Numerical stability analysis and control of umbilical-ROV systems in one-degree-of-freedom taut-slack condition

Abstract

In this paper, the stability of an umbilical-ROV system under nonlinear oscillations in heave motion is analyzed using numerical methods for the uncontrolled and controlled cases comparatively. Mainly the appearance of the so-called taut-slack phenomenon on the umbilical cable produced by interactions of monochromatic waves and an operated ROV is specially focused. Nonlinear elements were considered as nonlinear drag damping, bilinear restoring force and saturation of the actuators. Free-of-taut/slack stability regions are investigated in a space of physical bifurcation parameters involving a set of both operation and design parameters. They indicate a wide diversity in qualitative behaviors, both in the periodicity and possible routes to chaos from the stability regions to outside. For detection of periodicity of the nonlinear oscillations inside and outside the stability regions, a method based on Cauchy series is developed. The first part of the results is dedicated to the stability of the uncontrolled dynamics. These results suggest the design of a control system that is able to counteract hefty hauls of the cable during the sinking/lifting operation under perturbation. A combination of a force and cinematic controller based on nonlinear model-reference control is proposed. Through a comparative study of the stability regions for uncontrolled and controlled dynamics, it is shown that the control system can extend considerably these regions without appearance of the taut-slack phenomenon despite the presence of wave perturbations. The limits between the taut and taut-slack zones are defined by the wave steepness and the available energy of the actuators.