direkt zum Inhalt springen

direkt zum Hauptnavigationsmenü

Sie sind hier

TU Berlin

Page Content

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

 

Programme
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

Structure preserving discretization of port-Hamiltonian systems

Elena Celledoni, Department of Mathematical Sciences NTNU, Norwegian University of Science and Technology Trondheim

In this talk we discuss discrete port-Hamiltonian systems from the view point of geometric numerical integration. Our starting point is a continuous port-Hamiltonian system which is discretized using a passivity-preserving numerical time integration method. We propose two different numerical approaches. We analyse these methods, focusing in particular on discrete energy-preserving and passivity-preserving interconnection of simpler systems. Connections to nonholonomic systems and their energy-preserving integration are considered. For nonholonomic systems, a (numerical) comparison with Lagrange-d’Alembert variational integrators will be presented.

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

Quick Access:

Schnellnavigation zur Seite über Nummerneingabe

Auxiliary Functions