Boundary control of two-dimensional marine risers with bending couplings

The aim of this paper is to design a boundary controller for global stabilization of two-dimensional marine risers under environmental disturbances. Based on the energy approach, equations of motion including bending couplings for the risers are derived. Due to the couplings, the riser dynamics exhibit mutual effects between transverse motions. The Lyapunov direct method is used to design the boundary controller. Proof of the existence and uniqueness of the solutions of the closed-loop system is provided based on the Galerkin approximation method. Stability analysis of the closed-loop system is carried out using the Lyapunov stability theory. Numerical simulations illustrate the results.