Question $4(20$ points, $4$ points$/$each$)$ Consider the following closed loop control system, where $\backslash ($ p $\backslash )$ is the design parameters.

$($a$).$ Draw the allowable region for $($i$)\backslash ($ T$\_\{$p$\}\backslash$leq $1\backslash$mathrm$\{$sec$\}\backslash )$ and $\backslash ($ T$\_\{$s$\}\backslash$leq $4\backslash$mathrm$\{$sec$\}\backslash ).$

$($b$).$ Find a value of $\backslash ($ p $\backslash )$ so that the resulting system satisfies both specifications.

$($c$).$ What is the pole location $($inside the allowable region$)$ of your design?

$($d$).$ What is the Type number of the system?

$($e$).$ What is the steady state error if we apply a unit ramp function?