科研之友
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摘要
Periodic solutions for a parametrically excited van der Pol system with nonlinear stiffness and under state feedback control with a time delay are investigated. Two slow flow equations for the amplitude and phase of the parametric resonance response are derived. It is well known that their fixed points correspond to phase-locked periodic solutions for the starting system. In the system without control, periodic solutions exist only for fixed values of amplitude and phase and depend on the system parameters and excitation amplitude. The stable condition for steady-state response is given by the Routh - Hurwitz criterion, but in many cases the amplitudes of periodic solutions do not correspond to the technical requirements. On the contrary, it is demonstrated that, if the vibration control terms are added, stable periodic solutions with arbitrarily chosen amplitude and phase can be accomplished. An effective vibration control is then possible if appropriate time delay and feedback gains are chosen.
- 出版日期2007-11
