Robust Nonlinear Observer And Observer‐Backstepping Control Design For Surface Ships

A robust passive non‐linear observer, utilizing the sliding mode concept and acceleration feedback (AFB) technique, is developed for ships. The main advantage of the proposed observer is that it is robust and that it takes the Coriolis‐centripetal matrix (C‐matrix) into account. The observer reconstructs velocities of ships and bias from slowly varying environmental disturbances. It also filters out the noise and wave frequency data from measurements to protect the actuators from wear and excessive fuel consumption. The sliding mode technique is introduced to improve robust performance against neglected disturbances, uncertainties, and unmodeled dynamics. The acceleration feedback technique and coordinate transformation are used for reshaping the inertia matrix and removing the C‐matrix from the mathematical model. Then, the observer design and stability analysis become simpler. An output feedback controller using observer backstepping and the Lyapunov redesign technique is derived, and the global stability of the observer and observer‐controller system is shown by Lyapunov stability theory. A set of simulations was carried out to verify the performance of the proposed observer and controller.