A transfer function giving the relation between the wave disturbance w(t) and the roll 0(t) for a vessel given as: O(s) G(s) = 0.25 W (s) s² + 0.35s + 0.25

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PD Controller Design
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)
Oo00
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.
Transcribed Image Text:PD Controller Design 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) Oo00 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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