Under the actions of ocean currents and/or waves, deep-sea flexible risers are often subject to vortex-induced vibration (VIV). The VIV can lead to severe fatigue and structural safety issues caused by oscillatory periodic stress and large-amplitude displacement. As flexible risers have natural modes with lower frequency and higher density, a multimode VIV is likely to occur in risers under the action of ocean currents, which is considered as shear flow. To decrease the response level of the VIV of the riser actively, a multimode control approach that uses a bending moment at the top end of the riser via an LQR optimal controller is developed in this study. The dynamic equations of a flexible riser including the control bending moment in shear flow are established both in the time and state-space domains. The LQR controllers are then designed to optimize the objective function, which indicates the minimum cost of the riser's VIV response and control input energy based on the Riccati equation of the closed-loop system under the assumption that the lift coefficient distribution is constant. Finally, the VIV responses of both the original and closed-loop systems under different flow velocities are examined through numerical simulations. The results demonstrate that the designed active control approaches can effectively reduce the riser displacement/angle by approximately 71%–89% compared with that of the original system. Further, for multimode control, the presented mode-weighted control is more effective than the mode-averaged control; the decrease in displacement is approximately 1.13 times than that of the mode-averaged control. Owing to the increase in flow velocity as more and higher-order modes are excited, the VIV response of the original system decreases slightly while the frequency response gradually increases. For the closed-loop system, the response becomes smaller and more complicated, and the efficiency of the controller becomes lower at a certain flow velocity.

在洋流和/或波浪的作用下，深海柔性立管经常受到涡激振动（VIV）的影响。VIV 可导致由振荡周期性应力和大振幅位移引起的严重疲劳和结构安全问题。由于柔性立管具有较低频率和较高密度的固有模式，在洋流的作用下，立管中很可能发生多模态VIV，这被认为是剪切流。为了主动降低立管VIV的响应水平，本研究开发了一种通过LQR优化控制器在立管顶端使用弯矩的多模式控制方法。在时间域和状态空间域中建立了包括剪切流中控制弯矩的柔性立管的动力学方程。然后设计 LQR 控制器以优化目标函数，该函数指示在升力系数分布恒定的假设下，基于闭环系统的 Riccati 方程的立管 VIV 响应和控制输入能量的最小成本。最后，通过数值模拟检查了原始系统和闭环系统在不同流速下的 VIV 响应。结果表明，与原始系统相比，所设计的主动控制方法可以有效地减少立管位移/角度约 71%–89%。此外，对于多模控制，所提出的模加权控制比模平均控制更有效；位移的减少大约是模式平均控制的 1.13 倍。由于随着更多和更高阶模式被激发，流速增加，原始系统的VIV响应略有下降，而频率响应逐渐增加。对于闭环系统，响应变得更小、更复杂，在一定流速下控制器的效率变低。