Distribution Control of Particulate Systems Based on Population Balance Equation Models

Manufacturing processes in which the desired product takes the form of individual particles are ubiquitous in the chemical, pharmaceutical and agricultural industries. Particulate processes often are modeled using a form of the population balance equation (PBE) which describes the evolution of the particle distribution. In many applications, control of the particle distribution is necessary to achieve the desired product properties. In this paper, a model predictive control strategy based on a discretized representation of a general onedimensional PBE is proposed for particle distribution control. The controller is formulated to minimize the least squares difference between the predicted and target distributions assuming the availability of particle distribution measurements. The proposed method is applied to the problem of cell mass distribution control in a continuous yeast fermentor.