The GATE Grind

GATE 2014 EE (EE1) – Question 55

Control Systems · Stability analysis using Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci · 2 marks · Numerical answer

The asymptotic Bode magnitude plot of $G(s)=K(1+0.5s)(1+as)/[s(1+s/8)(1+bs)(1+s/36)]$ is shown. Note −6 dB/octave = −20 dB/decade. Find a/(bK).

Diagram for GATE 2014 EE (EE1) question 55

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 0.7 to 0.8

Explanation

Slope changes identify zeros at2and4rad/s and poles at8,24,36rad/s, alongside the integrator. Since the first zero is fixed by1+0.5s, the other gives a=1/4and the unknown pole gives b=1/24. The low-frequency asymptote K/ωcrosses0dBatω=8, so K=8. Therefore **a/(bK)=(1/4)/[(1/24)×8]=0.75**.