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 \mathrm{rad} / \mathrm{s}.$ At this frequency, the gain amplification provided by the controller, assuming asymptotic Bode-magnitude plot of $K(s),$ is $6 \mathrm{~dB}$. The values of $\alpha, \beta,$ respectively, are
- $1,16$
- $2,4$
- $3,5$
- $2.66,2.25$