Active Control of Flexible Riser Vibration by Boundary Control Based on LQR Controller

Abstract

The lateral displacement and the rotational angle of marine riser are likely to get larger as it is in stronger ocean current and, particularly, undergoes the consequences such as vortex-induced vibration or collisions between individual risers. The riser vibration with large amplitude value will lead to fatigue or coating damage of the structural body. In this study, the active vibration control, in terms of its angle and the displacement reductions, of a flexible riser under time-varying distributed load are considered using boundary control. The governing equations of the structural dynamics involving the control system of a flexible riser are built. The riser is modeled as an Euler-Bernoulli beam under the actions of ocean loads and the feedback controller. A torque actuator is introduced at the upper riser boundary, and the control law is employed to generate the required signal for riser angle control and displacement reduction. The feed-back control law is designed in state space, and the optimization of the control law is implemented based on the LQR approach. The linear quadratic regulator is used to determine the gain matrix, which can calculate the boundary control law by solving the Recatti equation. Based on the numerical simulations, the responses of the open-loop system and closed-loop system are presented and compared. The effectiveness of the vibration suppression of the flexible riser is examined.