A$.$ Given the nominal steady$-$state values w$1,$SS $=40$ g$/$min$,$ w$2,$SS $=60$ g$/$min$,$ x$1,$SS $=0\mathrm{.}5,$ T$1,$SS $=315$K$,$ and QSS $=50$ J$/$min$,$ determine the steady$-$state exit conditions, wSS$,$ xSS$,$ andTSS.

You wish to control the temperature T of this process by means of a feedforward control loop:This feedforward control loop measures the inlet temperature T$1$ to the process, and converts$/$transmits that temperature into an electrical signal T$1$m$.$ The temperature controller Gf takes T$1$m and produces a control signal P$,$ which is sent to a heat regulator. The regulator produces a heat output Q in a heating coil, which raises or lowers the temperature in the vessel.

B$.$ Calculate the calibration constants for the temperature transmitter KM and the heat regulator KR if the range of measurable temperatures is $280$K$-360$K and the current span $($for both$)$ is $4-20$ mA$.$ What are the units of each calibration constant?C$.$ Derive the linear expressions that relate T$1($t$)$ to T$1$m$($t$)$ and P$($t$)$ to Q$($t$)$ in terms of the calibration constants you calculated above. Your final expressions should be of the form: T$1($t$)=...$ and Q$($t$)=...$D$.$ Determine the signal P$[$mA$]$ if T$1$m $=10$ mA$,$ assuming the nominal steady state w$1,$SS $=40$ g$/$min$,$ w$2,$SS $=60$ g$/$min and desired tank temperature TSP $=315$K$.$ Hint: Substitute your expressions from

C$.)$ into the steady$-$state energy balance you derived in A$.)$ and solve for the pressure signal P$($t$)[$mA$]$E$.$ Given the choice, would you swap out the current tank heater for a more powerful or less powerful one? Explain, drawing upon your answer from

D$.)$ and the concept of controller saturation