Abstract
Broaching-to is a phenomenon in which a ship cannot keep her desired course despite the maximum steering effort. Once this dangerous phenomenon happens, she could capsize due to violent yaw motion. Generally a PID autopilot, however, has been used in model experiments and numerical simulations for investigating broaching-to although PID auto-pilot does not properly represent the "maximum steering effort". This paper attempts to apply an optimal rudder control for a ship in following and quartering seas with high speed. We performed the numerical optimization of rudder control for higher speed region which includes surf-riding threshold,i.e. heteroclinic bifurcation point. To the trajectory optimization nonlinear programming method was applied in conjunction of the method based on calculus of variation, e.g. Sequential Conjugate Gradient-Restoration Algorithm (SCGRA). Numerical results indicate an example that a ship cannot prevent significant course deviation even with course keeping rudder control based on the optimal control theory. Calculation results also showed that the optimal rudder control during surf-riding takes opposite maximum value. As a result, it was concluded that if the yaw motion became unstable around stable equilibrium point, she could consequently face broaching-to in spite of rudder control process before a ship is surf-ridden.
