root locus in control system

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root locus always starts from pole and end at either zero or infinity
Steps
step 1- locate poles and zeros
step 2- find root locus on real axis
step 3- find asymptotes and centroid
step 4- find break away and break in point
step 5- find crossing point on imaginary axis

00:10 locate poles and zeros
for getting poles equate denominator = 0, & find roots
for getting zeros equate numerate=0, & find roots

01:47 find root locus on real axis
take a test point and check whether you have odd number of poles or zeros on the right side of that test point. then root locus exist
if even number of poles and zeros there , then root locus does not exist

03:03 find asymptotes and centroid
for getting asymptotes find angle of asymptote
number of asymptote= P-Z
then find centroid and draw angle of asymptote

06:08 find break away and break in point
find the characteristic equation
from that find K
differentiate K and equate it to zero
find the roots of equation
check the roots obtained exist in the root locus in real axis
put the values of roots in the equation and check whether you are getting positive value
if there are two adjacent pole you will get break away point
if there are two adjacent zeros you will get break in point

11:03 find crossing point on imaginary axis
from the characteristic equation
either find Routh Hurwitz stability criterion
or put jw in place of S and equate real and imaginary parts
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