The figure below shows the Bode magnitude and phase plots of a stable transfer function

\({\rm{G}}\left( {\rm{s}} \right) = \frac{{{{\rm{n}}_0}}}{{{{\rm{s}}^3} + {{\rm{d}}_2}{{\rm{s}}^2} + {{\rm{d}}_1}{\rm{s}} + {{\rm{d}}_0}}}\)

Consider the negative unity feedback configuration with gain in the feedforward path. The closed loop is stable for 𝑘 < 𝑘₀. The maximum value of 𝑘₀ is ______.

Question

Question

This question was previously asked in

GATE EC 2018 Official Paper

Answer 1

According to figure

Gain = 20 dB (at phase cross over frequency)

Gian margin = -20 dB

System make to marginally stable G.M = 0 or Gain = 0 dB

i.e 20 log K = -20

log K = -1

K = 10^-1 = 0.1

So for K < 0.1 system will be stable