Hopf分岔的劳斯判据及磁悬浮系统的振动分析

Louts Criterion for Hopf Bifurcation and Analysis of Vibration of Maglev System

利用 Hopf分岔的劳斯判据 ,给出了由于参数变化而导致非线性系统产生自激振动的临界条件以及自激振动的频率。这种方法克服了以前方法在计算 Hopf分岔点时 ,对于参数的每一次变化都要通过求解系统 Jacobian矩阵特征根的庞大计算量。利用这一方法 ,对磁悬浮系统的稳定性进行了研究 ,得到了该系统产生自激振动的临界条件和振动频率。计算机仿真得到的磁悬浮系统自激振动的临界条件和振动频率与理论分析的结果基本一致 。

By using the louts criterion for Hopf bifurcation,a critical condition for the appearance of the self excited vibration caused by the change of the parameters in a nonlinear system and the corresponding frequency at this point were given.This method overcomes the drawback of previous ones which involve a good deal of computation of the eigenvalues of system's Jacobian matrix when there exist any changes of the parameters in the system.It was successfully applied to the stability analysis of a Maglev system,and the critical condition for the self excited vibration,as well as the frequency of the vibration at this point was attained.Subsequent computer simulation gave out the same results on the whole,which proves the effectiveness of the method.