Stability, performance and power flow of active U-tube anti-roll tank

Abstract Active control of ship roll using a U-tube anti-roll tank (ART) is considered. A linearized model of the ship and active ART with two degrees of freedom is formulated. The two degrees of freedom are the ART fluid free surface angle and the ship roll angle. The active control approach is based on the absolute roll-rate feedback assuming an idealized pump located in the connecting conduit of the U-tube. The pump generates a pressure difference proportional to the roll rate via a negative feedback gain. First, the stability of the feedback loop is analysed using the Nyquist criterion. The stability analysis indicates that the ART natural frequency should be set well below the ship roll natural frequency. The performance analysis is carried out in terms of the reductions of the frequency response function between the wave slope exciting the ship roll and the roll angle. It is found that also the active control performance improves with reducing the natural frequency of the ART. Finally, the analysis of the power flow through the system indicates that the pump power can be reduced with the reduction of the ART natural frequency. Also, it is shown that it is possible to reduce the wave power input into the ship plus ART system by engaging the active control.