Application of Optimal Control Theory to Course Keeping Problem in Following Seas

Abstract

When a ship runs in following and quartering seas, she could occasionally face broaching-to, which is a major threat of ship capsizing, or difficulty to keep her desired course due to wave-induce forces. It is noteworthy that usually a PID auto-pilot is used in model experiments and numerical simulations for investigating broaching-to but a PID auto-pilot is not so suitable for identifying operational limits. Thus, in this paper, the optimal control problem for ship maneuvering motion in following and quartering seas was discussed. As a result, while a proportional auto-pilot fails to keep the desired course,optimal control obtained here successfully keeps the desired course as a Bang-Bang control. If wave steepness further increases, even this optimal control may face a difficulty to keep her desired course and then broaching-to could be more rigorously identified.