Answered: Ships at sea undergo motion about their…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Ships at sea undergo motion about their roll axis, as shown in Fig. The stabilizers can be positioned by a closed-loop roll control system that consists of components, such as fin actuators and sensors, as well as the ship's roll dynamics. Assume the roll dynamics, which relates the roll-angle output, θ(s), to a disturbance-torque input, TD(s)

Find the natural frequency, damping ratio, peak time and percent overshoot.

Question 5 options:

ωn=2.8 rad/s, ξ=0.5Peak time 5.12sOvershoot 69.26%

ωn=0.5 rad/s, ξ=2.25Peak time 4.16sOvershoot 49.1%

ωn=2.25 rad/s, ξ=0.5Peak time 3.45sOvershoot 30.85%

Ships at sea undergo motion about their roll axis, as shown in Fig. The stabilizers can be positioned by a closed-
loop roll control system that consists of components, such as fin actuators and sensors, as well as the ship's roll
dynamics. Assume the roll dynamics, which relates the roll-angle output, 0(s), to a disturbance-torque input,
TD(s),
0 (s)
2.25
TD (s) (s² +0.5s +2.25)
Find the natural frequency, damping ratio, peak time and percent overshoot.
Own
Roll axis.
wn = 2.8 rad/s, = 0.5
§
Peak time 5.12s
Overshoot 69.26%
-
Tp(t) 0(t)
CCC
Oooo
0.5 rad/s, § = 2.25
&
Peak time 4. 16s
Overshoot 49.1%
wn = 2.25 rad/s, = 0.5
Peak time 3. 45s
Overshoot 30.85%
wn = 1.5 rad/s, § = 0.167
Peak time 2. 124s
Overshoot 59.6%

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