Chaos Of Ships Rolling Motions And Its Robust Control

When ships navigate in waves,there will be large amplitude rolling which contains complex nonlinearity.The serious nonlinear rolling,acted by outside forces or other factors, will lead ships to capsizing.In this paper,chaos is used to try to explain complex nonlinear phenomena of the ship rolling motion and a robust controller is designed to make the ship rolling motions get rid of the chaotic state.Firstly,on the basis of Newton's Second law,the equations for linear rolling motions in waves are established.Taking into account the nonlinear characteristics of the damping and righting moment in large amplitude rolling motions,mathematical expressions of them are established separately.Waves are looked as the only outside disturbance,then,referring to ship specific parameters,the specific equations for nonlinear rolling motions are established.Secondly,the bifurcation diagram,time response diagram and phase-space diagram are separately drawn by Matlab.Then some chaos characteristics are found by the diagram.Then,correlation dimension and Lyapunov features index are got by Matlab in order to confirm that chaos is exist in the system.Lastly,the nonlinear mathematic chaos model for ships rolling motion is linearized via exact feedback linearization,and then the robust controller based on closed-loop gain shaping algorithm is designed to control the chaos model for ships rolling motion.