基于Washout滤波器的Rssler系统Hopf分岔控制

Hopf bifurcation control of the Rssler system based on Washout filter controller

针对Rssler系统平衡点的Hopf分岔,以Washout滤波器为控制器,详细讨论了控制器参数对Hopf分岔点位置、分岔类型以及周期解振幅的控制问题.首先根据Routh-Hurwitz判据计算了受控系统的参数空间稳定域,找出了对应的Hopf分岔边界,并由此分析了滤波器时间常数、线性控制增益对分岔点位置的影响.然后,引入NormalForm直接法方便地求出系统Hopf分岔Normal Form系数,由此确定出改变分岔类型和周期解振幅的控制器非线性增益选择原则.最后用数值计算验证了本文的结论.

The Washout filter is adopted to control Hopf bifurcation in Rssler system.The effect of its parameters on the position of bifurcation point,the bifurcation type,and the amplitude of periodic solution is discussed in detail.Based on Routh criterion,the stability region in parameter space is found out firstly.Then the influence of the filter＇s time constant and the linear gain on the location of bifurcation point is analyzed.By using the Direct Normal Form method,the normal form of the controlled Rssler system is deduced and the coefficient of resonant term is expressed as a function of the nonlinear gain.It is revealed that,by changing the sign and the absolute value of the real part of the coefficient,the nonlinear gain can modify the periodic solution＇s amplitude and Hopf bifurcation type.All the results obtained are verified by numerical simulation.