Sliding Mode Controls in Partial Feedback Linearization applied to Unstable Ship Steering

This paper focuses on a sliding mode controller for a partial feedback linearization applied unstable ship steering system. The ship steering system is analyzed in this study considering a nonlinear mathematical model that is derived by the second-order linear Nomoto model under unstable maneuverability conditions. The partial feedback linearization approach is proposed to simplify the nonlinear steering system, in which the rudder rate effects are removed. This separates the vessel steering system into two sectors of: linearized dynamics and internal dynamics. The sliding mode controller is applied to linearized dynamics. The stability of zero dynamics in internal dynamics is analyzed, as a part of the feedback linearization process. It is shown that the proposed sliding mode controller in vessel steering is robust against parameter and unstructured uncertainties, and bounded external disturbances. The robustness of the sliding mode controller is analyzed considering the Lyapunov stability theorem. Finally, the proposed controllers are simulated with respect to unstable steering conditions and successful computational results are also reported in this paper.