Energy-Based Modeling of Complex Systems

The module introduces to a structured, network- and energy-based methodology for the modeling and coupling of multi-physical systems. Departing from the bond-graph formalism, a graphical language illustrating power flows and interconnections in complex systems, the port-Hamiltonian (PH) approach highlights the exchange, conversion, and storage of energy in control-oriented state space models. In its modularity, it is an ideal vehicle to set up complex system models. In the context of simulation and control design or implementation, preserving the physical structure in numerical approximations is of major interest. The course gives, based on the example of hyperbolic systems of conservation laws, insights in the structure-preserving discretization in space and time. Conditions to preserve the port-Hamiltonian structure in projective model order reduction are given.

The attendance of the module prepares interested students for research internships and theses in the Energy-Based Modeling and Control group of the Chair of Automatic Control.

The following topics are presented:

1. Bond graphs for the graphical description of multi-physics systems

2. Port-based modeling, Dirac structures, energy storage and other modules

3. PH systems and passivity

4. PH representation of spatially distributed systems in one dimension, beam models

5. Integration and calculus with differential forms

6. Conservation and balance laws in PH form on higher dimensional spatial domains

7. Structure-preserving spatial discretization of PH systems

8. Numerical time integration of (port-)Hamiltonian systems


The lecture given in English in the summer semester, is a Master degree module. After having passed the exam,  you will get 5 ECTS.

The module consists of the weekly
exercise course
and an optional revision exercise.

The revision exercise gives the opportunity
a) to clarify open questions concerning the course's contents and/or to deepen further topics going beyond the scope of the lecture and
b) to prepare for the exam.