It is important to ensure passenger comfort on ships by stabilizing the ship's oscillations due to waves [13]. Most ship stabilization systems use fins or hydrofoils projecting into the water to generate a stabilization torque on the ship. A simple diagram of a ship stabilization system is shown in Figure P4.2. The rolling motion of a ship can be regarded as an oscillating pendulum with a deviation from the vertical of θ degrees and a typical period of 3 seconds. The transfer function of a typical ship is

where wn = 3 rad/s and Ï‚ = 0.20. With this low damping factor Ï‚, the oscillations continue for several cycles, and the rolling amplitude can reach 18° for the expected amplitude of waves in a normal sea. Determine and compare the open-loop and closed-loop system for
(a) Sensitivity to changes in the actuator constant Ka and the roll sensor K1, and
(b) The ability to reduce the effects of step disturbances of the waves. The desired roll θd(s) is zero degrees.
Figure P4.2
Ship stabilization system. The effect of the waves is a torque Td(s) on the ship.

Transcribed Image Text:

Wave effec T4S) Fin TAs) | Ship → Roll Ku Fin Roll sensor * Ki