Stability of delayed oscillators subjected to digital PD control

David Lehotzky, Tamas Insperger

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

1 Citation (Scopus)

Abstract

Stabilization of time-delayed oscillators via digital PD controller is analyzed. The system under analysis is described by the delay-differential equation ẍ(t) + a 1ẋ (t) + a 0x(t) = b 0x(t - τ) - P x(t j-1) - Dẋ (t j-1), t ∈ [t j, t j+1), (1) where t j = jΔt with Δt being a sampling period for the digital controller. The point-delay term x(t-τ) is assumed to be inherently present in the governing equation of the uncontrolled system, while the term x(t j-1) is present due to the digital controller. Since the term x(t j-1) can be represented as a term with a piecewise linearly varying time delay, the system is time-periodic at period Δt. The stability analysis for the system is performed using the semi-discretization method. Case studies are presented for the stabilization of the turning process via digital PD controller.

Original languageEnglish
Title of host publicationBook of Abstracts - 10th IFAC Workshop on Time Delay Systems, TDS-2012
Pages73-78
Number of pages6
EditionPART 1
DOIs
Publication statusPublished - Sep 17 2012
Event10th IFAC Workshop on Time Delay Systems, TDS-2012 - Boston, MA, United States
Duration: Jun 22 2012Jun 24 2012

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
NumberPART 1
Volume10
ISSN (Print)1474-6670

Other

Other10th IFAC Workshop on Time Delay Systems, TDS-2012
CountryUnited States
CityBoston, MA
Period6/22/126/24/12

Keywords

  • Digital control
  • Sampled data
  • Semi-discretization
  • Stability
  • Time delay

ASJC Scopus subject areas

  • Control and Systems Engineering

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  • Cite this

    Lehotzky, D., & Insperger, T. (2012). Stability of delayed oscillators subjected to digital PD control. In Book of Abstracts - 10th IFAC Workshop on Time Delay Systems, TDS-2012 (PART 1 ed., pp. 73-78). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 10, No. PART 1). https://doi.org/10.3182/20120622-3-US-4021.00038