Discrete IDA-PBC control law for Newtonian mechanical port-Hamiltonian systems

Authors

Said Aoues, Damien Eberard, Wilfrid Marquis-Favre

Abstract

This paper deals with the stability of discrete closed-loop dynamics arising from digital IDA-PBC controller design. This work concerns the class of Newtonian mechanical port-Hamiltonian systems (PHSs), that is those having separable energy being quadrating in momentum (with constant mass matrix). We first introduce a discretization scheme which ensures a passivity equation relatively to the same storage and dissipation functions as the continuous-time PHS. A discrete controller is then obtained following the IDA-PBC design procedure applied to the discrete PHS system. This method guarantees that, from an energetic viewpoint, the discrete closed-loop behavior is similar to the continuous one. Under zero-state observability assumption, closed-loop stability then follows from LaSalle principle. The method is illustrated on an inertia wheel pendulum model.

Citation

• Journal: 2015 54th IEEE Conference on Decision and Control (CDC)
• Year: 2015
• Volume:
• Issue:
• Pages: 4388–4393
• Publisher: IEEE
• DOI: 10.1109/cdc.2015.7402904

BibTeX

@inproceedings{Aoues_2015,
  title={{Discrete IDA-PBC control law for Newtonian mechanical port-Hamiltonian systems}},
  DOI={10.1109/cdc.2015.7402904},
  booktitle={{2015 54th IEEE Conference on Decision and Control (CDC)}},
  publisher={IEEE},
  author={Aoues, Said and Eberard, Damien and Marquis-Favre, Wilfrid},
  year={2015},
  pages={4388--4393}
}

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