Anti-Disturbance Performance of Maglev Rotor Using Model Assisted Extended State Observer
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摘要:
随着正弦干扰频率的提高，扩张状态观测器（extended state observer，ESO）的性能会下降，为提高磁悬浮转子系统中ESO的干扰抑制能力，首先，建立单自由度磁悬浮轴承转子系统数学模型；其次，设计ESO并分析其干扰抑制效果下降的原因；在此基础上，提出一种模型辅助扩张状态观测器(model assisted extended state observer, MESO)以改进带宽配置方式，提高干扰抑制效果；然后，在频域内分析基于MESO的自抗扰控制器的稳定性；最后，通过仿真与试验验证了所提出观测器的有效性. 研究结果表明：带宽的增加会放大系统噪声的影响，使系统的控制电压增加；随着干扰频率的提高，MESO对高频正弦干扰的抑制效果会下降，但仍可以降低转子的模态振幅；对50 Hz旋转频率下的转子分别施加频率为10 Hz、振幅为2 mm的基础简谐干扰与1
g 的基础冲击干扰， 相比ESO，MESO控制下的转子位移分别降低了16.3%与22.6%，控制电压降低了约14%.Abstract:With the increase in sinusoidal disturbance frequency, the performance of extended state observers (ESOs) will decrease. In order to improve the disturbance suppression ability of the ESO in the maglev rotor system, firstly, the mathematical model of a one-degree-of-freedom (1-DOF) maglev bearing rotor system was built. Secondly, ESO was designed, and the reasons for its reduced disturbance suppression effects were analyzed. On this basis, a model assisted ESO (MESO) was proposed to improve the bandwidth configuration and enhance the disturbance suppression effects. Then, the stability of the active disturbance rejection controller based on MESO was analyzed in the frequency domain. The effectiveness of the proposed observer was finally verified through simulation and experiments. The research results indicate that an increase in bandwidth amplifies the impact of system noises and increases the control voltage of the system. As the disturbance frequency increases, the suppression effect of MESO on high-frequency sinusoidal disturbance will decrease, but it can still reduce the modal amplitude of the rotor. After applying fundamental harmonic disturbance of 10 Hz−2 mm and fundamental impulse disturbance of 1
g to the rotor at a rotating frequency of 50 Hz respectively, the rotor displacement under MESO control is reduced by 16.3% and 22.6%, respectively compared with that under ESO control, and the control voltage is reduced by about 14%. -
图 5 100～3000带宽下闭环系统特征根轨迹
Figure 5. Characteristic root locus of closed-loop system under bandwidth of 100−3 000
图 7 不同带宽下转子位移与控制电压对比
Figure 7. Comparison of rotor displacement and control voltage under different bandwidths
图 9 0～200 Hz扫频转子位移仿真
Figure 9. Simulation of rotor displacement under sweep frequency of 0−200 Hz
图 10 基础激励下磁悬浮转子系统实验平台现场
Figure 10. Experimental platform of maglev rotor system under fundamental excitation
图 12 0～200 Hz扫频转子位移对比
Figure 12. Comparison of rotor displacement under sweep frequency of 0−200 Hz
图 13 基础简谐激励下控制效果对比
Figure 13. Comparison of control effects under fundamental harmonic excitation
图 14 基础冲击激励下控制效果对比
Figure 14. Comparison of control effects under fundamental impulse excitation
表 1 AMB转子系统参数
Table 1. Parameters of AMB rotor system
符号 参数值 m/kg 3.55 A/m2 2 × 10−4 N/匝 150 g0/mm 0.2 保护轴承单边间隙 gmin/mm 0.125 I0/A 1.3 α/（°） 22.5 μ0/（N·A−2） 4π × 10−7 ka/（A·V−1） 0.26 ks/（V·m−1） 20000 转子转速 n/（r·min−1） 3000 kp 1.8 kd 0.002 ω 3000 
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表 2 转子位移二范数
Table 2. 2-Norm of rotor displacement
名称 二范数大小 相比 PID 控制器振幅降低比例/% ||ePID||2 7261.6 ||eESO||2 5684.6 21.7 ||eMESO||2 4608.7 36.5
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