Root Locus Effect of Addition of zeros and poles

Addition of zeros

The addition of a zero to the open-loop transfer function has the effect of pulling the root locus to the left, tending to make the system more stable and to speed up the settling of the response. 

Physically, the addition of a zero in the feed forward transfer function means the addition of derivative control to the system.

The effect of such control is to introduce a degree of anticipation into the system and speed up the transient response.

The Figure 1(a) shows the root loci for a system that is stable for small gain but unstable for large gain. 

Figures 1(b), (c), and (d) show root-locus plots for the system when a zero is added to the open-loop transfer function. It becomes stable for all values of gain.

However, it is not possible to add an isolated zero to a transfer function because of physical non-realizability.

Therefore, in order to realize the compensating network a pair of pole-zero has to be incorporated.

Addition of poles

The Figure The addition of a pole to the open-loop transfer function has the effect of pulling the root locus to the right, tending to lower the system's relative stability and to slow down the settling of the response.

Remember that the addition of integral control adds a pole at the origin, thus making the system less stable.

Figure 2 shows examples of root loci illustrating the effects of the addition of a pole

to a single-pole system and the addition of two poles to a single-pole system.