Bode plot of a stable system is shown in figure below. The

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Bode plot of a stable system is shown in figure below. The transfer function of the system is—

1. 4
  s(1 + 0.5s)
2. 4(1 + 0.5s)
  s
3. 4s
  (1 + 0.5s)
4. None of these

Correct Option: B

From figure
ω_c = 2
Since after decreasing from 20 dB/d gain becomes cons-tant it means one zero i.e., (1 + sT)
where,
T = 1/ω_n
= 1/2 = 0·5
Transfer function = K(1 + 0·5s)/s
20 log₁₀ K/s| _{s = 2} = 6
or
^K/s| _{s = 2} = 10^6/20 = 2
or
K = 2s = 2 × 2
K=4
Now,
T.F. = 4(1 + 0·5s)/s
Hence alternative (B) is the correct choice.