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The closed loop system having the open loop transfer function,
 is
  • a)
    unstable    
  • b)
    stable
  • c)
    marginally stable
  • d)
    conditionally stable
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The closed loop system having the open loop transfer function,isa)unst...
Given,


For finding ωgc, Img[G(jω)H(jω)] = 0
or, 
Now,


Thus, Nyquist plot will cut real axis at -0.66.
The given system:

of type-1 and order-3.
Therefore, Nyquist plot will be as shown below:

Now, from above Nyquist plot,
N = 0 = Number of encirclements.
Also, P = number of open loop poles in RH s-plane = 0
Now, N = P-Z
or, 0 = 0 - Z or Z = 0
Thus, no. of closed loop poles in RH s-plane = 0.
Hence, system is stable.
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The closed loop system having the open loop transfer function,isa)unstable b)stablec)marginally stabled)conditionally stableCorrect answer is option 'B'. Can you explain this answer?
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