Boundary control of a flexible marine riser with vessel dynamics

In this paper, boundary control of a flexible marine riser with vessel dynamics is developed to reduce the riser's vibrations. To provide an accurate and concise representation of the riser's dynamic behavior, the distributed parameter model of the flexible marine riser with vessel dynamics is described by a partial differential equation (PDE) coupled with ordinary differential equations (ODEs) involving functions of space and time. Boundary control is developed at the top boundary of the riser based on Lyapunov's direct method to regulate the riser's vibrations. With the proposed boundary control, uniform boundedness is achieved. The boundary control is implementable with actual instrumentation since all the signals in the control can be measured by sensors or calculated by a backwards difference algorithm. Simulations are provided to illustrate the effectiveness of the proposed control.