A block diagram of a closed$-$loop system is shown in the Figure

$($a$)$ Derive a closed$-$loop transfer function for disturbance changes, Y $($s$)/$D$($s$)$

$($b$)$ Derive a closed$-$loop transfer function for reference changes, Y $($s$)/$Ysp$($s$)$

$($c$)$ For the following transfer functions, what values of K$\_$c will result in a stable closed$-$loop system of Y $($s$)/$Ysp$($s$)?$

G$1($s$)=3,$ G$2($s$)=2/(5$s$+1),$ G$3($s$)=1/($s$-1),$ K$\_$m $=1$