Question

For the unity feedback system with;

G(s) = K(s²+5s+6)/(s²+s)
Do the following:
a). Sketch the root locus by finding break-in and breakaway points.

Answer 1

The student's question involves creating a root locus diagram for a specific transfer function by identifying poles and zeros, plotting them, applying root locus rules, and calculating break-in and breakaway points.

Step-by-step explanation:

The problem involves sketching the root locus for a given unity feedback system with the transfer function G(s) = K(s²+5s+6)/(s²+s). To sketch the root locus, one needs to find the break-in and breakaway points, which are determined by calculating the points where the root locus branches enter or leave the real axis.

Steps to sketch the root locus:

1. Identify poles and zeros of G(s).
2. Plot the poles and zeros on the complex s-plane.
3. Apply root locus rules to determine the path of the root locus.
4. Use the appropriate equations to find break-in and breakaway points.

Since this is a theoretical and computational exercise in control system design, it is assumed that the student can utilize root locus rules and the characteristic equation to sketch the root locus diagram.