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Given a unity feedback system with open-loop transfer function.
G(s) = K s(s + 1)(s + 2)
the root locus plot of the system is of the form—
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- Fig:- A
- Fig:- B
- Fig:- C
- Fig:- D
- Fig:- A
Correct Option: A
Given that
| G(s)H(s) = | |
| s(s + 1)(s + 2) |
∴ H(s) = 1
C.E. 1 + G(s) H(s) = 0
⇒ s3 + 3s2 + 2s + K = 0
Routh Hurwitz array
s3 1 2 s2 3 K s1 6 – K 6 s0 K 6 – K 6 ≥ 0 K=6
since there is nothing given in question in the form of numerical value, so we must calculate the intersection of root locus on the imaginary axis by using auxiliary equation i.e.,
3s2 + K = 0
3s2 + 6 = 0
or
s2 = 2
s = ± √2 j
since only plot (A) intersects imaginary axis.
Hence plot (A) is the correct choice.
