Interconnection of the Kirchhoff plate within the port-Hamiltonian framework

Authors

Andrea Brugnoli, Daniel Alazard, Valerie Pommier-Budinger, Denis Matignon

Abstract

The Kirchhoff plate model is detailed by using a tensorial port-Hamiltonian (pH) formulation. A structure-preserving discretization of this model is then achieved by using the partitioned finite element (PFEM). This methodology easily accounts for the boundary variables and the finite-dimensional system can be interconnected to the surrounding environment in a simple and structured manner. The algebraic constraints to be considered are deduced from the boundary conditions, that may be homogeneous or defined by an interconnection with another pH system.The versatility of the proposed approach is assessed by means of numerical simulations. A first illustration considers a rectangular plate clamped on one side and interconnected to a rigid rod welded to the opposite side. A second example exploits the collocated output feature of pH systems to perform damping injection in a plate undergoing an external forcing. A stability proof is obtained by the application of the LaSalle’s invariance principle.

Citation

• Journal: 2019 IEEE 58th Conference on Decision and Control (CDC)
• Year: 2019
• Volume:
• Issue:
• Pages: 6857–6862
• Publisher: IEEE
• DOI: 10.1109/cdc40024.2019.9029487

BibTeX

@inproceedings{Brugnoli_2019,
  title={{Interconnection of the Kirchhoff plate within the port-Hamiltonian framework}},
  DOI={10.1109/cdc40024.2019.9029487},
  booktitle={{2019 IEEE 58th Conference on Decision and Control (CDC)}},
  publisher={IEEE},
  author={Brugnoli, Andrea and Alazard, Daniel and Pommier-Budinger, Valerie and Matignon, Denis},
  year={2019},
  pages={6857--6862}
}

Download the bib file

References

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