Stabilisation of parametric roll resonance by combined speed and fin stabiliser control

Parametric roll resonance on a ship is a condition where large roll motion develops rapidly in moderate head or following seas. The phenomenon is caused by bifurcation in the nonlinear equations of motion when a restoring moment is subject to periodic variation. This paper analyzes the stability of the nonlinear system and suggests active control of both ship speed and fin stabilizers to stabilise the roll resonance condition. Lyapunov and backstepping designs are employed to achieve two nonlinear controllers, which are proved to stabilise the nonlinear system. The designed controllers are validated employing a high fidelity simulation model. The combined speed and fin stabiliser control is shown to efficiently drive the vessel out of the bifurcation condition and to quickly damp the residual roll motion.