$8\mathrm{.}1.$ Determine the analytical expression for a step set point change in the following processes under P$-$only and PI feedback control. You should select values for the tuning constant that give acceptable performance.

$($a$)$ Example $3\mathrm{.}1$ with $C_A$ as the controlled variable, $C_{A0}$ as the manipulated variable, and $\frac{?}{{?}_{\frac{?}{?}}SP}=0\mathrm{.}1$mol$\frac{e}{m^3}.$

$($b$)$ Example $3\mathrm{.}7$ with $T$ as the controlled variable, $F$ as the manipulated variable, and $\frac{?}{{?}_{\frac{?}{?}}SP}=3C.(F_6$ is constant.$)$

$($c$)$ Example $3\mathrm{.}3$ with $C_{A2}$ as the controlled variable, $C_{A0}$ as the manipulated variable, and $SP=0\mathrm{.}05$mol$\frac{e}{m^3}.$