标题： 磁流体动力学流动的实时控制 显示英文标题

标题： Real-time control of a magnetohydrodynamic flow

摘要： 我们通过外部施加的电场和磁场产生的洛伦兹力，展示了对弱导电磁流体动力学(MHD)流动的反馈控制。 具体而言，我们使用围绕和位于流体储层周围的电极和电磁铁阵列，将电解质的流动引导至预定的速度或涡度模式，反馈由平面粒子图像测速(PIV)提供。 控制是通过模型预测控制(MPC)框架实现的，在该框架中，通过最小化流动预测演变的代价函数来计算控制信号。 预测器完全通过数据构建，使用Koopman算子理论，这使得底层非线性流体动力学能够以线性表示。 这种线性允许通过在两个小且高效可解的凸二次规划(QP)之间交替来解决MPC问题：一个用于电极，另一个用于电磁铁。 结果控制器在标准笔记本电脑上以闭环运行，实现了对流动的实时控制。 我们通过实验演示了该方法的功能，其中流动被塑造成与一系列参考速度场和时变涡度场相匹配。 显示英文摘要

摘要： We demonstrate the feedback control of a weakly conducting magnetohydrodynamic (MHD) flow via Lorentz forces generated by externally applied electric and magnetic fields. Specifically, we steer the flow of an electrolyte toward prescribed velocity or vorticity patterns using arrays of electrodes and electromagnets positioned around and beneath a fluid reservoir, with feedback provided by planar particle image velocimetry (PIV). Control is implemented using a model predictive control (MPC) framework, in which control signals are computed by minimizing a cost function over the predicted evolution of the flow. The predictor is constructed entirely from data using Koopman operator theory, which enables a linear representation of the underlying nonlinear fluid dynamics. This linearity allows the MPC problem to be solved by alternating between two small and efficiently solvable convex quadratic programs (QPs): one for the electrodes and one for the electromagnets. The resulting controller runs in a closed loop on a standard laptop, enabling real-time control of the flow. We demonstrate the functionality of the approach through experiments in which the flow is shaped to match a range of reference velocity fields and a time-varying vorticity field.