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Complex balancing motions of an inverted pendulum subject to delayed feedback control

Research output: Working paperWorking paper and Preprints

  • J Sieber
  • B Krauskopf
Original languageEnglish
Publication date2003
DOIs
StateUnpublished

Abstract

We show that an inverted pendulum that is balanced on a cart by state-dependent delayed control may exhibit small chaotic motion about the upside-down position while the velocity of the cart performs a random walk. In periodic windows associated with this chaotic regime we find periodic orbits of arbitrarily high period that correspond to complex balancing motion of the pendulum with bounded velocity of the cart. This result is obtained by studying homoclinic bifurcations of a reduced three-dimensional vector field near a triple-zero eigenvalue singularity.

Additional information

Additional information: Later published by Elsevier Science, (2004) Physica D: Non Linear Phenomena, 197(3-4), pp. 332-345. ISSN 0167-2789 Sponsorship: The research of J.S. is supported by EPSRC grant GR/R72020/01 and that of B.K. by an EPSRC Advanced Research Fellowship.

Research areas

  • feedback control, homoclinic tangency, balancing motion, delay differential equation, inverted pendulum, triple-zero singularity

Documents

Documents

  • Siekra

    Preprint (usually an early version) , 2 MB, PDF-document

DOI

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