An empirical approach for delayed oscillator stability and parametric identification

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Mann, BP; Young, KA

Published Date

  • 2006

Published In

Volume / Issue

  • 462 / 2071

Start / End Page

  • 2145 - 2160

International Standard Serial Number (ISSN)

  • 1364-5021

Digital Object Identifier (DOI)

  • 10.1098/rspa.2006.1677