60 Magnitude 40 20 9 -20 -40 -60 -80 -100 104 103 102 101 100 101 102 103 104 105 Frequency [rad/s]
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F672bf286-8abe-4b07-9ca1-0d5b2612956c%2F94ad2b8c-b176-455c-be7d-0720ed70b257%2Fj3lt3il_processed.png&w=3840&q=75)
Transcribed Image Text: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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