4.6 Riser Angle Position Reference System
In Fig.10 the proposed calculation steps in the computation of the vessel position are shown. There are two main phases of operation: initialization mode and running mode. At start up the initialization procedure has to be run in order to establish a mathematical model of the riser at the prevailing site. Input signals to the RAPR system are measurements of the top and bottom riser angles (αt and αb), bearing angles (βt and βb), top tension Tt, and the Earth-fixed vessel position signals η provided by GNSS or HPR. The operator should be allowed to supervise the calculation steps and to provide additional input such as water depth, riser dimensions and particular mud characteristics. After the initialization has been completed a RAPR observer computing the North and East position of the vessel relative to the field zero point will be activated. Input signals to the RAPR observer are only measurements of the top and bottom riser angles, bearing angles, and top tension. At certain intervals and events (e.g. major change in current direction and velocity, positioning deviation alarms, and major changes of riser characteristics) the RAPR model needs to be updated. Robustness analysis of the RAPR accuracy subject to varying current profiles (velocity and direction) indicates that only bias adjustment is needed. This operation requires that measurements of vessel position are available. Hence, following the RAPR calculation procedure proposed in this paper, the RAPR will be periodically dependent on other position reference systems. Beyond that the RAPR will be able to operate as a separate position reference system.
Fig.10 RAPR system.
As shown in , the position estimates based on the top and bottom riser angle measurements become
bx and by are the North and East bias offsets, respectively. From (7) it is seen that we are able to calculate the Earth-fixed positions, rvxt,rvyt,rvxb, and rvyb using either the bottom or top riser angle respectively. The final vessel position estimates may be found by a weighted sum of both the top and bottom riser angle based position estimates according to
where wt and wb are appropriate weighting factors for the top and bottom riser angle estimates, respectively.
4.7 Simulation Results
A random walk is used to generate the surface current velocity about 1 m/s. It is furthermore assumed that the sea current velocity at the mid-depth is 75% and at the sea bottom 15% of the surface current velocity. The direction of the current at the surface is 25°. Further down in the water column (middle and bottom) the current changes direction to-155°. The significant wave height is 7m with peak period 14sec and wave direction 20°. The mean wind velocity is 15m/s with mean direction 20°.
Fig.11 North: position estimates using RAPR system.
Initially in the simulations, the setpoint for the DP system is set equal to the field zero point (0,0). At 500sec, 1000sec, 1500sec and 2000sec the setpoint is changed respectively to (-20m North, -10m East), (20m North, -10m East), (20m North, 10m East) and (-10m North, -20m East). As seen in Fig. 11, the RAPR observer follows the actual North position within ±2m during the maneuvering operation. For larger deviations this may initiate update of the bias estimates in (7). In Fig.12 snapshots of the riser profile at each 10sec are shown. In the figure it is also shown how the upper and lower riser angles will change during the maneuvering. In the simulations the variations of α1 and αb are within ±80°,indicating the good robustness of the observer subject to large variations in the riser angle offsets.
Fig.12 Snapshots of riser profile as each 10sec.
In this paper a new initiative on modular multidisciplinary simulator based on Matlab/Simulink has been presented. The simulator is named Marine Cybernetics Simulator (MCSim) and is used in education and research activities. The simulator integrates modules of hydrodynamics, structural mechanics, machinery systems, automatic control systems, and navigation and sensors systems. An example of a DP operated drilling rig is shown as a case in how the simulator may be adapted for a marine application.
Japan Society for the Promotion of Science (JSPS) is acknowledged for supporting the second author by a post-doctoral fellowship.
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Professor Asgeir J. Sørensen obtained MSc degree in Naval Architecture (1988) and dr. ing. degree in Engineering Cybernetics (1993) at NTNU. In the period 1989- 1992 Sørensen was employed at MARINTEK. In 1993 Sørensen was employed at ABB Corporate Research. In 1996 he was appointed to Manager of Positioning Systems at ABB Marine. From 1998 to April 2001 Sørensen was assigned to the position Technical Manager in the Business Area Automation Marine and Turbochargers, ABB Automation (Zürich). Since 1999 Sørensen has held the position of Professor of Marine Cybernetics at the Department of Marine Technology, NTNU.
Dr Egil Pedersen received a doctorate in Nautical Science from NTNU in 1997. He is a fully trained merchant ship navigational officer and has practical marine experience that includes various positions on board ocean going fishing vessels and marine seismic surveying vessels. He has been lecturing in nautical subjects at NTNU and Royal Norwegian Navy Academy since 1997 and 2000, respectively. Dr. Pedersen is currently a visiting researcher to National Maritime Research Institute in Tokyo.
Øyvind N. Smogeli received the M.Sc. degree in Marine Technology in 2002 at NTNU. He is currently working as a Ph.D. student in the field of Marine Cybernetics at NTNU.