Authors

Jeanne Redaud, Jean Auriol

Abstract

In this paper, we consider the stabilization of a clamped string with actuation located inside the domain. Such a model can represent the simplified dynamics of a microendoscope. Inspired by the Port Hamiltonian framework, we use the Riemann invariants of the energy states to reformulate this problem as stabilizing a chain of two coupled hyperbolic subsystems with actuation at the in-between boundary. After applying successive transforms, it is shown to be equivalent to stabilizing a neutral-type delay-differential equation. A suitable controller is derived using the backstepping methodology with a Fredholm integral transform. Some simulations illustrate this approach.

Keywords

Infinite-dimensional system; flexible structures; in-domain actuation; backstepping

Citation

  • Journal: IFAC-PapersOnLine
  • Year: 2023
  • Volume: 56
  • Issue: 2
  • Pages: 9936–9941
  • Publisher: Elsevier BV
  • DOI: 10.1016/j.ifacol.2023.10.692
  • Note: 22nd IFAC World Congress- Yokohama, Japan, July 9-14, 2023

BibTeX

@article{Redaud_2023,
  title={{Backstepping stabilization of a clamped string with actuation inside the domain}},
  volume={56},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2023.10.692},
  number={2},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Redaud, Jeanne and Auriol, Jean},
  year={2023},
  pages={9936--9941}
}

Download the bib file

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