Feedback Control of Fluid-Structure Interaction via Koopman-based Reduced-Order Model

This study proposes an active flow control framework for fluid–structure interaction (FSI) systems involving a flexible flag in the wake of a cylinder by integrating Koopman-based reduced-order models (ROMs) with model predictive control (MPC). A novel switched-system control strategy employs kernel dynamic mode decomposition (KDMD) and residual DMD are employed to construct accurate ROMs that capture nonlinear FSI dynamics while suppressing spurious modes. These ROMs provide efficient state predictions over a receding horizon, allowing the MPC optimizer to compute real-time actuation inputs. To enhance control performance, resolvent analysis determines optimal actuator and probe placement, and three strategically placed structural probes are sufficient to capture dominant Koopman modes. The framework successfully stabilizes three characteristic dynamic regimes: large-amplitude flapping (LAF), small-deflection flapping (SDF), and small-amplitude flapping (SAF). Koopman modal decomposition and energy analysis reveal distinct control mechanisms. LAF and SAF regimes are stabilized by locally modulating existing saturated modes, requiring low actuation energy. In contrast, SDF control generates new Koopman modes that disrupt symmetry-breaking dynamics, demanding higher control energy. Compared to reinforcement learning, the proposed Koopman-MPC framework achieves comparable control performance with significantly reduced computational cost. 本研究通过将基于库夫曼的降阶模型(ROM)与模型预测控制(MPC)相结合,提出了一种用于流固耦合(FSI)系统的主动流动控制框架,该系统涉及圆柱体尾流的柔性标志。一种新的开关系统控制策略采用核动态模态分解(KDMD),并采用残差DMD来构建精确的ROM,在抑制杂散模式的同时捕获非线性FSI动力学。这些ROM可在后退的视界内提供有效的状态预测,使MPC优化器能够计算实时驱动输入。为了提高控制性能,分辨率分析确定了最佳的致动器和探头位置,并且战略性放置的三个结构探头足以捕获占主导地位的 Koopman 模式。该框架成功稳定了三种特征动态状态:大振幅扑动(LAF)、小挠度扑动(SDF)和小振幅扑动(SAF)。考夫曼模态分解和能量分析揭示了不同的控制机制。LAF 和 SAF 状态通过局部调节现有饱和模式来稳定,需要低驱动能量。相比之下,SDF 控制会产生新的库夫曼模式,破坏破坏对称的动力学,需要更高的控制能量。与强化学习相比,所提出的Koopman-MPC框架在显著降低计算成本的情况下实现了相当的控制性能。