In this research, the periodic response and stability of a nonlinear maglev system under the combined effects of steady and unsteady aerodynamic lifts is investigated, considering time delay in the feedback control loop. First, a nonlinear maglev system with a single levitation point that accounts for the nonlinearity of the electromagnetic force, time delay in the feedback control loop, and effect of aerodynamic lift is established. Then the periodic solutions of the maglev system with aerodynamic lift and time delays are obtained by an incremental harmonic balance analysis, in which the explicit time-delay action matrices used indicate that the effect of time delay on the response of the maglev system is periodic. The stability of the periodic solutions based on a finite difference continuous time approximation method and Floquet theory is studied, from which the critical time delay is obtained. Also, the relationship between the periodic vibration amplitude and the time delay is examined, along with the steady aerodynamic lift coefficient, and frequency of the unsteady aerodynamic lift, as well as the variation of critical delay with respect to the position feedback and velocity feedback with the control gain parameters. In addition, the stability boundary for the simultaneous time-delayed position and velocity feedback is obtained.

中文翻译：

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气动升力下延迟反馈控制磁悬浮系统的周期响应与稳定性

在这项研究中，考虑反馈控制回路中的时间延迟，研究了非线性磁悬浮系统在稳态和非稳态气动升力联合作用下的周期响应和稳定性。首先，建立了一个具有单悬浮点的非线性磁悬浮系统，该系统考虑了电磁力的非线性、反馈控制回路中的时间延迟和气动升力的影响。然后通过增量谐波平衡分析得到具有气动升力和时滞的磁悬浮系统的周期解，其中使用的显式时滞作用矩阵表明时滞对磁悬浮系统响应的影响是周期性的。基于有限差分连续时间逼近法和Floquet理论研究了周期解的稳定性，从中得到了临界时滞。此外，还研究了周期振动幅度与时间延迟之间的关系，以及稳态气动升力系数和非定常气动升力频率，以及临界延迟相对于位置反馈和速度反馈的变化控制增益参数。此外，还获得了同时时间延迟位置和速度反馈的稳定性边界。非定常气动升力的频率和频率，以及临界延迟相对于位置反馈和速度反馈随控制增益参数的变化。此外，还获得了同时时间延迟位置和速度反馈的稳定性边界。非定常气动升力的频率和频率，以及临界延迟相对于位置反馈和速度反馈随控制增益参数的变化。此外，还获得了同时时间延迟位置和速度反馈的稳定性边界。