Optimal control for batch crystallization with size-dependent growth kinetics

An efficient algorithm for the optimal control of a batch crystallization process with size-dependent growth kinetics is proposed. By means of a unique diffeomorphism, new independent coordinates for the time and size variables of the underlying population balance equation are introduced, leading to a closed infinite dimensional moment model. The posed optimal control problem is solved using the minimum principle for a simplified model with neglected natural feedback of the nucleation mass into the crystallization kinetics. The solution is obtained in analytical form, and it is shown to be unique. Additionally, for the original optimization problem involving the full process dynamics, a simple feasible sub-optimal solution, as well as a lower and an upper bound for the cost, are suggested.