Applying LQR to control cross vortex-induced vibration of cylinders based on wake oscillators

Active control of a cylinder's vortex-induced vibration is a research hotspot, and proposing a theoretical model for real-time control of a cylinder's vortex-induced vibration is the foundation of engineering applications. Therefore, this article studies applying the LQR method to control the cross vortex-induced vibration of a single cylinder based on wake oscillators. Firstly, a theoretical control model of the LQR method and wake oscillator was established, and then the model's correctness and numerical solution were verified. Finally, numerical analysis was conducted to investigate the influence of different control parameters on the control of a cylinder's vortex-induced vibration. During the control process, there was no nonlinear bifurcation frequency doubling phenomenon caused by the wake oscillator. Controlling the displacement of a cylinder is more effective than controlling its speed, and the controlled displacement of the cylinder is close to a stationary state, with a lift force close to 2.0. The maximum displacement and lift suppression efficiency is 98.64% and 55.16%. In some cases, the maximum value of hydrodynamic energy at the original system is around 43.85 times that of control systems.