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要旨:
In this contribution, we investigate feedforward control synthesis for a batch cooling crystalliser based on a simple population balance model. Population balance models are multidimensional dynamical systems, where one of the independent variables represents time, the other(s) "property coordinate(s)" as, e.g. particle size. They typically describe the temporal evolution of number density functions and are therefore naturally suited to model particulate processes in chemical engineering. Crystallisation represents an important class of particulate processes. It is well established in the chemical and pharmaceutical industry as a purification and separation technique. The quality of crystalline products is strongly influenced by physical properties, such as crystal size distribution (CSD). In batch cooling crystallisers, the fact that solubility depends on temperature is exploited. In this contribution, the process is described by a standard population balance model consisting of a partial differential equation and an ordinary differential equation. The model describes the temporal evolution of both crystal size distribution and solute concentration. Temperature in the crystalliser is considered to be the control input, and the control objective is to achieve a desired crystal size distribution at the end of the batch. The suggested procedure uses a time scaling which transforms the partial differential equation into a simple transport equation and makes the associated (finite dimensional) moment model a flat systems. It checks whether the desired final CSD is achievable, i. e. whether it is compatible with the model assumptions and, if the outcome is affirmative, generates the appropriate control signal.
