Stabilisation of a Nonlinear Flexible Beam in Port-Hamiltonian Form

Authors

Abstract

The aim of this paper is to present a simple extension of the theory of linear, distributed, port-Hamiltonian systems to the nonlinear scenario. More precisely, an algebraic nonlinear skew-symmetric term has now been included in the PDE. It is then shown that the system can be equivalently written in terms of the scattering variables, and that these variables are strictly related with the Riemann invariants that appear in quasi-linear hyperbolic PDEs. For this class of PDEs, several results about the existence of solutions, and asymptotic stability of equilibria have already been presented in literature. Here, these results have been extended and applied within the port-Hamiltonian framework, where are suitable of a nice physical interpretation. The final scope is the boundary asymptotic stabilisation of a nonlinear flexible beam with a free-end, and full actuation on the other side.

Keywords

Passivity; stabilisation; nonlinear distributed parameter systems

Citation

Journal: IFAC Proceedings Volumes
Year: 2013
Volume: 46
Issue: 23
Pages: 412–417
Publisher: Elsevier BV
DOI: 10.3182/20130904-3-fr-2041.00115
Note: 9th IFAC Symposium on Nonlinear Control Systems

BibTeX

@article{Macchelli_2013,
  title={{Stabilisation of a Nonlinear Flexible Beam in Port-Hamiltonian Form}},
  volume={46},
  ISSN={1474-6670},
  DOI={10.3182/20130904-3-fr-2041.00115},
  number={23},
  journal={IFAC Proceedings Volumes},
  publisher={Elsevier BV},
  author={Macchelli, Alessandro},
  year={2013},
  pages={412--417}
}

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