Hydrocarbon Processing - May 2021 - 78

Process Controls, Instrumentation and Automation
At the Execution cycle n, the controller has made the last
move of size x, which will cause the rate-of-change of the level
to become 0 at the high limit. Therefore, at Row n in TABLE 2,
the value of the level is H and the rate-of-change is 0.
To calculate the level at Execution cycle n in terms of x,
PV0 and ROC0 , Column 3 of TABLE 2 is set equal to H. In calculating the equation in Column 3, Row n, the coefficient of
PV0 should be 1 and the coefficient of ROC0 should be n. The
series of coefficients for the term x.G (0, 1, 3, 6, 10...) shown
in Column 3 can be calculated as 0.5n2 - 0.5n. Therefore, the
value of the level at Cycle n can be expressed as PV0 + n.ROC0
- (0.5.n2 - 0.5n)x.G, as shown in the last row of Column 3 in
TABLE 2.

Combining H = PV0 + n.ROC0 - (0.5.n2 - 0.5n)x.G and Eq.
8 yields Eq. 9:
x = 0.5 × ROC0 × ROC0 / [G × (H - PV0 - 0.5 × ROC0 )](9)
Eq. 9 calculates by how much the OP must be changed during every execution cycle to balance the level at the high limit.
As stated before, dynamics on the level model may cause inaccuracies, but as the value and rate-of-change of the level are
measured every execution cycle, the inaccuracies are remedied.
In the same way, it can be calculated in Eq. 10 that:
x = 0.5 × ROC0 × ROC0 /[G × (L - PV0 - 0.5 × ROC0 )](10)
will balance the level at the low limit (L) if the level is moving
downward.
75

Level, %

50
Non-linear PV

Ramp horizon PV

SOALC PV

FIG. 2. Level response to a step disturbance of 5 m3/hr.

SIMULATION RESULTS
To test the ramp horizon and SOALC, a level was simulated
and subjected to step disturbances of different sizes. A standard
non-linear or error-squared PID controller2 was used as comparison and tuned to handle a maximum disturbance of 5 m3/hr.
To measure the success of the control, the variance of the
OP derivative (VOD) was measured.2,12,13,14
If a control method can minimize total OP movement over
time or prevent the OP from moving in one direction initially and then moving back later when the limits would not
have been exceeded if no moves were made, this would be a
big advantage in improving plant stability. There were no performance metrics in literature that highlighted this behavior.
To test to what extent this occurs, the average of the absolute
moves (AAM) of the OP of a controller, as shown in Eq. 11,
was developed as an additional performance indicator:
AAM =[∑iN abs(OPi - OPi-1)] / N
(11)
Positive step disturbance of 5 m3/hr. When responding to

a positive step of 5 m3/hr in the feed to the drum, FIG. 2 shows
how the controllers all managed to keep the level below the high
limit of 70%. FIG. 3 shows how all the controllers moved their
OPs by the same total amount. This is as expected, because the
volume balance must be restored to bring the rate-of-change of
the different levels to zero.
TABLE 3 shows that the controllers performed similarly when
considering the VOD and the same on the AAM. This is because all the controllers moved their OPs by exactly 5% over the
time horizon considered.
Positive step disturbance of 6.25 m3/hr. If the disturbance size is increased by 25%, FIG. 4 shows how the non-linear
controller was unable to keep its level below the high limit of
70%. This is because it was tuned to accommodate an assumed
maximum disturbance of 5 m3/hr. Both the ramp horizon controller and the SOALC managed to keep the level within the
limit. TABLE 4 indicates how the VOD showed slightly poorer
performance from the SOALC and ramp horizon controllers,
while the AAM is the same as before. FIG. 5 also shows how the
ramp horizon controller and SOALC initially moved their OP
faster to prevent the level from exceeding the limit. The VOD
shows slightly poorer performance from the SOALC, while the
AAM is the same as before.15,16,17
75

48
Level, %

OP, %

65
47

60
46
55

50
Non-linear OP

Ramp horizon OP

SOALC OP

FIG. 3. OP response to a step disturbance of 5 m /hr.
3

78 MAY 2021 | HydrocarbonProcessing.com

Non-linear PV

Ramp horizon PV

SOALC PV

FIG. 4. Level response to a step disturbance of 6.25 m3/hr.

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