Nonlinear model-based control of a semi-industrial batch crystallizer using a population balance modeling framework

This paper presents an output feedback nonlinear model-based control approach for optimal operation of industrial batch crystallizers. A full population balance model is utilized as the cornerstone of the control approach. The modeling framework allows us to describe the dynamics of a wide range of industrial batch crystallizers. In addition, it facilitates the use of performance objectives expressed in terms of crystal size distribution. The core component of the control approach is an optimal control problem, which is solved by the direct multiple shooting strategy. To ensure the effectiveness of the optimal operating policies in the presence of model imperfections and process uncertainties, the model predictions are adapted on the basis of online measurements using a moving horizon state estimator. The nonlinear model-based control approach is applied to a semi-industrial crystallizer. The simulation results suggest that the feasibility of real-time control of the crystallizer is largely dependent on the discretization coarseness of the population balance model. The control performance can be greatly deteriorated due to inadequate discretization of the population balance equation. This results from structural model imperfection, which is effectively compensated for by using the online measurements to confer an integrating action to the dynamic optimizer. The real-time feasibility of the output feedback control approach is experimentally corroborated for fed-batch evaporative crystallization of ammonium sulphate. It is observed that the use of the control approach leads to a substantial increase, i.e., up to 15%, in the batch crystal content as the product quality is sustained