b-nmpc control strategy for batch/semibatch crystallization processes. AIChE Journal, 63(11):5007–5018, 2017.

[3] J. S. I. Kwon, M. Nayhouse, G. Orkoulas, D. Ni, and P. D. Christofides. A method for handling batch-to-batch parametric drift using moving horizon estimation: application to run-to-run MPC of batch crystallization. Chemical Engineering Science, 127, 210-219, 2015

[4] T. Zhao, Y. Zheng, J. Gong, and Z. Wu. Machine learning-based reduced-order modeling and predictive control of nonlinear processes. Chemical Engineering Research and Design, 179:435–451, 2022.

[5] Y. Zheng, X. Wang, and Z. Wu. Machine learning modeling and predictive control of batch crystallization process. Industrial & Engineering Chemistry Research, in press, 2022.

[6] M. Trampuž, D. Teslić, and B. Likozar. Crystallization of fesoterodine fumarate active pharmaceutical ingredient: Modelling of thermodynamic equilibrium, nucleation, growth, agglomeration and dissolution kinetics and temperature cycling. Chemical Engineering Science, 201:97–111, 2019.