Micro-Chaos in Digital Control

G. Haller, G. Stépán

Research output: Contribution to journalArticle

58 Citations (Scopus)

Abstract

In this paper we analyze a model for the effect of digital control on one-dimensional, linearly unstable dynamical systems. Our goal is to explain the existence of small, irregular oscillations that are frequently observed near the desired equilibrium. We derive a one-dimensional map that captures exactly the dynamics of the continuous system. Using this micro-chaos map, we prove the existence of a hyperbolic strange attractor for a large set of parameter values. We also construct an "instability chart" on the parameter plane to describe how the size and structure of the chaotic attractor changes as the parameters are varied. The applications of our results include the stick-and-slip motion of machine tools and other mechanical problems with locally negative dissipation.

Original languageEnglish
Pages (from-to)415-448
Number of pages34
JournalJournal of Nonlinear Science
Volume6
Issue number5
Publication statusPublished - Sep 1996

Fingerprint

Digital Control
Chaos theory
chaos
Chaos
Machine tools
machine tools
strange attractors
Dynamical systems
One-dimensional Maps
Strange attractor
Machine Tool
Chaotic Attractor
Continuous System
charts
Chart
Large Set
Slip
dynamical systems
Irregular
Dissipation

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mathematics(all)
  • Applied Mathematics
  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Micro-Chaos in Digital Control. / Haller, G.; Stépán, G.

In: Journal of Nonlinear Science, Vol. 6, No. 5, 09.1996, p. 415-448.

Research output: Contribution to journalArticle

Haller, G & Stépán, G 1996, 'Micro-Chaos in Digital Control', Journal of Nonlinear Science, vol. 6, no. 5, pp. 415-448.
Haller, G. ; Stépán, G. / Micro-Chaos in Digital Control. In: Journal of Nonlinear Science. 1996 ; Vol. 6, No. 5. pp. 415-448.
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