Skip to main content
SpringerLink
Log in

Stabilization of port-controlled Hamiltonian systems via energy balancing

  • Conference paper
  • First Online:
Stability and Stabilization of Nonlinear Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 246))

Abstract

Passivity-based control (PBC) for regulation of mechanical systems is a well established tehcnique that yields robust controllers that have a clear physical interpretation in terms of interconnection of the system with its environment. In particular, the total energy of the closed-loop is the difference between the energy of the system and the energy supplied by the controller. Furthermore, since the Euler-Lagrange (EL) structure is preserved in closed-loop, PBC is robustly stable vis á vis unmodeled dissipative effects and inherits some robust performance measures from its inverse optimality. Unfortunately, these nice properties are lost when PBC is used in other applications, for instance, in electrical and electromechanical systems. Our main objective in this paper is to develop a new PBC theory for port-controlled Hamiltonian (PCH) systems, which result from the network modeling of energy-conserving lumped-parameter physical systems with independent storage elements, and strictly contain the class of EL models. We identify a class of PCH models for which PBC ensures the Hamiltonian structure is preserved, with storage function the energy balance. One final advantage of the method is that it is rather systematic and the controller can be easily derived using symbolic computation

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Ailon and R. Ortega, An observer-based set-point controller for robot manipulators with flexible joints, System & Control Letters, Vol. 21,No. 4, pp. 329–335, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Bloch, P. Krishnaprasad, J. Marsden and G. Sanchez, Stabilization of rigid body dynamics by internal nad external torques, Automatica, Vol. 28,No. 4, pp. 745–756, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  3. M. Dalsmo and A.J. van der Schaft, On representations and integrability of mathematical structures in energy-conserving physical systems, SIAM J. on Optimization and Control), Vol.37,No. 1, 1999.

    Google Scholar 

  4. G. Escobar, A. van der Schaft and R. Ortega, A hamiltonian viewpoint in the modeling of switching power converters, Automatica, Vol. 35, 1999.

    Google Scholar 

  5. H. Khalil, Nonlinear systems, Second Ed. Prentice-Hall, New Jersey, 1996.

    Google Scholar 

  6. P. C. Krause, Analysis of Electric Machinery, McGraw-Hill, 1986.

    Google Scholar 

  7. P. Libermann and C.M. Marle, Symplectic Geometry and Analytical Mechanics. Reidel, Dordrecht, 1987.

    MATH  Google Scholar 

  8. A. Bloch, N. Leonhard and J. Marsden, Controlled Lagrangians and the stabilization of mechanical systems, Proc. IEEE Conf. Decision and Control, Tampa, FL, USA, Dec. 1998.

    Google Scholar 

  9. A. Loria, R. Kelly, R. Ortega and V. Santibanez, On output feedback control of Euler-Lagrange systems with bounded inputs, IEEE Trans. Automat. Contr., Vol. 42,No. 8, 1997, pp. 1138–1143.

    Article  MATH  MathSciNet  Google Scholar 

  10. J. Marsden and T. Ratiu, Introduction to mechanics and symmetry, Springer, NY, 1994.

    MATH  Google Scholar 

  11. B. M. Maschke and A.J. van der Schaft, Port controlled Hamiltonian systems: modeling origins and system theoretic properties, Proc. 2nd IFAC Symp. on Nonlinear Control Systems design, NOLCOS’92, pp.282–288, Bordeaux, June 1992.

    Google Scholar 

  12. B. M. Maschke, A. J. van der Schaft and P. Breedveld, An intrinsic Hamiltonian formulation of network dynamics: Non-standard Poisson structures and gyrators, J. Franklin Inst., 329 (1992), pp. 923–926.

    Article  MATH  MathSciNet  Google Scholar 

  13. B. M. Maschke, Interconnection and structure in physical systems’ dynamics, 4th IFAC Symp. on Nonlinear Control Systems Design, NOLCOS’98, pp.291–296, Enschede, the Netherlands, July 1–3, 1998

    Google Scholar 

  14. B. M. Maschke, R. Ortega and A. J. van der Schaft, Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation, IEEE Conf. Dec. and Control, Tampa, FL, USA, Dec. 1998.

    Google Scholar 

  15. R. Ortega and M. Spong, Adaptive motion control of rigid robots: A tutorial, Automatica, Vol. 25,No.6, pp. 877–888, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  16. R. Ortega, A. Loria, P. J. Nicklasson and H. Sira-Ramirez, Passivity-based control of Euler-Lagrange systems, Springer-Verlag, Berlin, Communications and Control Engineering, Sept. 1998.

    Google Scholar 

  17. R. Ortega, A. Loria, R. Kelly and L. Praly, On output feedback global stabilization of Euler-Lagrange systems, Int. J. of Robust and Nonlinear Cont., Special Issue on Mechanical Systems, Eds. H. Nijmeijer and A. van der Schaft, Vol. 5,No.4, pp. 313–324, July 1995.

    Google Scholar 

  18. R. Ortega, A. Astolfi, G. Bastin and H. Rodriguez, Output feedback stabilization of mass-balance systems, in Output-feedback stabilization of nonlinear systems, Eds. H. Nijmeijer and T. Fossen, Springer-Verlag, 1999.

    Google Scholar 

  19. R. Ortega, A.J. van der Schaft, B. Maschke and G. Escobar, Stabilization of port-controlled Hamiltonian systems: Energy-balancing and passivation, CDC’99, Phoenix, AZ, USA, Dec. 7–10, 1999.

    Google Scholar 

  20. V. Petrovic, R. Ortega and A. Stankovic, An energy-based globally stable controller for PM synchronous motors, Northeastern University Int. Report, Boston, USA, 1999.

    Google Scholar 

  21. H. Rodriguez, R. Ortega and G. Escobar, A Robustly Stable Output Feedback Saturated Controller for the Boost DC-to-DC Converter, Rap. Int. LSS-Supelec, May 1999.

    Google Scholar 

  22. S. Stramigioli, B. M. Maschke and A. J. van der Schaft, Passive output feedback and port interconnection, Proc. 4th IFAC Symp. on Nonlinear Control Systems design, NOLCOS’98, pp. 613–618, Enschede, NL, July 1–3, 1998.

    Google Scholar 

  23. M. Takegaki and S. Arimoto, A new feedback method for dynamic control of manipulators, ASME J. Dyn. Syst. Meas. Cont., Vol. 102, pp. 119–125, 1981.

    Article  Google Scholar 

  24. van der Schaft, A. J., L 2-Gain and Passivity Techniques in Nonlinear Control, Lect. Notes in Contr. and Inf. Sc., Vol. 218, Springer-Verlag, Berlin, 1996.

    Google Scholar 

  25. van der Schaft, A. J., System theory and mechanics, in Three Decades of Mathematical System Theory, H. Nijmeijer and J. M. Schumacher eds., Lect. Notes Contr. Inf. Sci., Vol. 135, pp. 426–452, Springer, Berlin, 1989.

    Chapter  Google Scholar 

  26. A. van der Schaft and B. Maschke, The Hamiltonian formulation of energy-conserving physical systems with external ports, Archiv für Elektronik und Übertragungstechnik, 49 (1995), pp. 362–371.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire des Signaux et Systèmes, C.N.R.S., SUPELEC, 91192, Gif-sur-Yvette, France

    Romeo Ortega

  2. Faculty of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Arjan J. van der Schaft

  3. Centre National des Arts et Métiers, Automatisme Industriel, 21, rue Pinel, 75013, Paris, France

    Bernhard M. Maschke

Authors
  1. Romeo Ortega
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Arjan J. van der Schaft
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bernhard M. Maschke
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Systems Dynamics, Universiteit Gent, Technologiepark-Zwijnaarde 9, 9052, Gent, Belgium

    Dirk Aeyels (Professor) (Professor)

  2. Laboratoire des Signaux et Systèmes, CNRS, SUPELEC, 91192, Gif-sur-Yvette, France

    Françoise Lamnabhi-Lagarrigue (Docteur d’état) (Docteur d’état)

  3. Dept. of Applied Mathematics, University of Twente, PO Box 217, 7500, Enschede, The Netherlands

    Arjan van der Schaft (Professor) (Professor)

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag London Limited

About this paper

Cite this paper

Ortega, R., van der Schaft, A.J., Maschke, B.M. (1999). Stabilization of port-controlled Hamiltonian systems via energy balancing. In: Aeyels, D., Lamnabhi-Lagarrigue, F., van der Schaft, A. (eds) Stability and Stabilization of Nonlinear Systems. Lecture Notes in Control and Information Sciences, vol 246. Springer, London. https://doi.org/10.1007/1-84628-577-1_13

Download citation

  • DOI: https://doi.org/10.1007/1-84628-577-1_13

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-638-7

  • Online ISBN: 978-1-84628-577-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation