Micro-chaotic behaviour in PD-controlled systems

Gábor Csernák, Gábor Stépán

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The nonlinearity caused by the application of digital control may lead to chaotic behaviour. Our goal is to analyse the problem of computer-controlled stabilization of unstable equilibria, with the application of the PD control law. We consider a linear equation of motion. However, as a consequence of the digital effects, i.e., the sampling and the round-off error, the solutions of the system can be described by a two dimensional piecewise linear map. We show that this system may perform chaotic behaviour. The amplitude of the evolving oscillations is usually very small, this is why these are called micro-chaotic vibrations.

Original languageEnglish
Title of host publication2nd IFAC Conference on Analysis and Control of Chaotic Systems, CHAOS09 - Proceedings
PublisherIFAC Secretariat
Number of pages3
EditionPART 1
ISBN (Print)9783902661654
Publication statusPublished - Jan 1 2009

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
NumberPART 1
ISSN (Print)1474-6670


  • Digital control
  • Micro-chaos
  • Proof of chaos
  • Two-dimensional map

ASJC Scopus subject areas

  • Control and Systems Engineering

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  • Cite this

    Csernák, G., & Stépán, G. (2009). Micro-chaotic behaviour in PD-controlled systems. In 2nd IFAC Conference on Analysis and Control of Chaotic Systems, CHAOS09 - Proceedings (PART 1 ed., pp. 144-146). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 2, No. PART 1). IFAC Secretariat. https://doi.org/10.3182/20090622-3-uk-3004.00029