以四轮转向汽车（4WS）为研究对象，利用分析力学方法，建立了二自由度动力模型。利用Hurwitz代数判据，对4WS系统Hopf分岔进行了计算，得到分岔点。利用中心流形理论将高维4WS汽车系统降到二维，并通过计算二维分岔稳定性指标的正负判定原系统Hopf分岔的类型。利用Matlab软件对系统进行了仿真。结果表明，4WS汽车在一定的参数组合下出现转向自动摆动的性质，对振动的控制研究具有重要的参考价值。
Abstract
The dynamic model of two degrees of freedom is established for an automobile with four-wheel steering (4ws) by analysis mechanics. The Hopf bifurcation of 4WS system was calculated and the bifurcation point was obtained with Hurwitz algebraic criterion. The high-dimensional 4WS system was transferred to a two-dimensional system in the light of center manifold theory, and the bifurcation stability coefficient of the two-dimensional system was calculated to determine the Hopf bifurcation type of original system. The system was simulated using Matlab software. The result shows that automatic swing of steering occurs for an automobile of 4WS under specific parameters, and it has important reference value for the research on control of vibration.
关键词
四轮转向 /
Hopf分岔 /
Hurwitz行列式 /
中心流形理论
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Key words
four-wheel steering /
Hopf bifurcation /
Hurwitz determinant /
center manifold theory
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