Comparison between collocation methods and spectral element approach for the stability of periodic delay systems ?

Firas A. Khasawneh, Brian P. Mann, Eric A. Butcher

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

6 Scopus citations

Abstract

This paper compares two methods that are commonly used to study the stability of delay systems. The first is a collocation technique while the second is a spectral element approach which uses the weighted residual method. Two distributions of the collocation points are compared: the first uses the extrema of Chebyshev polynomials of the first kind whereas the second uses the Legendre-Gauss-Lobatto points. The spectral element approach uses the Legendre-Gauss-Lobatto points and higher-order trial functions to discretize the delay equations while Gauss quadrature rules are used to evaluate the resulting weighted residual integrals. Two case studies are used to compare the different methods. The first case study is a 3rd order autonomous DDE while the second is a DDE describing the midspan deflections of an unbalanced rotating shaft with feedback gain (nonautonomous DDE). Convergence plots that compare the different rates of convergence of the described methods are also provided.

Original languageEnglish (US)
Title of host publication9th IFAC Workshop on Time Delay Systems, TDS 2010 - Proceedings
Pages69-74
Number of pages6
EditionPART 1
StatePublished - Dec 1 2010
Externally publishedYes
Event9th IFAC Workshop on Time Delay Systems, TDS 2010 - Prague, Czech Republic
Duration: Jun 7 2010Jun 9 2010

Publication series

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

Other

Other9th IFAC Workshop on Time Delay Systems, TDS 2010
CountryCzech Republic
CityPrague
Period6/7/106/9/10

ASJC Scopus subject areas

  • Control and Systems Engineering

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  • Cite this

    Khasawneh, F. A., Mann, B. P., & Butcher, E. A. (2010). Comparison between collocation methods and spectral element approach for the stability of periodic delay systems ? In 9th IFAC Workshop on Time Delay Systems, TDS 2010 - Proceedings (PART 1 ed., pp. 69-74). (IFAC Proceedings Volumes (IFAC-PapersOnline); No. PART 1).