Vol. 25, No. 3 (2026), Sim26874 https://doi.org/10.24275/rmiq/Sim26874

Experimental implementation of MPC strategy by manipulating the stirring speed to control secondary nucleation in continuous crystallization

 

Authors

M. Presenda-de Dios, A. Reyes-Obando, L. A. Ricardez-Sandoval, P. A. Quintana-Hernández

Abstract

This paper presents the experimental implementation of a multivariable model predictive control (MPC) for the continuous crystallization of ammonium sulfate in a Mixed-Suspension, Mixed-Product-Removal (MSMPR) crystallizer. The strategy employs a dynamic model based on balances of mass, energy and population and coordinates stirring speed and coolant flow as manipulated variables for the simultaneous control of average crystal diameter D(4,3) and the crystallizer temperature. This multivariable control strategy is innovative because incorporates hydrodynamics effects on mechanically induced secondary nucleation. The experiments were conducted in a pilot plant equipped with Process Analytical Technology (PAT) for online monitoring of Crystal Size Distribution (CSD), temperature and solution concentration. The results demonstrated that the MPC was able to maintain operation within the metastable zone, reduced process oscillations, and improved setpoint tracking. Furthermore, the implementation of digital filtering and the adjustment of predictive horizons reduced the error associated with the CSD and stabilized control actions, validating the feasibility of the active use of agitation in the control of continuous crystallization systems.

Keywords

multivariable control, crystallization, ammonium sulfate, secondary nucleation, metastable zone operation.

References
  • Bal, V., & Peters, B. (2020). Crystallization with sinusoidal modulation of stirrer speed: Frequency response analysis and secondary nucleation kinetics. Crystal Growth & Design, 21(1), 235–242. https://doi.org/10.1021/acs.cgd.0c01048
  • Cao, Y., Acevedo, D., Nagy, Z. K., & Laird, C. D. (2017). Real-time feasible multi-objective optimization based nonlinear model predictive control of particle size and shape in a batch crystallization process. Control Engineering Practice, 69, 1–8. https://doi.org/10.1016/j.conengprac.2017.08.008
  • Diab, S., & Gerogiorgis, D. (2017). Technoeconomic evaluation of multiple MSMPR crystalliser configurations for continuous cyclosporine crystallisation. Organic Process Research and Development, 21(10), 1571. https://doi.org/10.1021/acs.oprd.7b00225
  • Enríquez-Torres, L. (2005). Análisis y control del proceso de cristalización de sulfato de amonio [Master's thesis, Instituto Tecnológico de Celaya].
  • Fisher, A. C., Lee, S. L., Harris, D. P., & Buhse, L. F. (2022). An audit of pharmaceutical continuous manufacturing regulatory submissions and outcomes in the US. International Journal of Pharmaceutics, 622, Article 121778. https://doi.org/10.1016/j.ijpharm.2022.121778
  • Gao, Y., Hou, B., Hu, L., Wang, Y., Jiang, Y., & Wang, J. (2021). Application of PAT-based feedback control approaches in pharmaceutical crystallization. Crystals, 11(3), Article 221. https://doi.org/10.3390/cryst11030221
  • Larson, M. A., & Mullin, J. W. (1973). Crystallization kinetics of ammonium sulphate. Journal of Crystal Growth, 20(3), 183–191. https://doi.org/10.1016/0022-0248(73)90002-X
  • Lee, S. L., O’Connor, T. F., Yang, X., Cruz, C. N., Chatterjee, S., Madurawe, R. D., Moore, C. M. V., Yu, L. X., & Woodcock, J. (2015). Modernizing pharmaceutical manufacturing: From batch to continuous production. Journal of Pharmaceutical Innovation, 10(3), 191–199. https://doi.org/10.1007/s12247-015-9215-8
  • Leeming, R., Mahmud, T., Roberts, K. J., George, N., Webb, J., Simone, E., & Brown, C. J. (2023). Development of a digital twin for the prediction and control of supersaturation during batch cooling crystallization. Industrial & Engineering Chemistry Research, 62(28), 11067-11081. https://doi.org/10.1021/acs.iecr.3c00371
  • Li, Y., Zhang, Y., & Wang, X. Z. (2020). Secondary nucleation kinetics of AIBN crystallisation in methanol: Online imaging-based measurement and modelling. Crystals, 10(6), Article 506. https://doi.org/10.3390/cryst10060506
  • Lima, F. A. R. D., de Moraes, M. G. F., Secchi, A. R., & de Souza, M. B. (2022). Development of a recurrent neural networks-based NMPC for controlling the concentration of a crystallization process. Digital Chemical Engineering, 5, 100052. https://doi.org/10.1016/j.dche.2022.100052
  • Lima, F. A. R. D., de Moraes, M. G. F., Secchi, A. R., de Souza, M. B., & Grover, M. A. (2025). Experimental nonlinear model predictive control of crystal size and yield in batch cooling crystallization enabled by soft sensor and symbolic-based calibration model. Industrial & Engineering Chemistry Research, 64(1), 100–112. https://doi.org/10.1021/acs.iecr.5c03894
  • Lugo-Martínez, J. R. (2005). Estudio para la determinación de la zona de saturación metaestable a través del análisis del proceso de nucleación de sulfato de amonio [Master's thesis, Instituto Tecnológico de Celaya].
  • Medina-Galván, X. M., Quintana-Hernández, P. A., Reyes-Valadez, J. N., & Fuentes-Cortés, L. F. (2020). Determination of kinetic parameters of nucleation and growth of acetylsalicylic acid crystals in ethanol. Revista Mexicana de Ingeniería Química, 19(1), 445–456. https://doi.org/10.24275/rmiq/Cat1574
  • Moldoványi, N., Lakatos, B. G., & Blickle, T. (2005). Model predictive control of MSMPR crystallizers. Journal of Crystal Growth, 275(1–2), e1349–e1354. https://doi.org/10.1016/j.jcrysgro.2004.11.170
  • Mullin, J. W. (2001). Crystallization (4th ed.). Butterworth-Heinemann.
  • Peng, J., Yang, Z., & Lian, P. (2024). Process optimization and crystallization kinetics of ammonium sulfate from wet ammonia-based desulfurization. Environmental Progress & Sustainable Energy, 43(1), Article e14310. https://doi.org/10.1002/ep.14310
  • Perry, R. H., & Green, D. W. (Eds.). (1997). Perry’s chemical engineers’ handbook (7th ed.). McGraw-Hill.
  • Qin, S. J., & Badgwell, T. A. (2003). A survey of industrial model predictive control technology. Control Engineering Practice, 11(7), 733–764. https://doi.org/10.1016/S0967-0661(02)00186-7
  • Quintana-Hernández, P. A., Aguilar-Madera, C. G., & Salcedo-Estrada, L. I. (2017). Development of a fuzzy control system for a non-isothermal continuous crystallizer. Revista Mexicana de Ingeniería Química, 16(2), 663–678.
  • Reyes-Obando, A. (2012). Control de cristalizadores continuos por enfriamiento usando control predictivo basado en modelos [Master's thesis, Instituto Tecnológico de Celaya].
  • Stoffan, G. N., Lorincz, Z., Pusztai, É., Madarász, L., Tacsi, K., Marosi, G., & Pataki, H. (2024). Development of Continuous Additive-Controlled MSMPR Crystallization by DoE-Based Batch Experiments. Industrial & Engineering Chemistry Research, 63(31), 13709-13722. https://doi.org/10.1021/acs.iecr.4c01933
  • Sun, F., Liu, T., Song, B., Cui, Y., Nagy, Z. K., & Findeisen, R. (2024). Multi-objective optimization based nonlinear model predictive control of seeded cooling crystallization with application to β form L-glutamic acid. Chemical Engineering Science, 299, Article 120475. https://doi.org/10.1016/j.ces.2024.120475
  • Tadayon, A., Rohani, S., & Bennett, M. K. (2002). Estimation of nucleation and growth kinetics of ammonium sulfate from transients of a cooling batch seeded crystallizer. Industrial & Engineering Chemistry Research, 41(24), 6181–6193. https://doi.org/10.1021/ie020163r
  • Tututi-Avila, S. (2010). Control del proceso de cristalización continuo no-isotérmico empleando lógica difusa [Doctoral dissertation, Instituto Tecnológico de Celaya].
  • Wang, L., Zhu, Y., & Gan, C. (2023). Nonlinear model predictive control of crystal size in batch cooling crystallization processes. Journal of Process Control, 126, Article 103020. https://doi.org/10.1016/j.jprocont.2023.103020
  • Wu, H., Dong, Z., Li, H., & Khan, M. (2015). An integrated process analytical technology (PAT) approach for pharmaceutical crystallization process understanding. Organic Process Research & Development, 19(1), 89–101. https://doi.org/10.1021/op500056a
  • Xiong, J., Han, J., Zhang, H., Liu, K., Yin, X., Zhang, S., & Chen, J. (2025). Effect of Stirring Paddle Geometry on Nucleation and Growth Crystal Size of Ammonium Sulfate Crystals. Journal of Chemical & Engineering Data, 70(9), 3602-3613. https://doi.org/10.1021/acs.jced.5c00367
  • Yousuf, M., & Frawley, P. J. (2019). Secondary nucleation from nuclei breeding and its quantitative link with fluid shear stress in mixing. Organic Process Research & Development, 23(5), 926–934. https://doi.org/10.1021/acs.oprd.9b00029
  • Zhao, B., Zang, H., Zhong, L., Ma, X., Wang, H., Zhang, H., & Li, L. (2023). Review of the application of PAT in the pharmaceutical continuous crystallization process. Current topics in medicinal chemistry, 23(18), 1699-1714. https://doi.org/10.2174/1568026623666230420112709