Q3. a) Consider the control system shown in Figure Q3. Controller E(s) R(s) C(s) Desired output Plant G(s) Y(s) Actual output K N(s) 4 C(s) = G(s) s+2 D(s) s²+5s-4 Figure Q3. Closed-loop system. (i) For the transfer function G(s), determine whether polynomial D(s) is Hurwitz. Justify your answer. (ii) Obtain the closed-loop transfer function P(s) = Y(s)/R(s) of the system. (iii) Based on your result for the previous question [Question 3a)-(ii)], use the Routh-Hurwitz stability criterion to determine the range of gain K for which the closed-loop system is stable.
Q3. a) Consider the control system shown in Figure Q3. Controller E(s) R(s) C(s) Desired output Plant G(s) Y(s) Actual output K N(s) 4 C(s) = G(s) s+2 D(s) s²+5s-4 Figure Q3. Closed-loop system. (i) For the transfer function G(s), determine whether polynomial D(s) is Hurwitz. Justify your answer. (ii) Obtain the closed-loop transfer function P(s) = Y(s)/R(s) of the system. (iii) Based on your result for the previous question [Question 3a)-(ii)], use the Routh-Hurwitz stability criterion to determine the range of gain K for which the closed-loop system is stable.
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
Question
![Q3.
a) Consider the control system shown in Figure Q3.
Controller
E(s)
R(s)
C(s)
Desired
output
Plant
G(s)
Y(s)
Actual
output
K
N(s)
4
C(s) =
G(s)
s+2
D(s) s²+5s-4
Figure Q3. Closed-loop system.
(i) For the transfer function G(s), determine whether polynomial D(s) is
Hurwitz. Justify your answer.
(ii) Obtain the closed-loop transfer function P(s) = Y(s)/R(s) of the
system.
(iii) Based on your result for the previous question [Question 3a)-(ii)], use
the Routh-Hurwitz stability criterion to determine the range of gain K
for which the closed-loop system is stable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e9f3fbc-f178-4c10-833f-0c2a76ea4b0d%2F1cd3c89b-d2d6-4aa3-9ffe-c2c159b4a148%2Fdejq6b3_processed.png&w=3840&q=75)
Transcribed Image Text:Q3.
a) Consider the control system shown in Figure Q3.
Controller
E(s)
R(s)
C(s)
Desired
output
Plant
G(s)
Y(s)
Actual
output
K
N(s)
4
C(s) =
G(s)
s+2
D(s) s²+5s-4
Figure Q3. Closed-loop system.
(i) For the transfer function G(s), determine whether polynomial D(s) is
Hurwitz. Justify your answer.
(ii) Obtain the closed-loop transfer function P(s) = Y(s)/R(s) of the
system.
(iii) Based on your result for the previous question [Question 3a)-(ii)], use
the Routh-Hurwitz stability criterion to determine the range of gain K
for which the closed-loop system is stable.
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