Effect of Time-delayed Displacement Feedback on AMD Vibration Control under Seismic Excitation
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摘要: 在传统被动TMD的基础上引入时滞位移反馈控制，将TMD转变为AMD。在AMD系统中，将时滞和反馈增益系数作为可调的控制参数。首先，建立AMD作用下两自由度耦合振动系统力学模型和数学模型；然后，采用特征值分析法判断控制参数平面上系统的稳定性；最后，以位移响应峰值、加速度响应峰值、位移均方根和加速度均方根为评价指标，基于Simulink仿真，分析控制参数对El Centro波作用下AMD振动控制效果的影响。研究结果表明，当系统物理参数固定时，控制参数取值决定了系统振动稳定性；相较于TMD作用的情况，合理的控制参数取值，可使AMD达到更佳的振动控制效果，主结构和阻尼器地震响应均在不同程度上得到抑制；在控制参数取值不合理的情况下，AMD振动控制效果变差。Abstract: A time-delayed displacement feedback is introduced to transform a traditional Tuned Mass Damper (TMD) system into an Active Mass Damper (AMD) system. The time delay and feedback gain coefficient are considered as adjustable control parameters for the AMD system. Firstly, the mechanical and mathematical models of the 2-degrees-of-freedom (2-DOF) coupling system with an AMD attached are established. Secondly, the stability of the system in the control parameter plane is determined using the eigenvalue analysis method. Finally, using Simulink simulations, the influence of control parameters on the vibration control effect of the AMD under EI Centro wave excitation is discussed, with evaluation indexes including the peak displacement response, peak acceleration response, root mean square (RMS) of displacement, and RMS of acceleration. The results show that the values of the control parameters determine the stability of the system with fixed physical parameters. An AMD with optimally tuned control parameters demonstrates a superior vibration control effect compared to a TMD. The seismic responses of both the primary structure and the damper are suppressed to varying degrees. However, if the control parameters are not optimally set, the vibration control effect of the AMD deteriorates.
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Key words:
- Time-delayed displacement feedback /
- Seismic excitation /
- Stability /
- Vibration control
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图 2 满足特征根为纯虚根的g和τ取值
Figure 2. Values of g and τ corresponding to the pure imaginary eigenroots
图 9 反馈增益系数对加速度峰值的影响
Figure 9. Effect of feedback gain coefficient on acceleration peak
图 10 反馈增益系数对位移均方根的影响
Figure 10. Effect of feedback gain coefficient on displacement root mean square
图 11 反馈增益系数对加速度均方根的影响
Figure 11. Effect of feedback gain coefficient on acceleration root mean square
表 1 不同情况下系统响应峰值及其均方根
Table 1. Peak and root mean square of system response in three cases
控制参数取值 位移峰值/cm 加速度峰值/cm 位移均方根/cm 加速度均方根/Gal g/（N·m−1） τ/s 主结构 TMD AMD 主结构 TMD AMD 主结构 TMD AMD 主结构 TMD AMD 无控 0.92 — — 294 — — 0.30 — — 98 — — 0 — 0.74 4.85 — 232 1519 — 0.23 1.39 — 71 447 — −1 000 0.20 0.63 — 4.10 200 — 1263 0.21 — 1.24 68 — 382 
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表 2 时滞对系统响应峰值及其均方根的影响
Table 2. Effect of τ on peak and root mean square of system response
控制参数取值 位移峰值/cm 加速度峰值/cm 位移均方根/cm 加速度均方根/Gal g/（N·m−1） τ/s 主结构 AMD 主结构 AMD 主结构 AMD 主结构 AMD −1 000 0.05 0.90 6.28 307 2 033 0.29 1.98 90 666 0.10 0.93 10.11 287 3 236 0.30 2.66 95 858 0.15 0.69 6.76 202 2 115 0.21 1.85 68 570 0.20 0.63 4.10 200 1 263 0.21 1.24 68 382 0.25 0.67 3.29 216 1 024 0.22 1.02 72 319 0.30 0.74 3.27 233 1 024 0.23 1.02 75 328 0.35 0.81 3.90 247 1 243 0.25 1.31 80 441 0.40 0.93 6.89 291 2 287 0.29 2.09 94 725
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