IV$.46$ Table PIV. $1$ shows the experimental process reaction curve of an openloop system with a PI controller. Using these values:

$($a$)$ Approximate the open$-$loop response with that of a first$-$order system plus dead time $($i$.$e$.,$ find the values of $K,,$ and $t_d).$

$($b$)$ Select the controller settings using the Cohen$-$Coon technique.

IV$.47$ Repeat Problem IV$.46$ using $(1)$ a PID controller instead of the PI$,$ and $(2)$ the process reaction curve data of Table PIV. $2.$