基于状态反馈参数激励系统的超谐共振分岔控制

设计了非线性参数控制器，改变了参数激励系统2 倍超谐共振时的稳态响应，减小了系统的响应幅值和消除了超谐共振时的鞍结分岔，从而消 除了跳跃和滞后现象.首先由多尺度法得到参数系统的近似频响方程，再进行分岔分析，从 而实现非线性控制的目标.通过数值模拟，说明状态反馈控制是可行的和有效的. 关键词： 参数激励 鞍结分岔 分岔控制 2倍超谐共振

Superharmonic resonance bifurcation control of parametrically excited system based on state feedback strategy

A nonlinear parametric feedback control is proposed to modify the steady_state resonance responses, thus to reduce the amplitude of the response and to eliminate the saddle_node bifurcations that take place in the resonance responses. The nonlinear gain of the feedback control is determined by analyzing the bifurcation function associated with the corresponding frequency_response equation and the Jacobian matrix. It is shown by illustrative examples that the proposed nonlinear feedback is effective for controlling superharmonic resonance responses.