含间隙超音速二元弹翼非线性颤振与主动控制

Nonlinear flutter and active control of the supersonic two-dimensional missile wings with a freeplay

研究含间隙超音速二元弹翼非线性颤振特性和主动控制问题.采用三阶活塞理论建立了含间隙二元弹翼非线性气动弹性动力学方程,利用Hopf分岔理论、谐波平衡法和数值方法,分析了系统的非线性颤振特性.应用基于微分几何法和二次型最优控制相结合的方法设计非线性系统控制器,推迟临界分岔速度.应用滑模变结构控制方法设计控制器,有效抑制非线性颤振,并讨论了控制参数对控制效果的影响.仿真结果表明,所设计的控制律可以有效地实现对含间隙超音速二元弹翼系统非线性颤振的控制.最后计算了在基础激励扰动下系统的动态响应,分别得到了周期运动、多周期运动、概周期运动以及混沌运动.

The nonlinear flutter characters and active control of the supersonic two-dimensional missile wings with a freeplay are investigated. Adopting the third-order piston, the nonlinear aeroelastic dynamic equations with freeplay nonlinearity are derived, nonlinear flutter character analysis of the systems are obtained by hopf bifurcation theory, harmonic balance method and numerical method respectively. The design method based on differential geometry and quadratic optimal control for nonlinear system controller is used to postpone the critical flutter speed. The sliding mode variable structure control for nonlinear system controller is used to stabilize the nonlinear flutter. Then, the influence of the controller and the parameters are analyzed. The simulation result shows that the two control methods are effective ways in control of nonlinear flutter. At last, the dynamical response with the base excitation disturbance are calculated, the single-periodic motion, the multi-periodic motion, the quasi-periodic motion and the chaotic motion are obtained.