Consider the feedback control system in Fig. $14\mathrm{.}8,$ and

the following transfer functions:

Gc $=$ Kc

$(2$s $+1$

$0\mathrm{.}1$s $+1$

$)$

Gv $=2$

$0\mathrm{.}5$s $+1$

Gp $=0\mathrm{.}4$

s$(5$s $+1)$

Gd $=3$

$5$s $+1$

Gm $=1$

$($a$)$ Plot a Bode diagram for the open$-$loop transfer function.

$($b$)$ Calculate the value of Kc that provides a phase margin

of $30.$

$($c$)$ What is the gain margin when Kc $=10?$