P4.2 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 stabi- lization system is shown in Figure P4.2. The rolling motion of a ship can be regarded as an oscillating pen- dulum with a deviation from the vertical of 0 degrees and a typical period of 3 seconds. The transfer function of a typical ship is G(s) = 5² + 25ws + w²² where w, = 3 rad/sec and = 0.20. With this low damping factor, the oscillations continue for several cycles, and the rolling amplitude can reach 18° for the expected amplitude of waves in a normal sea. Deter- mine and compare the open-loop and closed-loop sys- tem for (a) sensitivity to changes in the actuator constant K, and the roll sensor K₁, and (b) the ability to reduce the effects of step disturbances of the waves. Note that the desired roll, 0d(s), is zero degrees.
P4.2 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 stabi- lization system is shown in Figure P4.2. The rolling motion of a ship can be regarded as an oscillating pen- dulum with a deviation from the vertical of 0 degrees and a typical period of 3 seconds. The transfer function of a typical ship is G(s) = 5² + 25ws + w²² where w, = 3 rad/sec and = 0.20. With this low damping factor, the oscillations continue for several cycles, and the rolling amplitude can reach 18° for the expected amplitude of waves in a normal sea. Deter- mine and compare the open-loop and closed-loop sys- tem for (a) sensitivity to changes in the actuator constant K, and the roll sensor K₁, and (b) the ability to reduce the effects of step disturbances of the waves. Note that the desired roll, 0d(s), is zero degrees.
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Transcribed Image Text:Problems
Wave effect
T„(s)
Fin
E(s)
actuator
Ship
G(s)
(s)
Roll
K.
Fin
FIGURE P4.2
Ship stabilization
system. The effect
of the waves is a
torque on the ship,
TAs).
Fin
Roll
sensor
(a)
(b)
![P4.2 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 stabi-
lization system is shown in Figure P4.2. The rolling
motion of a ship can be regarded as an oscillating pen-
dulum with a deviation from the vertical of 0 degrees
and a typical period of 3 seconds. The transfer function
of a typical ship is
G(s)
s2 + 25w,s + w
3 rad/sec and
damping factor 7, the oscillations continue for several
cycles, and the rolling amplitude can reach 18° for the
expected amplitude of waves in a normal sea. Deter-
mine and compare the open-loop and closed-loop sys-
tem for (a) sensitivity to changes in the actuator
constant K, and the roll sensor K1, and (b) the ability
to reduce the effects of step disturbances of the waves.
Note that the desired roll, 0d(s), is zero degrees.
where w, = ġ = 0.20. With this low](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb6e49c2-d01d-4438-a99a-92f670cec770%2F3b45ffe0-40ac-47fb-a8af-53c378026aa0%2F4cfy80o_processed.png&w=3840&q=75)
Transcribed Image Text:P4.2 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 stabi-
lization system is shown in Figure P4.2. The rolling
motion of a ship can be regarded as an oscillating pen-
dulum with a deviation from the vertical of 0 degrees
and a typical period of 3 seconds. The transfer function
of a typical ship is
G(s)
s2 + 25w,s + w
3 rad/sec and
damping factor 7, the oscillations continue for several
cycles, and the rolling amplitude can reach 18° for the
expected amplitude of waves in a normal sea. Deter-
mine and compare the open-loop and closed-loop sys-
tem for (a) sensitivity to changes in the actuator
constant K, and the roll sensor K1, and (b) the ability
to reduce the effects of step disturbances of the waves.
Note that the desired roll, 0d(s), is zero degrees.
where w, = ġ = 0.20. With this low
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VIEWStep 4: a) sensitivity to changes in the closed loop;
VIEWStep 5: b) the ability to reduce the effects of step disturbances of the waves.
VIEWStep 6: b) the ability to reduce the effects of step disturbances of the waves.
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