Time-domain Simulation of Multibody Floating Systems based on State-space Modeling Technology



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A numerical scheme to simulate time-domain motion responses of multibody floating systems has been successfully proposed. This scheme is integrated into a time-domain simulation tool, with fully coupled hydrodynamic coefficients obtained from the hydrodynamic software - WAMIT which solves the Boundary Value Problem (BVP). The equations of motion are transformed into standard state-space format, using the constant coefficient approximation and the impulse response function method. Thus the Ordinary Differential Equation (ODE) solvers in MATLAB can be directly employed. The time-domain responses of a single spar at sea are initially obtained. The optimal Linear Quadratic Regulator (LQR) controller is further applied to this single spar, by assuming that the Dynamic Positioning (DP) system can provide the optimized thruster forces. Various factors that affect the controlling efficiency, e.g., the time steps ?? and ?t, the weighting factors(Q,R), are further investigated in detail. Next, a two-body floating system is studied. The response amplitude operators (RAOs) of each body are calculated and compared with the single body case. Then the effects of the body-to-body interaction coefficients on the time-domain responses are further investigated. Moreover, the mean drift force is incorporated in the DP system to further mitigate the motion responses of each body. Finally, this tool is extended to a three-body floating system, with the relative motions between them derived.