On the Synthesis of Boundary Control Laws for Distributed Port-Hamiltonian Systems

Authors

Alessandro Macchelli, Yann Le Gorrec, Hector Ramirez, Hans Zwart

Abstract

This paper is concerned with the energy shaping of 1-D linear boundary controlled port-Hamiltonian systems. The energy-Casimir method is first proposed to deal with power preserving systems. It is shown how to use finite dimensional dynamic boundary controllers and closed-loop structural invariants to partially shape the closed-loop energy function and how such controller finally reduces to a state feedback. When dissipative port-Hamiltonian systems are considered, the Casimir functions do not exist anymore (dissipation obstacle) and the immersion (via a dynamic controller)/reduction (through invariants) method cannot be applied. The main contribution of this paper is to show how to use the same ideas and state functions to shape the closed-loop energy function of dissipative systems through direct state feedback i.e. without relying on a dynamic controller and a reduction step. In both cases, the existence of solution and the asymptotic stability (by additional damping injection) of the closed-loop system are proven. The general theory and achievable closed-loop performances are illustrated with the help of a concluding example, the boundary stabilization of a longitudinal beam vibrations.

Citation

• Journal: IEEE Transactions on Automatic Control
• Year: 2017
• Volume: 62
• Issue: 4
• Pages: 1700–1713
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/tac.2016.2595263

BibTeX

@article{Macchelli_2017,
  title={{On the Synthesis of Boundary Control Laws for Distributed Port-Hamiltonian Systems}},
  volume={62},
  ISSN={1558-2523},
  DOI={10.1109/tac.2016.2595263},
  number={4},
  journal={IEEE Transactions on Automatic Control},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Macchelli, Alessandro and Le Gorrec, Yann and Ramirez, Hector and Zwart, Hans},
  year={2017},
  pages={1700--1713}
}

Download the bib file

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