This paper is concerned with the non-linear characteristics of an auto-pilot in improving the stability of ships in following seas. The theory is developed for optimizing the auto-pilot, accounting for the non-linearities introduced by limitations on rudder angle and rudder angular velocity. The yaw and rudder angles are assumed to be stationary random processes, and the Wiener–Hopf integral is used to obtain the transfer function relating them in a system of waves, hence yielding the optimum rudder behaviour. For given auto-pilot characteristics, it is shown how root-mean-square yaw angles may be estimated for a ship in a given course in a known sea state.
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References
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