气动伺服弹性系统数据驱动LPV低阶模型的平衡模态分解算法
The Balanced Mode Decomposition Algorithm for Data-Driven LPV Low-Order Models of Aeroservoelastic Systems
摘要：
提出了一种新的高维时变系统降阶建模方法。它利用了动态模式分解技术的形式主义以及平衡实现的概念。假设系统上唯一可用的信息来自数值模拟生成的输入、状态和输出轨迹，或在实验期间记录和估计，因此该方法完全是数据驱动的。我们的目标是获得一个输入-输出低维线性模型，该模型近似于整个系统的操作范围。由于气动伺服弹性系统的动态特性在运行中会发生显著变化（例如，由于飞行速度或高度的变化），因此在所构造的模型中保留了随时间变化的特征。这是通过生成由状态一致的线性时不变降阶模型的集合组成的线性变参数表示来实现的。该算法的制定取决于这样的想法，即用完全从数据构建的平衡斜投影来替换在基于动态模式分解的方法中使用的到固有正交分解模式上的正交投影。因此，与到相同或更低大小的子空间上的其他投影相比，在较低维度表示中捕获的输入-输出信息增加。此外，参数变化的投影是可能的，同时还实现状态一致性。所提出的方法的有效性证明了对最近在文献中提出的两种算法的性能比较变形机翼的机载风能应用。比较涵盖了模型预测控制应用中的预测精度和性能。
英文摘要：
A novel approach to reduced-order modeling of high-dimensional time varying systems is proposed. It leverages the formalism of the Dynamic Mode Decomposition technique together with the concept of balanced realization. It is assumed that the only information available on the system comes from input, state, and output trajectories generated by numerical simulations or recorded and estimated during experiments, thus the approach is fully data-driven. The goal is to obtain an input-output low dimensional linear model which approximates the system across its operating range. Since the dynamics of aeroservoelastic systems markedly changes in operation (e.g. due to change in flight speed or altitude), time-varying features are retained in the constructed models. This is achieved by generating a Linear Parameter-Varying representation made of a collection of state-consistent linear time-invariant reduced-order models. The algorithm formulation hinges on the idea of replacing the orthogonal projection onto the Proper Orthogonal Decomposition modes, used in Dynamic Mode Decomposition-based approaches, with a balancing oblique projection constructed entirely from data. As a consequence, the input-output information captured in the lower-dimensional representation is increased compared to other projections onto subspaces of same or lower size. Moreover, a parameter-varying projection is possible while also achieving state-consistency. The validity of the proposed approach is demonstrated on a morphing wing for airborne wind energy applications by comparing the performance against two algorithms recently proposed in the literature. Comparisons cover both prediction accuracy and performance in model predictive control applications.
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