一类离心调速器系统的分岔与混沌特性

BIFURCATION AND CHAOS OF A TYPE OF CENTRIFUGAL GOVERNOR SYSTEM

研究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,建立离心调速器系统的动力学方程。由Taylor级数展开得到离心调速器系统的扰动方程,应用Lyapunov直接方法分析该系统平衡点的稳定性。用四阶Runge-Kutta算法计算系统的全局分岔图,借助Poincar啨截面和Lyapunov指数对系统的运动形态进行分析。结果发现离心调速器系统中有周期泡现象。数值仿真进一步研究系统的Hopf分岔,通过对系统参数的不断变化,分析得出系统由Hopf分岔通向混沌的演化过程,并且验证该系统的全局分岔图与Lyapunov指数谱是完全吻合的.

The complex dynamic behavior of the centrifugal flywheel governor system subjected to external disturbance is studied. The dynamical equation of the system is established using Lagrangian and Newton＇s second law. By the Taylor series truncation, the disturbed differential equations of the above system are obtained. The Lyapunov direct method is applied to obtain conditions of stability of the equilibrium points of system. The bifurcation diagram of the system is obtained by the fourth order Runge-Kutta method. The characteristics of the system responses are analyzed by means of Poincaré sections and the Lyapunov exponents. Numerical simulation results show that Hopf bifurcation exists in the bifurcation diagram of the system. And the bubbling bifurcation sequence of peried-1-2-1 cycles occasionally occurs in the bifurcation diagram. The evolution from Hopf bifurcation to chaos is shown by the bifurcation diagrams and a series of Poincaré sections under different sets of system parameters, and the bifurcation diagrams are verified by the related Lya： punov exponent spectra.