An open loop transfer function G(s) of a system isG(s) =

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An open loop transfer function G(s) of a system is
G(s) = K
s (s + 1)(s + 2)

For a unity feedback system, the breakaway point of the root loci on the real axis occurs at,

1. – 0.42
2. – 1.58
3. – 0.42 and – 1.58
4. None of the above

Correct Option: A

The characterstic equation of given function is
1 + G(s) H(s) = 0
∴ s(s² + 3s + 2) + K = 0 ( &becuse; H(s) = 1)
∴ – k = s³ + 3s² +2s
In order to find break away point

We have	dK	= 0
	ds

∴ 3s² + 6s + 2 = 0
∴ S = – 0.42 is the solution that makes k > 0

G(s) =	K
	s (s + 1)(s + 2)