Effect of adding a zero to a second order system

The standard second-order system has no zeros in the transfer function. If the system is modified to include a zero in it, the overshoot and settling time are greatly affected by the location of that zero.

1. What is the effect of zeros on system stability?
2. What happens when a zero is added to the open loop transfer function?
3. Do zeros affect settling time?
4. How overshoot is affected by adding a zero in the forward path transfer function?

What is the effect of zeros on system stability?

Addition of poles to the transfer function has the effect of pulling the root locus to the right, making the system less stable. Addition of zeros to the transfer function has the effect of pulling the root locus to the left, making the system more stable.

What happens when a zero is added to the open loop transfer function?

If we include a zero in the open loop transfer function, then some of root locus branches will move towards left half of 's' plane. So, it will increase the control system stability. In this case, the damping ratio δ increases.

Do zeros affect settling time?

LHP Zeros: Increase overshoot, decrease rise time, and have no effect on settling time. The effects are small if the zero is far in the LHP. RHP Zeros: Cause undershoot but no effect on settling time.

How overshoot is affected by adding a zero in the forward path transfer function?

Adding a zero to the forward path transfer function reduces the maximum overshoot of the system.