Bias$/$Feedforward: An acidic waste stream is neutralized in tank T$-3$ using a

sodium hydroxide $($caustic$)$ solution with $pH12.$ A cascade control scheme shown in the

diagram adjusts the flow of the caustic to achieve a neutral $(pH7)$ effluent leaving $T-3$

past sensor AT$-$T$3,$ but it is hard to react to sudden changes to the flow or $pH$ of the inlet

acidic stream in time using only feedback. The plant has installed a flowmeter and a pH

meter on the acidic waste stream. Propose a bias$/$feedforward control scheme to

augment this feedback controller by predicting the flow of caustic needed. Both

flowmeters measure in $k\frac{g}{m}in.$

Assume $[H_{+}]=$both $10-$ pHstreams in moll are; $\{$:$[Hessentially{]}_{+-}][OH-]=$ water $10-($i$.$e$\mathrm{.}14$; the

$H+$ same$)+OH$ for $-$ density $H_{2}O$ and molecular

weight purposes. Spell out the mass balance below to calculate the bias, and diagram

how the feedforward$/$bias scheme works on this drawing. Feel free to use a block titled

MATH if you specify the equation elsewhere.