Modeling and Control of Parametric Roll Resonance

Abstract

Parametric roll resonance is a dangerous resonance phenomenon affecting several types of ships, such as destroyers, RO-RO paxes, cruise ships, fishing vessels and especially container ships. Worst case, parametric roll is capable of causing roll angles of at least 50 degrees, and damage in the tens of millions of US dollars.

Empirical and mathematical investigations have concluded that parametric roll occurs due to periodic changes in the waterplane area of the ship. If the vessel is sailing in longitudinal seas, with waves of approximately the same length as the ship, and encounter frequency of about twice the natural roll frequency, then parametric resonance can occur.

While there is a significant amount of literature on the hydrodynamics of parametric roll, there is less on controlling and stopping the phenomenon through active control. The main goal of this thesis has been to develop controllers capable of stopping parametric roll. Two main results on control are presented.

To derive, analyze and simulate the controllers, it proved necessary to develop novel models. The thesis thus contains four major contributions on modeling.

The main results are (presented in order of appearance in the thesis): Six-DOF computer model for parametric rollOne-DOF model of parametric roll for non-constant velocityThree-DOF model of parametric rollSeven-DOF model for ships with u-tanks of arbitrary shapeFrequency detuning controllerActive u-tank based controller for parametric roll