Max Planck Institute for Dynamics of Complex Technical Systems
Model Reduction and Control of 2D Crystallization Processes
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].
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.
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.
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.
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.