Multi-Baker Map as a Model of Digital PD Control

Gábor Csernák, Gergely Gyebrószki, G. Stépán

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Digital stabilization of unstable equilibria of linear systems may lead to small amplitude stochastic-like oscillations. We show that these vibrations can be related to a deterministic chaotic dynamics induced by sampling and quantization. A detailed analytical proof of chaos is presented for the case of a PD controlled oscillator: it is shown that there exists a finite attracting domain in the phase-space, the largest Lyapunov exponent is positive and the existence of a Smale horseshoe is also pointed out. The corresponding two-dimensional micro-chaos map is a multi-baker map, i.e. it consists of a finite series of baker's maps.

Original languageEnglish
Article number1650023
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume26
Issue number2
DOIs
Publication statusPublished - Feb 1 2016

Fingerprint

Digital Control
Chaos theory
Chaos
Smale Horseshoe
Largest Lyapunov Exponent
Chaotic Dynamics
Linear systems
Phase Space
Quantization
Stabilization
Vibration
Unstable
Linear Systems
Model
Oscillation
Sampling
Series

Keywords

  • chaos proof
  • Digital control
  • hybrid system
  • micro-chaos
  • Smale horseshoe

ASJC Scopus subject areas

  • Applied Mathematics
  • General
  • Engineering(all)
  • Modelling and Simulation

Cite this

Multi-Baker Map as a Model of Digital PD Control. / Csernák, Gábor; Gyebrószki, Gergely; Stépán, G.

In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 26, No. 2, 1650023, 01.02.2016.

Research output: Contribution to journalArticle

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