摘要
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。
A nonlinear parametric feedback control is proposed to modify the steady-state responses, which can reduce the amplitude of the response and can eliminate the saddle-node bifurcations. 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 comparing the response curves of the uncontrolled and the controlled systems, 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.
出处
《振动工程学报》
EI
CSCD
北大核心
2004年第3期365-368,共4页
Journal of Vibration Engineering
基金
湖南省自然科学基金资助项目 (编号 :0 1JJY2 0 0 7)
关键词
非线性振动
分岔控制
非线性反馈控制
强迫Duffing系统
主共振
Bifurcation (mathematics)
Computer simulation
Feedback control
Frequency response
Nonlinear control systems
Resonance
