摘要
考虑二元非线性机翼颤振系统,利用多尺度法研究系统的Hopf分岔类型和周期解的稳定性.设计非线性时滞控制器抑制Hopf分岔引起的颤振,将原系统的亚临界Hopf分岔变为超临界Hopf分岔,将原系统的超临界Hopf分岔控制为稳定.理论分析和数值模拟结果验证了所给控制方法的有效性.
We considered a two-variable nonlinear system,namely,the flutter of airfoil.The type of Hopf bifurcation and the stability of periodic solution were analyzed with the method of multiple scales.The nonlinear time delay controller was designed to restrain the flutter caused by Hopf bifurcation.Thus the nonlinear control gain can be determined to transform subcritical Hopf bifurcation into supercritical one and transform supercritical Hopf bifurcation into steady points.The results of the theory analysis and numerical simulation show that the designed controller is valid.
出处
《吉林大学学报（理学版）》
CAS
CSCD
北大核心
2015年第4期647-654,共8页
Journal of Jilin University:Science Edition
基金
国家自然科学基金(批准号:11072085)
吉林省科技发展计划项目(批准号:20130101065JC)
关键词
亚临界Hopf分岔
超临界Hopf分岔
非线性控制
多尺度法
subcritical Hopf bifurcation
supercritical Hopf bifurcation
nonlinear control
method of multiple scale
