Today's industrial applications comprise a large number of different, highly interconnected, non-trivial subsystems. Their efficient overall operation is an important factor for economic growth and environmental protection. Conservation laws govern the dynamics of a large variety of phenomena in energy, production and process industry which evolve in space and time. They describe, for example, mass and heat transport, or the evolution of concentrations in chemical reactions. The efficient operation of such complex processes requires mathematical models that reproduce the dominant system properties.
The EasyEBC project is based on the port-Hamiltonian (PH) perspective with its exciting conceptual simplicity: The storage of energy (a “Hamiltonian”), dissipation and power exchange between subsystems and the environment via power interfaces (“ports”) are the key modeling paradigms. They make the PH approach suited for modeling and control of complex multi-physics systems. The development of transparent and easy-to-handle – as a prerequisite for industrial deployment – control design methods for systems of conservation laws based on the PH representation is the ultimate goal of EasyEBC.
A series of spatial discretization methods hat preserve the PH structure have been proposed in the last decade. Their properties and accuracy, their parametrization and the relations to classical schemes from numerical mathematics, pose, however, a series of open questions. These issues, together with the benchmark problem suggested by the host laboratory, namely the modelling of heat and mass transport in catalytic foams, motivated us to re-orientate the action. Instead of control design for 1D hyperbolic systems based on given models, we concentrated on the elaboration of discrete systems of conservation laws, augmented with boundary port variables in higher spatial dimensions, and the analysis and adaptation of classical numerical approximation methods for this purpose. This research on more fundamental questions paves the way to develop EasyEBC control methods for a much wider class of complex dynamical systems.
Besides the research project, the scientific training of the fellow, and the dissemination of the results, the consolidation of the scientific cooperation and the organization of a summer school on PH systems were the main objectives of the action.
Clarifications on structure-preserving discretization with respect to the state of the art, the extensions of existing and the development of new discretization methods for open and/or controlled physical systems, are the scientific results of the action. They serve as a solid basis for a control design methodology in the spirit of EasyEBC. The successful application for a French-German research grant (DFG-ANR project INFIDHEM, 2017-2020), impulsed by the fellow’s and the supervisor’s labs and four partner groups, is an outcome of the project. It founds the follow-up of the results towards geometrical model order reduction and control with the elaborated models and guarantees the continuity of our collaboration beyond the MSCA action. Research, training, scientific collaboration and the integration into an excellent research network, allowed the fellow to strengthen his academic qualification and to significantly advance in his Habilitation project.
