Hydrocarbon Processing - July 2021 - 63

The Digital Plant
averaging level control, the performance indicators considered
typically focus on minimizing the movement of the OP,
like the variance of the OP derivative (VOD)5,6,7
as shown in
Eq. 3 or the average of the absolute move of the OP (AAMO)
shown in Eq. 4:
1
VOD =
N ∑ ⎣⎡( OPi − OPi−1
i=1
N
)−µ⎦⎤
2
(3)
where:
N = number of execution cycles
OP = controller output
µ = mean of the OP for all execution cycles.
If the IGC is tuned aggressively, the controller will move
the OP past the steady-state value and then change direction.
To show this behavior, the AAMO metric (as shown in Eq. 4)
was developed as an additional performance indicator.
AAM = ∑ OPi − OPi−1
⎡
⎣
N
i abs (
)
⎤
⎦
/ N
(4)
where:
N = number of execution cycles
OP = controller output.
As the advantage of the IGC is that it repositions the system
quicker by bringing PV back to SP faster than a normal PI
controller, it is worthwhile to also consider performance metrics
that measure the control performance, such as integrated
absolute error (IAE) and integrated squared error (ISE). Specifically,
the ISE should be considered, as the IGC will aggressively
counteract PV error when the PV is outside the integral
gap while acting less aggressively when the PV is inside the
gap. The ISE will provide a better indication of whether the
IGC does this successfully.
The difference between a PI averaging level controller with
typical tuning and an IGC is shown in FIGS. 1 and 2. Both controllers
were tuned to reject a 5-m3
/hr step disturbance with a
high limit set at 70%.
The IGC was tuned with a 10% gap on either side of SP:
Ti outside gap = 96 and Ti in gap
= 256.
The IGC gap was set to 10% and FIGS. 1 and 2 show how
the more aggressive control action decreased when the PV
returned to less than 60%. Studying the OP trajectory also
shows how the proportional action that was increasing the OP
on the return of the PV towards SP made larger OP moves
than the decreased integral action that was still moving the OP
downwards. This caused the PI controller to overtake the IGC
and have less remaining PV error towards the end of the test.
Even though the intent of the IGC is to reach SP sooner
than the traditional PI controller, tuning the IGC this way has
merit as small disturbances that occur while the PV is close to
SP will be rejected less aggressively, and return to SP will also
be done slowly, leading to improved averaging level control on
smaller disturbances.
FIG. 2 also shows the obvious disadvantage that bringing the
level back to SP sooner will require slightly larger OP moves.
This disadvantage must be offset by the advantage of being
ready for a subsequent disturbance sooner.
TABLE 1 shows that the IGC performed better on the
squared error metric, as it brought the PV closer to the SP in
a shorter time. The VOD showed that the IGC was slightly
51
50
49
46
47
48
45
44
43
PI OP
Integral gap OP
FIG. 4. OP response of PI and more aggressive IGC to a
positive disturbance.
Hydrocarbon Processing | JULY 2021 63
gentler with the OP movements, while the AAMO penalized
the IGC for overshooting the steady-state value more than
the PI controller.
This could be a typical way of tuning the IGC controller
that would quickly bring the PV back into the gap and then act
less aggressively to prevent overshooting SP. This would also
enable the controller to be gentler when smaller disturbances
occur that do not push the PV outside the gap.
For the IGC to reach SP sooner than the PI controller, either
the integral action in the gap can be increased or the size
of the gap can be decreased.
FIGS. 3 and 4 compare the performance of the IGC with
more aggressive integral action in the gap with the PI controller.
These figures show how the IGC was able to get to SP sooner
but had to move its OP faster to do so.
TABLE 1. Performance metrics, gap = 10%, Ti outside gap
= 256
IAE
PI
IGC
75
70
65
60
55
50
45
PI PV
Integral gap PV
FIG. 3. PV response of PI and more aggressive IGC to a
positive disturbance.
3,139
3,204
ISE
40,519
37,546
VOD
0.0395
0.0392
= 96 and
Ti in gap
AAMO
0.0142
0.0149
Hydrocarbon Processing - July 2021

Table of Contents for the Digital Edition of Hydrocarbon Processing - July 2021
