Optimal Universal Controllers for Rudder Roll Stabilization
Roll stabilization (damping) is an important problem of ship motion control since excessive roll motion may cause motion sickness of human occupants and damage fragile cargo. This problem becomes especially non trivial in situations where the same actuators are used for the vessel's roll and yaw stabilization. To keep the "trade off" between the concurrent goals of accurate course steering and roll stabilization, an optimization problem is usually solved where the cost functional penalizes the roll angle, the steering error and the control effort. Since the vessel's motion is influenced by the uncertain wave disturbance, the optimal value of this functional and the optimal process are also uncertain. A standard approach, prevailing in the literature, is to approximate the wave disturbance by the "colored noise" with a known spectral density, reducing the optimization problem to conventional LQG control. In this paper, we propose a novel approach to optimal roll damping, approximating the disturbance by the polyharmonic signal with known frequencies yet uncertain amplitudes and phase shifts. For this class of external disturbances, an optimal universal controller (OUC) can be found. Unlike the LQG controller, minimizing only the expected value of the cost function, the OUC delivers the optimal solution for any uncertain parameters of the signal. The practical applicability of our algorithms is illustrated by numerical simulations.
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