Authors

A. Venkatraman, A.J. van der Schaft

Abstract

We consider a special class of port-Hamiltonian systems for which we propose a design methodology for constructing globally exponentially stable full-order observers using a passivity based approach. The essential idea is to make the augmented system consisting of the plant and the observer dynamics to become strictly passive with respect to an invariant manifold defined on the extended state-space, on which the state estimation error is zero. We first introduce the concept of passivity of a system with respect to a manifold by defining a new input and output on the extended state-space and then perform a partial state feedback passivation which leads to the construction of the observer. We then illustrate this observer design procedure on two physical examples, the magnetic levitation system and the inverted pendulum on the cart system.

Keywords

Port-Hamiltonian systems; Observer design; Passivity

Citation

BibTeX

@article{Venkatraman_2010,
  title={{Full-order observer design for a class of port-Hamiltonian systems}},
  volume={46},
  ISSN={0005-1098},
  DOI={10.1016/j.automatica.2010.01.019},
  number={3},
  journal={Automatica},
  publisher={Elsevier BV},
  author={Venkatraman, A. and van der Schaft, A.J.},
  year={2010},
  pages={555--561}
}

Download the bib file

References

  • 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
  • Arcak, M. & Kokotović, P. Nonlinear observers: a circle criterion design and robustness analysis. Automatica vol. 37 1923–1930 (2001) – 10.1016/s0005-1098(01)00160-1
  • Arcak, M. & Kokotovic, P. Observer-based control of systems with slope-restricted nonlinearities. IEEE Transactions on Automatic Control vol. 46 1146–1150 (2001) – 10.1109/9.935073
  • Astolfi, (2008)
  • Besancon, G. On output transformations for state linearization up to output injection. IEEE Transactions on Automatic Control vol. 44 1975–1981 (1999) – 10.1109/9.793789
  • Byrnes, C. I., Isidori, A. & Willems, J. C. Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems. IEEE Transactions on Automatic Control vol. 36 1228–1240 (1991) – 10.1109/9.100932
  • Fan, X. & Arcak, M. Observer design for systems with multivariable monotone nonlinearities. Systems & Control Letters vol. 50 319–330 (2003) – 10.1016/s0167-6911(03)00170-1
  • Hammouri, Bilinearization up to output injection. Systems & Control Letters (1989)
  • Zhong-Ping Jiang & Hill, D. J. Passivity and disturbance attenuation via output feedback for uncertain nonlinear systems. IEEE Transactions on Automatic Control vol. 43 992–997 (1998) – 10.1109/9.701109
  • Karagiannis, D. & Astolfi, A. Observer design for a class of nonlinear systems using dynamic scaling with application to adaptive control. 2008 47th IEEE Conference on Decision and Control 2314–2319 (2008) doi:10.1109/cdc.2008.4739140 – 10.1109/cdc.2008.4739140
  • Krener, A. J. & Respondek, W. Nonlinear Observers with Linearizable Error Dynamics. SIAM Journal on Control and Optimization vol. 23 197–216 (1985) – 10.1137/0323016
  • Levine, J. & Marino, R. Nonlinear system immersion, observers and finite-dimensional filters. Systems & Control Letters vol. 7 133–142 (1986) – 10.1016/0167-6911(86)90019-8
  • Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
  • Rajamani, R. Observers for Lipschitz nonlinear systems. IEEE Transactions on Automatic Control vol. 43 397–401 (1998) – 10.1109/9.661604
  • Shastry, (1999)
  • Shim, H., Seo, J. H. & Teel, A. R. Nonlinear observer design via passivation of error dynamics. Automatica vol. 39 885–892 (2003) – 10.1016/s0005-1098(03)00023-2
  • Teel, A. R. A nonlinear small gain theorem for the analysis of control systems with saturation. IEEE Transactions on Automatic Control vol. 41 1256–1270 (1996) – 10.1109/9.536496
  • THAU, F. E. Observing the state of non-linear dynamic systems. International Journal of Control vol. 17 471–479 (1973) – 10.1080/00207177308932395
  • Tsinias, J. Observer design for nonlinear systems. Systems & Control Letters vol. 13 135–142 (1989) – 10.1016/0167-6911(89)90030-3
  • van der Schaft, (1999)
  • Venkatraman, A., Ortega, R., Sarras, I. & van der Schaft, A. Control of underactuated mechanical systems: Observer design and position feedback stabilization. 2008 47th IEEE Conference on Decision and Control 4969–4975 (2008) doi:10.1109/cdc.2008.4738912 – 10.1109/cdc.2008.4738912
  • Xia, X.-H. & Gao, W.-B. Nonlinear Observer Design by Observer Error Linearization. SIAM Journal on Control and Optimization vol. 27 199–216 (1989) – 10.1137/0327011