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| 时滞反馈控制对弹簧摆动力学行为的影响 | |
| 引用本文： | 李欣业,管啸天,张华彪,李金华.时滞反馈控制对弹簧摆动力学行为的影响[J].应用力学学报,2012,29(4):421-425,486. |
| 作者姓名： | 李欣业 管啸天 张华彪 李金华 |
| 作者单位： | 1. 河北工业大学机械工程学院天津300130 2. 哈尔滨工业大学航天学院,哈尔滨,150001 3. 哈尔滨工程大学船舶工程学院,哈尔滨,150001 |
| 摘 要： | 利用解析和数值方法,以弹簧摆为对象讨论了线性的时滞位移反馈控制对一类平方非线性系统动力学行为的影响。根据多尺度法得到了1:2内共振情况下一次近似解的慢变方程,基于此讨论了反馈控制参数对零解的稳定性和周期解振幅的影响。结果表明:耦合的反馈项在平均方程中并不出现。根据罗斯-霍尔维茨判据发现,没有反馈控制时该系统的零解总是不稳定的,而通过调整反馈增益或反馈时滞就可以很容易地使零解稳定。反馈时滞对周期解振幅的影响呈现周期性,反馈增益或时滞发生变化时,周期解振幅的变化会表现出鞍结分岔现象;同时基于MATLAB软件的数值计算结果验证了该理论分析的正确性。 |
| 关 键 词： | 弹簧摆 内共振 反馈控制 时滞 多尺度法 |
Delayed feedback control of dynamics of spring pendulums |
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| Li Xinye,Guan Xiaotian,Zhang Huabiao,Li Jinhua.Delayed feedback control of dynamics of spring pendulums[J].Chinese Journal of Applied Mechanics,2012,29(4):421-425,486. | |
| Authors: | Li Xinye Guan Xiaotian Zhang Huabiao Li Jinhua |
| Institution: | 3(School of Mechanical Engineering,Hebei University of Technology,300130,Tianjin,China) 1(School of Astronautics,Harbin Institute of Technology,150001,Harbin,China) 2(College of Shipbuilding Engineering,Harbin Engineering University,150001,Harbin,China) 3 |
| Abstract: | Based on the assumption that quadratic nonlinear terms and 1:2 internal resonance are considered,the influence of linear feedback control with time delay on the dynamics of spring-pendulum systems is investigated analytically and numerically.By means of the method of multiple scales,the slow-flow equations for the first order approximation,which can be used to discuss the stability of the trivial solution and the variation of amplitude of periodic solutions with control parameters,are obtained.It is shown that there are no the coupled feedback terms in the slow-flow equations.According to Routh-Hurwitz criterion,the trivial solution can be easily stabilized by feedback control although it is always unstable when no feedback control is applied to it.The influence of time delay in feedback control on amplitude of periodic solutions is periodic,and the saddle-node bifurcation may occur when control parameters are varied.Some simulations by MATLAB are presented to verify those analytical results. |
| Keywords: | spring pendulums internal resonance feedback control time delay method of multiple scales |
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