Observer design for a class of nonlinear Hamiltonian systems based on energy function structure

Authors

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

Abstract

In this paper the observer design problem for a class of nonlinear Port-Controlled Hamiltonian (PCH) systems is addressed. The approached class is characterized, first, by considering that the state vector can be divided into measurable and non measurable components and, second, in terms of the structure of the Hamiltonian energy function. Under these conditions, the main contribution of this paper is to propose an observer design methodology that considers as a basic feature the decomposition of the system as the interconnection of two PCH subsystems to obtain a reduced order observer. Regarding the Hamiltonian function, it is proved that the proposed methodology is able to deal with the same energy function that, to be best of the authors knowledge, is considered as the state-of-the-art contribution of the field. The proposed observer design is evaluated in a magnetic levitation system comparing its convergence characteristics with respect to another kind of observer that is reported in the literature.

Keywords

magnetic levitation system, nonlinear observers, port-controlled hamiltonian systems, reduced order observer

Citation

• Journal: IFAC-PapersOnLine
• Year: 2024
• Volume: 58
• Issue: 6
• Pages: 178–183
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2024.08.277
• Note: 8th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2024- Besançon, France, June 10 – 12, 2024

BibTeX

@article{Granados_Salazar_2024,
  title={{Observer design for a class of nonlinear Hamiltonian systems based on energy function structure}},
  volume={58},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2024.08.277},
  number={6},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Granados-Salazar, Christian and Rojas, Michael and Espinosa-Pérez, Gerardo},
  year={2024},
  pages={178--183}
}

Download the bib file

References

• Biedermann B, Meurer T (2021) Observer design for a class of nonlinear systems combining dissipativity with interconnection and damping assignment. Intl J Robust & Nonlinear 31(9):4064–4080. https://doi.org/10.1002/rnc.546 – 10.1002/rnc.5461
• Espinosa-Pérez G, Maya-Ortíz P, Dòria-Cerezo A, Moreno JA (2010) Output-feedback IDA stabilisation of an SMIB system using a TCSC. International Journal of Control 83(12):2471–2482. https://doi.org/10.1080/00207179.2010.53114 – 10.1080/00207179.2010.531145
• Maschke BM, van der Schaft AJ (1993) PORT-CONTROLLED HAMILTONIAN SYSTEMS: MODELLING ORIGINS AND SYSTEMTHEORETIC PROPERTIES. Nonlinear Control Systems Design 1992 359–36 – 10.1016/b978-0-08-041901-5.50064-6
• Maya‐Ortiz P, Espinosa‐Pérez G (2004) Output feedback excitation control of synchronous generators. Intl J Robust & Nonlinear 14(9–10):879–890. https://doi.org/10.1002/rnc.91 – 10.1002/rnc.912
• Ortega R, van der Schaft A, Maschke B, Escobar G (2002) Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38(4):585–596. https://doi.org/10.1016/s0005-1098(01)00278- – 10.1016/s0005-1098(01)00278-3
• Pfeifer M, Caspart S, Strehle F, Hohmann S (2021) Full-Order Observer Design for a Class of Nonlinear Port-Hamiltonian Systems. IFAC-PapersOnLine 54(19):149–154. https://doi.org/10.1016/j.ifacol.2021.11.07 – 10.1016/j.ifacol.2021.11.070
• Rojas M, Granados-Salazar C, Espinosa-Pérez G (2021) Observer Design for a Class of Nonlinear Hamiltonian Systems. IFAC-PapersOnLine 54(19):125–130. https://doi.org/10.1016/j.ifacol.2021.11.06 – 10.1016/j.ifacol.2021.11.066
• Venkatraman A, van der Schaft AJ (2010) Full-order observer design for a class of port-Hamiltonian systems. Automatica 46(3):555–561. https://doi.org/10.1016/j.automatica.2010.01.01 – 10.1016/j.automatica.2010.01.019
• Venkatraman A, Ortega R, Sarras I, van der Schaft A (2010) Speed Observation and Position Feedback Stabilization of Partially Linearizable Mechanical Systems. IEEE Trans Automat Contr 55(5):1059–1074. https://doi.org/10.1109/tac.2010.204201 – 10.1109/tac.2010.2042010
• Vincent B, Hudon N, Lefèvre L, Dochain D (2016) Port-Hamiltonian observer design for plasma profile estimation in tokamaks. IFAC-PapersOnLine 49(24):93–98. https://doi.org/10.1016/j.ifacol.2016.10.76 – 10.1016/j.ifacol.2016.10.761
• Yaghmaei A, Yazdanpanah MJ (2019) Structure Preserving Observer Design for Port-Hamiltonian Systems. IEEE Trans Automat Contr 64(3):1214–1220. https://doi.org/10.1109/tac.2018.284790 – 10.1109/tac.2018.2847904
• Zenfari S, Laabissi M, Achhab ME (2021) Proportional observer design for port Hamiltonian systems using the contraction analysis approach. Int J Dynam Control 10(2):403–408. https://doi.org/10.1007/s40435-021-00830- – 10.1007/s40435-021-00830-3