Control of near-grazing dynamics in impact oscillators

Harry Dankowicz, Jenny Jerrelind

Research output: Contribution to journalArticlepeer-review

Abstract

A method is presented for controlling the persistence of a local attractor near a grazing periodic trajectory in a piecewise smooth dynamical system in the presence of discontinuous jumps in the state associated with intersections with system discontinuities. In particular, it is shown that a discrete, linear feedback strategy may be employed to retain the existence of an attractor near the grazing trajectory, such that the deviation of the attractor from the grazing trajectory goes to zero as the system parameters approach those corresponding to grazing contact. The implementation relies on a local analysis of the near-grazing dynamics using the concept of discontinuity mappings. Numerical results are presented for a linear and a nonlinear oscillator. copy; 2005 The Royal Society.

Original languageEnglish (US)
Pages (from-to)3365-3380
Number of pages16
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume461
Issue number2063
DOIs
StatePublished - Nov 8 2005
Externally publishedYes

Keywords

  • Control
  • Discontinuity mappings
  • Grazing bifurcations
  • Grazing trajectories
  • Piecewise smooth systems

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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