Mathematical Ship Modeling for Control Applications

In this report, we review the models for describing the motion of a ship in four degrees of freedom suitable for control applications. We present the hydrodynamic models of two ships: a container and a multi-role naval vessel. The models are based on experimental results in the four degrees of freedom roll planar motion mechanism (RPMM) facility at the Danish Maritime Institute, and have also been validated via extensive full scale trials. Based on the RPMM hydrodynamic models, we also present non-linear and linearized state space models suitable for simulation and control applications. Finally, we evaluate the quality of the linearized models with respect to their nonlinear counterparts and analyze sensitivity to parameter variations.