迟滞非线性气动弹性反馈线性化自适应控制

Aadptive control with feedback linearization of hysteresis nonlinear aeroelasticity

首先将含操纵面二元机翼的动态方程以状态空间形式描述,基于Lie导数对其进行了输入/输出局部反馈线性化;然后考虑迟滞非线性模型存在参数不确定性的情况下,利用Lyapunov稳定性理论进行了自适应控制律设计.仿真结果显示:在内动态稳定的情况下,所设计的控制律能够使开环不稳定气动弹性系统受扰后快速地回复到原来的稳定状态,并且在控制面偏转存在限制的情况下仍能实现对非线性颤振的控制.

The question of active flutter control of prototypical aeroelastic wing section in subsonic uncompressible flow is investigated. The dynamic equations of a two-dimensional airfoil with control surface are described in state space. Then based on Lie derivative, the partial input/output feedback linearization was obtained. Suppose that there is parametric uncertainty in the hysteresis nonlinear model, Lyapunov function was used to design an adaptive control law. The simulation results show that the unstable aeroelastic system exhibit limit circle oscillation while the closed loop system, including the adaptive control law, become stable. It should be emphasized that the control law can be used only when the internal dynamics is stable. Even if there is a hard constraint on the control input, satisfactory responses can be achieved.