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摘要: 将磁悬浮车轨耦合振动系统简化为单磁铁-Bernoulli-Euler梁模型, 设计了5种状态变量的反馈控制器, 分别在时、频域上研究了系统的动力学特性。依据相似理论建立了单磁铁车轨耦合系统的小比例模型, 推导了动力学系统的相似关系, 分析了小比例模型的相似特性。研究结果表明: 提出的磁悬浮控制方法利用轨道梁低阶模态与电磁铁振动信息得出控制器输出, 方法有效; 利用所设计的控制器, 系统能够在0.27s达到稳定状态, 最大超调量为2%;在单磁铁的车轨耦合振动系统中, 取其3阶模态即可较精确地反映其振动特性, 而当轨道梁各阶频率相差较大时, 对系统的低频特性分析, 在仅取第1阶模态时也可得出较精确的结果; 通过相似理论得到的小比例磁悬浮车轨耦合振动模型的动力学特性与原模型一致。Abstract: Simplified as a model composed of single magnet and Bernoulli-Euler beam, the maglevguideway coupling vibration system with 5-state-variable feedback controller was designed to study the dynamics performances of the system in the time and frequency domain. A small-scale model of single magnet-guideway coupling vibration system was established based on the similarity theory, its similarity performances were studied, and the similarity relationship of the dynamics systems was analyzed. Study result shows that the maglev control method, calculating the controller output with the vibration informations of guideway's low order mode and magnet, is effective and can keep the system stable. The step response of the system indicates that the developed controller can stabilize the system in 0.27 swith the overshot 2%. The first 3 order modes can be used to accurately describe the dynamics characteristics of coupling vibration system. For analyzing the lower frequency characteristics of the system, the first 1 order mode is sufficient when the large difference among the lower frequencies exists. The small-scale model obtained according to the similarity theory is coincident with the original model in the dynamics performances.
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图 13 电磁铁加速度频域响应的比较
Figure 13. Frequency domain response comparison of electromagnet accelerations
图 14 轨道梁位移频域响应的比较
Figure 14. Frequency domain response comparison of guideway displacements
图 15 轨道梁加速度频域响应的比较
Figure 15. Frequency domain response comparison of guideway accelerations
表 2 车轨耦合振动系统的等效参数
Table 2. Equivalent parameters of vehicle-guideway coupling vibration model
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