Hydrocarbon Processing - May 2021 - 76

Process Controls, Instrumentation and Automation
Ln + RH = Ln + ΔL(3)

* They do not exceed limits if larger than expected
disturbances occur.
Ramp horizon controller. Ramp horizon control is a simplifi-

cation of the way level buffering is done by an APC.5 A timespan
or ramp horizon is selected during which the high and low limits imposed on the level may not be exceeded. The trajectory of
the level is estimated, based on the current position and current
rate-of-change. OP moves are only made if the estimated trajectory will violate a limit within the ramp horizon. If no violation
is predicted, no OP moves are made.
The algorithm is initiated by calculating the current ramp
rate (Eq. 1):
RR = (Ln - Ln-i )/ i(1)
where:
RR = Current ramp rate, % per execution cycle
Ln = Level at current execution cycle, n (%)
Ln-i = Level at execution cycle, n-i (%)
i = Number of execution cycles used to calculate ramp rate.
Consider the example shown in FIG. 1. The ramp rate is calculated by subtracting the current process value (PV) of the
level (which is 50) from a previous value of 45 at Time 2 and
dividing that by the time difference of two intervals to obtain
the current rate-of-change of the level of 2.5% per interval. The
value of i should be large enough to minimize noise and small
enough to limit the amount of lag introduced.
Next, the change in level over the ramp horizon is calculated
by Eq. 2:
ΔL = RR × RH(2)
where:
ΔL = Amount that the level is predicted to change over the
ramp horizon
RH = Ramp horizon.
In the example, the ramp rate of 2.5%/cycle is multiplied
by the ramp horizon of 10 execution cycles. This calculates the
change in level over the ramp horizon to be 25% (Eq. 3):
90

Level, %

PV error

High limit

Ramp horizon
40

30
-5

-4

-3

-2

-1

Time in execution intervals
Level (predicted)

Level (desired)

FIG. 1. Ramp horizon controller.

76 MAY 2021 | HydrocarbonProcessing.com

where:
Ln + RH = Predicted value of level at ramp horizon.
In the example, 25% is added to the current value of the
level of 50% to calculate the predicted value of the level at the
ramp horizon to be 75%. If this predicted value does not violate
the high or low limit, no OP moves are made. However, the
predicted value violates the high limit of 70%, so an OP move
will be calculated and implemented.
A controller gain is calculated initially by either using step
test data or calculating the volume of liquid between the high
and low limits on the drum. The gain is the change in the level
rate-of-change that will result when the OP is moved up by one
engineering unit (Eq. 4):
Gain = (RR SS - RRinitial )/∆OP(4)
where:
Gain = Ramp horizon controller gain, % level/
execution cycle/% OP
RR SS = Ramp rate when steady state is reached after step
was made
RRinitial = Ramp rate at steady state before step change
was made
ΔOP = Step change in OP that was made.
For this example, a step test was conducted with the ramp
rate of the level at -2 initially. The OP was stepped up by 4 and
the ramp rate reached steady state at 6. The gain is calculated
as 2 using Eq. 4. This indicates a 2%/execution cycle change in
the rate-of-change of the level for every 1% change in OP.
Using the controller gain, it was possible to calculate how
much the OP must be changed to prevent the limit being exceeded (Eq. 5):
∆OP = (Ln + RH - Limit)/ RH / Gain(5)
where:
Limit = Limit towards which the level is moving.
In the example, the PV error is calculated by taking the difference between the predicted value of the level at the ramp
horizon and the exceeded limit-this is 5% in the example. We
now need to calculate how much the OP should be moved so
that the level will be at 70% at the ramp horizon. Dividing the
error by the ramp horizon calculates the desired change in the
rate-of-change for the level to be 0.5%/interval. Dividing this
value by the controller gain shows that the OP must be moved
up by 0.25% to change the trajectory of the level just enough so
it will be on the limit at the ramp horizon.
This will prevent the level from exceeding the limit at the
ramp horizon. However, as the level will still be approaching the
limit, the controller during the next execution cycle will once
again predict that the limit will be exceeded. It will implement
another controller move to ensure that at the ramp horizon, the
level will still be inside the limit. If no other process influences
the trajectory of the level, this process will be repeated until the
rate-of-change of the level reaches 0 as it reaches the high limit.
When a relatively small disturbance causes a change on a level
that is controlled by using the ramp horizon method, the prediction will initially not show that a limit will be exceeded within
the ramp horizon. As the level then goes towards a limit, no OP

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Hydrocarbon Processing - May 2021

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