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Time-delayed feedback control of improved friction-induced model: application to moving belt of particle supply device

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Abstract

In this paper, based on the original friction-induced oscillation, we propose a new friction-induced mathematical model associated with moving belt of particle supply device. Two delay feedback control methods are provided to make the new model be stable. Linear stability analysis is carried out to obtain the stability of equilibrium and the stability boundary, corresponding to the critical value of Hopf bifurcation, dividing stable and unstable regimes of equilibrium. Next, we derive explicit formulae for determining the stability of Hopf bifurcating periodic solutions and the direction of Hopf bifurcation. Finally, detailed numerical simulations using MATLAB software are presented to demonstrate the application of the theoretical results, and we also compare the efficacy of the two control forces in new friction-induced models.

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Funding

This study was funded by Fundamental Research Funds for the Central Universities (Grant No. 2572019BC14), the Heilongjiang Provincial Natural Science Foundation (Grant No. LH2019A001) and Heilongjiang Provincial Postdoctoral Scientific Research Foundation (Grant No. LBH-Q17007).

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Authors and Affiliations

  1. Department of Mathematics, Northeast Forestry University, Harbin, 150040, People’s Republic of China

    Yuting Ding & Ruizhi Yang

  2. Library, Northeast Forestry University, Harbin, 150040, People’s Republic of China

    Liyuan Zheng

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  1. Yuting Ding
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  2. Liyuan Zheng
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  3. Ruizhi Yang
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Correspondence to Ruizhi Yang.

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Ding, Y., Zheng, L. & Yang, R. Time-delayed feedback control of improved friction-induced model: application to moving belt of particle supply device. Nonlinear Dyn 100, 423–434 (2020). https://doi.org/10.1007/s11071-020-05523-8

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  • DOI: https://doi.org/10.1007/s11071-020-05523-8

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