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The open loop transfer function of a unity feedback control system is given by
Find the value of ‘K’ at which the root locus diagram of the system intersects the imaginary axis.
  • a)
    50
  • b)
    60
  • c)
    70
  • d)
    80
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The open loop transfer function of a unity feedback control system is...
After crossing the imaginary axis from LHP to RHP the system will become unstable, thus imaginary axis crossing point is a marginal stable situation. It can be found by Routh-Hurwitz criterion.
Characteristic equation system is
1 + G(s) = 0
⇒ s(s + 2)(s + 5) + K = 0
⇒ s3 + 7s2 + 10s + K = 0
Making Routh Table,
s3s2s1s01107K1/7(70−k)0K0
When its marginal stable then,
1/7(70−K)=0 ⇒ K = 70
Hence, the value of ‘K’ at the crossing point of imaginary axis is 70.
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The open loop transfer function of a unity feedback control system is given byFind the value of ‘K’ at which the root locus diagram of the system intersects the imaginary axis.a)50b)60c)70d)80Correct answer is option 'C'. Can you explain this answer?
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