Hey there all,
I'm hoping to get some help on how to calculate the gain of a level
control loop at the bottom of a distillation tower. The tower is

actually a condensate stabilizer, and this is what I have:
Easy things first - The valve is capable of 0 - 500m3/day of liquid
flow, the transmitter output is 0-100%, and the level transmitter is
0-100%. Because it's going in and out of the DCS, the signals are 4-20
mA.
So for a valve gain I have 5m3/day/%(valve opening)
The volume of the well is 13.1 m3 with a 0-100% Level Transmitter.
This means that I have 0.131m3/%Level.
I know that it is difficult (or impossible??) to calculate the gain of
an integrating process, as this is. I have no trouble calculating the
time constant, so I know how fast the process will act (slope of line
assuming constant inlet flow) with a valve position change.
Even though I don't want tight level control, I'm just kind of
playing around, figuring out how everything interacts, and responds.
If I did want tight level control, how would I get process parameters
to tune it?
Any thoughts/comments?
Thanks.

Clearly you need a copy of my book (still in preparation) 'Design of Averaging
Level Controls'.
Assuming P+I Control, then in nearly all practical process applications it is
possible to calculate
liquid level-controller tuning parameters for the case of level control cascaded
to flow control, to
achieve any desired degree of tuning on what is a continuous spectrum of
behaviour between 'tight' level
control (limited by noise and stability) and averaging level control (limited by
the need to keep
worst-case level disturbances within alarm limits), at any pre-defined loop
damping ratio. The
information required to calculate the tuning settings includes change in fluid
volume between 0-100% of
level controller range, and between upper and lower level alarm (or operating)
limits; together with the
volumetric flow rates corresponding with upper and lower ranges of the flow
controller.
The design principles are simple: First select a target damping ratio for the
loop: the choice determines
the size of the resonant peak in the system's I/O response to flow disturbances.
Next calculate loop
gain, Kl from the flow and volume ranges and controller integral-action time,
Ti. The chosen damping
ratio sets the relationship between K and Ti; e.g. Kl*Ti=4 for critical damping
is suitable for >95% of
process applications. Controller gain Kc (which is one component of Kl) can then
be adjusted for any
desired degree of 'tightness' of level control (within the limits described
above). Indeed, it is
possible to conceive of a level controller having just one tuning knob for
adjustment between 'averaging'
and 'tight', with the calculation of appropriate Kc and Ti settings taking place
behind the panel. When I
worked for a major oil company I produced a simple Excel spreadsheet for the
calculations, and we still
use the same method here for calculating level-controller settings in our
process simulation studies.
Unfortunately, it is not so easy to do a numerical design with level control
cascaded to a control valve;
because, except in the special circumstances of constant-pressure operation and
linear installed valve
characteristic, there is not the well-defined linear relationship between flow
and demand (output) from
the level controller that is provided by a slave flow controller. Nevertheless,
the design principles are
essentially the same; but one needs to check the calcs. for a range of
valve-gains under extreme
operating conditions - then choose a worst-case.
The single most common fault in on-site level-controller tuning is that
engineers do not understand the
need to keep the product Kl*Ti (e.g. =4) constant to achieve a defined constant
loop damping. Very many
level control loops in industry are therefore very poorly damped (underdamped)
with low natural
frequencies, leading to under-damped oscillation in response to transients,
often with very long
oscillation periods; sometimes so long that operators don't even realise that
the slow ups and downs
(sometimes on a time-scale of several hours) are not an inherent feature of the
process behaviour.
Kelvin B. Hales
Kelvin Hales Associates Limited
Consulting Process Control Engineers
Web: www.khace.com

Hi Curtis,
The easyest way to tune a integrating process is to make a step response
experiment, and then tune the controller.
Follow this link to se how to do
http://hem.fyristorg.com/PI_Tune/helpfile.htm go to the section called
Integrating process to see how to perform the experiment. At the bottom of
the page press the HOME link and Download or open the Tune program. Sellect
Lambda Tune or the Amigo tuning method.
Curtis
wrote:

Kelvin,
Thanks for your reply. You state in the first paragraph:
Next calculate loop

This is the part I'm having trouble with. To make a move on the valve
and watch the level change obviously will not work because the process
is integrating. Also, I'm not sure what the controller integral time
has to do with the process -- the process gain should be independent
of anything in the controller. I have the flow and volume range do I
just divide full scale volume over full scale flow?
If so I get 13m3/(500m3/day). But that really doesn't give me much.
When your book is done let me know. It sounds like it would help me
out a lot.
Thanks.
Curtis

I started on a reply to your reply (IYSWIM); but I got side-tracked. I'll try
and finish it, otherwise maybe an
E-mail correspondence might be best.
Kelvin B. Hales
Kelvin Hales Associates Limited
Consulting Process Control Engineers
Web: www.khace.com

Hey there Kelvin,
Actually and email would be great. I have a couple pages of notes I
wrote and scanned into pdf that maybe you could look at.
Tim, maybe you'd be interested? They're pretty simple...
Curtis

Assuming that it's truly integrating, i.e. that the head on the valve
doesn't change with tank level, then your integrator gain is
(5m3/day/%opening)/(0.131m3/%level) = 38.2 * %level / %opening / day,
which is a perfectly valid integrator gain. It says (for instance) that
with 100% opening the tank level should change by 100% in 1/38.2 of a
day, or that for a 1% valve opening the tank level should change by
38.2% in a day. Assuming linearity you should be able to plug this into
just about any control model and design a controller on paper.
Actually having it follow such a simple model would be a surprise, but
that's your problem.
I suspect that your problem with integrator gains is that you want to
see something like level vs. opening. Integrator outputs are rates of
change, so there needs to be a time factor in the denominator of the
integrator gain, or a frequency in the numerator.

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