Objective  In order to solve the problem of an underactuated ship responding slowly to heading changes during rudder roll stabilization (RRS) caused by fixed weight values in model predictive control (MPC), a RRS control method based on the finite time extended states observer (FTESO), fuzzy rules and robust predictive control is proposed.

  Methods  A fixed speed linear underactuated ship model is established for controller design. The FTESO is used to estimate the ship's motion states and external disturbances. By analyzing the conditions of the ship's course-keeping and heading change, the objective function weights under the two conditions and the fuzzy rules between the states and weights are designed respectively. Robust predictive control is used to solve the multi-objective cooperative control problem with constraints. The closed-loop stability of the proposed control method is then proven theoretically.

  Results  According to a numerical simulation of a multi-purpose naval vessel, the proposed control method is compared with a disturbance compensation MPC and disturbance observer enhanced MPC, and is shown to have a higher roll stabilization rate by 5.74% and 0.898 3%, respectively. The response time of the proposed method for a 30° heading change is also reduced by 1.8 s and 7.3 s respectively.

  Conclusion  The effectiveness of the proposed method in underactuated ship rolling reduction is proven.