一类参数激励系统的非线性时滞反馈分岔控制

Bifurcation control for a kind of parametric system using the time delay controller

采用平均化方法,研究参数激励和强迫激励联合作用的非线性动力系统.以平均方程研究系统平衡点附近流形,利用分岔响应方程,研究系统的分岔动力特性与主要参数的关系.通过对两种非线性时滞控制器与线性时滞控制器的比较,分析非线性时滞控制器的分岔控制特点,比较与线性时滞控制器的优劣性.结果表明,两种平方非线性时滞控制器的控制效果均与激励幅值有关,在同等增益的条件下,激励幅值越大控制效果越好,但对于没有强迫激励的参数激励系统,该类非线性时滞控制器失效.

The averaged method is used to study the bifurcations of a kind of nonlinear dynamical system which is excited the parametric and forced combination excitation.The averaged equations are obtained and used to study the manifold near the equilibrium points.The bifurcation equation is used to analyze the relationship between the bifurcation points and system parameters.Linear and nonlinear time delay controllers are compared to study controller design.Based on the bifurcation control characteristics of the linear and nonlinear time delay controllers,the merits and demerits of the time delay controllers are analyzed.It shows that the efficiency of these two kind nonlinear controller in our work is related to the forced excitation.For the nonlinear controller,the larger amplitude of the excitation induce the better control effect of the controller.But,the nonlinear controller may be invalid for the nonlinear parametric system without forced excitation.