Control of Product Quality in Batch Crystallization of Pharmaceuticals and Fine Chemicals. Part 2: External Control

Abstract

We use the term “external control” to refer to two process control configurations: First, the “direct or inferential feedback control” of a given product quality index such as the crystal size distribution. Second, the “optimal control” of a process variable such as the control of the cooling policy (temperature) or the reactants addition rate to optimize an objective function defined in terms of the product quality. The intent of this two-part contribution is to discuss the various approaches used for the control of crystal quality. In Part 1, the design of the crystallization process and the selection of the process variables affecting the product quality were presented. In this part the implementation of an “external controller” will be presented. Initially, state-of-the-art instrumentation in crystallization research and technology is discussed. Mathematical models involving the population density and moments equation are presented and evaluated. Feedback control of crystal size distribution and supersaturation is presented in some detail. Polymorphic outcome of pharmaceuticals is dictated by the choice of solvent, presence of impurities, and the operating variables such as the temperature and the degree of supersaturation that are controlled by the implementation of an “external controller”. A new algorithm for the solution of the integro-hyperbolic partial differential equation representing the population balance is discussed, and its potential use in the design of real-time optimal control policies for the control of batch crystallizers is highlighted. Open-loop and real-time optimal control policies in cooling batch crystallizers are presented, and their efficacy is evaluated.