GATE Electrical Engineering (EE) 2023 Solved Paper

Consider a lead compensator of the form
$\mathit{K}\left(\mathit{s}\right)=\frac{1+\frac{\mathit{s}}{\mathit{a}}}{1+\frac{\mathit{s}}{\mathit{\beta }\mathit{a}}}$, β > 1, α > 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, 𝛽, respectively, are