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For example, using ACD = 4.12, CoeffA value can be calculated to be equal to:

4.766911E-15 * EXP (-5.392648 * 4.12) = 1.06957E-24

And CoeffB value can be calculated to be equal to:

0.37109091 * 4.12 + 12.26236364 = 13.7913

If 3 hours after the last observation, the value of the noise free normalized cell

voltage is estimated to be equal to 4.100 V, the concentration of the dissolved alumina
can in turn be estimated to be equal to:

1.06957E-24* EXP (13.7913 * 4.100) = 3.8557

1 / 3.8557 + 1.965 = 2.22 %

PID controller

The last part of the In Situ control logic is straightforward. After a no feed

observation period, the concentration of the dissolved alumina in the bath is estimated
every 5 minutes or so. Next, the error between a selected target value and the current
estimated value is used to adjust the alumina feeding rate using the standard PID
controller equation [10, 11]:

For example, starting with no integral and derivative contributions at the end of

the observation period, a K

value of 2000 kg/min% and a target alumina

concentration of 2.30 % would translate into an additional feeding rate of:

2000 * (2.30 2.21) = 180 kg/hr

Since the nominal feeding rate of the demo Dyna/Marc test case is about 180

kg/hr, this means that the initial total feeding rate at the end of the observation period
would be about 200% of the nominal rate (180 + 180). That feeding rate would be
maintained for 5 minutes and then readjusted based on the new estimated value of the
dissolved alumina concentration at the time.

This summarizes the theory behind the In Situ control logic. It is clearly an

example of "out of the box" thinking as nothing even remotely similar was ever
imagined to control the alumina concentration of a H.H. cell. Would this innovative
control logic work in a real cell? It is difficult to say with absolute certainty at this
stage as a number of assumptions are built into the logic. Continued testing in the
Dyna/Marc cell simulator will provide these answers in a risk free environment! This
is one of the reasons why cell simulators have been developed in the first place.

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