Open Access

Ruven Weiß, Moritz Diehl, Harald Rieger, Johannes Reuter

• In many industrial applications a workpiece is continuously fed through a heating zone in order to reach a desired temperature to obtain specific material properties. Many examples of such distributed parameter systems exist in heavy industry and also in furniture production such processes can be found. In this paper, a real-time capable model for a heating process with application to industrial furniture production is modeled. As the model is intended to be used in a Model Predictive Control (MPC) application, the main focus is to achieve minimum computational runtime while maintaining a sufficient amount of accuracy. Thus, the governing Partial Differential Equation (PDE) is discretized using finite differences on a grid, specifically tailored to this application. The grid is optimized to yield acceptable accuracy with a minimum number of grid nodes such that a relatively low order model is obtained. Subsequently, an explicit Runge-Kutta ODE (Ordinary Differential Equation) solver of fourth order is compared to the Crank-Nicolson integration scheme presented in Weiss et al. (2022) in terms of runtime and accuracy. Finally, the unknown thermal parameters of the process are estimated using real-world measurement data that was obtained from an experimental setup. The final model yields acceptable accuracy while at the same time shows promising computation time, which enables its use in an MPC controller.