一类离心调速器的Hopf分岔及其混沌控制

研究了受外部扰动的离心调速器系统的复杂动力学行为。通过系统运动的拉格朗日方程和牛顿第二定律,建立了离心调速器系统的动力学方程,应用Lyapunov直接方法分析了该系统平衡点的稳定性。利用相图分析了系统超混沌吸引子的特性,通过Poincaré截面和Lyapunov指数研究了系统的超混沌行为,通过仿真系统的分岔图和相图分析了系统通向混沌的道路,并且验证了该系统的分岔图与Lyapunov指数谱是完全吻合的。通过对系统施加非线性反馈控制器,并选取合适的反馈系数,可以获得各种不同的所需的稳定周期轨道。对受外部扰动的离心调速器系统施于此控制,计算机数值模拟结果表明,这种控制方法简便有效,控制范围广。

Hopf Bifurcation and Chaos Control for A Type of Centrifugal Governor

The dynamics behavior of a centrifugal flywheel governor system which is subjected to external disturbance is studied here.By mechanical analyzing,the dynamical equation of the system are established,the Lyapunov direct method is applied to obtain stability conditions of the equilibrium points of the system.The characteristic of hyperchaotic attractors of the system are analyzed by phase portraits.Poincare sections and Lyapunov exponents are used to analyze the hyperchaotic behavior of the system.Two positive Lyapunov exponents along with one zero and one negative Lyapunov exponent are obtained.Routes from Hopf bifurcation to chaos are analyzed by bifurcation diagrams and phase portraits,and Lyapunov exponents corresponding to bifurcation diagrams of the system are confirmed.By two methods,hyperchaotic behavior of the system is controlled.Steady periodic orbits of the system are obtained under effective control. Based on non-linear feedback control and adjusting feedback coefficients,different stable periodic orbits are obtained.Numerical simulation results show that the control methods are effective and the control range is broad.