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Proportional observer design for port Hamiltonian systems using the contraction analysis approach

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Abstract

A simple proportional observer design method is presented for a class of linear port Hamiltonian systems. This observer design approach is based on the use of a powerful tool derived from continuum mechanics and differential geometry, known as contraction analysis. Under two verifiable assumptions, it is shown that error dynamics between the plant and the observer states converges exponentially to zero. Finally, our design method is applied to two physical systems arising from different domains: The DC motor and the RLC circuit.

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References

  1. Duindam V, Macchelli A, Stramigioli S, Bruyninckx H (2009) Modeling and control of complex physical systems-the port-hamiltonian approach. Springer, Berlin

    Book  Google Scholar 

  2. Maschke B, Van Der Schaft A, Breedveld PC (1992) An intrinsic Hamiltonian formulation of network dynamics: non-standard Poisson structures and gyrators. J Franklin Inst 329(5):923–966

    Article  MathSciNet  Google Scholar 

  3. Van Der Schaft A, Maschke B (1995) The Hamiltonian formulation of energy conserving physical systems with external ports. AEÜ Int J Electron Commun 49:362–371

    Google Scholar 

  4. Van Der Schaft A, Jeltsema D (2014) Port-Hamiltonian systems theory: an introductory overview. Found Trends Syst Control 1(2):173–378

    Article  Google Scholar 

  5. Lohmiller W, Slotine JJE (1998) On contraction analysis for nonlinear-systems. Automatica 34(06):683–696

    Article  MathSciNet  Google Scholar 

  6. Shim H, Seo JH, Teel AR (2003) Nonlinear observer design via passivation of error dynamics. Automatica 39(5):885–892

    Article  MathSciNet  Google Scholar 

  7. Venkatraman A, Van Der Schaft A (2010) Full order observer design for a class of port hamiltonian systems. Automatica 46:555–561

    Article  MathSciNet  Google Scholar 

  8. Vincent B, Hudon N, Lefevre L, Dochain D (2016) Port-Hamiltonian observer design for plasma profile estimation in tokamaks. Ifac-PapersOnline 49(24):093–098

    Article  Google Scholar 

  9. Wang Y, Ge SS, Cheng D (2005) Observer and observer-based H\(\infty \) control of generalized Hamiltonian systems. Sci China Ser F 48(2):211–224

    MathSciNet  MATH  Google Scholar 

  10. Bakhshande F, Söffker D (2015) Proportional-integral-observer: a brief survey with special attention to the actual methods using ACC Benchmark. Ifac-PapersOnLine 48(1):532–537. https://doi.org/10.1016/j.ifacol.2015.05.049

    Article  Google Scholar 

  11. Rakesh PB, Maghade DK, Sondkar SY, Pawar SN (2021) A review of PID control, tuning methods and applications. Int J Dynam Control 9:818–827. https://doi.org/10.1007/s40435-020-00665-4

    Article  MathSciNet  Google Scholar 

  12. Lohmiller W, Slotine JJE (1998) On contraction analysis for nonlinear-systems. Automatica 34(06):683–696

    Article  MathSciNet  Google Scholar 

  13. Lohmiller W, Slotine JJE (2000) Control system design for mechanical systems using contraction theory. IEEE Trans Automat Control 45(05):984–989

    Article  MathSciNet  Google Scholar 

  14. Van Der Schaft A (2000) L2- gain and passivity techniques in nonlinear control. Springer, Berlin

    Book  Google Scholar 

  15. Ortega R, Garçia-Canseco E (2004) Interconnection and damping assignment passivity-based control: a survey. Eur J Control 10(5):432–450

    Article  MathSciNet  Google Scholar 

  16. Khalil HK (2002) Nonlinear systems, 3rd edn. Prentice Hall, New York

    MATH  Google Scholar 

  17. Van Der Schaft A, Maschke B (1995) The Hamiltonian formulation of energy conserving physical systems with external ports. AEÜ Int J Electron Commun 49:362–371

    Google Scholar 

  18. Van Der Schaft A, Jeltsema D (2014) Port-Hamiltonian systems theory: an introductory overview. Found Trends Syst Control 1(2):173–378

    Article  Google Scholar 

  19. Venkatraman A, Van Der Schaft A (2010) Full order observer design for a class of port hamiltonian systems. Automatica 46:555–561

    Article  MathSciNet  Google Scholar 

  20. Medianu S, Lefèvre L (2021) Structural identifiability of linear Port Hamiltonian systems. Syst Control Lett. https://doi.org/10.1016/j.sysconle.2021.104915

    Article  MathSciNet  MATH  Google Scholar 

  21. Navarro D, Cortes D, Galaz-Larios M (2017) A port-Hamiltonian approach to control DC-DC power Ccnverters. Stud Inf Control 26(3):269–276. https://doi.org/10.24846/v26i3y201702

    Article  Google Scholar 

  22. Zhang M, Ortega R, Jeltsema D, Su H (2015) Further deleterious effects of the dissipation obstacle in control-by-interconnection of port Hamiltonian systems. Automatica 61:227–231

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University Chouaib Doukkali, B.P. 20, 24000, El Jadida, Morocco

    Saida Zenfari, Mohamed Laabissi & Mohammed Elarbi Achhab

Authors
  1. Saida Zenfari
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  2. Mohamed Laabissi
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  3. Mohammed Elarbi Achhab
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Correspondence to Saida Zenfari.

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Zenfari, S., Laabissi, M. & Achhab, M.E. Proportional observer design for port Hamiltonian systems using the contraction analysis approach. Int. J. Dynam. Control 10, 403–408 (2022). https://doi.org/10.1007/s40435-021-00830-3

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  • DOI: https://doi.org/10.1007/s40435-021-00830-3

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