$2.$ Tuning constants for a PI controller for the following process are to be determined.Gp$($s$)$ Gi$($s$)$Gm$($s$)=$Table $2$TuningK$(5$s $+1)(2$s $+1)$A colleague has calculated several sets of values for the controller gain and integraltime $($Table $2).$ Determine which of these sets of constants, if any, is acceptable andexplain why not.Case ASe$2$s$12\mathrm{.}06\mathrm{.}0$Case B$12\mathrm{.}0$G L$($S$)=1\mathrm{.}01000\mathrm{.}35$s $+1$Case C Case D$6\mathrm{.}00\mathrm{.}31\mathrm{.}0$Hint: Find the characteristic equation of the control system. Using Pad$$approximation rearrange the equation and check for the coefficients first.Find a FOPDT model for Gp$($s$)$ Gv$($s$)$Gm$($s$)$ by Skogestad half rule method and byusing ITAE $($set$-$point$)$ methods, find tuning constants fora PI controller. Comparethem with the appropriate one given in Table $2.$