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Question

# The gain at the breakaway point of the root locus of a unity feedback system with open loop transfer function G(s)=Ks(sā1)(sā4) is

A
1
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B
2
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C
5
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D
9
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Solution

## The correct option is A 1OLTF⇒G(s)=Ks(s−1)(s−4) Now, characteristics equation, 1+G(s)H(s)=0 Ks(s−1)(s−4)+1=0 ⇒Ks+(s2−5s+4)=0 K=−(s2−5s+4)s=[s−5+4s] For break away point : dKds=0 dKds=−[1+0−4s2]=0 we get, s=±2 Therefore valid break away point is s = 2. Now gain at s = 2 is ⇒K=Product of distance from all poles to break away pointproduct of distance from all the zeros to break away point Gain,K=1×22=1

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