关键词: 亚临界Hopf分岔, 超临界Hopf分岔, 非线性控制, 多尺度法

Abstract:

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.

Key words: subcritical Hopf bifurcation, supercritical Hopf bifurcation, nonlinear control, method of multiple scale