Control of batch crystallization—A system inversion approach

In this article, a new approach to the control of batch cooling crystallizers is presented. In batch cooling crystallization, the crucial control problem is to design a temperature trajectory which produces a desired crystal size distribution at the end of the batch. Traditionally, this problem is addressed in an optimization framework. Here, a completely different solution is presented. It is shown that the standard population balance model can be inverted analytically. System inversion is performed making use of a state-dependent time scaling of the population balance model. Consequently, for any achievable crystal size distribution at the end of the batch, the corresponding temperature trajectory can be determined in a straightforward way as a feedforward control signal. Furthermore, exploiting the properties of the corresponding time-scaled moment model, a nonlinear feedback controller is designed for the batch crystallizer to ensure tracking of the previously generated feedforward trajectories in the presence of uncertainty.