Nonlinear Observers for Parametric Roll

Abstract

Parametric roll resonance is a dangerous resonance phenomenon affecting several kinds of ships, such as cruise ships, fishing vessels and container ships. In a worst case scenario parametric roll resonance may lead to roll angles of up to 50 degrees, capsizing of the vessel, or damage of goods and ship for tens of millions of dollars, citep{Ginsberg1998}.Accurate equations in the model for the ship motion are important because they are directly related to the observer design. There has been done allot of mathematical investigations on the problem. In this work, we use a standard model for parametric roll, and express it in state-space form. We establish an augmented state-space model by adding wave-induced forces to the nonlinear state-space model.We revise Lie Derivatives, and use an observability check for nonlinear systems, to derive conditions for nonlinear observability of our system.A Matlab/Simulink model is implemented, and shows that the state space modelis good for simulation of a ship exhibiting parametric roll.The main goal of this thesis has been to investigate different observers for state estimation of a ship exhibiting parametric roll. The wave encounter frequency is estimated by implementing an extended Kalman filter, and in turn an unscented Kalman filter. By comparing the two filters, we conclude that the unscented Kalman filter has better empirical results for estimation of the states of a ship in parametric roll resonance condition. Also attention has been paid to estimation of the direction of the incoming waves.In this thesis the wave direction has been estimated by implementing an extended Kalman filter, and consequently by implementing speed and heading controllers.