I wanted to model a column's bottom level (as CV) with the column's bottom draw flow (as MV). I can do a step test and use a model identification software to generate model for me. However, I'm unable to do the step test due to some limitation. How can I develop a model (maybe in Laplace form) between the level and draw flow whereby the level is known to be an integrating process? Perhaps in more specific is that, how can I obtain the process gain and integral time so that I can simply punch in them onto the identification software?
Your confusion confuses me. So I assume I'm not getting something.
If you have a column of known dimensions, and you're truly controlling the outlet flow (as opposed to the position of the valve or some other indirect method), and you're working with an incompressible fluid and a rigid column, then deriving the level vs. flow should be a problem from a 1st-year calculus class.
Taking level = 0 as an empty tank, then
level / volume = | area(x) dx = f(level) / 0
So level = f^-1(volume)
If the column has a constant cross section then
volume = level * area,
and
level = volume / area.
You must have some inflow, or your problem will become pretty boring once all the fluid is drawn out. so
The final equation doesn't help me much. If you ever use or deal with software like RMPCT or DMCplus, you would understand my question. Yes the column has a known dimension based on mechanical drawing while under basic control, the level is managed by cascading to the flow controller. I'm dealing with real hydrocarbon here. Reason why I mentioned basic control is because I'm working on APC. Therefore, I'm more interested with equation like;
G(s) = Kp * (1/S+1) * e^-s
that tells me relationship between the level response to a step change in bottom flow.
No, I haven't had the pleasure (?) of working with commercial industrial control software. All of the control systems I've built have been purpose-built to be embedded in manufactured products, and I've been given (or designed) a board with ADC(s), processor(s), DAC(s) and driver(s). The most purchased code that I've ever used has been real-time OS code, and the most pre-made control code I've ever used has been stuff that I've written for reuse. So I am, for the most part, blissfully unaware of the limitations imposed by your environment.
Be that as it may, if the column area is constant and known, and if you're looking at level change vs. flow change (_not_ flow command), and if your sensors don't introduce any significant delay, then your equation is just
G(s) = Kp * (1/S) * e^0,
and Kp should be easy to calculate from your known column area and your known sensor gains -- hence my confusion over your confusion.
If your sensors have delay thats a significant fraction of your intended closed-loop response time, and you don't know what it is, then I can see your concern, and my confusion is resolved.
Does your practical problem with system ID stem from the fact that you cannot take the plant off-line to do the test, or that it hasn't been commissioned yet, or some other such thing?
If it were me, and if the system performance requirements allowed it, I would investigate determining my expected plant transfer function from first principals. Then I'd make the World's Most Conservative tuning that accommodates the performance requirements and what I know about the plant and see if it works.
If the plant were running I think I'd also investigate whether I could monitor the input/output relationship of the column, to see if I could collect enough ambient data to pour into an ARMA model and determine the plant parameters. This does require that there be _some_ tuning information available, it is fraught with errors, and it makes you _really_ want to know what the inflow is -- but it may give you a model that's enough better than a first-principals model to let you proceed.
Is it correct for me to reword it by saying the time taken to drain the level from 100 to 0% by 1m3/hr of bottom flow?
Once I obtained the rate, where do I specify the value presuming I can enter the information onto the offline ID software such as Profit Suite? I know the software provides direct entry in the following form;
Based on the rest of the thread, assuming that this is to be treated as an integrating CV then all the control package should need to know is some variant of the time it takes the level signal to travel full scale for a nominated change in the bottoms flow. The bottom flow is an easy MV, you can calculate it as described earlier simply based on the vessel diameter and LT span. Then you just need to know what form the resulting integral time is to be specified in, the package documentation will cover this.
The other models - base level vs other tower MVs - can be more difficult, because the level controller needs to be out of play during the plant tests, and there are likely to be significant additional dynamics on top of the level integrator.
The response of a level system is characterised by the hold-up time, which is the time taken to raise the level from 0% to 100% (or vice versa) when the manipulated flow (read "control valve stroke") is at 100%.
The reciprocal of this time gives the coefficient of the integral term in normalised form.
Level (pu) = 1/TH x integral(inflow(pu) - outflow(pu))
That's the one. e^s refers to dead time (take a look at your college control text). You need to go to the documentation for your particular MVC to find out specifically what it means.
Occurred to me later that I'm not sure why you'd actually go to the effort to get this model in your controller. The bottoms level doesn't (AFAIK) have a significant effect on the operation of the column as long as it stays within working limits. It's common to have a simple LC on the base, and apply the MVC to the interacting, performance-sensitive variables such as reflux, bottoms heat, etc.
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