Resumen
Focusing on dynamic positioning (DP) systems for ships, which are subject to environmental disturbances and actuator constraints, this paper presents a finite-time controller that uses a disturbance observer with the aid of a backstepping technique. First, to estimate the time-varying and unknown environmental disturbances in finite time, two sliding-mode disturbance observers are constructed. Specifically, an adaptive disturbance observer (ADO) effectively decreases undesired chattering without the need for prior information on environmental disturbances. Then, to handle the actuator constraints, the designed control forces are distributed into multiple actuators using a control allocation algorithm to obtain the actual forces. Next, an auxiliary dynamic system is built to compensate for velocity tracking errors induced by the mismatch of the DP control law and thruster forces. Then, with the designed ADO and the auxiliary dynamic system, a finite-time controller with a fast exponential-reaching law is designed; this ensures that the positioning errors and the sliding surface converge to zero at a fast convergence rate. Finally, numerical simulations are presented: these present a cable-laying ship experiencing wind, currents, and waves in different sea states. The results show the effectiveness of the presented control scheme.