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:

Aiming at the mechanical centrifugal flywheel governor system, we studied the type of Hopf bifurcation and the stability of periodic solution by using the method of multiple scales. A nonlinear controller was designed to restrain the flutter caused by Hopf bifurcation. The nonlinear control gain could be determined to transform subcritical Hopf bifurcation into supercritical one and transform large amplitude of supercritical Hopf bifurcation into small
amplitude of supercritical one. The results of the theoretic 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