摘要惯容和接地刚度可以通过改变振动系统的固有频率对系统的一部分振动起到抑制作用，在被动控制系统中耦合时滞反馈主动控制是一种相对操作简单且有效的振动主动控制技术。本文通过对含惯容的接地刚度时滞反馈动力吸振器系统进行多目标优化设计，通过对系统结构参数和控制参数进行优化，实现了对主系统共振峰幅值、反共振峰幅值、反共振频带对称性的有效控制。首先,通过固定点理论得到接地刚度系统的最优结构参数。其次,通过Cluster Treatment of Characteristic Roots(CTCR)方法对控制系统进行稳定性分析，得到振动系统稳定的反馈增益系数和时滞控制参数的稳定区域。再次，在满足优化准则的前提下，根据反共振频带的对称性得到最优惯容比。最后，结合最优结构参数和准则，得到满足优化目标的控制参数区域。研究表明，针对任意一个外激励频率，在控制参数区域内存在一对反馈增益系数和时滞的最优参数，能够将主系统的振幅抑制到最小值。幅频响应曲线和时间历程响应曲线的数值模拟结果与解析结果吻合，证明了本文结果的可靠性。本文研究结果为时滞主动控制动力吸振器的优化和设计提供了理论依据。
Abstract：The vibration of the vibrating system can be suppressed partly by using inerter and grounded stiffness components. The natural frequency of the vibrating system could be changed by inerter and grounded stiffness. Delayed feedback control technology is a simple and effective active vibration control technology. Delayed feedback control is commonly coupled to passive control systems to suppress vibration. In this paper, the multi-objective optimization design of the grounded stiffness coupled delayed feedback dynamic vibration absorber system with inerter is studied. The amplitude of the resonance peaks and anti-resonance peak, anti-resonance frequency band can be effectively controlled by optimizing the system structure parameters and control parameters. Firstly, the optimal structural parameters of the inerter and grounded stiffness system are obtained by the fixed-point theory. Secondly, the stability analysis of the control system is analyzed by the Cluster Treatment of Characteristic Roots (CTCR) method. The stable region of the feedback gain and delayed coefficient are obtained. Thirdly, the optimal inerter coefficient is obtained according to the symmetry of the anti-resonance frequency band in the perspective of satisfying the optimization criteria. Finally, the region of control parameters satisfying optimization goal is obtained considering optimal structural parameters and criteria. The research shows that for a certain external excitation frequency, there is a pair of optimal parameters of feedback gain coefficient and time-delay in control parameter region. The amplitude of the primary system can be suppressed to the minimum by selecting this pair of optimal parameters of feedback gain coefficient and time-delay. The numerical simulation results of amplitude frequency response curve and time history response curve are agree with the analytical results well. The reliability of the results in this paper is approved from the above results. The theory foundation of optimization and design is provided for active delayed feedback control system.
杨柳青，赵艳影. 一种含惯容的接地刚度时滞反馈动力吸振器的多目标优化设计[J]. 振动与冲击, 2023, 42(23): 133-143.
YANG Liuqing,ZHAO Yanying. Multi-objective optimization design of a grounded stiffness time delay feedback dynamic vibration absorber with inerter. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(23): 133-143.
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