Multi-stage model predictive control for slug flow crystallizers using uncertainty-aware surrogate models

This paper presents a novel dynamic model for slug flow crystallizers that addresses the challenges of spatial distribution without backmixing or diffusion, potentially enabling advanced model-based control. The developed model can accurately describe the main characteristics of slug flow crystallizers, including slug-to-slug variability but leads to a high computational complexity due to the consideration of partial differential equations and population balance equations. For that reason, the model cannot be directly used for process optimization and control. To solve this challenge, we propose two different approaches, conformalized quantile regression and Bayesian last layer neural networks, to develop surrogate models with uncertainty quantification capabilities. These surrogates output a prediction of the system states together with an uncertainty of these predictions to account for process variability and model uncertainty. We use the uncertainty of the predictions to formulate a robust model predictive control approach, enabling robust real-time advanced control of a slug flow crystallizer.