CAJ | 학술논문

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。
고필일류비선성마찰조니력작용하상대전동계통적 Hopf 분차류형급분차공제문제。선운용중심류형이론장원계통강유，통과계산강유후계통적은정성지표판정원계통적 Hopf분차류형；재설계기우 Washout려파기적립방비선성항공제기대계통진행 Hopf 분차공제，병토론공제삼수대 Hopf분차류형급겁한배폭치적영향。결과표명，당공제삼수만족일정조건시，가장원계통구유잠재위협적아림계Hopf분차공제위초림계Hopf분차，보증계통정상운행，병차운행폭치수공제삼수적감소이감소。
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.