Energy shaping control revisited

  • Romeo Ortega
  • Arjan J. van der Schaft
  • Iven Mareels
  • Bernhard Maschke
Part IV Physics In Control
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 264)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. C. Willems, “Paradigms and puzzles in the theory of dynamical systems,” IEEE Trans. Automat. Contr., 36, pp. 259–294, 1991.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    A. J., van der Schaft, L 2-Gain and Passivity Techniques in Nonlinear Control, Springer-Verlag, Berlin, 1999.Google Scholar
  3. 3.
    M. Takegaki and S. Arimoto, “A new feedback method for dynamic control of manipulators,” ASME J. Dyn. Syst. Meas. Cont., 102, pp. 119–125, 1981.Google Scholar
  4. 4.
    E. Jonckheere, “Lagrangian theory of large scale systems,” Proc. European Conf. Circuit Th. and Design, The Hague, The Netherlands, pp. 626–629, 1981.Google Scholar
  5. 5.
    J. J. Slotine, “Putting physics in control — The example of robotics,” IEEE Control Syst. Magazine, 8, 6, pp. 12–17, 1988.CrossRefGoogle Scholar
  6. 6.
    N. Hogan, “Impedance control: an approach to manipulation: part 1 — Theory,” ASME J. Dyn. Syst. Measure and Control, 107, pp 1–7, March 1985.MATHCrossRefGoogle Scholar
  7. 7.
    R. Ortega and M. Spong, “Adaptive motion control of rigid robots: A tutorial,” Automatica, 25, 6, pp. 877–888, 1989.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    R. Ortega, A. van der Schaft, B. Maschke and G. Escobar, “Interconnection and damping assignment passivity based control of port-controlled Hamiltonian systems,” Automatica, (to be published).Google Scholar
  9. 9.
    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
  10. 10.
    V. Petrovic, R. Ortega, A. Stankovic and G. Tadmor, “Design and implementation of an adaptive controller for torque ripple minimization in PM synchronous motors”, IEEE Trans. on Power Electronics, Vol. 15, No. 5, Sept. 2000, pp. 871–880.CrossRefGoogle Scholar
  11. 11.
    H. Berghuis and H. Nijmeijer, “A passivity approach to controller-observer design for robots,” IEEE Trans. on Robotics and Automation, 9, 6, pp. 740–754, 1993.CrossRefGoogle Scholar
  12. 12.
    L. Lanari and J. Wen, “Asymptotically stable set point control laws for flexible robots,” Systems and Control Letters, 19, 1992.Google Scholar
  13. 13.
    A. Sorensen and O. Egeland, “Design of ride control system for surface effect ships using dissipative control,” Automatica, 31, 2, pp. 183–1999, 1995.CrossRefMathSciNetGoogle Scholar
  14. 14.
    R. Prasanth and R. Mehra, “Nonlinear servoelastic control using Euler-Lagrange theory,” Proc. Int. Conf. American Inst. Aeronautics and Astronautics, Detroit, pp. 837–847, Aug, 1999.Google Scholar
  15. 15.
    R. Akemialwati and I. Mareels, “Flight control systems using passivity-based control: Disturbance rejection and robustness analysis,” Proc. Int. Conf. American Inst. Aeronautics and Astronautics, Detroit, Aug, 1999.Google Scholar
  16. 16.
    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, Dec. 1998. Also IEEE Trans. Automat. Contr., (to appear).Google Scholar
  17. 17.
    R. Ortega, A. van der Schaft, B. Maschke and G. Escobar, “Energy-shaping of port-controlled Hamiltonian systems by interconnection,” IEEE Conf. Dec. and Control, Phoenix, AZ, Dec. 1999.Google Scholar
  18. 18.
    R. Ortega, A. Astolfi, G. Bastin and H. Rodriguez, “Output-feedback regulation of mass-balance systems,” in New Directions in Nonlinear Observer Design, eds. H. Nijmeijer and T. Fossen, Springer-Verlag, Berlin, 1999.Google Scholar
  19. 19.
    V. Petrovic, R. Ortega and A. Stankovic, “A globally convergent energy-based controller for PM synchronous motors,” CDC'99, Phoenix, AZ, Dec. 7–10, 1999. Also to appear in IEEE Trans. on Control Syst. Technology.Google Scholar
  20. 20.
    R. Ortega, M. Galaz, A. Bazanella and A. Stankovic, “Output feedback stabilization of the single-generator-infinite-bus system,” (under preparation).Google Scholar
  21. 21.
    H. Rodriguez, R. Ortega and I. Mareels, “Nonlinear control of magnetic levitation sysstems via energy balancing,” ACC 2000, Chicago, June 2000.Google Scholar
  22. 22.
    H. Rodriguez, R. Ortega, G. Escobar and N. Barabanov, “A robustly stable output feedback saturated controller for the boost DC-to-DC converter,” Systems and Control Letters, 40, 1, pp. 1–6, 2000.MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    J. Scherpen, and R. Ortega, “Disturbance attenuation properties of nonlinear controllers for Euler-Lagrange systems,” Systems and Control Letters., 29, 6, pp. 300–308, March 1997.MathSciNetGoogle Scholar
  24. 24.
    A. Rodriguez, R. Ortega and G. Espinosa, “Adaptive control of nonfeedback linearizable systems,” 11th World IFAC Congress, Aug. 13–17, Tallinn, 1990.Google Scholar
  25. 25.
    P. Kokotovic and H. Sussmann, “A positive real condition for global stabilization of Nonlinear systems,” Systems and Control Letters, 13, 4, pp. 125–133, 1989.MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    R. Sepulchre, M. Jankovic and P. Kokotovic, Constructive Nonlinear Control, Springer-Verlag Series on Communications and Control Engineering, Springer-Verlag, London, 1997.Google Scholar
  27. 27.
    M. Krstić, I. Kanellakopoulos and P. V. Kokotović, Nonlinear and Adaptive Control Design, Wiley, New York, 1995.Google Scholar
  28. 28.
    R. Ortega and M. Spong, “Stabilization of underactuated mechanical systems using interconnection and damping assignment,” IFAC Work. on Lagrangian and Hamiltonian Methods in Nonlinear Control, Princeton, NJ, March 15–17, 2000.Google Scholar
  29. 29.
    A. Bloch, N. Leonhard and J. Marsden, “Controlled Lagrangians and the stabilization of mechanical systems,” Proc. IEEE Conf. Decision and Control, Tampa, FL, Dec. 1998.Google Scholar
  30. 30.
    M. Spong and L. Praly, “Control of underactuated mechanical systems using switching and saturation,” in Control Using Logic-based Switching, Ed. A. S. Morse, Springer, Lecture Notes No. 222, pp. 162–172, 1996.Google Scholar
  31. 31.
    D. Hill and P. Moylan, “The stability of nonlinear dissipative systems,” IEEE Trans. Automat. Contr., pp. 708–711, 1976.Google Scholar
  32. 32.
    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
  33. 33.
    J. Marsden and T. Ratiu, Introduction to Mechanics and Symmetry, Springer, New York, 1994.MATHGoogle Scholar
  34. 34.
    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, 5, 4, pp. 313–324, July 1995.Google Scholar
  35. 35.
    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, July 1–3, 1998.Google Scholar
  36. 36.
    A.M. Bloch, N.E. Leonard, J.E. Marsden, “Potential shaping and the method of controlled Lagrangians,” 38th Conf. Decision and Control, Phoenix, Arizona, pp. 1652–1657, 1999.Google Scholar
  37. 37.
    D. Auckly, L. Kapitanski, W. White, “Control of nonlinear underactuated systems,” Communications on Pure and Applied Mathematics, Vol. LIII, 2000.Google Scholar
  38. 38.
    J. Hamberg, “General matching conditions in the theory of controlled Lagrangians,” 38th Conf. Decision and Control, Phoenix, Arizona, pp. 2519–2523, 1999.Google Scholar

Copyright information

© Springer-Verlag London Limited 2001

Authors and Affiliations

  • Romeo Ortega
    • 1
  • Arjan J. van der Schaft
    • 2
  • Iven Mareels
    • 3
  • Bernhard Maschke
    • 4
  1. 1.Lab. des Signaux et Systèmes, CNRS-SUPELECGif-sur-YvetteFrance
  2. 2.Fac. of Mathematical SciencesUniversity of TwenteEnschedeThe Netherlands
  3. 3.Dept. Electrical and Computer EngineeringUniversity of MelbourneAustralia
  4. 4.Automatisme IndustrielParisFrance

Personalised recommendations