Observer Design for a Class of Nonlinear Hamiltonian Systems

Authors

Michael Rojas, Christian Granados-Salazar, Gerardo Espinosa-Pérez

Abstract

In this paper, the observer design problem for Port-Controlled Hamiltonian systems is approached. It is considered a particular class of these systems and a full-order order observer is proposed which belongs to the Structure Preserving approach since it is a copy of the original system with an output corrective term. Concerning the class of systems, it corresponds to nonlinear systems that exhibit nonlinearities given by the products between components of the state vector. The fact that this kind of behavior corresponds to a special property of the interconnection matrix is exploited to obtain a representation for the estimation error dynamics that is suitable to formally state the convergence properties of the observer. The usefulness of the contribution is illustrated by solving the speed observation problem for a Permanent Magnet Synchronous Motor.

Keywords

Port-Controlled Hamiltonian System; Nonlinear observers; Structure preserving observers

Citation

• Journal: IFAC-PapersOnLine
• Year: 2021
• Volume: 54
• Issue: 19
• Pages: 125–130
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2021.11.066
• Note: 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021- Berlin, Germany, 11-13 October 2021

BibTeX

@article{Rojas_2021,
  title={{Observer Design for a Class of Nonlinear Hamiltonian Systems}},
  volume={54},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2021.11.066},
  number={19},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Rojas, Michael and Granados-Salazar, Christian and Espinosa-Pérez, Gerardo},
  year={2021},
  pages={125--130}
}

Download the bib file

References

• Arcak, Nonlinear observers: a circle criterion design and robustness analysis. Auto-matica (2001)
• Astolfi, (2007)
• Besancon, G. & Tsiclea, A. Regularization approach for an immersion-based observer design. 2018 European Control Conference (ECC) 1951–1956 (2018) doi:10.23919/ecc.2018.8550112 – 10.23919/ecc.2018.8550112
• Lohmiller, W. & Slotine, J.-J. E. Simple observers for Hamiltonian systems. Proceedings of the 1997 American Control Conference (Cat. No.97CH36041) 2748–2753 vol.5 (1997) doi:10.1109/acc.1997.611955 – 10.1109/acc.1997.611955
• Osorio, M. & Moreno, J. A. Dissipative Design of Observers for Multivalued Nonlinear Systems. Proceedings of the 45th IEEE Conference on Decision and Control 5400–5405 (2006) doi:10.1109/cdc.2006.377335 – 10.1109/cdc.2006.377335
• Rajamani, R. Observers for Lipschitz nonlinear systems. IEEE Trans. Automat. Contr. 43, 397–401 (1998) – 10.1109/9.661604
• Shah, D., Espinosa–Pérez, G., Ortega, R. & Hilairet, M. An asymptotically stable sensorless speed controller for non‐salient permanent magnet synchronous motors. Intl J Robust & Nonlinear 24, 644–668 (2012) – 10.1002/rnc.2910
• Venkatraman, A. & van der Schaft, A. J. Full-order observer design for a class of port-Hamiltonian systems. Automatica 46, 555–561 (2010) – 10.1016/j.automatica.2010.01.019
• Yaghmaei, A. & Yazdanpanah, M. J. Structure Preserving Observer Design for Port-Hamiltonian Systems. IEEE Trans. Automat. Contr. 64, 1214–1220 (2019) – 10.1109/tac.2018.2847904