PD Controller DesignA transfer function giving the relation between the wave disturbance w(t) and the roll 0(t)for a vessel given as:O(s)0.25G(s)W (s) s² + 0.35s + 0.25w(t) 0(t)Oo00Roll axisa. Show the roots on root-locus plot and find the damping 3, and natural frequency wnb. Show plot of the system's response to unit step input and explain the resultc. 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 toprovide feedback system with 3 = 0.707 and Kp > 0, please evaluate?e. Switch the controller with proportional-derivative controller and evaluate Kp and a Kagains to provide 3 = 0.707 damping.

Gs=θsWs=0.25s2+0.35s+0.25Characteristics…

Answered: A transfer function giving the relation…

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

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

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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