Micro-chaotic behaviour in PD-controlled systems

Gábor Csernák, G. Stépán

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

Abstract

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 publicationIFAC Proceedings Volumes (IFAC-PapersOnline)
Pages144-146
Number of pages3
Volume2
EditionPART 1
Publication statusPublished - 2009
Event2nd IFAC Conference on Analysis and Control of Chaotic Systems, CHAOS09 - London, United Kingdom
Duration: Jun 22 2009Jun 24 2009

Other

Other2nd IFAC Conference on Analysis and Control of Chaotic Systems, CHAOS09
CountryUnited Kingdom
CityLondon
Period6/22/096/24/09

Fingerprint

Linear equations
Equations of motion
Stabilization
Sampling

Keywords

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

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Csernák, G., & Stépán, G. (2009). Micro-chaotic behaviour in PD-controlled systems. In IFAC Proceedings Volumes (IFAC-PapersOnline) (PART 1 ed., Vol. 2, pp. 144-146)

Micro-chaotic behaviour in PD-controlled systems. / Csernák, Gábor; Stépán, G.

IFAC Proceedings Volumes (IFAC-PapersOnline). Vol. 2 PART 1. ed. 2009. p. 144-146.

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

Csernák, G & Stépán, G 2009, Micro-chaotic behaviour in PD-controlled systems. in IFAC Proceedings Volumes (IFAC-PapersOnline). PART 1 edn, vol. 2, pp. 144-146, 2nd IFAC Conference on Analysis and Control of Chaotic Systems, CHAOS09, London, United Kingdom, 6/22/09.
Csernák G, Stépán G. Micro-chaotic behaviour in PD-controlled systems. In IFAC Proceedings Volumes (IFAC-PapersOnline). PART 1 ed. Vol. 2. 2009. p. 144-146
Csernák, Gábor ; Stépán, G. / Micro-chaotic behaviour in PD-controlled systems. IFAC Proceedings Volumes (IFAC-PapersOnline). Vol. 2 PART 1. ed. 2009. pp. 144-146
@inproceedings{0cb8da1406804cd0b2a3adea1a8a33f5,
title = "Micro-chaotic behaviour in PD-controlled systems",
abstract = "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.",
keywords = "Digital control, Micro-chaos, Proof of chaos, Two-dimensional map",
author = "G{\'a}bor Csern{\'a}k and G. St{\'e}p{\'a}n",
year = "2009",
language = "English",
isbn = "9783902661654",
volume = "2",
pages = "144--146",
booktitle = "IFAC Proceedings Volumes (IFAC-PapersOnline)",
edition = "PART 1",

}

TY - GEN

T1 - Micro-chaotic behaviour in PD-controlled systems

AU - Csernák, Gábor

AU - Stépán, G.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Digital control

KW - Micro-chaos

KW - Proof of chaos

KW - Two-dimensional map

UR - http://www.scopus.com/inward/record.url?scp=79960943017&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960943017&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:79960943017

SN - 9783902661654

VL - 2

SP - 144

EP - 146

BT - IFAC Proceedings Volumes (IFAC-PapersOnline)

ER -