Global stabilization of three-dimensional flexible marine risers by boundary control

A method to design a boundary controller for global stabilization of three-dimensional nonlinear dynamics of flexible marine risers is presented in this paper. Equations of motion of the risers are first developed in a vector form. The boundary controller at the top end of the risers is then designed based on Lyapunov's direct method. Proof of existence and uniqueness of the solutions of the closed loop control system is carried out by using the Galerkin approximation method. It is shown that when there are no environmental disturbances, the proposed boundary controller is able to force the riser to be globally exponentially stable at its equilibrium position. When there are environmental disturbances, the riser is stabilized in the neighborhood of its equilibrium position by the proposed boundary controller.