(240f) Optimal Distributional Control of Crystal Size and Shape

This paper considers the problem of optimally controlling the characteristics of pharmaceutical crystals that vary in size and shape as the crystals nucleate and grow. The computational expense of the batch optimal control problem is greatly reduced by applying the method of characteristics to compute the multidimensional crystal size distribution by solving a set of ordinary differential equations. The temperature profile and seed characteristics are optimized for a class of distributional control objective functions designed to minimize the number of small crystals at the end of the batch for a proprietary Merck pharmaceutical. For the highly nucleating system considered in this study, the optimal control policy consisted of the smallest seed mass and the largest mean size, which is in sharp contrast to the optimal seeding for most other crystallizations. The paper explores a tradeoff between producing crystals of uniform shape and minimizing the number of small crystals.