含时滞半主动天棚悬架系统的解析研究

Analytical Study on Semi-active Skyhook Suspension with Time Delay

研究了含时滞的半主动天棚悬架系统的非线性动力学。首先,采用平均法求出了半主动悬架系统的近似解析解,并通过Matlab仿真得到了数值解,以位移传递率作为评判指标对二者进行了比较,发现近似解析解具有令人满意的精度;然后,利用Lyapunov理论对该系统进行了稳定性分析,发现无时滞时系统始终是稳定的,含时滞系统的稳定性是随着时滞大小周期变化的,且变化周期等于激励周期,说明时滞对半主动天棚悬架系统有着重要的影响。

The nonlinear dynamics of a semi-active suspension system under skyhook control with time delay are studied.First,the approximate analytical solution for the semi-active suspension system is obtained using the averaging method.The numerical solution is also obtained through simulation in Matlab software.The comparison between the displacement transmissibilities for the two methods verifies that the approximate analytical solution has satisfactory precision.Furthermore,the stability analysis for this system is completed based on the Lyapunov stability theory.The results show that the system without time delay is unconditionally stable,while the stability of the delayed system varies periodically with time delay.The variation period is the same as that of the excitation.The results verify that time delay is important in the semi-active suspension system under skyhook control.