Effects of poles and zeroes

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 Consider the system with G(s)H(s) = This is the corresponding root locus

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

4. Now, if one more pole is added at 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. Addition of Pole

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

8. Addition of Zeroes Adding one more zero at s= -6. G(s)H(s)= 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.