数据驱动的颤振抑制：基于HODMD、DMDc与约束MPC
Data-Driven Flutter Suppression via HODMD, DMDcand Constrained MPC
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- Facultad Politecnica, Universidad Nacional de Asuncion（亚松森国立大学技术学院）
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中文总结 AI 辅助
本工作提出结合HODMD、DMDc与约束MPC的数据驱动框架，用于执行器约束下的颤振抑制，在噪声下实现低误差识别与稳定控制，并通过多项仿真验证其可行性。
中文摘要 AI 辅助
本工作提出了一种可解释的数据到控制框架，用于执行器约束下的颤振抑制，该框架结合了高阶动态模态分解（HODMD）、带控制的动态模态分解（DMDc）和模型预测控制（MPC）。主要案例是一个带有后缘襟翼和有理非定常气动力的俯仰-沉浮典型截面。HODMD从四个测量的结构通道中识别出亚临界、近临界和超临界状态下的主导频率和增长率。在2% RMS传感器噪声下，近临界增长率误差为1.8 x 10^-3 s^-1，显著低于未采用延迟嵌入的标准DMD。由HODMD子空间形成一个五状态实降阶模型，其襟翼输入矩阵通过DMDc从小幅PRBS记录中估计。对于独立的啁啾输入，所有通道的归一化误差为2.4 x 10^-3。约束MPC在初始俯仰扰动为8度、襟翼限制为1度的情况下稳定了真实的超临界对象，而由同一模型设计的饱和LQR则达到规定的有效性极限。三项辅助研究评估了可迁移性。SU2模拟显示HODMD频率恢复与可用的频谱分辨率一致；OpenFOAM动态网格计算显示铰接襟翼力矩权限在2至8度范围内近似线性，且增益随频率变化；一个双向SU2 Python-FSI案例展示了基于比例-微分基线的有界扰动抑制。这些研究支持模态识别、执行器权限和闭环可行性，但并未作为CFD级别的MPC验证。该框架提供了一条从早期测量到约束气动弹性控制的可复现路径。
英文摘要
This work presents an interpretable data-to-control framework for actuator-constrained flutter suppression by combining higher-order dynamic mode decomposition (HODMD), dynamic mode decomposition with control (DMDc), and model predictive control (MPC). The primary case is a pitch-plunge typical section with a trailing-edge flap and rational unsteady aerodynamics. HODMD identifies the dominant frequency and growth rate in subcritical, near-critical, and post-critical regimes from four measured structural channels. With 2% RMS sensor noise, the near-critical growth-rate error is 1.8 x 10^-3 s^-1, substantially lower than with standard DMD without delay embedding. A five-state real reduced-order model is formed from the HODMD subspace, and its flap-input matrix is estimated from a small-amplitude PRBS record using DMDc. For an independent chirp input, the normalized error over all channels is 2.4 x 10^-3. The constrained MPC stabilizes the true post-critical plant for an initial pitch perturbation of 8 degrees with a flap limit of 1 degree, whereas saturated LQR designed from the same model reaches the prescribed validity limit. Three supporting studies assess transferability. SU2 simulations show HODMD frequency recovery consistent with the available spectral resolution; OpenFOAM dynamic-mesh calculations show nearly linear articulated-flap moment authority from 2 to 8 degrees with frequency-dependent gain; and a two-way SU2 Python-FSI case demonstrates bounded disturbance rejection using a proportional-derivative baseline. These studies support modal identification, actuator authority, and closed-loop feasibility, but are not presented as CFD-level MPC validation. The framework provides a reproducible route from early-time measurements to constrained aeroelastic control.
