# Integrating Processes

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.
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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
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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:

Averaging Level Controls'.

is possible to calculate

behaviour between 'tight' level

(limited by the need to keep

loop damping ratio. The

fluid volume between 0-100% of

operating) limits; together with the

flow controller.

the loop: the choice determines

disturbances. Next calculate loop

time, Ti. The chosen damping

damping is suitable for >95% of

can then be adjusted for any

described above). Indeed, it is

place behind the panel. When I

the calculations, and we still

process simulation studies.

control cascaded to a control valve;

operation and linear installed valve

flow and demand (output) from

Nevertheless, the design principles are

valve-gains under extreme

engineers do not understand the

constant loop damping. Very many

(underdamped) with low natural

transients, often with very long

that the slow ups and downs

of the process behaviour.

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Kelvin,
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
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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
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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
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Curtis wrote:

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.
--

Tim Wescott
Wescott Design Services