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 twopart 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 integrohyperbolic 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.

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

“…Mazzotti et al [166,167] used model-based optimization techniques to control CSD in batch cooling crystallisation of paracetamol in ethanol and also the combined cooling/antisolvent crystallisation of acetylsalicylic acid in ethanol-water mixtures. Rohani and co-workers (see for example [168][169][170][171][172][173][174]) minimized the optimization objective function with respect to a parameter vector temperature input, subject to the mass balance dynamics as well as the PB equation to obtain optimal cooling policy for product quality control. They also developed real-time model-based optimal control of anti-solvent semi-batch crystallisation processes and seeded batch crystallisation processes using real-time single and multi-objective optimization, rigid logic and fuzzy logic control methods [171][172][173][174][175].…”

Optimal Control of Polymorphic Transformation in Batch Pharmaceutical Crystallization

“…For j>1, the temperature parameters were determined from a genetic algorithm applied to the optimization of the robust objective function subject to all operating constraints for the full range of uncertain parameters. V. C -CONTROL In many experimental and simulation studies of nonpolymorphic batch crystallizations, the C-control strategy ( Figure 2) has resulted in low sensitivity of the product quality to most practical disturbances and variations in kinetic parameters [3], [8], [11], [12], [17]. C-control can be interpreted as nonlinear state feedback control [17], in which the nonlinear master controller acts on the concentration C as a measured state to produce the setpoint temperature T set as its manipulated variable.…”

“…The most widely studied approach is to determine a temperature profile (Tcontrol) that optimizes an objective function based on an offline nominal model [5], [6]. Although T-control is simple to implement, it has become well-known in recent years that Tcontrol can be very sensitive to variations in the kinetic parameters [7], [8]. This motivated the development of robust Tcontrol which explicitly includes the impact of uncertainties in the objective while determining the optimal temperaturetime trajectory to be followed during batch operation [9], [10].…”

“…This motivated the development of robust Tcontrol which explicitly includes the impact of uncertainties in the objective while determining the optimal temperaturetime trajectory to be followed during batch operation [9], [10]. With advances in sensor technologies, another control strategy developed to provide improved robustness to model uncertainty is C-control, which follows an optimal or nearly optimal concentration-temperature trajectory [3], [8], [11], [12].…”

Applications of the crystallization process in the pharmaceutical industry

“…These properties can be controlled either by proper selection of the process variables such as the solvent type, the degree of local and average supersaturation, degree of mixing (macro-, meso-and micro-mixing), crystallizer geometry, and seeding policy (loading, dry or slurry form, time of addition, etc. ), or by implementing external control [3,4].…”