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Algorithm for Robust Stability of Delayed Multi-Degree-of-Freedom Systems

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Time Delay Systems

Part of the book series: Advances in Delays and Dynamics ((ADVSDD,volume 7))

Abstract

Computation of the stability limits of systems with time delay is essential in many research and industrial applications. Most of the computational methods consider the exact model of the system, and do not take into account the uncertainties. However, the stability charts are highly sensitive to the change of some input parameters, especially to time delays. An algorithm has been developed to determine the robust stability limits of delayed dynamical systems, which is not sensitive to the fluctuations of selected parameters in the dynamic system. The algorithm is combined with the efficient Multi-Dimensional Bisection Method. The single-degree-of-freedom delayed oscillator is investigated first and the resultant robust stability limits are compared to the derived analytical results. For multi-degree-of-freedom systems, the system of equations of the robust stability limits are modified with the aim to reduce the computational complexity. The method is tested for the 2-cutter turning system with process damping.

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Acknowledgements

The research leading to these results has received funding from the European Research Council under the European Unions Seventh Framework Programme (FP7/2007–2013) ERC Advanced grant agreement No. 340889. Furthermore, this paper was supported by the Hungarian Scientific Research Fund—OTKA PD-112983 and the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences.

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Authors and Affiliations

  1. Department of Applied Mechanics, BME, Műegyetem rkp. 5., Budapest, 1111, Hungary

    Daniel Bachrathy, Marta Janka Reith & Gabor Stepan

Authors
  1. Daniel Bachrathy
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  2. Marta Janka Reith
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  3. Gabor Stepan
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Correspondence to Daniel Bachrathy .

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Editors and Affiliations

  1. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary

    Tamás Insperger

  2. Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, USA

    Tulga Ersal

  3. Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, USA

    Gábor Orosz

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Bachrathy, D., Reith, M.J., Stepan, G. (2017). Algorithm for Robust Stability of Delayed Multi-Degree-of-Freedom Systems. In: Insperger, T., Ersal, T., Orosz, G. (eds) Time Delay Systems. Advances in Delays and Dynamics, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-53426-8_10

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  • DOI: https://doi.org/10.1007/978-3-319-53426-8_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53425-1

  • Online ISBN: 978-3-319-53426-8

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