高斯白噪声激励下含分数阶PD控制器广义DVP系统的随机P-分岔  

Stochastic P-bifurcation of Generalized DVP System with Fractional Order PD Controller under Gaussian White Noise Excitation

作　　者：王慧男 盛正大 王媛 王芳 WANG Hui-nan;SHENG Zheng-da;WANG Yuan;WANG Fang(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《兰州文理学院学报（自然科学版）》2023年第6期30-35,66,共7页Journal of Lanzhou University of Arts and Science(Natural Sciences)

基　　金：国家自然科学基金项目(61863022)。

摘　　要：研究了高斯白噪声激励下含分数阶PD控制器广义DVP系统的随机P-分岔.依据均方最小误差原理将含分数阶PD控制器系统转化为等价的整数阶系统,利用随机平均法求得系统幅值的稳态概率密度函数,且分析了分数阶PD控制器的相关参数及系数对系统的影响,结合稳态概率密度函数曲线图发现改变其参数及系数会诱导系统发生随机P-分岔行为.The stochastic P-bifurcation of generalized DVP system with fractional order PD controller under Gaussian white noise excitation is investigated.According to the principle of minimal mean square error,the system with fractional order PD controller is transformed into an equivalent integer order system,and the stationary probability density function of the system’s amplitude is obtained by stochastic averaging method.The effects of the parameter and coefficient of the fractional order PD controller on the system are analyzed,and it is found that changing the parameter and coefficient of the system will induce stochastic P-bifurcation in the system by combining with the stationary probability density function diagram.

关 键 词：高斯白噪声 分数阶PD控制器 广义DVP系统 随机平均法 随机P-分岔 

分 类 号：O324[理学—一般力学与力学基础]