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The problem of automatic steering control of a large tanker in a seaway is formulated within the framework of linear quadratic Gaussian (LQG) control theory. Wave disturbance are characterized by shaping filters, and Kalman filters are designed using these disturbance noise models. LQG controllers are designed to minimize a performance criterion commonly thought to be representative of propulsion losses due to steering. Performance of the controllers is determined by simulation results, which apply for deep water and are based on data from scale model tests.