Study on a Dynamic Positioning System of n-footings Type Semi-submersible Platform

Abstract

In this paper authors focused attention on a dynamic positioning system of n-footings type semi-submersible platform using a mathematical model which is very simple but can simulate well an actual model experiment. The mathematical model is based on following assumptions. 1) Our platform is a pancake shape n-footings type with a thruster installed under each footing. 2) Hydrodynamic forces of submersible bodies except for drags are negligible. 3) Forces acting on each footing are homogenious in direction and can be superposed. Strictly speaking the model must be shown by nonlinear equations. But closed form mathematical expressions for the optimal control equation in nonlinear problem cannot be obtained analytically except in very special case. Therefore a linear approximate equation was introduced. For this linear equation, it is not difficult to research optimal control gains. From the optimal control theory, it is well known that the solution minimizing a quadratic form performance measure is a feed back control system. In the present paper, some numerical calculations on the motion of platform which was tried to keep the position by P.I.D feed back control were carried out and compared with the results of model experiments. And it was found that the theoretical results agree with experimental values.