Boundary control of vibration in coupled nonlinear three dimensional marine risers

Abstract

This paper presents a design of boundary controllers implemented at the top end for global stabilization of a marine riser in three dimensional space under environmental loadings. Based on the energy approach, nonlinear partial differential equations of motion including bending-bending and longitudinal-bending couplings for the risers are derived. These couplings cause mutual effects between the three independent directions in the riser’s motions and make it difficult to minimize its vibrations. The Lyapunov direct method is employed to design the boundary controller. It is shown that the proposed boundary controllers can effectively reduce the riser’s vibration. Stability analysis of the closed-loop system is performed using the Lyapunov direct method. Numerical simulations illustrate the results.