Model identification and reduction for the control of an ice cream crystallization process

Ice cream crystallization processes can be modeled by some population and energy balance equations. Due to the infinite dimensional and nonlinear characteristics, such models are highly complex, especially when all the phenomena of nucleation, growth and breakage are considered. Depending on the control problem under consideration, such a complexity can be useless and the control law can be designed on the basis of an input-output reduced order model of the process. In the present paper, we first consider a reduced order model of 6 ordinary differential equations obtained by the method of moments. By means of a sensitivity analysis and a parameter identification, it is shown that, to accurately describe the input-output behavior of the system whatever the conditions are, it is sufficient to change the values of only two parameters of this model, which is really interesting from a control point of view. However, when looking at the simulated data, the complexity of this moments model appears useless, from the input-output point of view. A second model reduction is therefore performed, based on physical assumptions. We finally get a new model with 3 ordinary differential equations, which is validated first on experimental data and then by comparison with the initial moments model.