Given is a feed-forward transfer function G(s) of some system, where K is an adjustable parameter. K G(s) s(s + 2) Assume you apply a unity feedback loop from the output of this system back to the input. a) Find the equivalent transfer function of the closed-loop system Heg (s) b) Using the text-book approximation for the rise-time of the system (t, = 1.8 s ), determine the Wn range of undamped natural frequencies that result in the rise time t, < 0.18 s and the range of values of parameter K that correspond to such frequencies. c) What is the settling time of this closed-loop system (assume that we settle within 1% of the final output value)? d) Can the settling time be modified by adjusting the parameter K? e) What is the maximum value of the damping factor { that can be achieved if the requirement under b) is satisfied? What is the corresponding overshoot (as a % of the final, steady-state value)? What would happen to the rise-time if you tried to reduce the overshoot by adjusting the parameter K? f) What type of system is this in terms of steady-state error? Diagram (applies to all subsequent problems): w(s) R(s) U(s) Y(s) Da (s) Gpl (s) H(s)

Given is a feed-forward transfer function G(s) of some system, where K is an adjustable parameter. K G(s) s(s + 2) Assume you apply a unity feedback loop from the output of this system back to the input. a) Find the equivalent transfer function of the closed-loop system Heg (s) b) Using the text-book approximation for the rise-time of the system (t, = 1.8 s ), determine the Wn range of undamped natural frequencies that result in the rise time t, < 0.18 s and the range of values of parameter K that correspond to such frequencies. c) What is the settling time of this closed-loop system (assume that we settle within 1% of the final output value)? d) Can the settling time be modified by adjusting the parameter K? e) What is the maximum value of the damping factor { that can be achieved if the requirement under b) is satisfied? What is the corresponding overshoot (as a % of the final, steady-state value)? What would happen to the rise-time if you tried to reduce the overshoot by adjusting the parameter K? f) What type of system is this in terms of steady-state error? Diagram (applies to all subsequent problems): w(s) R(s) U(s) Y(s) Da (s) Gpl (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

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Question

Given is a feed-forward transfer function G(s) of some system, where K is an adjustable parameter.
K
G(s)
s(s + 2)
Assume you apply a unity feedback loop from the output of this system back to the input.
a) Find the equivalent transfer function of the closed-loop system Heg (s)
b) Using the text-book approximation for the rise-time of the system (t, =
1.8
s ), determine the
Wn
range of undamped natural frequencies that result in the rise time t, < 0.18 s and the range of
values of parameter K that correspond to such frequencies.
c)
What is the settling time of this closed-loop system (assume that we settle within 1% of the
final output value)?
d) Can the settling time be modified by adjusting the parameter K?
e) What is the maximum value of the damping factor { that can be achieved if the requirement
under b) is satisfied? What is the corresponding overshoot (as a % of the final, steady-state
value)? What would happen to the rise-time if you tried to reduce the overshoot by adjusting
the parameter K?
f) What type of system is this in terms of steady-state error?
Diagram (applies to all subsequent problems):
w(s)
R(s)
U(s)
Y(s)
Dci (s)
Gpl (s)
H(s)

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