Confused with region where root locus lies and sketch

1. How do you determine if a point lies on the root locus?
2. What are the rules to sketch root locus?
3. Where does root locus start and end?

How do you determine if a point lies on the root locus?

If the angle of the open loop transfer function at a point is an odd multiple of 180⁰, then that point is on the root locus. If odd number of the open loop poles and zeros exist to the left side of a point on the real axis, then that point is on the root locus branch.

What are the rules to sketch root locus?

If a branch on the real axis lies between a pair of poles, the root locus must break away from the real axis somewhere between the poles. Similarly, if a branch on the real axis lies between a pair of zeros, there must be an entry point between that pair of zeros.

Where does root locus start and end?

Key Concept: Rule 3 – Starting and Ending Points of Root Locus. The locus starts (when K=0) at poles of the loop gain, and ends (when K→∞ ) at the zeros.