Abstract: This paper presents an active control system design based on LQR (Linear Quadratic Regulator) method for hypersonic airfoil flutter. Firstly, based on hypersonic two-dimensional airfoil model with cubic physical nonlinearity and aerodynamic nonlinearity, eigenvalues at the zero equilibrium point are analyzed, and a Hopf-bifurcation point is obtained. Then, a quadratic performance index of system is given, and an active control system based on the LQR method for hypersonic airfoil flutter is designed. The control algorithm can effectively inhibit the continuous oscillation at the Hopf-bifurcation point, moreover, it is simple and easy to realize in engineering. Finally, the simulation results verify the effectivity of the control method.

摘要： 基于LQR（Linear Quadratic Regulator）方法研究了高超声速机翼颤振的主动控制系统的设计。首先，针对同时具有结构立方非线性和气动非线性的高超声速飞行器的二元机翼模型，通过对其在零平衡点的特征值进行分析，得到系统的Hopf分叉点。然后确定系统的性能指标，基于LQR方法设计了高超声速机翼颤振主动控制系统，有效地抑制了Hopf分叉点处持续振荡的颤振，算法简单，易于工程实现。最后通过仿真验证了控制方法的有效性。

关键词: 振动与波, 高超声速, 机翼颤振, 主动控制, Hopf分叉, LQR