Need help designing a simple control system

This problem probably amounts to determining the constants of a curve. Furthermore, the "curve" is most likely a line:

Y = mX + K

Now, the fun part. I am trying to synthesize/derive a formula that will tell me how much insulin should a diabetic patient use: the OPTIMAL dosage.

Let's say that the person measures his glucose level every night and depending on its value, he injects himself some units of insulin. The target output is that the following morning the glucose should be between 100-120 mg/dl.

The more insulin the person uses, the lower the glucose BUT we don't want him to go into hypoglycemia.

I took a Control System class and recall that when some output is simultaneously input, we have a feedback control system. This seems to be the case here, as the sugar level is measured (input) in order to achieve a desired level (output).

I would like to start with the simplest case, with 3 parameters:

(1) The glucose level, G (2) The injected insulin, I (3) The time, t.

After taking many measurements (the number of them is fortunately not a constraint, can take them for weeks or months, for improved accuracy) a formula is derived, and we have reverse-engineered the glucose Control System.

That is all I have so far. Can you folks give me a hand?



Reply to
Ramon F Herrera
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So we have a value of I(t) that depends on G(t-1).

I will allow you to take a peek at the future (more complex) problem.

In reality the patient administers the insulin TWICE a day: before going to bed and first thing in the morning. Pinching himself is a pain (not in the butt :-) and therefore there are times in which a default dose is applied (specially in the night).

The doctor simply prescribed "50 units at night and 60 in the morning" but this is terribly inaccurate! An airplane (*) would crash with this kind of "rule of thumb!" If we can place "Curiosity" on the surface of Mars, we can certainly come up with a better system.

Thanks again,


(*) When I took the Analog Control Systems and Digital Control Systems courses, my professors worked across the street in McDonnell-Douglas, designing the F-18 Hornet, Tomahawks, etc.

Reply to
Ramon F Herrera

Are you certain that your "curve" is linear? I would expect either an exponential or logarithmic curve for these kinds of situations. Also, I hope you are talking about a hypothetical patient here. I wouldn't use a living being to experiment with this.

And finally, this doesn't seem like an Electronics problem, but a math and biology problem.

Reply to
Daniel Pitts

I figured I would start with a straight line. The range is actually pretty short and the dosages are not critical at all.

That would be yours truly. We are not talking Marie Curie type of experiments here. Insulin is over an the counter medication and the doc authorized me to do trial and error. I am trying to come up with a better method than his constants.

If a person injects himself too much, he feels weak and all he has to do is drink orange juice or something. If too little, there is no short-term effect.

This is definitely a control system.


Reply to
Ramon F Herrera

Thanks for your interest, Daniel.

A big issue here is the period, P: the time between the measurement and the correction. In the F-18 examples my professor used, it was measured in milliseconds (flap angle). A human being cannot possibly respond fast enough and fly-by-wire is required.

In the diabetes case the period is about 6 months! The doctor measures your Hb A1C (*) level and says: "Ramon, instead of 50/60 units go up to

60/70" and 6 months later he checks again.

Many people don't even bother measuring anything. All measures are done at the doctor's place, and they simply inject merrily.

For people who can afford it, there is some pancreas clone gizmo: a device that is permanently attached to your body, measures the glucose levels and emits the necessary insulin. It checks every half hour or something.

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Those are the 2 extremes of P. Since I have this little glocumeter gadget that allows home measurement of glucose, I figure I can come up with something in between: a period less than 6 months and more than 1/2 hour. About 24 hours would be nice.


(*) Glycated hemoglobin which measures the average insulin level. I was floored when I found out how similar it is to a man-made circuit: God imitates humans!.

Reply to
Ramon F Herrera

There are many dosage calculators available on the google app store that use just this type of equation BUT it is more complex than that. A persons insulin sensitivity changes according to the amount of glycogen/glucose already stored in the muscles and liver.

Reply to
David Eather

There are newsgroups for diabetics.

Anyone wanting to run for any political office in the US should have to 
have a DD214, and a honorable discharge.
Reply to
Michael A. Terrell

So. You are your own test subject. That is very dangerous. Simple measuring a bit more often may help you understand better the less than a day, daily, monthly, and the yearly cycles. Of course if you have not been logging the data you have some logging to do. Party and other irregular (and a few annual) disruptions are up to you, but understanding the cycles better will help you deal with them.

Most of this stuff is second order ODE and a few second order heterogeneous non-linear PDE.


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