基于降阶模型的气动弹性主动控制律设计

流体/结构耦合数值模拟是目前解决复杂气动弹性问题精度最高的方法。但由于计算效率比较低,模型阶数过高,不能直接用于气动弹性系统的主动控制律设计。为了对主动控制系统设计提供高效高精度状态空间模型,研究了气动弹性系统的时域正则正交分解(POD)/降阶模型(ROM)方法,并引入平衡截断(BT)技术进一步降低时域POD/ROM的阶数,从而有效克服了时域POD/ROM阶数过高的缺点。在此基础上建立了基于POD-BT/ROM的气动伺服弹性降阶方程。以AGARD445.6机翼为例,说明了时域POD/ROM建模的各个细节,并将其用于气动弹性主动控制律的设计。计算结果表明,POD/ROM具有接近计算流体力学(CFD)/计算结构动力学(CSD)耦合计算的精度,同时又大大提高了计算效率约1～2个量级,是一种高精度高效率的气动弹性主动控制系统设计工具。

Design of Active Control Law for Aeroelastic Systems via Reduced Order Models

Currently the method of highest accuracy for complex aeroelastic systems is fluid-structure coupled numerical simulation. However, because of its low efficiency and higher order, it cannot be directly used to design the active control law for an aeroelastic system. To deal with the problem, a reduced order model (ROM) based on time-domain proper orthogonal decomposition (POD) is investigated. The order of time-domain POD/ROM is much higher than that of the frequency-domain POD/ROM;therefore a POD-BT/ROM is developed by introducing the balanced truncation (BT) method in control theory. Then a reduced-order aeroservoelastic model based on POD-BT/ROM is built. Details of the construction of time-domain POD/ROM and the design of active control law are demonstrated by AGARD 445.6 wing. The numerical results show that the POD/ROM has nearly the same accuracy as the computational fluid dynamics (CFD)/computational structure dynamics (CSD) coupled method and it improves the computation efficiency by about 1-2 orders of magnitude. It is a highly efficient and accurate active control law design tool for aeroelastic systems.