a$.$ Use Process Reaction Curve method $($PRC$)$ to find the FOPDT process model, for the data collected by a step change of magnitude $M=0\mathrm{.}5$ in input, that is given in Table $1.$

b$.$ If $G_m(s)=G_m(s)=1\mathrm{.}0,$ using ITAE tuning method, design a PI controller for load and set$-$point changes. Which controller seems to be better for model$/$plant mismatch i$.$e$.$ more robust and why?

$\backslash$table$[[$Table $1($t$,$ time in minutes and y output in$],[$meters$),],[t,y,t,y,t,y,t,y,,],[0,3,4,3\mathrm{.}6,8,5\mathrm{.}4,12,6\mathrm{.}0,,],[1,3,5,3\mathrm{.}9,9,5\mathrm{.}7,13,6\mathrm{.}0,,],[2,3,6,4\mathrm{.}3,10,5\mathrm{.}8,14,6\mathrm{.}0,,],[3,3\mathrm{.}3,7,4\mathrm{.}8,11,5\mathrm{.}9,15,6\mathrm{.}0,,]]$