Control Strategy of In-Port U-Turn for Ships Based on Arctangent Function Nonlinear Feedback

This study presents an innovative control strategy for enabling ships to perform automatic U-turns in restricted waters, with a focus on minimizing energy consumption and reducing wear on the steering gear. The strategy integrates a closed-loop gain-shaping algorithm with nonlinear feedback control, applied to a nonlinear motion mathematical model specifically designed for low-speed operations in shallow waters. The simulations, conducted under a Beaufort wind scale conditions up to No. 5 and water depths of 15 m, demonstrate that ships can successfully execute automatic U-turns within a distance three times their length. The incorporation of nonlinear feedback technology significantly reduces energy consumption and steering gear wear, with specific improvements including a reduction in the average rudder angle by up to 18.26%, a reduction in the mean absolute error (MAE) by up to 3.6%, a reduction in the mean integrated absolute (MIA) by up to 13.55%, and a reduction in the mean total variation (MTV) by up to 36.36%. These enhancements not only optimize the control effect but also extend the service life of the steering gear, thereby contributing to more sustainable maritime operations. Theoretical proofs and Matlab-based simulations validate the effectiveness of the controller, highlighting its potential for energy savings and improved navigational efficiency in challenging maritime environments.