a$.$ Use proportional control, P$,$ with Dc$($s$)=$ kP $,$ and give the range of values for kP for which the system will be stable.

b$.$ Use PD control and let Dc$($s$)=($kP $+$ kDs$)$ and determine the system type and error constant with respect to reference inputs.

c$.$ Use PD control, let Dc$($s$)=($kP $+$kDs$)$ and determine the system type and error constant with respect to disturbance inputs.

d$.$ Use PI control, let Dc$($s$)=($kP $+$ kI $/$s$),$ and determine the system type and error constant with respect to reference inputs.

e$.$ Use PI control, let Dc$($s$)=($kP $+$ kI $/$s$),$ and determine the system type and error constant with respect to disturbance inputs.

f$.$ Use PID control, let Dc$($s$)=($kP $+$ kI $/$s $+$ kDs$)$ and determine the system type and error constant with respect to reference inputs.

g$.$ Use PID control, let Dc$($s$)=($kP $+$ kI $/$s $+$ kDs$)$ and determine the system type and error constant with respect to disturbance inputs.