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Identifying and mitigating residual vibrations in wave-based control of lumped, flexible systems

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Abstract

Wave-based control (WBC) is a technique for motion control of under-actuated flexible systems. It envisages actuator motion as launching a motion wave into the system, while simultaneously absorbing any wave returning from the system. For rest-to-rest motion the net launch displacement is set at half the target displacement. In absorbing the returning wave and vibrations, WBC moves the system the remaining distance to the target, with zero steady-state error. The focus of this paper is on very small residual vibrations around the target position which can endure for a long time after arrival at target. This issue was discovered through a recent development within WBC context on controlling complex two-dimensional, mass-spring, beam-like arrays. To date their existence has been unidentified. This paper investigates and interprets the nature of these vibrations, explains and identifies them based on wave ideas, and finally offers a new wave-based approach to mitigate or suppress them. It also discusses their implication, not just for WBC but for the general problem of control of flexible systems.

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Authors and Affiliations

  1. School of Computing, Engineering and Digital Technologies, Teesside University, Tees Valley, Middlesbrough, TS1 3BX, UK

    Hossein Habibi

  2. UCD School of Mechanical and Materials Engineering, Engineering Building, UCD Belfield, Dublin 4, Ireland

    William O’Connor

  3. School of Engineering and Sustainable Development, De Montfort University, Gateway House, Leicester, LE1 9BH, UK

    S. Abolfazl Zahedi

Authors
  1. Hossein Habibi
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  2. William O’Connor
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  3. S. Abolfazl Zahedi
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Correspondence to Hossein Habibi.

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Habibi, H., O’Connor, W. & Zahedi, S.A. Identifying and mitigating residual vibrations in wave-based control of lumped, flexible systems. Meccanica 55, 1693–1705 (2020). https://doi.org/10.1007/s11012-020-01207-0

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  • DOI: https://doi.org/10.1007/s11012-020-01207-0

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