Question $1$

A third$-$order transfer function below governs a flow control system, assuming the flow

sensor is collocated with a field$-$excited DC motor$-$actuated flow control valve.

$g(s)=\frac{4}{s(s+3)(s+1)}[l\frac{s^{-1}}{V}]$

a$.$ What type number is the plant

b$.$ Compute and sketch the time function of the system to a unit impulse input.

c$.$ Design a controller for the systems to track a constantly increasing flow rate $(1$

$\{$:$[\frac{l}{s^2}])$ with steady$-$state error of less than $0\mathrm{.}002\frac{l}{s}$