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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.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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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)
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
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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