Floating Production Storage and Offloading (FPSO) vessels for offshore operations use a Dynamic Positioning system (DP), which includes a controller to correct the position variation of the FPSO subject to internal and external disturbances. Most of these positioning systems use a classic Proportional Integral Derivative controllers (PID) and their deferent variants, where the control law is determined adjusting three control gains: proportional, integral and derivative, usually heuristic techniques are employed to determine the control gains. In this study we propose a theoretical tuning procedure in order to determine the control gains in a simple way, analyzing the boundary conditions in the matrices of the FPSO dynamic model, as well as the relation they have with the control gains for the FPSO motion in an adjust domain. In order to guarantee the semi-global stability of the closed-loop system, a stability proof in the Lyapunov sense is carried out. The theoretical results were validated in numerical simulations using Matlab. These results show that the methodology presented in this work is highly satisfactory for the control gain selection in the trajectory tracking control problem for FPSO motion.


A Floating Production, Storage and Offloading (FPSO) system is considered in this paper. In the last two decades FPSOs have been the dominant offshore platforms used in oil and gas fields. Fig. 1 shows the Ta'Kuntah FPSO, which was the first FPSO operated in the Cantarell Field in the Gulf of Mexico. A FPSO can be operated in deep water and sometimes must perform maneuvering movements and marine activities with other vessels as shown in Fig. 2 (Tamuri, 2009), these activities involve huge risks due to the environmental random forces presence, affecting the normal operation and sometimes causing severe accidents (Moan, 2002) and lack stability (Chen, 2008). In offshore basically there are two ways to maintain the FPSO position, the first is by Mooring Positioning (MP) and the second by Dynamic Positioning (DP) (Sorensen, 1996; Sorensen, 1997). In DP the principal advantage is the immediate positioning on a required set point, in other hand the MP systems are limited to operate about 500m (Veksler, 2016).

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