Extremum Seeking Speed and Heading Control Applied to Parametric Roll Resonance

Parametric roll is a dangerous resonance phenomenon for ships caused by time-varying restoring forces. The resulting large roll oscillations may endanger the ship's safety and possibly lead to capsizing. The susceptibility of container ships to parametric roll resonance has caused considerable research activities in the development of control and operational strategies to avoid large roll motions. In this paper, a novel approach to the active control of ships experiencing parametric roll resonance is presented. The methodology of extremum seeking control is used to iteratively determine the set-point for the wave encounter frequency in order to avoid the conditions for the onset and build-up of parametric roll. The desired trajectory for the wave encounter frequency is tracked by mapping it to the ship speed and heading angle by a control allocation, formulated as a constrained optimization problem, and consequently by implementing speed and heading controllers. The combined variation of the speed and heading angle is shown to efficiently drive the ship out of the parametric roll resonance region.