Complex dynamics in a relay feedback system with hysteresis and delay

A Colombo, M Di Bernardo, SJ Hogan, P Kowalczyk

Research output: Contribution to journalArticle (Academic Journal)peer-review

19 Citations (Scopus)

Abstract

Relay feedback systems are used to control engineering devices. In practice the switching between different functional forms of the system is never instantaneous, but takes place after a small delay. In this paper we analyse the dynamics and bifurcations of a representative example of such systems. In the absence of delay, negative feedback results only in unimodal symmetric limit cycles, but positive feedback can lead to aperiodic trajectories and chaos. In the presence of delay, the system can behave as an equivalent system without delay, provided that the delay is small in a sense which we define precisely. For larger delays, we identify a new bifurcation phenomenon, an event collision, where the delayed switching manifold intersects the relay hysteretic lines. In this case the dynamics become much more complicated.
Translated title of the contributionComplex Dynamics in a relay feedback system with hysteresis and delay
Original languageEnglish
Pages (from-to)85 - 108
Number of pages24
JournalJournal of Nonlinear Science
Volume17
Issue number2
DOIs
Publication statusPublished - Apr 2007

Bibliographical note

Publisher: Springer New York

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