Control of distributed-parameter solidifaction and melting processes

• Applicant: Professor Dr.-Ing. Joachim Deutscher
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 555284045

This research project considers the control of 1d and 2d solidification and melting processes on time-varying spatial domains, which are very important for applications. For this, the flatness property of these processes is used to systematically determine nonlinear feedforward controllers. Thereby, disturbances and modell uncertainty are taken into account by designing backstepping-based tracking controllers. This results in new powerful tools for the control of solidification and melting processes. Thereby, new interesting challenges arise both for flatness-based and backstepping-based control. The starting point of the project is the extension of previous results concerning the linear backstepping-based tracking controller design for 1d two-phase problems with a time-varying spatial domain. In order to take model uncertainty and disturbances into account, disturbance feedforward controllers are combined with the linear tracking controllers. Besides linear controllers also new nonlinear flatness-based controllers are investigated, which ensure a desired exactly linear tracking error dynamics. The desinged state feedback controllers are implemented by using a disturbance observer. Thereby, both boundary measurements as well as a measurement of the position of the liquid-solid interface are utilized. For this, new backstepping methods for the design of observers with a time-varying 1d spatial domain are derived. In many applications it is of interest to shape the form as well as the time evolution of 2d the liquid-solid interface, which was not investigated using control theory so far. Therefore, the results for 1d two-phase problems are extended to a 2d spatial domain. This requires a detailed flatness analysis of the 2d two-phase problem in order to determine flatness-based feedforward controllers. With this, not only the control of the motion but also of the form of the 2d liquid-solid interface is possible. The stabilization of the tracking error dynamics is achieved by extending the backstepping-based tracking controller design from 1d to 2d spatial domains. Then, an output tracking controller is obtained by designing a tracking observer for 2d time-varying spatial domains. The experimental validation of the new tracking control methods are of particular importance in the research project. This ensures that the new results are also applicable to real-world problems appearing in industrial applications. For this, a laboratory setup is developed, which uses Paraffin for solidifaction and melting. The new setup allows to both study 1d and 2d two-phase problems experimentally.

• DFG Programme: Research Grants