GATE 2023 Electrical Engineering Q38

Question

Consider a lead compensator of the form
$K(s) = \frac{1 + \frac{s}{a}}{1 + \frac{s}{\beta a}}, \beta > 1, a > 0$
The frequency at which this compensator produces maximum phase lead is 4 rad/s.
At this frequency, the gain amplification provided by the controller, assuming
asymptotic Bode-magnitude plot of K(s), is 6 dB. The values of $a, \beta$, respectively,
are

Answer

1, 16

Answer

2, 4

Answer

3, 5

Answer

2.66, 2.25