一类准周期参激非线性相对转动动力系统的稳定性与时滞反馈控制

摘要

建立了一类含准周期参数激励和时滞反馈的相对转动非线性系统的动力学方程.采用多尺度法求解1/2亚谐波主参数共振下的分岔响应方程,并分析了系统的稳定性.在求解非受控系统的定常解的基础上,通过讨论系统的动力学特性,研究了准周期参数激励对系统响应的影响.采用时滞反馈控制的方法对系统分岔和极限环（域）进行控制,数值模拟的结果表明通过改变时滞参数可以实现对系统分岔的控制,并能有效地控制极限环（域）的幅值和稳定性.%The dynamical equation of a relative-rotation nonlinear dynamic system, which contains quasi-periodic parametric excitation and time delays, is established. Bifurcation response equation of 1/2 subharmonic primary parametric resonance is obtained by the method of multiple scales, and the stability of the system is analyzed. By solving the steady state solutions of the uncontrolled system, the effect of quasi-periodic parametric excitation on system response is studied through discussing the dynamics of the system. Time-delay feedback control method is used to control the bifurcation and limit cycle（region）. Numerical results show that the bifurcation and the stability of the limit cycle（region） are controlled effectively by changing the time-delay parameters.