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Figure 2.
Cell response to a 100 kg AlF3 addition
As we will see below, the time lag between the collection of the
bath sample and the introduction of the results in the cell controller
database can also lead to significant oscillations in the excess AlF3
concentration in the bath.
Case no 1: 100 days response without feedback control
In Figure 3, we can see the 100 days cell response to a constant 1.2
kg per hour direct AlF3
feeding rate. Since 1.2 kg per hour is a bit
more than what the cell needs to maintain a 8.5% excess AlF3
concentration, that concentration increases for about 50 days before
an equilibrium at 9.2% is reached.
Figure 3.
100 days response without feedback control
Case no 2: Integral control, 1 sample per day, 1 day delay
Continuously readjusting the base direct AlF3 feeding rate every
day based on the results of the analysis of the previous day sample
analysis is an example of integral control feedback loop with a time
lag. As we can see in Figure 4, when a 10% adjustment is made on
the base direct AlF3
feeding rate each day for each 1% excess AlF3
concentration offset for the bath sample of the previous day, an
oscillation pattern emerges.
Figure 4.
Integral control, 1 sample per day, 1 day delay.
Case no 3: Proportional control, 1 sample per day, 1 day delay
Clearly, it is better to keep the base direct AlF3 feeding rate
constant over time and rather make a one time adjustment
proportional to the current concentration offset. Figure 5 presents
the obtained results, there are no more oscillations but by using a
proportional 1 kg/hr% proportional adjustment constant on a base
1.2 kg/hr feeding rate, we are ending up with a 0.5% permanent
error as with a proportional only control mode, it takes an offset to
make a correction.
Figure 5.
Proportional control, 1 sample per day, 1 day delay.
Case no 4: PI control, 1 sample per day, 1 day delay
As it is presented in Figure 6, the permanent error can be
eliminated by reintroducing the integral part of the feedback
control (i.e. readjusting the base feeding rate at each feedback
loop). This PI feedback control works so well that that could very
well be the end of the story! Unfortunately, it relies on the fact that
we are taking 1 bath sample per cell per day and that the results are
available to the cell controller in 24 hours. Many smelters cannot
keep up with this kind of schedule, so they have to reduce the bath
sampling frequency introducing a longer time lag in the control
feedback loop.