Effect of Control Delay on Dynamic Characteristics of Negative Stiffness Duffing System

李辉光 1; 刘恒 1; 杨利花 1; 2; 虞烈 1

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Effect of Control Delay on Dynamic Characteristics of Negative Stiffness Duffing System

更新时间：2025-12-08

- Effect of Control Delay on Dynamic Characteristics of Negative Stiffness Duffing System
- Vol. 41, Issue 7, Pages: 811-814(2007)
- 作者机构：
  
  西安交通大学机械电子及信息系统研究所,西安,710049
- 作者简介：
- 基金信息：
- DOI：
  CLC： O322;TH113.1
- Online First：10 July 2007，
  
  Published：2007
- 稿件说明：
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李辉光 1, 刘恒 1, 杨利花 1, et al. Effect of Control Delay on Dynamic Characteristics of Negative Stiffness Duffing System[J]. 2007, 41(7): 811-814.
DOI：

李辉光 1, 刘恒 1, 杨利花 1, et al. Effect of Control Delay on Dynamic Characteristics of Negative Stiffness Duffing System[J]. 2007, 41(7): 811-814. DOI：

摘要

对时滞反馈控制负刚度Duffing系统的动力学特性进行了研究.以时滞量为参数

通过分析对应线性系统特征方程的根的分布

讨论了平凡解的稳定性

得到了平凡解发生Hopf分岔而失稳的临界时滞量以及临界时滞量与系统控制参数的关系.采用数值方法研究了时滞对系统强迫振动的影响

结果表明时滞量的增加不仅导致系统稳态周期运动的振幅增加

而且会导致出现概周期运动、多倍周期运动等复杂的动力学行为

并能引起系统失控.因此

在系统控制环节设计时应充分考虑时滞的影响.

Abstract

The dynamic characteristics of negative stiffness Duffing system with delayed feedback control are investigated. Choosing time delay as the control parameter

the stability of trivial equilibrium is discussed by analyzing distribution of the roots of the associated characteristic equation. It is found that Hopf bifurcation occurs from trivial equilibrium when the delay passes through critical values

then the critical values and their relations with system control parameters are obtained. The effect of time delay on the forced vibration of system is evaluated with numerical method. The results show that the amplitude of stable period motion increases

some complex dynamical behaviors such as quasi-periodic motion and multiple periodic motion may occur

and the system gets out of control with the increase of time delay. Therefore the effect of time delay ought to be taken into sufficient consideration in the design of system control loop.

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references

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Xu J, Chung K W. Effects of time delayed position feedback on a van derPol-Duffing oscillator[J]. Physica: D, 2003, 180(1):17-39.

钱长照, 唐驾时. 一类非自治时滞反馈系统的分岔控制[J].物理学报, 2006,55(2): 617-621.

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Li Xinye, Ji J C, Hansen C H, et al. The response of a Duffing-van derPol oscillator under delayed feedback control[J]. Journal of Sound and Vibration, 2006, 291(3): 644-655.

Hu H Y, Dowell E H, Virgin L N. Resonance of a harmonically forced Duffing oscillator with time delay state feedback[J]. Nonlinear Dynamics, 1998, 15(4):311-327.

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