强非线性振动系统极限环振幅控制研究  

Amplitude control of limit cycles in a class of strongly nonlinear oscillation systems

作　　者：蔡萍[1,2] 唐驾时[1] 

机构地区：[1]湖南大学机械与运载工程学院,长沙410082 [2]漳州师范学院数学与信息科学系,福建漳州363000

出　　处：《振动与冲击》2013年第9期110-112,共3页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(11172093,11032004);高等学校博士学科点专项科研基金资助课题(20100161110024)

摘　　要：研究一类强非线性振动系统极限环振幅控制。利用改进的多尺度法求解系统极限环振幅表达式;构造几类线性、非线性反馈控制器,获得反馈系数与极限环振幅的近似解析关系;通过选择适当的反馈系数,可对极限环振幅进行控制;讨论并比较不同控制器的控制效果;数值模拟结果验证了幅值预测的正确性与控制的有效性。对较大参数ε仍具有较高精确度。A new method was presented for studying the controlling of amplitude of limit cycles. The amplitudes of limit cycles were determined by using the modified multiple scale method and the analytical expressions regarding the amplitudes of controlled limit cycles and the feedback gains were also obtained. The control of amplitudes of limit cycles was realized by choosing suitable feedback gains and the efficiencies of different controllers were discussed and compared. The validity of the analytical conclusions was verified by numerical simulations and the method still maintains high accuracy for the case of larger parameter Ε.

关 键 词：强非线性 极限环 振幅控制 改进多尺度法 

分 类 号：O322[理学—一般力学与力学基础]