Stabilization of floating platform by boundary tracking control

In this work, a boundary tracking control scheme is investigated for the stabilization of a floating platform connected to a traditional mooring system. The system is composed of a floating platform and several mooring lines which are designed for station keeping of the former on the sea surface. Since the floating platform is subject to excitation forces from waves and currents, a coupled boundary-tracking controller is proposed for the tip payload of mooring lines in two-dimensional direction to reduce the effect of boundary vertical and horizontal displacement. Firstly, a boundary controller is proposed to the boundary oscillation in horizontal direction. Secondly, in order to efficiently suppress the heave motions of the platform, an auxiliary exo-system is introduced to generate the desired time-varying reference trajectory in the vertical direction. Furthermore, a tracking error system is derived by integrating the reference trajectory. According to this error system, the boundary motion of mooring lines in vertical direction can track the reference trajectory which is to achieve the target of vibration suppression. In addition, the stability of the system is guaranteed by Lyapunov's method. Finally, numerical simulation results show that efficacy of the proposed control scheme, that is, the boundary displacement of z-axis can accurately track a bounded periodic time-varying reference trajectory and the horizontal boundary vibration can be suppressed within a small range.