Authors

Paul Kotyczka, Delgado L. Sergio

Abstract

A well-known problem in controller design for underactuated mechanical systems using the Interconnection and Damping Assignment (IDA-PBC) technique is friction in unactuated degrees of freedom. For certain equilibria the definiteness requirements on the virtual energy of the port-Hamiltonian (pH) target system and the closed-loop dissipation matrix can not be satisfied simultaneously. In this contribution a modification of the pH target system is proposed, where particularly the total energy function is augmented by a cross term between coordinates and momenta. The approach stems from the fact that, although IDA-PBC may fail, unstable equilibria of underactuated mechanical systems are stabilized by linear state feedback, if the linearization is stabilizable. Then the solution of a Lyapunov equation for the linearized closed-loop system is not block diagonal, which gives rise to the proposed structure of the energy.

Keywords

Underactuated mechanical systems; port-Hamiltonian systems; passivity based control; physical damping.

Citation

  • Journal: IFAC Proceedings Volumes
  • Year: 2012
  • Volume: 45
  • Issue: 19
  • Pages: 149–154
  • Publisher: Elsevier BV
  • DOI: 10.3182/20120829-3-it-4022.00007
  • Note: 4th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control

BibTeX

@article{Kotyczka_2012,
  title={{On a generalized port-Hamiltonian representation for the control of damped underactuated mechanical systems}},
  volume={45},
  ISSN={1474-6670},
  DOI={10.3182/20120829-3-it-4022.00007},
  number={19},
  journal={IFAC Proceedings Volumes},
  publisher={Elsevier BV},
  author={Kotyczka, Paul and Sergio, Delgado L.},
  year={2012},
  pages={149--154}
}

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References