Modeling and identification of temperature fields in multi-zone-furnaces

The following article describes a model for the thermodynamic transient temperature field in multi-zone-furnaces. Such plants have a wide range of application, especially in material sciences. Conventionally, one-dimensional approaches are used to define an input/output relation between heaters and sensors for each zone. Driven by the application of measuring diffusion coefficients in metallic and semiconductor melts, additional sensors can be placed near the sample. This necessitates more complex temperature models. Here, a state space representation created by a semi-discrete finite difference discretization of the temperature field is explained. It will be shown that an empirical identification process achieves good results for the approximation of the real plant.