Rudder Roll Stabilization Based on Arc Tangent Nonlinear Feedback for Ships

Jian Zhao,Cailei Liang,Xianku Zhang

doi:10.3390/jmse8040245

Abstract

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.

Highlights

Roll motion will inevitably occur when a ship is sailing in rough seas
Rudder roll damping technology has prevailed as a hot topic in recent years
Kapitanyuk designed an optimal controller that had a good performance when the rudder turn rate is limited within 7◦/s [13]

Summary

Introduction

Roll motion will inevitably occur when a ship is sailing in rough seas. Violent roll motion endangers the comfort of crew and passengers onboard and the safety of the ship as well. Hickey et al [4] transferred the rolling model of a ship to a second order transfer function and used H∞ theory to design controllers for a fin stabilizer system, which laid the theoretical foundation for roll damping control. Facilities such as fin stabilizers and anti-roll tanks occupied quite a lot space onboard a ship that were not economical, ad hoc for commercial ships. Zhou et al [11] proposed a robust H∞ controller for rudder roll damping system It researched the selection method of weight function to restrain the disturbances and keep course precisely. Simulation results verified that the ZOH component could further lower the steer frequency of steering gear to the acceptable ranges for most commercial ships

Ship Model

Controller Design

Effect on Stability of the System

Findings

Conclusions