基于Wash-out滤波器技术的机翼颤振控制

研究应用wash-out滤波器技术对具有立方非线性俯仰刚度的二元机翼颤振的控制。首先，确定需要引入Hopf分岔的点，并在该点将原系统方程Jordan化；其次，对于引入的wash-out滤波控制器，先按Hopf分岔条件确定线性控制增益，再用规范型直接法得到受控系统的规范型，由分岔类型与规范型系数的关系确定非线性控制增益，从而将原系统的亚临界Hopf分岔变为超临界Hopf分岔；最后通过数值模拟验证了控制的有效性，并发现受控系统的颤振幅值（极限环大小）大大降低。

Flutter Control of a Two-dimensional Airfoil Using Wash-out Filter Technique

The wash-out filter (WF) technique is used to control the flutter of a two dimensional airfoil with cubic non-linearity in incompressible flow. Firstly, Hopf bifurcation theory is used to determine the point at which the nonlinear controller is introduced. The system is then transformed into Jordan canonical form, based on analysis of linearized eigenvalues of the system. Secondly, for the introduced WF controller, the linear control gain is determined according to Hopf bifurcation condition. The symbolic computing program of normal form direct method (NFDM) is also used to obtain the normal form of the controlled system. The non-linear control gain can be determined based on the relation of the type of bifurcation and the parameters of the normal form, to transform sub-critical Hopf bifurcation to be super-critical one. Lastly, numerical simulations are used to certify the validity of theoretical analysis, in which the amplitude of flutter or limit cycle of the controlled system is reduced greatly, comparing to the original system.