Temperature-Dependent Dynamic Behavior of Process Temperature Sensors

For a number of applications in control and safety value monitoring, a profound knowledge of the dynamic behavior of process temperature sensors is of great importance. Sensor test procedures and model identification methods are state of the art for small temperature changes, i.e., steps. For wider temperature ranges, the temperature dependency of the material characteristics is significant, too. The resulting non-linearities limit the utilization of classical model concepts. In this paper, we introduce and solve a non-linear ordinary differential equation for the linear dependency of the material characteristic parameters, i.e., for the basic case of non-constant material parameters. The analytic solution will be explained, and the results are discussed and compared to a finite element method model of a basic cylinder.