An adaptive bi-limit homogeneous sliding mode control for 3-DOF stabilized system of ship propulsion-assisted sail with prescribed performance

Sail-assisted ships have garnered widespread interest as a sustainable technology. The three-degree-of-freedom (3-DOF) stabilized system of ship propulsion-assisted sail is used to track the optimal azimuth of the sail and isolate the swaying of the ship's hull. In this paper, the problem of tracking control for the system with prescribed performance is investigated. By using an appointed-time prescribed performance function (APPF), a novel bi-limit homogeneous sliding surface with expected trajectory is proposed to improve the convergence rate, accuracy, and overshoot. Considering the external disturbance, a wind resistance model is established and compensated to reduce the conservatism and chattering. Adaptive extreme learning machines (AELMs) are employed to estimate the mismatch parameters caused by Reynolds number fluctuations and unmodelled dynamics. Finally, an adaptive bi-limit homogeneous sliding mode controller is constructed, by which the system can track the 3-DOF target signals with prescribed performance and suppress disturbances. The fixed-time reachability of the system is verified by Lyapunov analysis and fixed-time theory. To validate the effectiveness of the presented controller, numerical simulations and principle prototype experiments are conducted. The results are compared with other algorithms and show that regardless of the control performance or energy-saving benefits, the proposed method has a better effect.