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Fractional-order time-delay feedback control for nonlinear dynamics in giant magnetostrictive actuators

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Abstract

In order to effectively manage the nonlinear dynamic response of giant magnetostrictive actuators (GMA), this study introduces a fractional-order time-delay feedback control scheme. Initially, we establish dimensionless dynamic equations for the controlled system, building upon prior research regarding the GMA’s nonlinear dynamic model. Subsequently, we employ the averaging method to resolve the primary resonance response equation and establish stability conditions for the controlled system. Moreover, we conduct numerical simulations to examine the impact of key structural parameters within the uncontrolled system and the control system’s regulating parameters, which include fractional order, feedback gain coefficient, and time-delay parameter, on the characteristics of the primary resonance response. Finally, we investigate the effects of excitation amplitude and regulating parameters on system bifurcation, chaos, and the basin of attraction. This research reveals that by selecting appropriate regulating parameters, it is possible to eliminate the jump phenomenon in the primary resonance curve, the chaos window, and chaotic attractors, thereby enhancing the system's stability. Consequently, this study lays the theoretical groundwork for implementing fractional-order time-delay feedback control within GMA systems.

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Funding

This work is supported by the National Natural Science Foundation of China under Grant No. 52266005 and Basic Research Funds for Universities (Research and engineering development of low frequency chaos in rare earth giant magnetostrictive bone conduction oscillators).

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  1. College of Mechanical Engineering, Inner Mongolia University of Science and Technology, Baotou, 014010, China

    Hongbo Yan, Qingzhen Ma, Jianxin Wang & Haitao Huang

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  1. Hongbo Yan
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Correspondence to Qingzhen Ma.

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Yan, H., Ma, Q., Wang, J. et al. Fractional-order time-delay feedback control for nonlinear dynamics in giant magnetostrictive actuators. Nonlinear Dyn 112, 3055–3079 (2024). https://doi.org/10.1007/s11071-023-09228-6

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