Optimal controllers for rudder roll damping with an autopilot in the loop*

:In this paper we propose a new approach to the design of a rudder roll stabilization system, integrated with a predesigned heading controller (autopilot). Whereas a number of methods for the roll oscillation damping have been proposed in the literature, this problem still remains challenging. In this paper we consider a linear-quadratic optimization problem, where the cost functional penalizes the roll angle, the heading deviation and the control effort (rudder angle). Approximating the wave disturbance by a polyharmonic signal with a known spectrum, we design a controller, which optimizes this quadratic performance index, providing thus a "tradeoff" between the maintenance of the desired heading, roll damping and the steering system utilization. The practical applicability of our algorithms is illustrated by numerical simulations.