Diagram (applies to all subsequent problems): W(s) Y(s) R(s) U(s) Da (s) Gpi (s) H(s)
Diagram (applies to all subsequent problems): W(s) Y(s) R(s) U(s) Da (s) Gpi (s) H(s)
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...
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![Diagram (applies to all subsequent problems):
W(s)
R(s)
U(s)
Y(s)
Da (s)
Gpl (s)
H(s)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03f00886-5b68-487c-98b2-407f8302b5ec%2F75d6acb4-b18e-48cd-b52f-7a2ab24167dd%2Fvmnxyef_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Diagram (applies to all subsequent problems):
W(s)
R(s)
U(s)
Y(s)
Da (s)
Gpl (s)
H(s)
![Given a system as in the diagram above, where K is an adjustable parameter.
1
K1
Det (s) = Kp +
Gpi(s)
H(s) = 1
s + 4
S
a) Assuming W=0, find the transfer function Y(s)/R(s)
b) Assuming R=0, find the transfer function Y(s)/W(s)
c) Assume r(t)=0, what is the response of the system to w(t) = u(t) (unit-step)? What is the steady-
state response to the disturbance (derive in terms of parameters ?
d) Ignoring the effects of the zero (numerator of the closed-loop function), determine the range
of constants Kp and Ki such that the rise-time of the closed-loop system is equal (or less than)
0.36 s and so that the damping factor { is equal to (or greater than) 0.8. Use the textbook
approximation for the rise-time.
e) For the values of constants Kp and Ki that correspond to the borderline cases of rise-time and
damping-factor in problem 2d), determine the settling time of the closed-loop system to within
1% of the final value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03f00886-5b68-487c-98b2-407f8302b5ec%2F75d6acb4-b18e-48cd-b52f-7a2ab24167dd%2Fmwigype_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given a system as in the diagram above, where K is an adjustable parameter.
1
K1
Det (s) = Kp +
Gpi(s)
H(s) = 1
s + 4
S
a) Assuming W=0, find the transfer function Y(s)/R(s)
b) Assuming R=0, find the transfer function Y(s)/W(s)
c) Assume r(t)=0, what is the response of the system to w(t) = u(t) (unit-step)? What is the steady-
state response to the disturbance (derive in terms of parameters ?
d) Ignoring the effects of the zero (numerator of the closed-loop function), determine the range
of constants Kp and Ki such that the rise-time of the closed-loop system is equal (or less than)
0.36 s and so that the damping factor { is equal to (or greater than) 0.8. Use the textbook
approximation for the rise-time.
e) For the values of constants Kp and Ki that correspond to the borderline cases of rise-time and
damping-factor in problem 2d), determine the settling time of the closed-loop system to within
1% of the final value.
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