$9\mathrm{.}7.$ Dye for our new line of blue jeans is being blended in a mixing tank. The desired color of blue

is produced using a concentration of $1500ppm$ blue dye, with a minimum acceptable con$-$

centration of $1400ppm.$ At $9$ A$.$M$.$ today the dye injector plugged, and the dye flow was inter$-$

rupted for $10$min, until we realized the problem and unclogged the nozzle. see Fig. P$9-7.$

FIGURE P$9-7$

Plot the controller ouput from $9$ A$.$M$.$ to $9$:$10$ A$.$M$.$ The steady$-$state controller output $($the bias

value$)$ is $8g.$ Does the controller output saturate $($output range is $3$ to $15g)?$ If so$,$ at what

time does it occur? The controller is a PI controller with $K_c=0\mathrm{.}001\frac{g}{p}pm$ and ${}_{\text{I}}=1$min.