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The open-loop transfer function of a system is given by
G(s) H(s) = K(s + 1)(s + 3) s2 + 4s + 8
Its root locus diagram is—
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- Fig:- A
- Fig:- B
- Fig:- C
- Fig:- D
- Fig:- A
Correct Option: A
The open-loop transfer function is
| G(s)H(s) = | |
| s2+ 4s + 8 |
Now s2 + 4s + 8 = 0
has the roots s1, 2 = – 2 ± j2
Number of zeros of G(s) H(s) is 2 at
s = – 1, s = – 3.
Number of poles of G(s) H(s) is 2 at
s = – 2 + j2, s = – 2 – j2.
The root locus will having two branches starting at s = – 2 + j2 and s = – 2 – j2 and terminating at s = – 1 and s = – 3.
Number of asymptotes = α = p (Number of finite poles) – Z (Number of finite zeros)
= 2 – 2 = 0.
