Inhalt des Dokuments
Energy based modeling, simulation and control
Friday, 25th October 2019
Location: Technische Universität Berlin
Main building, Room H
3005
Straße des 17. Juni 135, 10623 Berlin
Guests are welcome!
Programme
Friday, 25. October 2019
15:00 |
Structure
preserving discretization of port-Hamiltonian
systems Elena Celledoni,
Department of Mathematical Sciences NTNU, Norwegian University of
Science and Technology Trondheim |
15:50 | Coffee
Break |
16:10 | Energy based modeling, simulation and control
using port-Hamiltonian descriptor
systems Riccardo Morandin, Inst. f.
Mathematik, TU Berlin |
16:35 | GENERIC structures with bulk-interface
interaction Marita Thomas,
Weierstrass Institut, Berlin |
17:00 | Informal get-together
("Stammtisch") |
Abstracts
Elena Celledoni, Department of Mathematical Sciences NTNU, Norwegian University of Science and Technology Trondheim
Energy based modeling, simulation and control using port-Hamiltonian descriptor systems
Riccardo Morandin, Inst. f. Mathematik, TU Berlin
Recent developments in the energy market require new mathematical
models and suitable algorithms for the efficient usage of the existing
networks. Starting from these real-world problems, it is necessary to
concentrate on methods for large-scale energy networks and, in
particular, address optimization and stability analysis, model
predictive control, model-order reduction, uncertainty quantification,
and related topics on energy networks. The abstract setting allows for
consideration of applications arising from both, gas and power
networks.
Our framework of choice is the one of
port-Hamiltonian descriptor systems, or pHDAEs. These are energy-based
equations with a special structure, that guarantees several beneficial
properties, e.g. inherent stability and passivity, physical
interpretation of variables, simple interconnection,
structure-preserving model reduction, robust numerical integration and
simplification of feedback stabilization.
In this talk, we
present a new formulation for port-Hamiltonian descriptor systems,
which extends previous models by including under- and overdetermined
systems, and arbitrary differentiable Hamiltonian functions. Every
system of this form is associated with a geometric object known as
Dirac structure, that encloses its energy balance properties.
Furthermore, we investigate the application of collocation methods for
time-discretization to these systems and we show that, under certain
assumptions, structure preservation can be achieved. Finally, we show
one example from the power network setting and some numerical
results.
GENERIC structures with bulk-interface
interaction
Marita Thomas, Weierstrass Institut,
Berlin
This talk is devoted to the thermodynamical modeling framework of GENERIC which was originally introduced by Öttinger and Grmela. GENERIC, the acronym for General Equations for Non-Equilibrium Reversible Irreversible Coupling, characterizes Hamiltonian systems for reversible dynamics and Onsager (or gradient) systems for irreversible dynamics in terms of triples given by suitable state spaces, driving functionals, and geometric structures. It allows for their thermodynamically consistent coupling by enforcing a non-interaction condition for the triples of reversible and irreversible dynamics. Originally introduced for thermodynamically closed systems, this concept was more recently extended by Öttinger to open systems. This talk reviews this approach in order to treat coupled systems in which processes that take place in the bulk interact with processes taking place along interfaces. This is illustrated with examples from fluid and solid mechanics. Directions towards mathematical analysis are outlined for specific examples and connections to related modeling concepts such as Port-Hamiltonian systems are adressed.
Zusatzinformationen / Extras
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https://www3.itp.tu-berlin.de/collaborative_research_center_910/sonderforschungsbereich_910/events/symposia/energy_based_modeling_simulation_and_control_251019/