基于BPOD的气动弹性降阶及其在主动控制中的应用

Model reduction using BPOD and its application to aeroelastic active control

流体动力系统是一个高阶的非线性复杂系统,这严重限制了优化和控制在该系统中的应用。模型降阶技术是解决这一问题的有效工具。将特征正交分解方法(Proper Orthogonal Decomposition,POD)和平衡截断方法结合起来,形成平衡特征正交分解方法(Balanced Proper Orthogonal Decomposition,BPOD),并应用到气动伺服弹性模型降阶中。该方法将由POD快照得到系统可控和可观Gramian矩阵的近似表达,通过该近似得到平衡降阶模型。以一个二维翼段的气动弹性系统为例,首先将流体控制方程线化;然后利用BPOD方法得到非定常气动力的降阶模型以及降阶的气动弹性系统;最后,对降阶系统设计主动控制律,通过控制面偏转来抑制翼型颤振。数值仿真结果表明BPOD降阶模型可以精确地模拟高阶非线性的流体动力系统并且可以有效地应用于气动弹性主动控制中。

It is badly limited to apply optimization and control into fluid dynamic system as its high-dimensional and nonlinear characteristic. Model reduction technique is a powerful tool to solve the problem. In this paper, the balanced proper orthogonal decomposition （BPOD） which is combined POD with balance truncation theory is applied to aeroservoelastic model reduction. The POD snapshot is used to obtain approximations to the system controllability and observability gramians. The approximations are then applied to obtain balanced reduced-order model. For a two-dimensional airfoil aeroelastic system, the unsteady aerodynamic reduced-order model and then the reduced aeroelastic model are constructed by BPOD method. Finally, an active control law is designed for the reduced-order system to suppress the airfoil flutter via the control surface deflection. The numerical results show that the BPOD reduced-order model can accurately simulate the high-dimensional nonlinear fluid dynamic system and effectively apply to aeroelastic active control.