Linear reduction of backstepping algorithm based on nonlinear decoration for ship course-keeping control system

In order to solve the practical application problems of high output energy and difficult cancellation of nonlinear function in the backstepping algorithm for ship course-keeping control, a closed loop gain shaping algorithm is employed to design the linear part of nonlinear backstepping controller firstly, then the backstepping algorithm is linear-reduced by ignoring the nonlinear part of the controller. Secondly, a novel nonlinear decoration algorithm with sine-function deduced from nonlinear feedback algorithm is proposed, where the sine function was embedded into the back of original linear controller. Then, taking training ship “YUKUN” of Dalian Maritime University as a test object, the simulation experiments are carried out to verify the effectiveness of the proposed algorithm and the results show the advantages of robustness, energy saving and safety in course-keeping practice. Compared with nonlinear feedback and the standard feedback, the energy cost performance specifications (MIA) of the proposed nonlinear decoration algorithm are reduced by −31.5% and −15.7%, respectively. Meanwhile, the response performance specification (MAE) and the smoothness performance specification (MTV) also show the satisfactory control effects.