Boundary control of three-dimensional inextensible marine risers

This paper present a design of boundary controllers actuated by hydraulic actuators at the top end for global stabilization of a three-dimensional riser system. First, a set of partial and ordinary differential equations describing motion of the riser and hydraulic systems is developed. Second, several important properties of the riser system are derived. Based on these properties, we show that the conventional formula to calculate the riser effective tension is oversimplified and a new formula is provided. Next, boundary controllers are designed based on Lyapunovʹs direct method, the backstepping technique, the derived properties of the riser system dynamics, and Poincareʹs inequalities. Finally, the Galerkin approximation method is used to prove existence and uniqueness of the solutions of the closed loop control system.