Optimal Control of Batch Crystallization Processes with Primary Nucleation

Multi-objectiveoptimization problems for batch crystallizationprocesses with primary nucleation are presented and solved using optimalcontrol theory. The mass of the nucleated crystals is tracked andincluded in the material balance. The resulting two-point boundary-valueproblems are difficult to solve because the expressions for the derivativesof the states and costates are highly non-linear. Conventional shootingmethods usually fail to converge. Therefore, a gradient-based algorithmis applied instead. The method is illustrated by computing Paretofronts for multi-objective optimization problems. An inherent trade-offis observed between the competing objectives of minimizing the numberof nucleated crystals and the nucleated mass or the weight mean size.The algorithm is found to be both fast and robust, suggesting thatit might be suitable for online model-based control.