Problem $1$

A unity feedback system with forward transfer function

G$($s$)=$ K

s$($s $+7)$

is operating with a closed$-$loop step response that has $20\%$ overshoot. Do the following:

a$.$ Evaluate the settling time.

b$.$ Evaluate the steady$-$state error for a unit ramp input.

c$.$ Design a lag$-$lead compensator to decrease the settling time by $2$ times and decrease the steady$-$

state error for a unit ramp input by $10$ times. Place the lead zero at $-3.$

$1$