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Model Reduction and Control of 2D Crystallization Processes

From Fachgebiet Regelungssysteme TU Berlin

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Crystallization models that take into account direction-dependent growth rates give rise to multi- dimensional population balance equations. We have investigated two problems for such systems: (i) D. Flockerzi has proposed a model reduction technique based on the quadrature method of moments [1], [2]. This method has been applied to a number of example problems, e.g., the direction-dependent growth of barium sulphate needle-shaped crystals, and has been shown to compare favorably to a number of alternative reduction methods. (ii) In practice, crystal shape is an important feature, and appropriate control schemes are therefore of paramount importance. Traditional techniques mostly use chemical additives for blocking or promoting the growth of certain crystal faces. In contrast, our work is based solely on the appropriate control of temperature. In particular, by “driving” the system through an appropriate sequence of growth and dissolution modes, it is possible to achieve morphologies which cannot be reached through a pure growth process. Switching is realized by determining suitable state manifolds. [3] investigates several optimal control problems for the single crystal case, and [4] proposes a convenient reformulation of the optimization problem as a convex program. These approaches have been carried over to crystal population systems in [5].

People involved


  • Christian Borchert (now with BASF)
  • Shamsul Qamar, Max-Planck-Institut für Dynamik komplexer technischer Systeme
  • Kai Sundmacher, Max-Planck-Institut für Dynamik komplexer technischer Systeme


  1. Voigt, A., Heineken, W., Flockerzi, D., Sundmacher, K.. Dimension reduction of two-dimensional population balances based on the quadrature method of moments. Computer Aided Chemical Engineering, 25 (1):913 - 918, 2008.
  2. Heineken, W., Flockerzi, D., Voigt, A., Sundmacher, K.. Dimension reduction of bivariate population balances using the quadrature method of moments. Computers & Chemical Engineering, 35 (1):50 - 62, 2011.
  3. Bajcinca, N., de Oliveira, V., Borchert, C., Raisch, J., Sundmacher, Kai. Optimal control solutions for crystal shape manipulation. In pages 751–756, 2010.
  4. Bajcinca, N., Perl, R., Sundmacher, K.. Convex optimization for shape manipulation of multidimensional crystal particles. In Proc. of ESCAPE-21, Halkidiki,Greece, pages 855–859, 2011.
  5. Bajcinca, N., Menarin, H., Hofmann, S.. Optimal control of multidimensional population balance systems for crystal shape manipulation. In 18th IFAC World Congress, Milano, Italy, pages 9842–9849, 2011.

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