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Old April 22nd, 2005, 11:59 AM   #6
Ron Beaufort
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in Figure 6 we have another type of “sealed system” ... again our controller is using only Proportional action ... and our Proportional gain has once again been given a setting of 1.00 ... and for consistency, our setpoint is once again dialed in at 60% (or 150 gallons) ...








and once again, we seem to be violating the popular textbook “rule” that says that “Proportional-only control will not maintain a setpoint” ... but by now you should be getting used to the trick involved in violating that particular “rule” ... specifically, we’re “cheating” just a little bit by keeping the drain valve closed ... under these special “sealed system” conditions, ANY amount of water entering the tank will raise the level ... and since the Proportional-only controller will not completely close off the fill valve until the setpoint is finally reached, then SOME amount of water will continue to flow into the tank until we’ve finally reached the target ... it might take a VERY long time, but eventually the target will be reached ... and the error will become zero ... and then the controller will finally completely close the inlet valve ...



but once again, this “sealed system” isn’t going to prove very useful in the real world ... someday somebody is going to open that drain valve ... we’ll cover that situation in the next post ... but first ...



warning! ... trick question coming up ... this next part has little if anything to do with the topic at hand but I find it mildly entertaining ... and maybe we can learn something useful from it ... and so a side-trip just for fun ...



suppose that we temporarily turn off our automatic controller for awhile ... and suppose that we start out with an empty tank ... and suppose that we open the fill valve SOME amount and then leave it at that setting ... and suppose that we also open the drain valve SOME amount and then leave it at that setting ... suppose that we see the level in the tank start to rise ... now ...



since the level is definitely rising, we CAN say with assurance that “the water is coming IN faster than it is going OUT” ... but (and here’s the trick question) can we also say with absolute assurance that the tank will eventually fill all the way up and then overflow? ... at first glance we might think “yes, eventually that will surely happen” ... because (as we said before) “the water is coming IN faster than it is going OUT” ... and so an overflow must be inevitable ...



but the correct answer is “the tank MIGHT NOT overflow – we can’t be sure without more information” ... why? ...



remember that the amount of water draining from the tank under the force of gravity relies on the level (the height in feet and inches) of the water level in the tank ... and so the amount of water draining from the tank will constantly be increasing as the tank continues to fill ... and so, depending on exactly how much water is coming in, and depending on the setting of the drain valve, and depending on the depth of the tank, then there COULD be a point (a specific level) at which the rate of draining would exactly equal the rate of filling ... big idea: the “rate of fill” is a straight line as shown in Figure 5 ... but the “rate of drain” is a curving line as shown in Figure 4 ... and so without further information, we can NOT say with assurance that the tank will eventually overflow ... regardless of the fact that at the start of the test the water is indeed coming in faster than it is going out ...



as I said earlier, this doesn’t really have a lot to do with the subject at hand ... but I thought that I’d bring this discussion up just to show that you have to keep your wits about you when you’re trying to determine the characteristics of any particular system that you’re planning to control ... specifically, one size does NOT fit all ... and your mileage may vary ... and first impressions are not always correct ...
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