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 that 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 the 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 the 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 to concentration and third-order moment values. The equation obtained by symbolic regression presented R2 values close to one for the training and validation data sets. The symbolic regression approach presented better performance than the traditional PLSR to calculate the paracetamol concentration in a new data set. 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 R2 values close to one and mean absolute percentage error (MAPE) around 7% for the training and validation data sets. The NMPC’s performance was tested in five experimental batches. The first two batches produced crystals that were close to the desired target specifications. In experiment 1, for example, 9.75 g of paracetamol was produced with mean size of 196.2 μm based on sieving and weighing, while the set-points were 9.00 g and 200.0 μm. 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.