摘要:研究一类非自治旋转机械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,建立了机械式离心调速é器系统的动力学方程.通过系统的分岔图和Lyapunov指数研究系统的混沌行为,通过仿真Poincaré截面分析系统通向混凝沌的道路,并且验证该系统的分岔图与Lyapunov指数谱是完全吻合的.基于Lyapunov稳定性理论,采用非线性控制方法进行一类不同阶非自治混沌系统之间的同步控制的研究.通过构造合适的控制函数,成功地实现两个不同阶混沌系统之间的同步控制,并用数值的仿真进一步证明该方法的有效性.
The complex dynamic behavior of the mechanical centrifugal flywheel governor system was studied.The dynamical equation of the sysablished using lagrangian and Newton's second law,The chaotic behavior of the system was analyzed by means of bifurcation diagram and Lyapunov exponents.The evolution from Hopf bifurcation to chaos was shown by the shown by the bifurcation diagrams and a series of Poincaré sections under different sets of system parameters,and the bifurcation diagrams were verified by the related Lyapunov exponent spectra.Based on Lyapunov stability theory theory,a method of non-linear control was proposed for synahronization between Duffing system and mechanical centrifugal flywheel govvernor system was realized by aonstructing the appropriate non-linear controller.Numerical simulation shows the effectiveness and feassibility of the proposed method.