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The nyquist plot for a unity feedback control system having open loop transfer function G(s) = K(1-s)/(s+1) is shown in figure below :

The system is
  • a)
    stable for all values of K
  • b)
    stable for K > 1
  • c)
    unstable for K > 1 and stable for K < 1
  • d)
    unstable for K < 1
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The nyquist plot for a unity feedback control system having open loop ...
Given,
G(s)H(s) = K(1-s)/(s+1)
or,



Thus, the radius of Nyquist plot will be K.
Now, no.of open loop poles in RH s-piane = 0.
When K > 1, no. of encirclement, N = -1
When K< 1, no. of encirclement, N = 0
Thus, for K > 1, N = P - Z
or,    -1 = 0 - Z or Z = 1
∴ System is unstable.
For K < 1, N = P - Z or 0 = 0 - Z or Z = 0
∴ System is stable..
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The nyquist plot for a unity feedback control system having open loop transfer function G(s) = K(1-s)/(s+1)is shown in figure below :The system isa)stable for all values of Kb)stable for K > 1c)unstable for K > 1 and stable for K < 1d)unstable for K < 1Correct answer is option 'C'. Can you explain this answer?
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