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Fractional-order time-delayed feedback control of nonlinear dynamics in a giant magnetostrictive actuator
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Hong-bo YAN1, Xin FU1, Jian-xin WANG1, Jun-cheng YU1, Qing-zhen MA1, Bo-jun YANG2
Journal of Vibration Engineering | 2024, 37(4) : 632 - 644
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Journal of Vibration Engineering | 2024, 37(4): 632-644
Fractional-order time-delayed feedback control of nonlinear dynamics in a giant magnetostrictive actuator
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Hong-bo YAN1, Xin FU1, Jian-xin WANG1, Jun-cheng YU1, Qing-zhen MA1, Bo-jun YANG2
Affiliations
  • 1College of Mechanical Engineering，Inner Mongolia University of Science & Technology，Baotou 014010，China
  • 2National Engineering Research Center for Technological Innovation Method and Tool，Hebei University of Technology，Tianjin 300131，China
Published: 2024-04-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.04.010
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In this paper，a fractional-order time-delayed feedback controller is designed to control the nonlinear dynamic response of a single-degree-of-freedom giant magnetostrictive actuator （GMA）. Considering the effect of geometric nonlinear factors introduced by the preloaded disc spring mechanism，a nonlinear mathematical model of the GMA system is established. The amplitude-frequency response equation of the main resonance of the system under the feedback control strategy with fractional-order time-delayed is obtained by the averaging method，and the stability condition of the system is obtained according to the Routh-Hurwitz criterion. The influence of key structural parameters in the GMA system on the amplitude-frequency response characteristics，as well as the characteristic law of the main resonance peak and system stability with each time-delayed feedback parameter are studied through numerical simulation. The bifurcation diagram and Lyapunov exponent diagram are obtained and the influence of the external excitation amplitude on the chaotic motion of the system is studied； finally，the time-delayed feedback gain and fractional order are used to suppress the chaotic motion of the system. The results show that the time-delayed feedback gain and fractional order can effectively suppress the main resonance peak and unstable region of the system，and the system response can be adjusted from chaotic motion to stable periodic movement to improve the stability of the system.

geometric nonlinearity  /  giant magnetostrictive actuator  /  chaos  /  time-delayed feedback  /  stability
Hong-bo YAN, Xin FU, Jian-xin WANG, Jun-cheng YU, Qing-zhen MA, Bo-jun YANG. Fractional-order time-delayed feedback control of nonlinear dynamics in a giant magnetostrictive actuator[J]. Journal of Vibration Engineering, 2024 , 37 (4) : 632 -644 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.04.010
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Year 2024 volume 37 Issue 4
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doi: 10.16385/j.cnki.issn.1004-4523.2024.04.010
  • Receive Date：2022-07-29
  • Online Date：2026-02-09
  • Published：2024-04-28
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  • Received：2022-07-29
  • Revised：2022-10-01
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Affiliations
    1College of Mechanical Engineering，Inner Mongolia University of Science & Technology，Baotou 014010，China
    2National Engineering Research Center for Technological Innovation Method and Tool，Hebei University of Technology，Tianjin 300131，China
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https://castjournals.cast.org.cn/joweb/zdgcxb/EN/10.16385/j.cnki.issn.1004-4523.2024.04.010
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表12种不同金属材料的力学参数
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小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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