(382b) Two Feedback Control Schemes for the Size and Shape of Needle-like Crystals Growing in Suspension

The purification and the solidification of products by batch crystallization from solution is an essential unit operation in the chemical and pharmaceutical industries. The particle size and shape distribution (PSSD) is considered to be one of the central attributes of the solid products of such a batch crystallization process, because it affects not only downstream operations, but also product quality [1].

Since feedback control-based approaches have the potential to provide robustness with respect to process disturbances and to mitigate batch-to-batch variations, they are considered to be promising for operating batch processes. Furthermore, online monitoring tools for the size and shape evolution of crystals growing in suspension have evolved significantly in the past few years [see, e.g., Ref. 2 and references therein], enabling the development of tailored feedback control schemes for such processes.

In this contribution, we present two different feedback controllers for the evolution of the average length and width of needle-like crystals during seeded, growth-dominated batch cooling crystallization, where both strategies rely on the capability to measure PSSDs online [2]. The first scheme is a path following controller (PFC) that operates without a kinetic model for crystal growth. The second scheme is a more complex nonlinear model predictive controller (NMPC) that relies on a multidimensional crystal growth rate model.

Both controllers were designed, and their performance was tested, using a custom process simulation framework that features a morphological population balance model based on a polyhedral model for the needle-like particles and a detailed model of the characteristics of the online PSSD monitoring device presented in Ref. [2]. Therefore, this framework takes into account the discrepancy between the faceted shape of real crystals and the simpler generic particle shape models commonly applied for monitoring and modeling purposes.

In terms of reaching target average sizes and shapes chosen to lie within the attainable region of a given seed population, both controllers performed similarly. The feedback mechanism in the NMPC scheme was able to compensate for the model-plant mismatch. Additionally, the PFC was able to robustly achieve final average dimensions with respect to variations in the crystal growth rates. Since acquiring multidimensional growth models requires considerable efforts [see, e.g., Ref. 3], we conclude that PFC is a more adequate feedback control scheme for the considered process.

References

[1] Davey, R.; Garside, J., From Molecules to Crystallizers: An Introduction to Crystallization. Oxford University Press: New York, NY, 2000.

[2] Rajagopalan, A. K.; Schneeberger, J.; Salvatori, F.; Bötschi, S.; Ochsenbein, D. R.; Oswald, M. R.; Pollefeys, M.; Mazzotti, M., A comprehensive shape analysis pipeline for stereoscopic measurements of particulate populations in suspension. Powder Technol. 2017, 321, 479-493.

[3] Eisenschmidt, H.; Voigt, A.; Sundmacher, K., Face-Specific Growth and Dissolution Kinetics of Potassium Dihydrogen Phosphate Crystals from Batch Crystallization Experiments. Cryst. Growth Des. 2015, 15, 219-227.