Lyapunov and Hurwitz based controls for input-output linearisation applied to nonlinear vessel steering

This paper focuses on the Lyapunov, Hurwitz and PID based control approaches for an input-output linearisation applied nonlinear vessel steering system. A mathematical model of the vessel steering system is derived considering a second-order Nomoto model with nonlinear manoeuvrability features. In general, the control design process of the nonlinear vessel steering system is affected by the nonlinearities that are related to rudder angle, rudder rate and vessel heading angle. Therefore, to simplify the nonlinear vessel steering system, input-output linearisation is proposed in this study. During this process (i.e. input-output linearization), the system is divided in a system with linear dynamics and a system with internal dynamics. Furthermore, the stability conditions of internal dynamics are analysed to observe overall stability of the vessel steering system. The Lyapunov, Hurwitz and PID based controllers are proposed for course keeping and course changing manoeuvres in vessel steering. Furthermore, the overall stability conditions of the proposed Lyapunov and Hurwitz based controller are analysed, considering a Lyapunov candidate function and the Hurwitz conditions, respectively. Finally, the proposed control algorithms are simulated on a vessel steering system and successful results with respect to course keeping and course changing manoeuvres are presented in this paper.