色噪声激励下水轮机调节系统的分岔

基于水轮机饱和非线性比例积分(proportional-integral, PI)调节系统,建立了色噪声激励下的水轮机调节系统,研究了该系统的随机分岔行为。利用统一色噪声近似原理将系统简化为一个等效非线性白噪声模型;利用中心流形定理对系统降维处理,依据随机平均法得到了伊藤微分方程及FPK方程,讨论了系统的随机分岔条件;通过数值模拟,分别讨论了系统在不同自相关时间及噪声强度影响下的随机分岔行为,验证了随机平均法理论的有效性及分岔现象的发生。

Bifurcation of hydraulic turbine governing system under color noise excitation

Based on the saturated nonlinear proportional-integral(PI)governing system of a hydraulic turbine, a hydraulic turbine governing system under the excitation of color noise is established, the stochastic bifurcation behavior of system is studied. The system is simplified to an equivalent nonlinear white noise model by using the uniform color noise approximation principle. The central manifold theorem is used to reduce the dimension of system, the Ito differential equations and FPK equations are obtained according to stochastic average method, the stochastic bifurcation condition of system is discussed. Through numerical simulation, the stochastic bifurcation behaviors of system under the influence of different autocorrelation time and noise intensity are discussed respectively, the validity of theory of stochastic averaging and the occurrence of bifurcation phenomenon are verified.