Port-Hamiltonian modelling and energy-based control of the Timoshenko beam

Authors

Andreas Siuka, Markus Schöberl, Kurt Schlacher

Abstract

This contribution deals with the port-Hamiltonian modelling and energy-based control of infinite-dimensional mechanical systems. Motivated by the physical interpretation offered by the port-controlled Hamiltonian system class in the finite-dimensional case, we analyse an extension of this framework to the infinite-dimensional scenario on the basis of the so-called evolutionary approach which is used for the port-Hamiltonian formulation of flexible beams modelled according to the Timoshenko theory. Furthermore, we adapt the well-known control via structural invariants method with respect to the presented port-Hamiltonian description such that this method is applied to the boundary control of the Timoshenko beam.

Keywords

Timoshenko Beam; Dirac Structure; Casimir Function; Timoshenko Theory; Hamiltonian System Class

Citation

• Journal: Acta Mechanica
• Year: 2011
• Volume: 222
• Issue: 1-2
• Pages: 69–89
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s00707-011-0510-2

BibTeX

@article{Siuka_2011,
  title={{Port-Hamiltonian modelling and energy-based control of the Timoshenko beam: An approach based on structural invariants}},
  volume={222},
  ISSN={1619-6937},
  DOI={10.1007/s00707-011-0510-2},
  number={1–2},
  journal={Acta Mechanica},
  publisher={Springer Science and Business Media LLC},
  author={Siuka, Andreas and Schöberl, Markus and Schlacher, Kurt},
  year={2011},
  pages={69--89}
}

Download the bib file

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