[期刊论文] 王在华,胡海岩,胥奇,Gabor Stepan, Effect of delay combinations on stability and Hopf bifurcation of an oscillator with acceleration-derivative feedback, International Journal of Non-Linear Mechanics, 2017, 94: 392-399.

发布者:孙加亮发布时间:2020-04-28浏览次数:390

Effect of delay combinations on stability and Hopf bifurcation of an oscillator 

with acceleration-derivative feedback

Zaihua Wang, Haiyan Hu, Qi Xu, Gabor Stepan

 

Abstract:This paper presents new observations of delayed AD (acceleration-derivative) controller in active vibration control and in bifurcation control of a Duffing oscillator. Based on the stability analysis of the linear delayed oscillator, it is found that combination of the two delays in acceleration feedback and velocity feedback has a significant influence on the stable region in the parameter plane of the gains. By calculating the real part of the rightmost characteristic roots of the controlled oscillator with fixed delays, it is shown that a delayed acceleration feedback with positive gain can work much better than the corresponding delayed negative acceleration feedback, which is used in classic control theory. For given feedback gains, by calculating the critical delay values, it is shown that a delayed positive acceleration feedback can result in a much larger stable delay interval than the corresponding delayed negative acceleration feedback does. As an application of these results to a delayed Duffing oscillator with acceleration-derivative feedback, a delayed positive acceleration feedback can be well used to postpone the occurrence of Hopf bifurcation in the delayed nonlinear oscillators.

 

原文链接: https://www.sciencedirect.com/science/article/abs/pii/S0020746216302499