### Abstract

It is shown how port-based modeling of lumped-parameter complex physical systems (multi-body systems, electrical circuits, electromechanical systems,..) naturally leads to a geometrically defined class of systems, called port-Hamiltonian systems. These are Hamiltonian systems defined with respect to a power-conserving geometric structure capturing the basic interconnection laws, and a Hamiltonian function given by the total stored energy. The structural properties of port-Hamiltonian systems are discussed, in particular the existence of Casimir functions and its implications for stability and stabilization. Furthermore it is shown how passivity-based control results from interconnecting the plant port-Hamiltonian system with a controller port-Hamiltonian system, leading to a closed-loop port-Hamiltonian system. Finally, extensions to the distributed-parameter case are provided by formulating boundary control systems as infinite-dimensional port-Hamiltonian systems.

Original language | English |
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Title of host publication | Advanced Dynamics and Control of Structures and Machines |

Editors | Hans Irshik, Kurt Schlacher |

Place of Publication | Wien, New York |

Publisher | Springer |

Pages | 127-168 |

Number of pages | 41 |

ISBN (Electronic) | 978-3-7091-2774-2 |

ISBN (Print) | 978-3-211-22867-8 |

DOIs | |

Publication status | Published - 2004 |

### Publication series

Name | CISM Courses and Lectures |
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Volume | 444 |

ISSN (Print) | 0254-1971 |

ISSN (Electronic) | 2309-3706 |

### Keywords

- METIS-223799
- Hamiltonian System
- Multibody System
- Kinematic Constraint
- Dirac Structure
- Bond Graph

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## Cite this

van der Schaft, A. J. (2004). Port-Hamiltonian systems: network modeling and control of nonlinear physical systems. In H. Irshik, & K. Schlacher (Eds.),

*Advanced Dynamics and Control of Structures and Machines*(pp. 127-168). (CISM Courses and Lectures; Vol. 444). Wien, New York: Springer. https://doi.org/10.1007/978-3-7091-2774-2_9