平衡特征正交分解及其在机翼气弹模型降阶中的应用

Balanced proper orthogonal decomposition and its application in order reduction of aeroelastic models of aircraft wing

将平衡特征正交分解方法(Balanced Proper Orthogonal Decomposition,BPOD)应用于气弹控制系统降阶。该方法是平衡截断(balance truncation theory)与特征正交分解(Proper Orthogonal Decomposition,POD)的结合,能克服高阶系统为控制方法应用所带来的局限性。先给出BPOD方法的理论推导与降阶过程,后以三元大展弦比机翼的有限元模型为例进行仿真验证。仿真结果分析,BPOD方法可有效减少系统阶数,计算经济并保留输入输出关系,非常适用于气弹控制系统。

Balanced proper orthogonal decomposition （BPOD） was introduced to reduce the order of aeroelastic control system. The BPOD method is a combination of the proper orthogonal decomposition （POD） and balanced realization theory and can overcome the limitations caused by high dimension characteristics. The theoretical derivation and order reduction process of BPOD were presented. Then, the proposed method was applied to reduce the order of the aeroelastic model of a three-dimensional wing. Based on the analysis of numerical simulation results, it is shown that, while keeping the input-output relationship, BPOD is able to effectively reduce the system order as well as the computational cost, and is very suitable for aeroelastic control systems.