$15\mathrm{.}3.$ The feedforward$-$feedback strategy has an additional sensor and controller. How is it possible to add these and not violate the degrees of freedom of the system? For the heat exchanger example in Section $15\mathrm{.}2,$

$($a$)$ Derive all equations describing the process and the feedforwardfeedback controllers.

$($b$)$ Analyze the degrees of freedom to verify that the system is exactly specified.

$($c$)$ Discuss how you would solve the equations in $($a$)$ numerically for a dynamic response $($simulate the process with a digital control system$).$

Stirred$-$tank heat exchanger with single$-$loop feedback temperature control.

Stirred$-$tank heat exchanger with feedforward$-$feedback control strategy.