Port-Hamiltonian modeling, discretization and feedback control of a circular water tank

Authors

Flavio Luiz Cardoso-Ribeiro, Andrea Brugnoli, Denis Matignon, Laurent Lefevre

Abstract

This work presents the development of the nonlinear 2D Shallow Water Equations (SWE) in polar coordinates as a boundary port controlled Hamiltonian system. A geometric reduction by symmetry is obtained, simplifying the system to one-dimension. The recently developed Partitioned Finite Element Method is applied to semi-discretize the equations, preserving the boundary power-product of both the original 2D and the reduced 1D system. The main advantage of this power-preserving semi-discretization method is that it can be applied using well-established finite element software. In this work, we use FEniCS to solve the variational formulation, including the nonlinearity provided by the non-quadratic Hamiltonian of the SWE. A passive output-feedback controller using damping injection is used to dissipate the water waves.

Citation

• Journal: 2019 IEEE 58th Conference on Decision and Control (CDC)
• Year: 2019
• Volume:
• Issue:
• Pages: 6881–6886
• Publisher: IEEE
• DOI: 10.1109/cdc40024.2019.9030007

BibTeX

@inproceedings{Cardoso_Ribeiro_2019,
  title={{Port-Hamiltonian modeling, discretization and feedback control of a circular water tank}},
  DOI={10.1109/cdc40024.2019.9030007},
  booktitle={{2019 IEEE 58th Conference on Decision and Control (CDC)}},
  publisher={IEEE},
  author={Cardoso-Ribeiro, Flavio Luiz and Brugnoli, Andrea and Matignon, Denis and Lefevre, Laurent},
  year={2019},
  pages={6881--6886}
}

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References

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