相对转动系统的Hopf分岔分析及分岔控制

Hopf Bifurcation Analysis and Bifurcation Control of a Relative Rotation System

考虑一类非线性摩擦阻尼力作用下相对转动系统的Hopf分岔类型及分岔控制问题.先运用中心流形理论将原系统降维,通过计算降维后系统的稳定性指标判定原系统的Hopf分岔类型;再设计基于Washout滤波器的立方非线性项控制器对系统进行Hopf分岔控制,并讨论控制参数对Hopf分岔类型及极限环幅值的影响.结果表明,当控制参数满足一定条件时,可将原系统具有潜在威胁的亚临界Hopf分岔控制为超临界Hopf分岔,保证系统正常运行,并且运行幅值随控制参数的减小而减小.

Hopf bifurcation type and Hopf bifurcation control of a relative rotation dynamical system with nonlinear damping force were mainly studied.Firstly,the original system was changed to a two-dimensional system via center manifold theory,and the stability coefficient of the two-dimensional system was calculated to determine the Hopf bifurcation type of the original system.Then,the cubic nonlinear controller based on Washout filter theory was designed to control Hopf bifurcation,and the effects of control parameter on Hopf bifurcation type and periodic solution ’s amplitude were discussed.The results show that when the control parameter satisfies certain condition,the potential threat subcritical Hopf bifurcation of original will be changed to supercritical Hopf bifurcation,thus the normal vibration of original system is guaranteed,and the amplitude of vibration will decrease with the reduction of the control parameter.