Vibration control by recursive time-delayed acceleration feedback
Vibration control by recursive time-delayed acceleration feedback
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DOI：
10.1016/j.jsv.2008.03.020
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发表时间：
2008-10
影响因子：
4.7
通讯作者：
S. Chatterjee
中科院分区：
文献类型：
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作者：
S. Chatterjee
本文给出了机械振荡器线性和非线性振动时滞加速度反馈控制的理论基础。控制信号是由过去以等时间间隔测量的振动系统加速度的无限加权和合成的。结果表明，该方法具有可控的线性谐振振动、低频非谐振振动、强制Duffing振荡器的主谐振和1/3次谐波谐振。引入了等效阻尼和系统固有频率的概念。结果表明，适当选择控制参数可以产生较大的阻尼。对于某些控制参数的组合，在小延迟极限下，系统的有效阻尼系数与时滞成反比。讨论了控制受迫振动和自由振动的最佳控制参数的选择。结果表明，采用单位递推增益和较小的时滞参数控制受迫振动效果最好。然而，可以通过根据增益适当选择时间延迟来优化控制瞬态响应。最佳强制响应的延迟值可能与最佳瞬态响应所需的延迟值不同。当两者都很重要时，建议选择具有单位递归增益的次优延迟参数。
This paper presents a theoretical basis of time-delayed acceleration feedback control of linear and nonlinear vibrations of mechanical oscillators. The control signal is synthesized by an infinite, weighted sum of the acceleration of the vibrating system measured at equal time intervals in the past. The proposed method is shown to have controlled linear resonant vibrations, low-frequency non-resonant vibrations, primary and 1/3 subharmonic resonances of a forced Duffing oscillator. The concept of an equivalent damping and natural frequency of the system is also introduced. It is shown that a large amount of damping can be produced by appropriately selecting the control parameters. For some combinations of the control parameters, the effective damping factor of the system is shown to be inversely related to the time-delay in the small delay limit. Selection of the optimum control parameters for controlling the forced and free vibrations is discussed. It is shown that forced vibration is best controlled by unity recursive gain and smaller values of the time-delay parameter. However, the transient response can be optimally controlled by suitably selecting the time delay depending upon the gain. The delay values for the optimal forced response may be different from that required for the optimum transient response. When both are important, a suboptimal choice of the delay parameters with unity recursive gain is recommended.