Rudder Roll Stabilization Based on Arc Tangent Nonlinear Feedback for Ships

The rudder is used for damping the roll motion of a ship. Study of this motion is the essence of this paper. The responses of yaw and roll motions are different as the rudder angle varies. The low frequency motion of the rudder mainly affects the ship’s yaw motion, whereas the high frequency motion of the rudder mainly affects the roll motion. As long as the controller is well designed, the characteristic of the rudder can be used to reduce the roll motion. In order to save energy and reduce steer frequency, a nonlinear feedback controller is proposed based on the arc tangent function processing feedback error to save energy consumption. In addition, a ZOH component is applied in the system to reduce the steer frequency. In heavy sea state, simulation results illustrate that controllers based on pole assignment with and without nonlinear feedback can reduce roll motion by 32.1% and 30.3%, respectively, when the rudder turn rate is limited within 7°/s. Furthermore, the former reduces the amplitude of rudder angle by 23.3% compared with the latter, which means the nonlinear feedback control consumes less energy. Consequently, the ZOH can lower steer frequency to once every 1 s, which protects steering gear from abrasion.