Generating self-excited oscillations for underactuated mechanical systems via two-relay controller

Luis T. Aguilar, Igor Boiko, Leonid Fridman, Rafael Iriarte

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


A tool for the design of a periodic motion in an underactuated mechanical system via generating a self-excited oscillation of a desired amplitude and frequency by means of the variable structure control is proposed. First, an approximate approach based on the describing function method is given, which requires that the mechanical plant should be a linear low-pass filter-the hypothesis that usually holds when the oscillations are relatively fast. The method based on the locus of a perturbed relay systems provides an exact model of the oscillations when the plant is linear. Finally, the Poincare map's design provides the value of the controller parameters ensuring the locally orbitally stable periodic motions for an arbitrary mechanical plant. The proposed approach is shown by the controller design and experiments on the Furuta pendulum.

Original languageBritish English
Pages (from-to)1678-1691
Number of pages14
JournalInternational Journal of Control
Issue number9
StatePublished - Sep 2009


  • Frequency domain methods
  • Periodic solution
  • Underactuated systems
  • Variable structure systems


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