Reduced order in domain control of distributed parameter port-Hamiltonian systems via energy shaping

Authors

Ning Liu, Yongxin Wu, Yann Le Gorrec, Laurent Lefèvre, Hector Ramirez

Abstract

An in-domain finite dimensional controller for a class of distributed parameter systems on a one-dimensional spatial domain formulated under the port-Hamiltonian framework is presented. Based on (Trenchant et al. 2017) where positive feedback and a late lumping approach is used, we extend the Control by Interconnection method and propose a new energy shaping methodology with an early lumping approach on the distributed spatial domain of the system. Our two main control objectives are to stabilize the closed-loop system, as well as to improve the closed-loop dynamic performances. With the early lumping approach, we investigate two cases of the controller design, the ideal case where each distributed controller acts independently on the spatial domain (fully-actuated), and the more realistic case where the control action is piecewise constant over certain intervals (under-actuated). We then analyze the asymptotic stability of the closed-loop system when the infinite dimensional plant system is connected with the finite dimensional controller. Furthermore we provide simulation results comparing the performance of the fully-actuated case and the under-actuated case with an example of an elastic vibrating string.

Keywords

Port-Hamiltonian systems; Distributed parameter systems; Passivity-based control; Casimir function; Optimization

Citation

• Journal: Automatica
• Year: 2024
• Volume: 161
• Issue:
• Pages: 111500
• Publisher: Elsevier BV
• DOI: 10.1016/j.automatica.2023.111500

BibTeX

@article{Liu_2024,
  title={{Reduced order in domain control of distributed parameter port-Hamiltonian systems via energy shaping}},
  volume={161},
  ISSN={0005-1098},
  DOI={10.1016/j.automatica.2023.111500},
  journal={Automatica},
  publisher={Elsevier BV},
  author={Liu, Ning and Wu, Yongxin and Le Gorrec, Yann and Lefèvre, Laurent and Ramirez, Hector},
  year={2024},
  pages={111500}
}

Download the bib file

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