Question

The transfer function of a compensator isgiven as
$G_c\left(s\right)=\frac{s+a}{s+b}$
$G_c\left(s\right)$ is a lead compensator if

• A. $a=1,b=2$
• B. $a=3,b=2$
• C. $a=-3,b=-1$
• D. $a=3,b=1$

Answer 1

The correct option is A $a=1,b=2$

$G_c\left(s\right)=\left(\frac{s+a}{s+b}\right)$
$PhaseP=ta{n}^{-1}\left(\omega /a\right)-ta{n}^{-1}\omega /b$
for lead comparators phase must be +ve.
for this $\frac{\omega }{a}>\frac{\omega }{b}\Rightarrow a<b$
$So,a=1,b=2$