Authors

D.A. Dirksz, J.M.A. Scherpen, R. Ortega

Abstract

A dynamic extension for position feedback of port-Hamiltonian mechanical systems is studied. First we look at the consequences for the matching equations when applying Inter-connection and Damping Assignment Passivity-Based Control (IDA-PBC). Then we look at the possibilities of asymptotically stabilizing a class of port-Hamiltonian mechanical systems without having to know the velocities, as once presented for Euler-Lagrange (EL) systems. Here it is shown how the idea of damping injection by dynamic extension works when shaping the total energy in the port-Hamiltonian framework.

Citation

  • Journal: 2008 47th IEEE Conference on Decision and Control
  • Year: 2008
  • Volume:
  • Issue:
  • Pages: 4957–4962
  • Publisher: IEEE
  • DOI: 10.1109/cdc.2008.4738841

BibTeX

@inproceedings{Dirksz_2008,
  title={{Interconnection and Damping Assignment Passivity-Based Control for port-Hamiltonian mechanical systems with only position measurements}},
  DOI={10.1109/cdc.2008.4738841},
  booktitle={{2008 47th IEEE Conference on Decision and Control}},
  publisher={IEEE},
  author={Dirksz, D.A. and Scherpen, J.M.A. and Ortega, R.},
  year={2008},
  pages={4957--4962}
}

Download the bib file

References

  • astolfi, dynamic extension is unnecessary for stabilization via interconnection and damping assignment passivity-based control. 40th IEEE Conf Decision and Control (2008)
  • Gómez-Estern, F. & Van der Schaft, A. J. Physical Damping in IDA-PBC Controlled Underactuated Mechanical Systems. European Journal of Control vol. 10 451–468 (2004) – 10.3166/ejc.10.451-468
  • Cheng, D., Astolfi, A. & Ortega, R. On feedback equivalence to port controlled Hamiltonian systems. Systems & Control Letters vol. 54 911–917 (2005) – 10.1016/j.sysconle.2005.02.005
  • van der Burg, J. C. M., Ortega, R., Scherpen, J. M. A., Acosta, J. A. & Siguerdidjane, H. B. An experimental application of Total Energy Shaping Control: Stabilization of the inverted pendulum on a cart in the presence of friction. 2007 European Control Conference (ECC) 1990–1996 (2007) doi:10.23919/ecc.2007.7068504 – 10.23919/ecc.2007.7068504
  • Acosta, J. A., Ortega, R., Astolfi, A. & Mahindrakar, A. D. Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one. IEEE Transactions on Automatic Control vol. 50 1936–1955 (2005) – 10.1109/tac.2005.860292
  • Ortega, R., Spong, M. W., Gomez-Estern, F. & Blankenstein, G. Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Transactions on Automatic Control vol. 47 1218–1233 (2002) – 10.1109/tac.2002.800770
  • Blankenstein, G., Ortega, R. & Van Der Schaft, A. J. The matching conditions of controlled Lagrangians and IDA-passivity based control. International Journal of Control vol. 75 645–665 (2002) – 10.1080/00207170210135939
  • Ortega, R. & García-Canseco, E. Interconnection and Damping Assignment Passivity-Based Control: A Survey. European Journal of Control vol. 10 432–450 (2004) – 10.3166/ejc.10.432-450
  • stramigioli, passive output feedback and port interconnection. Proceedings of 4th IFAC Symposium on Nonlinear Control Systems (1998)
  • Ortega, R., Loría, A., Nicklasson, P. J. & Sira-Ramírez, H. Passivity-Based Control of Euler-Lagrange Systems. Communications and Control Engineering (Springer London, 1998). doi:10.1007/978-1-4471-3603-3 – 10.1007/978-1-4471-3603-3
  • Bloch, A. M., Leonard, N. E. & Marsden, J. E. Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem. IEEE Transactions on Automatic Control vol. 45 2253–2270 (2000) – 10.1109/9.895562
  • satoru sakai, Dynamic Output Feedback Stabilization for a class of Nonholonomic Hamiltonian Systems. SICE 2004 Annual Conference (2004)
  • van der schaft, theory of port-hamiltonian systems. Network Modeling and Control of Physical Systems DISC course (2005)