GIVEN: The below system:

Y

R $-$

$+$

where

$2$

$32$

$42$

$()3225$

s s

G s s s s

$+$

$=+++.$ The closed loop system is easily verified to be

strictly stable for $0$T $=($via Routh, e$.$g$.).$

Point E: $(-0\mathrm{.}9107,+0\mathrm{.}4131).2\mathrm{.}66/$E rad s

$=.$

Point F: $(-0\mathrm{.}9845,+0\mathrm{.}1754).2\mathrm{.}32/$F rad s

$=+.$

The dashed curved is the unit circle $($circle of radius $1\mathrm{.}0$ and center at the origin$).$

REQUESTED:

a$.$What is the phase margin when $0$T $=?$

b$.$What is the maximum value that the delay T can take

before the closed loop system becomes unstable?

c$.$What is the phase margin when $0\mathrm{.}05$secondsT $=?$

$1$