非线性时滞反馈控制系统超谐共振分析  

Superharmonic resonance response of the control system with time-delayed feedback

作　　者：孙清[1] 刘正伟[1] 伍晓红[2] 张斌[1] 

机构地区：[1]西安交通大学土木工程系,西安710049 [2]西安交通大学航天航空学院,西安710049

出　　处：《应用力学学报》2010年第2期274-279,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(10772141)

摘　　要：采用增量谐波平衡法求解了非线性时滞微分方程的超谐共振解,研究了时滞、反馈控制增益、激励幅值、非线性项系数等系统参数对系统超谐共振响应的影响,分析了超谐共振响应随系统参数变化的规律。结果表明:三次谐波与一次谐波振幅的比值随时滞量呈周期性变化;反馈控制增益对系统超谐共振的影响与非线性项系数和激励幅值有关;随着非线性项系数和激励幅值的不断增大,三次谐波项与一次谐波项振幅的比值都是先增大后减小,而且减小的趋势逐渐减弱;一次谐波成份在振幅中占主导地位。The superharmonic resonance response of the strongly nonlinear delay differential equation is solved by using the incremental harmonic balance method.The influences of the time delay,the feedback gain,the excitation amplitude and the coefficient of nonlinear term on the system superharmonic resonance response are studied.The variation of the superharmonic resonance response with the system parameters is obtained.The results show that the variation of the amplitude ratio of the third harmonic to the first harmonic is of wavy type.The influence of the feedback gain on the system superharmonic resonance response relates to the excitation amplitude and the coefficient of nonlinear term.The amplitude ratio of the third harmonic to the first harmonic increases first then decreases and the decreasing trend weakens gradually with increasing the excitation amplitude and the coefficient of nonlinear term.The first harmonic in the amplitude is dominant in the superharmonic resonance response.

关 键 词：时滞 非线性动力系统 增量谐波平衡法 超谐共振 

分 类 号：O322[理学—一般力学与力学基础]