The modeling and dynamics of nonlinear, large-amplitude motions of vessels in regular beam seas are studied. By using a wave-fixed coordinate system, a three-degree-of-freedom ship model which contains roll, sway, and heave motions is obtained. This model systematically includes various factors that contribute to ship motions. After nondimensionalization and rescaling, it is transformed into a form that is amenable to analysis that takes advantage of various time scales in the problem. This analysis provides a systematic reduction of the full system to a single-degree-of-freedom (DOF) dynamics problem in which roll is dominant. The analysis is based on invariant manifold theory of dynamical systems, and allows one to account for coupling to the quasi-static heave dynamics and the sway velocity. Numerical simulations of a model for a typical fishing vessel are presented and demonstrate that the traditional single DOF roll model represents approximately the dynamics on a special subset—an invariant manifold—of the higher dimensional state space of the full three-DOF model. This work points the way towards a systematic means of modeling general, large-amplitude motions of vessels in a variety of sea states.

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The dynamics and control of a strongly nonlinear 3-DOF model for ship motion are investigated. The model describes the roll, sway, and heave motions occurring in a vertical plane when the vessel is subjected to beam seas. The ship is installed with active antiroll tanks as a means of preventing large amplitude roll motions. A robust state feedback controller for the pumps is designed that can handle model uncertainties, which arise primarily from unknown hydrodynamic loads. 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 this design can effectively control roll motions of large amplitude, including capsize prevention. Numerical simulation results for an existing fishing vessel, the twice-capsized Patti-B, are used to verify the analysis. [S0022-0434(00)02701-5]

This study is concerned with the contouring control of biaxial motion systems. It is well known that contour errors depend not only on the controller, but also on the reference command. Two problems are investigated in this paper. First, it is to find the reference command that will yield the minimum contour error. This is the problem of interpolation and acceleration/deceleration. Second, given a reference command, it is to find a modified reference command so that the system output will be as close to the reference command as possible. The design of the modified reference command utilizes the inverse model of the closed-loop system. In other words, the modified reference command can be considered as the output of the inverse system with the desired reference command as the input. It can be obtained by the convolution technique.