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Keywords:

  • batch crystallization;
  • nonlinear moment model;
  • seeding;
  • model-based control;
  • dynamic optimization;
  • state estimation;
  • real-time implementation

Abstract

This article presents a model-based control approach for optimal operation of a seeded fed-batch evaporative crystallizer. Various direct optimization strategies, namely, single shooting, multiple shooting, and simultaneous strategies, are used to examine real-time implementation of the control approach on a semi-industrial crystallizer. The dynamic optimizer utilizes a nonlinear moment model for on-line computation of the optimal operating policy. An extended Luenberger-type observer is designed to enable closed-loop implementation of the dynamic optimizer. In addition, the observer estimates the unmeasured process variable, namely, the solute concentration, which is essential for the intended control application. The model-based control approach aims to maximize the batch productivity, as satisfying the product quality requirements. Optimal control of crystal growth rate is the key to fulfill this objective. This is due to the close relation of the crystal growth rate to product attributes and batch productivity. The experimental results suggest that real-time application of the control approach leads to a substantial increase, i.e., up to 30%, in the batch productivity. The reproducibility of batch runs with respect to the product crystal size distribution is achieved by thorough seeding. The simulation and experimental results indicate that the direct optimization strategies perform similarly in terms of optimal process operation. However, the single shooting strategy is computationally more expensive. © 2010 American Institute of Chemical Engineers AIChE J, 57: 1557–1569, 2011