Complete nonlinear dynamic manoeuvering models of ships, with numerical values, are hard to find in the literature. This paper presents a modeling, identification, and control design where the objective is to manoeuver a ship along desired paths at different velocities. Material from a variety of references have been used to describe the ship model, its difficulties, limitations, and possible simplifications for the purpose of automatic control design. The numerical values of the parameters in the model is identified in towing tests and adaptive manoeuvering experiments for a small ship in a marine control laboratory.
IntroductionModel-based control for steering and positioning of ships has become state-ofthe-art since LQG and similar state-space techniques were applied in the 1960s. For a rigid-body the dynamic equations of motion are divided into two distinctive parts: kinematics, which is the study of motion without reference to the forces that cause motion, and kinetics, which relates the action of forces on bodies to their resulting motions (Meriam & Kraige, 1993). The rigid-body and hydrodynamic equations of motion for a ship are in reality given by a set of (very complicated) differential equations describing the 6 degrees-of-freedom (6 DOF); surge, sway, and heave for translation, and roll, pitch, and yaw for rotation. The models used to represent the physics of the real world, however, vary as much as the underlying control objectives vary. Roughly divided these control objectives are either slow speed positioning or high speed steering. The first is called dynamical positioning (DP) and includes station keeping, position mooring, and slow speed reference tracking. For DP the 6 DOF model is reduced to a simpler 3 DOF model that is linear in the kinetic part. Such applications with references are thoroughly described by Strand (1999) and Lindegaard (2003). High speed steering, on the other hand, includes automatic course control, high speed position tracking, and path following; see for instance Holzhü ter (1997), Lefeber et al. (2003) and Fossen et al. (2003). For these applications, Coriolis and centripetal forces together with nonlinear viscous effects become increasingly important and therefore make the kinetic part nonlinear. By port-starboard symmetry, the longitudinal (surge) dynamics are essentially decoupled from the lateral (steering; sway-yaw) dynamics and can therefore be controlled independently by
