A transfer function giving the relation between the wave disturbance w(t) and the roll 0(t) for a vessel given as: O(s) 0.25 G(s) = W (s) s² + 0.35s + 0.25 w(t) 0(t) Roll axis a. Show the roots on root-locus plot and find the damping 7, and natural frequency w, b. Show plot of the system's response to unit step input and explain the result c. Shade/Show the region on a root-locus plot where the damping ratio be at least 7 = 0.707 (hint: independent from the system) To provide the roll stability, mostly fins are used in vessels with their feedback systems.
A transfer function giving the relation between the wave disturbance w(t) and the roll 0(t) for a vessel given as: O(s) 0.25 G(s) = W (s) s² + 0.35s + 0.25 w(t) 0(t) Roll axis a. Show the roots on root-locus plot and find the damping 7, and natural frequency w, b. Show plot of the system's response to unit step input and explain the result c. Shade/Show the region on a root-locus plot where the damping ratio be at least 7 = 0.707 (hint: independent from the system) To provide the roll stability, mostly fins are used in vessels with their feedback systems.
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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Transcribed Image Text:A transfer function giving the relation between the wave disturbance w(t) and the roll 0(t)
for a vessel given as:
O(s)
0.25
G(s)
W (s) s2 + 0.35s + 0.25
w(t) 0(t)
00
Roll axis
a. Show the roots on root-locus plot and find the damping 3, and natural frequency wn
b. Show plot of the system's response to unit step input and explain the result
c. Shade/Show the region on a root-locus plot where the damping ratio be at least 3 =
0.707 (hint: independent from the system)
To provide the roll stability, mostly fins are used in vessels with their feedback systems.
d. Through applying proportional control and negative unit feedback, is it possible to
provide feedback system with 3 = 0.707 and Kp > 0, please evaluate?
e. Switch the controller with proportional-derivative controller and evaluate Kp and a Ka
gains to provide 3 = 0.707 damping.
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