The ongoing development of deep-sea resources has contributed toward the widespread use of dynamic positioning (DP) systems that can operate in arbitrary sea areas without the limitation of operating water depth compared to mooring systems. The second-order slowly varying forces can be compensated by DP feedback control. Wave filtering techniques are crucial for designing the DP controller, which can improve the positioning performance and service of multiple actuators. The objective of wave filtering is to separate the motion induced by the first-order high-frequency oscillatory waves from the motion caused by the second-order low-frequency (LF) slowly varying disturbances. This paper proposes a novel real-time wave filtering approach for DP systems on the basis of the discrete wavelet transform without relying on the previous knowledge of dynamics of the vessel. Meanwhile, to suppress the end effects of wavelet filtering and achieve real-time application, symmetric boundary extension and the sliding window method are investigated in order to capture the slow time-varying LF motion of DP vessels. The proposed real-time wavelet filtering approach can significantly improve the quality of the separated components by selecting the optimal decomposition level, wavelet function parameters, and threshold denoising method. The real-time and filtering performance of the proposed approach is verified using a scaled model of an offshore supply vessel as well as full-scale experiments on the EXPLOERE I scientific investigation vessel under the action of winds, currents, and waves. The experimental results confirm that the proposed wave filtering algorithm is efficient and that the LF component waveform can be effectively recovered after wavelet filtering.

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.