具有时滞反馈控制的非线性主动悬架系统的稳定性、分岔和混沌

Stability,bifurcation and chaos of nonlinear active suspension system with time delay feedback control

研究了具有时滞反馈控制的非线性主动悬架系统模型,该模型考虑了悬架弹簧和阻尼的非线性特性。运用广义Sturm准则推导了时滞无关稳定区域的临界增益和稳定性开关的临界时滞。在不同稳定性区间内选取参数组合进行数值模拟,验证理论分析的有效性。在动力学方程的基础上,利用分岔图、庞加莱映射图和时域图,研究了在路面激励下的悬架系统的非线性动力学行为。结果表明,在增益系数和阻尼系数g~ζ1平面内存在一个小的参数区间来实现时滞无关稳定性,并且区间范围随着悬架阻尼系数的增加而增大。当受控系统不具有时滞无关稳定性时,系统会随着时滞的变化而发生稳定性切换,这些稳定性开关对应时滞跨越临界值时发生的Hopf分岔。数值仿真验证了理论分析的正确性。时滞作为分岔参数,观察到系统由准周期运动通往混沌运动的途径:准周期环面破裂。

Here,a nonlinear active suspension system model with time delay feedback control was studied considering nonlinear characteristics of suspension spring and damping.The critical gain of delay independent stable region and the critical delay of stability switch were derived by using the generalized Sturm criterion.The effectiveness of the theoretical analysis was verified using numerical simulation with chosen parametric combinations in different stability intervals.Based on dynamic equations,nonlinear dynamic behavior of the suspension system under road excitation was studied by using bifurcation diagram,Poincare map and time domain diagram.The results showed that there is a small parameter interval in gain coefficient-damping coefficient plane to realize delay independent stability,and the interval range increases with increase in suspension damping coefficient;when the controlled system has no delay independent stability,the system can have stability switching with change of time delay;these stability switches correspond to Hopf bifurcations when time delay crosses critical value;numerical simulation verifies the correctness of the theoretical analysis;when time delay is taken as a bifurcation parameter,the system’s path from quasi-periodic motion to chaotic one is observed,i.e.,rupture of quasi-periodic torus.