Interfacial energy estimation in a precipitation reaction using the flatness based control of the moment trajectories

In this paper, we consider a model for precipitation experiments based on the population balance equation. The study revealed a high sensitivity of the system with respect to the modeling of intrinsic parameters, motivating a comprehensive validation of the estimates. In the forward simulation the impact of the influencing parameters including surface energy, nucleus size and distribution is investigated. Subsequently we construct a simplified model of the precipitation process in such a way that it is orbitally flat in terms of control theory, which enables the inverse calculation of the parameters. The numerical results of the inverse simulation for the interfacial energy have been compared to a physical model. The possibility of solving the inverse problem provides a promising way of estimating hardly measurable quantities for more complex molecules.