Question

Sketch the root locus for a unity-feedback system where

G(s) = K(s-2)(s-3) / s(s+2)(s+3)
Then find the following:
a). The break-away and break​​​​​​​-in points.

Answer 1

The root locus of the given unity-feedback system can be plotted to show the paths of the poles as gain K varies, and break-away points are found where the root locus departs from the real axis.

Step-by-step explanation:

The root locus of a unity-feedback system where G(s) = K(s-2)(s-3) / s(s+2)(s+3) involves plotting the paths of the closed-loop system poles on the s-plane as the gain K varies from 0 to infinity. The root locus method helps determine system stability and response characteristics by observing the loci of the system poles in the complex plane.

To find the break-away and break-in points, one would typically set the derivative of the characteristic equation of the closed-loop transfer function equal to zero, and solve for the points where the root locus breaks away from the real axis or comes back into the real axis.