Optimal Control of Crystal Size and Shape in Batch Crystallization Using a Bivariate Population Balance Modeling

An optimal control framework was employed to obtain optimal supersaturation/temperature policies for controlling the crystal mass, size, and shape that meet target product specifications. It uses a bivariate population balance model that includes crystal nucleation, growth, dissolution, and disappearance. The optimal control scheme, solving a dynamic optimization problem, was applied to the batch cooling crystallization of potassium dihydrogen phosphate. The population balance model was evaluated in open-loop experiments, showing good prediction for the mean characteristic lengths and number of particles, both for the supersaturation and undersaturation zones. The deterministic optimal control simulations demonstrated the application of the control action policies to produce crystals of desired mass and average shape for different control targets. Copyright (C) 2021 The Authors.