Control of coupled tanks

Hi, Does anyone have any practical thoughts or experience with the following control situation?
2 identical tanks side by side, inflows are separate, wild and unmeasured.
Outflows are separate and controlled. About half way up the tanks there is a large equalising line, big enough that the level in a tank will more or less be pinned upwards if that tank is overflowing through the equaliser into the other one. So there are effectively 3 modes of operation, if symmetries are rolled in:
Both tanks below equalising line, ie. 2 separate tanks. One tank above, one below the equaliser, overflowing Both tanks above, effectively one tank.
What's required is a level control strategy adjusting the two outflows that will allow the levels to float somewhat in the middle, but keep both within working limits. The upper working limit has to be above the equaliser for residence time reasons.
Appreciate that the problem is somewhat underspecified. Also that there's a fundamental observability problem while the overflow is active. I just thought that someone somewhere might have tackled this already. TIA
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I don't see why you don't treat the two tanks like one big tank when the level is above the equalizing line and as two separate tanks below. Tank level control using pumps on the outfeed has been covered here in the last year. There are other here like Fred Thomasson that seem to have practical experience. I can help with the theortical or model based control.
The previous threads have shown that level control is usually very simple. A simle P gain will work most of the time. The only reason why you would have problem is if the pumps can keep up with the peak inflow.
Peter Nachtwey
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Are you measuring the outflow on the tanks and the level in each tank? From that, you can deduce the inflow.
Going further, if you look at the Cv of the control valves, and measure the flow rates, then you will know the head and hence the depth in the tank.
We need to know a bit about the exit flows. What are they being controlled to optimize?
Michael
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On Mon, 28 Jan 2008 12:37:42 +0900, Bruce Varley wrote:

How wild is "wild"? Peter's suggestion of simple proportional control (at least if it's proportional control on the outflow valve position or pump rate) should work well if you can use a high enough gain to keep things within limits while still keeping the system stable. With simple proportional control I don't even think you need to worry about the equalizer -- just operate each outflow from the level of it's tank.
If you can't get away with a simple proportional controller then you'll have to accept using something like a PI controller -- only if you have a integrators in there does the cross-flow become an issue, and then only if both tanks are above the equalizer. Were I doing this I'd consider implementing PI controllers that stayed independent whenever the equalizer was not in play, but slaved the two integrators together whenever the level was above the equalizer in both tanks.
Come to think of it, you may be able to keep independent PI control on both tanks, unless the equalizing line is huge: as long as the level in each tank is at least somewhat dependent on the inflow, a PI controller should work. Your apparent plant gains will vary depending on whether the level is below or above the lip of the equalizer tube, so you'll have to tune it up to be well behaved in both circumstances, but it ought to work.
This sounds like something that should be considered, and modeled, and simulated well before you start implementing your control rules...
--
Tim Wescott
Control systems and communications consulting
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Thanks for the comments guys, I appreciate your input. This was a bit of a fishing post, unfortunately I can't post more details, of which there are some. Basically what we need is an inner control shell that will enable us to present the system as stable linear models across the whole operating range, for an overarching controller that extends beyond the tanks, and which needs to have access to the discharge handles.
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Bruce,
I'm not convinced there is an especial problem here: since each tank has its own outflow controller, and the inflows are wild, then any flow (in or out) between tanks through the equalising line is simply a variation of the net inflow as seen by each individual tank.
Industry standard methods of calculating the level-controller tuning settings on the basis of expected flow excursions and vessel dimensions should be applicable.
Having said that, it is very easy in a thought experiment to miss some unexpected behaviour, and since this arrangement would be trivially simple to model and simulate in something like Simulink, I'd probably do just that to demonstrate to myself (and prove to the client) that there is no untoward behaviour.
Best Regards, Kelvin B. Hales Kelvin Hales Associates Limited Consulting Process Control Engineers Web: www.khace.com
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