Optimal Control of Batch Crystallization Processes with Primary Nucleation

Abstract

Multi-objective optimization problems for batch crystallization processes with primary nucleation are presented and solved using optimal control theory. The mass of the nucleated crystals is tracked and included in the material balance. The resulting two-point boundary-value problems are difficult to solve because the expressions for the derivatives of the states and costates are highly non-linear. Conventional shooting methods usually fail to converge. Therefore, a gradient-based algorithm is applied instead. The method is illustrated by computing Pareto fronts for multi-objective optimization problems. An inherent trade-off is observed between the competing objectives of minimizing the number of nucleated crystals and the nucleated mass or the weight mean size. The algorithm is found to be both fast and robust, suggesting that it might be suitable for online model-based control.