© 1961 by Oxford University Press
ON THE OPTIMUM CONTROL OF SHIPS' STABILIZERS
( Southampton University )
It is becoming an increasingly common practice to fit one or more pairs of fins to the sides of ships so as to reduce rolling in a rough sea.The anti-rolling moment generated by the fins depends on their attitude, and in all existing systems this attitude is controlled, not by a direct recording of the state of the sea, but by a continuous measurement of the angle of roll and of the rate-of-roll of the ship. In the literature one finds references to the relative amounts of feedback from the roll and from the rate-of-roll which have been adopted in particular commercial control systems; it appears that these relative amounts have been determoined, and may be adjusted during the voyage, on empiricasl grounds, but that no theoretical predictions have been made of the optimum combination of these two types of control.
The special feature of what may appear at first sight as a simple application of existing control theory lies in the fact that there is a definit limit, imposed by the mechanical design and by the hydrodynamic characteristies, to the deflexion of the fins; in other words, the magnitude as often as possible so as to achieve the greatest degree of stabilization, and it is the aim of a theoretical investigation to determine the feedback coefficients of the roll and rate-of-roll to satisfy this requirement.
So posed, the problem some intractable for a random sea— that is, with a random forcing function in the governing differential equation for the roll angle. But for the special case of a simusoidal forcing function, the solution is simple and is given in this paper. The final result, once it is obtained, seems intuitively obvious: the roll can be reduced by exactly, but by no more than, the roll angle which the stabilizing fins could produce (by a sinusoidal movement over their whole range) in a calm sea. The values of the feedback coefficients are given for this optimum control, and suggestions are made as to the procedure which might be adopted in a realistic, random sea.