索-梁耦合结构Hopf分岔的反控制

Anti-Control of Hopf Bifurcations of Cable-Stayed Beam

论文研究了索-梁耦合结构的Hopf分岔的反控制,动态窗口滤波反馈控制器在反控制领域有着很广泛的应用.论文通过使用这种控制器,可以使得受控系统在指定的平衡点处产生Hopf分岔.最后,根据庞加莱截面和级数展开法,证明了上述方法的有效性及可行性.

In recent years, there has been increasing interest in bifurcation control. Anti-control of bi furcation, as opposed to the bifurcation control, which means to design a controller to reduce some of the existing bifurcation dynamics of a given nonlinear system, refers to a task of creating a certain bifurcation at a desired location with preferred properties by appropriate controls. In this study, the anti-control of Hopf bifurcations was investigated. A Hopf bifurcation was introduced at a designed stable equilibrium point, followed by employing a washout-filter-aided controller. The effectiveness and feasibility of using the washout-filter-aided controller to obtain a certain Hopf bifurcation at the desired location were proved based on the Poincare map and expansion method of power series. By defining a mapping, the （2 ＋ 1）-di- mensional system was created, in which the Poincare section could be suitably selected. The number of fixed points was then determined by using the second derivative of the function. In addition, the fixed points were solved using the Poincare map. The parameters of feedback controller were modified to keep the locations of equilibrium points fixed. Then, by using the washout filter-aided dynamic feedback con troller, a Hopf bifurcation was created at the desired location with preferable properties. According to the calculation of Poincare map, there existed at most one fixed point in the system. The equilibrium point co incided with the fixed point of the system designed to operate with the use of washout-filter-aided dynamic feedback controller. The periodic solution near the bifurcation point could also be obtained using the Poin care map. Based on the Poincare map theory, a Hopf bifurcation could be created at a desired location with preferred properties using the dynamic feedback controller. The finding can trigger further studies on ap- plications of the anti-control of bifurcations.