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.1K1Det (s) = Kp +Gpi(s)H(s) = 1s + 4Sa) 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 rangeof 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 textbookapproximation for the rise-time.e) For the values of constants Kp and Ki that correspond to the borderline cases of rise-time anddamping-factor in problem 2d), determine the settling time of the closed-loop system to within1% of the final value.

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Answered: W(s) R(s) U(s) Y(s) Da (s) Gpi (s) H(s)

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Electrical Engineering

W(s) R(s) U(s) Y(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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Question

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.

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