10:36a) Consider the feedback system in Figure Q4 with controller G.(s)= and plants+a100G,(s)=s+25Specify K and a of G,(s) such that the overall closed-loop response to aunity step reference input has a maximum percentage overshoot (%OS) of 25% and a 1%settling time of 0.1sec. [Hint: use the approximate relationship %OS = 1-x 100%]0.6b) To make the steady-state error to a unit step reference input zero, add an integrator tothe controller of Q4a, ie. G.(s)Assuming that a has the value derived ins(s+a)Q4a do the following:() Draw the root-locus of the closed-loop system, as K takes all positive real values, bycomputing the locus on the real axis, the angles of asymptotes, the point ofintersection of the asymptotes with the real axis and the break points. Show clearlywith arrows the direction of the loci.(ü) Find the value of K so the closed-loop system becomes marginally stable. In that casecompute the points of intersection of the loci with the imaginary axis.R(s) +a Els)Y(s)G,(s)G,(s)Figure Q4: Unity feedback system

Answered: Image /qna-images/answer/7c6b5ce2-aadc-44ec-85dc-ef90c76f5b7f.jpg

a) Consider the feedback system in Figure Q4 with controller G.(s)= K and plant s+o 100 G,(s)= Specify K and a of G̟(s) such that the overall closed-loop response to a S+25 unity step reference input has a maximum percentage overshoot (%O5) of 25% and a 1% settling time of 0.1sec. [Hint: use the approximate relationship %oS = 1. x100%] 0.6 b) To make the steady-state error to a unit step reference input zero, add an integrator to K the controller of Q4a, Le. Ĝ,(s) = Assuming that a has the value derived in s(s+o Q4a do the following: (0 Draw the root-locus of the closed-loop system, as K takes all positive real values, by computing the locus on the real axis, the angles of asymptotes, the point of intersection of the asymptotes with the real axis and the break points. Show clearly with arrows the direction of the loci. (i) Find the value of K so the closed-loop system becomes marginally stable. In that case compute the points of intersection of the loci with the imaginary axis. R(s)+a Els) Yls) G,(s) Figure Q4: Unity feedback system

a) Consider the feedback system in Figure Q4 with controller G.(s)= K and plant s+o 100 G,(s)= Specify K and a of G̟(s) such that the overall closed-loop response to a S+25 unity step reference input has a maximum percentage overshoot (%O5) of 25% and a 1% settling time of 0.1sec. [Hint: use the approximate relationship %oS = 1. x100%] 0.6 b) To make the steady-state error to a unit step reference input zero, add an integrator to K the controller of Q4a, Le. Ĝ,(s) = Assuming that a has the value derived in s(s+o Q4a do the following: (0 Draw the root-locus of the closed-loop system, as K takes all positive real values, by computing the locus on the real axis, the angles of asymptotes, the point of intersection of the asymptotes with the real axis and the break points. Show clearly with arrows the direction of the loci. (i) Find the value of K so the closed-loop system becomes marginally stable. In that case compute the points of intersection of the loci with the imaginary axis. R(s)+a Els) Yls) G,(s) Figure Q4: Unity feedback system

Introductory Circuit Analysis (13th Edition)

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ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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Question

10:36
a) Consider the feedback system in Figure Q4 with controller G.(s)= and plant
s+a
100
G,(s)=
s+25
Specify K and a of G,(s) such that the overall closed-loop response to a
unity step reference input has a maximum percentage overshoot (%OS) of 25% and a 1%
settling time of 0.1sec. [Hint: use the approximate relationship %OS = 1-x 100%]
0.6
b) To make the steady-state error to a unit step reference input zero, add an integrator to
the controller of Q4a, ie. G.(s)
Assuming that a has the value derived in
s(s+a)
Q4a do the following:
() Draw the root-locus of the closed-loop system, as K takes all positive real values, by
computing the locus on the real axis, the angles of asymptotes, the point of
intersection of the asymptotes with the real axis and the break points. Show clearly
with arrows the direction of the loci.
(ü) Find the value of K so the closed-loop system becomes marginally stable. In that case
compute the points of intersection of the loci with the imaginary axis.
R(s) +a Els)
Y(s)
G,(s)
G,(s)
Figure Q4: Unity feedback system

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