A Family of Pumping-Damping Smooth Strategies for Swinging Up a Pendulum

  • Javier Aracil
  • Francisco Gordillo
  • Karl J. Åström
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 366)


In this paper we present some additional results regarding the pumping-damping strategy for swinging up a pendulum introduced in [3]. Here, the family of energy functions is enlarged and the corresponding pumping-damping functions are proposed giving rise to new smooth controllers that swing up and stabilize the pendulum. Furthermore, a generalization of the stability criterion is introduced for this larger class of controllers.


Pendulum Shaping Hamiltonians Swing-up Energy management 


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  1. 1.
    José Ángel Acosta. Nonlinear control of underactuated systems. PhD thesis, University of Seville, 2004. In Spanish.Google Scholar
  2. 2.
    J. Aracil and F. Gordillo. The inverted pendulum: A challenge for nonlinear control (in Spanish). Revista Iberoamericana de Automätica e Informätica Industrial, 2(2): 8–19, 2005.Google Scholar
  3. 3.
    K. J. Åström, J. Aracil, and F. Gordillo. A new family of smooth strategies for swinging up a pendulum. In 16 th IFAC World Congress. Prague, 2005.Google Scholar
  4. 4.
    K.J. Åström and K. Furuta. Swinging up a pendulum by energy control. Automatica, 36:287–295, 2000.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Javier Aracil
    • 1
  • Francisco Gordillo
    • 1
  • Karl J. Åström
    • 2
  1. 1.Escuela Superior de IngenierosUniversidad de SevillaSevillaSpain
  2. 2.Department of Automatic Control LTHLund UniversityLund.Sweden

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