Problem Statement

Proportional$-$plus$-$integral$-$plus$-$derivative $($PID$)$ may be recommended for TYPE $3$ systems when the output in a

feedback loop system is required to perfectly track parabolic and step and ramp reference signals $($Papadopoulos

$2013.)$ The system pictured below$($ Figure P$7\mathrm{.}23),$ the transfer functions of a plant $Gp(s)$ and recommended

controller, $Gc(s),$ are given by: