Question

Consider a unity feedback control system with open loop transfer function :

KG(S) = K / s(s + 2)(s + 5)

Determine the segments of root locus on real axis

Answer 1

The root locus segments on the real axis are determined by the open loop poles of the transfer function. For the unity feedback control system with KG(S) = K / s(s + 2)(s + 5), the real axis segment between -2 and -5 will belong to the root locus.

Step-by-step explanation:

The segments of the real axis that will belong to the root locus of a unity feedback control system with an open loop transfer function KG(S) = K / s(s + 2)(s + 5) can be determined by the number of poles to the right of any segment on the real axis. In this transfer function, there are three poles located at 0, -2, and -5. According to the rules of root locus, the segments of the real axis that will belong to the root locus are those that have an odd number of poles to their right.

For this particular function:

• The segment between the origin (0) and -2 will not be part of the root locus because there are two poles to the right (0 and -2).
• The segment between -2 and -5 will be part of the root locus, as there is only one pole to the right (-2).
• The segment to the left of -5 will not be part of the root locus, as there are no poles to its right.