机翼颤振的 Hopf 分岔分析与控制

摘要

We considered a two-variable nonlinear system,namely,the flutter of airfoil.The type of Hopf bifurcation and the stability of periodic solution were analyzed with the method of multiple scales.The nonlinear time delay controller was designed to restrain the flutter caused by Hopf bifurcation.Thus the nonlinear control gain can be determined to transform subcritical Hopf bifurcation into supercritical one and transform supercritical Hopf bifurcation into steady points.The results of the theory analysis and numerical simulation show that the designed controller is valid.%考虑二元非线性机翼颤振系统，利用多尺度法研究系统的 Hopf 分岔类型和周期解的稳定性。设计非线性时滞控制器抑制 Hopf 分岔引起的颤振，将原系统的亚临界 Hopf 分岔变为超临界 Hopf 分岔，将原系统的超临界 Hopf 分岔控制为稳定。理论分析和数值模拟结果验证了所给控制方法的有效性。