Problem $6.$ Consider the general form of a phase compensator given below,

$G_c(s)=\frac{1}{}\frac{s+\frac{1}{T}}{s+\frac{1}{T}}$

where, $=0\mathrm{.}1$ and $T=1$

$($a$)$ Write analytical expressions for the magnitude, $M()$ and phase, $()$ responses of $G_c(s).$

$($b$)$ Sketch the asymptotic magnitude $M(),$ in dB $,$ and phase $(),$ degrees, responses of $G_c(s).$

$($c$)$ Draw the actual magnitude and phase plots on the asymptotic sketches you provided in $($b$).$

$($d$)$ Fill in the table with the magnitudes in dB and phase angles in degrees at the corresponding frequencies from the asymptotic plots you sketched in $($b$).$

$\backslash$table$[[$Frequency $($rad$/$s$),0\mathrm{.}1,2,3,20,100,1000],[$Magnitude $($dB$),,,,,,],[$Phase $($degrees$),,,,,,]]$

$($e$)$ What is this phase compensator called? What is its function?