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Delay Systems pp 271–284Cite as

Analysis and Control of Time Delay Systems Using the LambertWDDE Toolbox

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Part of the book series: Advances in Delays and Dynamics ((ADVSDD,volume 1))

Abstract

This chapter provides an overview of the Lambert W function approach. The approach has been developed for analysis and control of linear time-invariant time delay systems with a single known delay. A solution in the time-domain is given in terms of an infinite series, with the important characteristic that truncating the series provides a dominant solution in terms of the rightmost eigenvalues. A solution via the Lambert W function approach is first presented for systems of order one, then extended to higher order systems using the matrix Lambert W function. Free and forced solutions are used to investigate key properties of time-delay systems, such as stability, controllability and observability. Through eigenvalue assignment, feedback controllers and state-observers are designed. All of these can be achieved using the Lambert W function-based framework. The use of the MATLAB-based open source software in the LambertWDDE Toolbox is also introduced using numerical examples.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, North Carolina AT State University, Greensboro, NC, 27411, USA

    Sun Yi

  2. Magna Powertrain, Troy, MI, 48083, USA

    Shiming Duan

  3. Department of Mathematics and Computer Science, Lawrence Technological University, Southfield, MI, 48075, USA

    Patrick W. Nelson

  4. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    Patrick W. Nelson

  5. Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, 48109-2125, USA

    A. Galip Ulsoy

Authors
  1. Sun Yi
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  2. Shiming Duan
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  3. Patrick W. Nelson
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  4. A. Galip Ulsoy
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Corresponding author

Correspondence to Sun Yi .

Editor information

Editors and Affiliations

  1. Dept. of Instrumentation & Control Eng. Faculty of Mechanical Engineering, Czech Technical University, Prague, Czech Republic

    Tomáš Vyhlídal

  2. Institut de Recherche en Communications et Cybernétique de Nantes, Nantes Cedex 3, France

    Jean-François Lafay

  3. Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts, USA

    Rifat Sipahi

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Yi, S., Duan, S., Nelson, P.W., Ulsoy, A.G. (2014). Analysis and Control of Time Delay Systems Using the LambertWDDE Toolbox. In: Vyhlídal, T., Lafay, JF., Sipahi, R. (eds) Delay Systems. Advances in Delays and Dynamics, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-01695-5_20

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  • DOI: https://doi.org/10.1007/978-3-319-01695-5_20

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-01694-8

  • Online ISBN: 978-3-319-01695-5

  • eBook Packages: EngineeringEngineering (R0)

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