Modeling, dynamics and control of large amplitude motions of vessels in beam seas

The modeling, dynamics and control of large amplitude motions of vessels traveling in regular beam seas are considered. We first derive a 3-DOF model that considers roll, sway and heave motions of arbitrary amplitude occurring in a (vertical) plane for a vessel subjected to excitation from regular beam seas. By exploiting natural time and force scales of the system, the equations of motion are transformed into a singularly perturbed form through a nondimensionalization and rescaling process. Analysis of this dynamical system using chaotic transport theory and a Melnikov analysis provides a ship capsizing criterion in terms of vessel parameters and the sea state. The coupling effects from sway and heave are examined in order to assess the validity of commonly used models which include only roll dynamics.;Next, active anti-roll tanks are added to the system as a means of preventing large amplitude roll motions. A robust state feedback controller is designed that can handle model uncertainties, which arise primarily from unknown hydrodynamic contributions. The approach for the controller design is a combination of sliding mode control and composite control for singularly perturbed systems, with the help of the backstepping technique. It is shown that a pump/tank system containing water representing less than 5% of the vessel displacement can effectively control roll motions.;Numerical simulation results for an existing fishing vessel, the twice-capsized Patti-B, are used to verify the analysis for the capsize criteria and the controller design.