Discrete IDA-PBC design for 2D port-Hamiltonian systems

Authors

Said Aoues, Damien Eberard, Wilfrid Marquis-Favre

Abstract

We address the discrete-time passivity-based control laws synthesis within port-Hamiltonian framework. We focus on IDA-PBC design for canonical port-Hamiltonian systems with separable energy being quadratic in momentum. For this class of systems, we define a discrete Hamiltonian dynamics that exactly satisfies a discrete energy balance. We then derive a discrete controller following the IDA-PBC procedure. The proposed methodology relies on an energy discretization scheme with suitable discrete conjugate port variables. The main result is illustrated on two examples: a nonlinear pendulum in order to compare with some simulation results of the literature, and the impact oscillator which requires robust discretization scheme.

Citation

Journal: IFAC Proceedings Volumes
Year: 2013
Volume: 46
Issue: 23
Pages: 134–139
Publisher: Elsevier BV
DOI: 10.3182/20130904-3-fr-2041.00088
Note: 9th IFAC Symposium on Nonlinear Control Systems

BibTeX

@article{Aoues_2013,
  title={{Discrete IDA-PBC design for 2D port-Hamiltonian systems}},
  volume={46},
  ISSN={1474-6670},
  DOI={10.3182/20130904-3-fr-2041.00088},
  number={23},
  journal={IFAC Proceedings Volumes},
  publisher={Elsevier BV},
  author={Aoues, Said and Eberard, Damien and Marquis-Favre, Wilfrid},
  year={2013},
  pages={134--139}
}

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References

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