A jacketed stirred tank is used to cool a process by causing cooling water to flow trhough the jackes as shown in Figure $1.$ The process input variable is the flow of cooling water $f_c(t),$ The inlet temperature of the process stream $T_i(t)$ is considered as a disturbance variable. The output of interest is the outlet temperature of the process and the water $T(t),T_c(t),$

Figure $1$ Jacketed process

$1-$ Desing a feedforward controller based on a steady$-$state design method

$2-$ Repeat the previous question, consider the dynamic behavior

$3-$ Simulate the closed$-$loop response to a unit step change in the disturbance variable using feedforward control of parts $(1)$ and $(2).$

$4-$ Using a selected controller from Part $3,$ study the closed loop stability for the feedforwardfeedback control scheme, use either feedforward controller from question $1$ or $2.$

$5-$ Repeat question $3,$ for the feedforward$-$feedback control scheme, and provide a comparison for steady$-$state vs dynamic design methods.

$6-$ Conclude

$($Please solve it in a peper$)$