A transfer function for a system for rudder control was obtained experimentally in frequencydomain and Bode-plots of the open-loop system are given below. The slopes of asymptotes canbe estimated from the diagrams. Assuming we use a unity-feedback to close the loop, analyze(with justification/explanation) the system:60Magnitude4020믐 20-40-60-80-10010410310210110°10102103104105Frequency [rad/s]Phase-30-60-90-120-150-180-210-240-270-300104103102101100101102103104105Frequency [rad/s]a) What is the type of the system (with respect to steady-state erroib) What is the steady-state error ess when a unit-step input is applied to the closed-loopsystem – provide the exact valuec) What is the crossover frequency we of the system?d) What is the Phase Margin of the system? Is this considered adequate for stability (e) What is the Gain Margin of the system approximatelyf) Briefly mention at least 2 possible options/controllers ana pros/cons of using them thatwould reduce the closed-loop steady-state error by say, factor of 10,g) Assume we added +60dB of gain to the system to improve the ess, what would be thenew w, and the Phase Margin (approximately)?Degrees

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Answered: 60 Magnitude 40 20 9 -20 -40 -60 -80…

Engineering

Electrical Engineering

60 Magnitude 40 20 9 -20 -40 -60 -80 -100 104 103 102 101 100 101 102 103 104 105 Frequency [rad/s]

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

A transfer function for a system for rudder control was obtained experimentally in frequency
domain and Bode-plots of the open-loop system are given below. The slopes of asymptotes can
be estimated from the diagrams. Assuming we use a unity-feedback to close the loop, analyze
(with justification/explanation) the system:
60
Magnitude
40
20
믐 20
-40
-60
-80
-100
104
103
102
101
10°
10
102
103
104
105
Frequency [rad/s]
Phase
-30
-60
-90
-120
-150
-180
-210
-240
-270
-300
104
103
102
101
100
101
102
103
104
105
Frequency [rad/s]
a) What is the type of the system (with respect to steady-state erroi
b) What is the steady-state error ess when a unit-step input is applied to the closed-loop
system – provide the exact value
c) What is the crossover frequency we of the system?
d) What is the Phase Margin of the system? Is this considered adequate for stability (
e) What is the Gain Margin of the system approximately
f) Briefly mention at least 2 possible options/controllers ana pros/cons of using them that
would reduce the closed-loop steady-state error by say, factor of 10,
g) Assume we added +60dB of gain to the system to improve the ess, what would be the
new w, and the Phase Margin (approximately)?
Degrees

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