强迫Duffing振动系统的主共振鞍结分岔控制

设计了非线性参数控制器来改变非线性系统的稳态响应，减小了系统的响应幅值并消除了共振时的鞍结分岔。首先由多尺度法得到系统的近似频响方程，再由奇异性理论来分析分岔特性，从而实现非线性控制的目标。最后对强迫Duffing系统的主共振形式进行了分析，由数值模拟来确定分岔控制是可行的和有效的。

Primary Resonance Saddle-Node Bifurcation Control of Forced Duffing System

A nonlinear parametric feedback control is proposed to modify the steady-state responses, thus to reduce the amplitude of the response and to eliminate the saddle-node bifurcations,which may arise in the nonlinear response of a forced Duffing system under the primary resonance. The nonlinear feedback gain is determined by the modulation equations from the singularity theory. By theoretically analyzing the modified modulation equations, the saddle-node bifurcation can be eliminated for the trivial steady state in the frequency response. Furthermore, by performing numerical simulations, and by comparing the response curves of the uncontrolled and the controlled system, we clarify that the proposed bifurcation control is available for removing the jump phenomenon and suppressing the steady-state responses in the primary resonance response.