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An empirical approach for delayed oscillator stability and parametric identification

Publication ,  Journal Article
Mann, BP; Young, KA
Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
January 1, 2006

This paper investigates a semi-empirical approach for determining the stability of systems that can be modelled by ordinary differential equations with a time delay. This type of model is relevant to biological oscillators, machining processes, feedback control systems and models for wave propagation and reflection, where the motion of the waves themselves is considered to be outside the system model. A primary aim is to investigate the extension of empirical Floquet theory to experimental or numerical data obtained from time-delayed oscillators. More specifically, the reconstructed time series from a numerical example and an experimental milling system are examined to obtain a finite number of characteristic multipliers from the reduced order dynamics. A secondary goal of this work is to demonstrate a benefit of empirical characteristic multiplier estimation by performing system identification on a delayed oscillator. The principal results from this study are the accurate estimation of delayed oscillator characteristic multipliers and the utilization the empirical results for parametric identification of model parameters. Combining these results with previous research on an experimental milling system provides a particularly relevant result-the first approach for identifying all model parameters for stability prediction directly from the cutting process vibration history. © 2006 The Royal Society.

Duke Scholars

Published In

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

DOI

EISSN

1471-2946

ISSN

1364-5021

Publication Date

January 1, 2006

Volume

462

Issue

2071

Start / End Page

2145 / 2160

Related Subject Headings

  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Mann, B. P., & Young, K. A. (2006). An empirical approach for delayed oscillator stability and parametric identification. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 462(2071), 2145–2160. https://doi.org/10.1098/rspa.2006.1677
Mann, B. P., and K. A. Young. “An empirical approach for delayed oscillator stability and parametric identification.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2071 (January 1, 2006): 2145–60. https://doi.org/10.1098/rspa.2006.1677.
Mann BP, Young KA. An empirical approach for delayed oscillator stability and parametric identification. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2006 Jan 1;462(2071):2145–60.
Mann, B. P., and K. A. Young. “An empirical approach for delayed oscillator stability and parametric identification.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 462, no. 2071, Jan. 2006, pp. 2145–60. Scopus, doi:10.1098/rspa.2006.1677.
Mann BP, Young KA. An empirical approach for delayed oscillator stability and parametric identification. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2006 Jan 1;462(2071):2145–2160.
Journal cover image

Published In

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

DOI

EISSN

1471-2946

ISSN

1364-5021

Publication Date

January 1, 2006

Volume

462

Issue

2071

Start / End Page

2145 / 2160

Related Subject Headings

  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences