非线性隔振系统反馈控制动力学特性研究

Study on the Dynamic Characteristics of Nonlinear Vibration Isolation Systems with Feedback Control

建立含速度反馈控制的两自由度非线性隔振系统模型,推导系统的幅频特性关系式;研究反馈控制增益对幅频特性曲线的影响,得到曲线共振峰随反馈增益变化的规律。当增益增大时,共振峰左移并逐渐消失,本质上反映了该反馈对大幅值振动的抑制过程。通过计算分析反馈控制时系统的Lypunov指数谱随控制参数变化的规律,得到可用于系统混沌控制的参数范围,表明系统在一定的参数条件下可以处于混沌状态和周期状态。通过实验研究观察到系统出现的基频和超谐波响应,通过控制可以使得线谱成分得到有效降低,从而可为非线性隔振系统混沌控制和设计提供有益参考。

A 2-DOF controlling model is presented to study the dynamic characteristics of the nonlinear vibration isolation system(NVIS)with feedback control.The amplitude frequency equation of the system is derived,and the corresponding curve of the relationship between the amplitude and frequency is obtained.The influence of the feedback gain on the curve is researched,and the variation of the resonant peaks against the feedback gain is found.Results show that there are two resonant peaks in the amplitude– frequency curve,one is in the low frequency band and the other in higher frequency band.The resonant frequency shifts towards the left obviously and disappears gradually with the increasing of the feedback control gain.The Lyapnov exponent curve of the system is calculated to discover the chaotic and periodic parameter regions.The basic frequency response and super-harmonic response are observed in the experiment,and the linear spectrum is controlled effectively.This work is beneficial to the design of nonlinear vibration isolation control systems.