The addition of poles to a system tends to shift the root locus towards the right side of the s-plane, lowering stability. Adding more poles further restricts stability by shifting the breakaway points more to the right. In contrast, the addition of zeros tends to pull the root locus left, improving stability by making the system less oscillatory and increasing the gain margin and range of k values.

1. Effect of addition of poles
The general effect of
addition of a pole is a
tendency to shift the locus
towards right side of s-plane
and this lowers the stability.

2. Addition of Pole
k
Consider the system with G(s)H(s) =
s (s 2)
This is the
corresponding
root locus

3. Addition of Pole
Now, let us add a pole s= -4.
k
G ( s) H ( s)
s ( s 2)( s 4)
Root locus
becomes:
It is seen that the root locus has
shifted to its right. Stability of
the system gets restricted.

4. Addition of Pole
Now, if one more pole is added at s= -6
k
G ( s) H ( s)
s ( s 2)( s 4)( s 6)
Breakaway point in section s=0 and s= -2
gets shifted towards right as compared to
previous case. So system stability further gets
restricted.

5. Summary
Effect of addition of open loop poles can be
summarised as follows:
The root locus changes its nature and
shifts towards imaginary axis.
The system becomes oscillatory.
Gain Margin enhances relatively, thus
stability decreases.
Range of k reduces.
Settling time increases.

6. Effect of Addition of
Zero
The general effect of
addition of zeroes is a
tendency to pull the root
locus to the left of s-plan
and hence improves
stability.

7. Addition of Zeroes
k
Consider the system with G(s)H(s)=
s (s 2)
It is the corresponding Root
loci.
Add a zero s= -4.
Now, G(s)H(s) becomes
k ( s 4)
s( s 2)
The root locus here, is shifted
to its left.

8. Addition of Zeroes
Adding one more zero at s= -6. G(s)H(s)=
k ( s 4)( s 6)
s ( s 2)
We can see, the root locus has shifted towards its left.
And, the breakaway points shifts towards left of the s plane.
So relatively stability of system increases.

9. Summary
The root locus changes its nature
and shifts to left away from
imaginary axis.
Relative stability of system
increases.
System becomes less oscillatory.
Gain margin increases and so
does the range of K.
Settling time decreases.