### Abstract

Infinite dimensional, or continuous systems, and their finite element method (FEM) representations have, for many applications in control and optimization, too many degrees of freedom to be of practical use. Model order reduction is an essential part of modelling such systems. What features to retain is determined by the dynamics of interest, which follow from the input to the system and the specifications of the model. The input is necessary to bring the system into a nontrivial dynamical state, the output does not always follow from the specifications.

The appropriate output to an input, in the port-based modelling, is the response to an input, which product is the power transfer in or out of the system. The input and output are therefore collocated in a single “port”. In continuous systems the variables of the input are usually not the same as the internal variables, or the state. For example, the input to an elastic system can be force or velocity, while the corresponding internal variables are the stress and strain tensors. The relation among boundary variables and internal variables can be formalized in the port-Hamiltonian H0. This extension of the Hamiltonian H of a physical system automatically dictates the appropriate boundary variables and

the correct boundary conditions to be set, even in the case of an open system, where energy flows in and out of the system through the boundaries.

The appropriate output to an input, in the port-based modelling, is the response to an input, which product is the power transfer in or out of the system. The input and output are therefore collocated in a single “port”. In continuous systems the variables of the input are usually not the same as the internal variables, or the state. For example, the input to an elastic system can be force or velocity, while the corresponding internal variables are the stress and strain tensors. The relation among boundary variables and internal variables can be formalized in the port-Hamiltonian H0. This extension of the Hamiltonian H of a physical system automatically dictates the appropriate boundary variables and

the correct boundary conditions to be set, even in the case of an open system, where energy flows in and out of the system through the boundaries.

Original language | English |
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Title of host publication | 25th Benelux Meeting on Systems and Control, March 13 – 15, 2006, Heeze, The Netherlands |

Subtitle of host publication | Book of Abstracts |

Editors | Bram de Jager, Gjerrit Meinsma |

Publisher | Technische Universiteit Eindhoven |

Pages | 57-57 |

ISBN (Print) | 978-90-386-2558-4 |

Publication status | Published - 13 Mar 2006 |

Event | 25th Benelux Meeting on Systems and Control 2006 - Heeze, Belgium Duration: 13 Mar 2006 → 15 Mar 2006 Conference number: 25 |

### Conference

Conference | 25th Benelux Meeting on Systems and Control 2006 |
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Country | Belgium |

City | Heeze |

Period | 13/03/06 → 15/03/06 |

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## Cite this

Ligterink, N. E., Breedveld, P. C., & van der Schaft, A. J. (2006). The minimal model of a continuous, physical system, and more. In B. de Jager, & G. Meinsma (Eds.),

*25th Benelux Meeting on Systems and Control, March 13 – 15, 2006, Heeze, The Netherlands: Book of Abstracts*(pp. 57-57). Technische Universiteit Eindhoven.