Nonlinear vectorial backstepping design for global exponential tracking of marine vessels in the presence of actuator dynamics

A nonlinear vectorial backstepping control law for commercial ships is derived by using the concept of vectorial backstepping. Vectorial backstepping is done in 3 steps corresponding to the state vectors of the ship dynamics, kinematics and actuator dynamics. Emphasis is placed on compensation of the actuator dynamics since the bandwidth of the propellers, thrusters and rudders often is close to the bandwidth of the ship dynamics. Global exponential tracking is proven by applying Lyapunov stability analysis. The case study is simultaneously global exponential tracking of the surge and sway positions (x,y) and the yaw angle ψ of a surface ship. This can only be done by applying nonlinear control theory due to the nonlinear structure of the kinematic equations, Coriolis and centripetal forces, and hydrodynamic damping forces