Coupled control of the horizontal and vertical plane motions of a semi-submersible platform by a dynamic positioning system

Abstract

Due to the small-waterplane-area of a semi-submersible platform, not only are the surge and sway responses affected by the roll and pitch damping, but also roll and pitch motions may be induced by the propeller activity of the dynamic positioning (DP) system. The coupling characteristics of the dynamic responses between the degrees-of-freedom (DOFs) of the horizontal plane and the vertical plane can no longer be neglected. Therefore, traditional DP control strategies based on the horizontal DOFs are not suitable for the DP of a semi-submersible platform. The Cummins equation is widely used to simulate the response in the time domain. This equation, in which the convolution integral terms are replaced by the state-space model, is directly used to design the DP control strategy used in this study. The advantage of this model is that the coupling effects of the horizontal plane motions and vertical plane motions are considered. Because the sensors can only measure the dynamic motions of the platform, a static output feedback controller using L ∞ performance is designed to reject persistent environmental disturbances for the fully coupled dynamic model. Lyapunov function-based stability analysis is used to guarantee the stability. Finally, simulation results in the time domain are provided to specify the proposed controller design.