Step-1: The first step in constructing a root-locus plot is to locate the open- loop poles and zeros in s-plane. Ri Cis) (s + 1)6 +2) a5- K -0.5- G(s)H(s): s(s+1)(s+2) -1
Step-1: The first step in constructing a root-locus plot is to locate the open- loop poles and zeros in s-plane. Ri Cis) (s + 1)6 +2) a5- K -0.5- G(s)H(s): s(s+1)(s+2) -1
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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![46.| 36.ill
Control Engineerin...
>
Control Engineering II/3rd Year/Electronic Engineering
LECTURE: 02
ROOT LOCUS TECHNIQUES AND DESIGN
Root locus is a graphical method in which roots of the characteristic
equation are plotted in s-plane for the different values of parameter. The
locus of the roots of the characteristic equation when gain is varied from
zero to infinity is called root locus.
<<<>>> Angle Condition:
4 G(s)H(s) = +180 (2k + 1)
(k = 1,2, 3, ...)
<<>> Magnitude Condition:
|G(s)H(s) = 1
>>> Rules for Construction of Root Loci
Following are the rules to sketch the root locus plot.
Step-1: The first step in constructing a root-locus plot is to locate the open-
loop poles and zeros in s-plane.
Ris)
Cs)
sis +1)(s+ 2)
0.5 -
K
-0.5-
G(s)H(s)=
s(s+1)(s+2)
-3
2.
-1
1|Page
Asst. Prof. Dr. Abbas H. Issa
Control Engineering II/3rd Year/Electronic Engineering
Step-2: Determine the root loci on the real axis.
•To determine the root loci on real axis we select some test points.
• e.g: p1 (on positive real axis).
/s = /s + 1 = /s + 2 = 0°
gle condition is not satisfied.
, there is no root locus on the positive real axis.
0.5-
0.5
P1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99e0cf9a-fa3b-438e-8bbf-82e0ea49eeb4%2Fc319db1d-5505-4be6-bdf1-a200a2b21ce4%2Fnye8ojb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:46.| 36.ill
Control Engineerin...
>
Control Engineering II/3rd Year/Electronic Engineering
LECTURE: 02
ROOT LOCUS TECHNIQUES AND DESIGN
Root locus is a graphical method in which roots of the characteristic
equation are plotted in s-plane for the different values of parameter. The
locus of the roots of the characteristic equation when gain is varied from
zero to infinity is called root locus.
<<<>>> Angle Condition:
4 G(s)H(s) = +180 (2k + 1)
(k = 1,2, 3, ...)
<<>> Magnitude Condition:
|G(s)H(s) = 1
>>> Rules for Construction of Root Loci
Following are the rules to sketch the root locus plot.
Step-1: The first step in constructing a root-locus plot is to locate the open-
loop poles and zeros in s-plane.
Ris)
Cs)
sis +1)(s+ 2)
0.5 -
K
-0.5-
G(s)H(s)=
s(s+1)(s+2)
-3
2.
-1
1|Page
Asst. Prof. Dr. Abbas H. Issa
Control Engineering II/3rd Year/Electronic Engineering
Step-2: Determine the root loci on the real axis.
•To determine the root loci on real axis we select some test points.
• e.g: p1 (on positive real axis).
/s = /s + 1 = /s + 2 = 0°
gle condition is not satisfied.
, there is no root locus on the positive real axis.
0.5-
0.5
P1
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