Experimental Nonlinear Model Predictive Control of Crystal Size and Yield in Batch Cooling Crystallization
Enabled by Soft Sensor and Symbolic-Based Calibration Model
Pregled programa
- Paracetamol batch crystallization experiments were controlled by an NMPC
- A symbolic regression model was used to convert the ATR-FTIR spectra into concentration
- ANNs were used to calculate CSD information from chord count measurements and close the control loop
Fernando Arrais Romero Dias Lima presents "Experimental Nonlinear Model Predictive Control of Crystal Size and Yield in Batch Cooling Crystallization Enabled by Soft Sensor and Symbolic-Based Calibration Model." Crystallization plays a key role in purification and product design in industries such as pharmaceuticals and food. Ensuring the crystals produced have a size distribution that meets regulatory standards requires an effective control system. However, most controllers developed for crystallization processes in the literature were tested only in simulations.
This study proposes a robust methodology to implement a nonlinear model predictive controller (NMPC) in a crystallizer and test it in batch experiments of unseeded paracetamol crystallization in ethanol. A validated population balance model (PBM) serves as the NMPC’s internal model, controlling crystal size and yield by manipulating temperature. The experimental setup included attenuated total reflectance-Fourier transform infrared (ATR-FTIR) and Focused Beam Reflectance Measurements (FBRM). However, these tools could not directly measure concentration and the first four moments of the crystal size distribution (CSD). To address this, a symbolic regression model was developed to convert ATR-FTIR spectra into concentration and third-order moment values. The equation obtained by symbolic regression presented R^2 values close to one for the training and validation datasets. The symbolic regression approach presented better performance than the traditional PLSR to calculate the paracetamol concentration in a new dataset.
Additionally, an approach based on artificial neural networks (ANNs) was applied to estimate the first three moments of the CSD based on FBRM data, concentration, and temperature. For the three variables, the ANNs presented R^2 values close to one and mean absolute percentage error (MAPE) around 7% for the training and validation datasets. The NMPC's performance was tested in five experimental batches. The first two batches produced crystals close to the desired target specifications.
In Experiment 1, for example, 9.75 g of paracetamol was produced with mean size of 196.2 micrometers based on sieving and weighing, while the set-points were 9.00 g and 200.0 micrometers. However, in the following two batches, the crystals were larger than expected as a result of temperature cycles causing crystal disappearance. To resolve this, a stopping criterion was introduced in the fifth experiment, halting the process based on model predictions. The resulting crystals met set-point specifications, showing that the proposed control strategy effectively controlled the paracetamol batch crystallization process.
About the Presenter
Fernando Arrais Romero Dias Lima, Ph.D.
Federal University of Rio de Janeiro
Fernando Arrais Romero Dias Lima is a chemical engineer and researcher whose work centers on the modeling, monitoring, and control of crystallization processes, with a strong emphasis on combining process systems engineering and machine learning. He holds two PhD degrees, one in Chemical Engineering from the Norwegian University of Science and Technology (NTNU) and another in Engineering of Chemical and Biochemical Processes from the Federal University of Rio de Janeiro (UFRJ). His research focuses on improving crystallization processes through model-based and data-driven approaches, including soft sensing, symbolic regression, neural networks, universal differential equations, and advanced control strategies. His research has addressed both the fundamental and applied sides of crystallization, spanning mechanistic and empirical modeling, uncertainty-aware prediction, nonlinear model predictive control, reinforcement learning, and experimental closed-loop control of batch systems such as paracetamol crystallization. He has also developed monitoring tools using spectroscopic and particle measurement data to support real-time control and optimization. Across his publications and research appointments, Fernando has built a profile focused on trustworthy and interpretable intelligent methods for crystallization engineering, aiming to bridge rigorous process understanding with modern machine learning tools for industrially relevant applications.
