Asymmetric control or how to get the maximum compatible output

Hi all.

Say you have a system you want to control, which has an output you want to maximize. When you increase the input variable, you can get two different results:

- either the variable is already at its maximum, so you get no variations

- or the variable drops a little, so you need to decrease the input variable to make it go up again

The problem is: you want your input variable to be the maximum you can get, as long as your output variable is increasing or staying at its max.

I solved the problem using some kind of "fuzzy" (say commonsense) control, but I'd like a more formal solution, for which I could study stability and performances.

Thanks for any help

Reply to
metiu uitem
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To clarify:

You want to find the minimum input that will cause the output to saturate, the output is a monotonically non-decreasing function of the input, and the output saturates in some clear-cut manner?

It sounds like probing the system with a varying input (which you seem to be doing) is the only way to go, short of installing sensors to tell you the output is saturated or otherwise changing your plant.

If you can stand a little bit of continuous variation on the output, and if the various speeds work out, you could try the following:

Vary the input with a small fixed amplitude, fixed frequency repetitive signal (I'd use a sine wave, or perhaps a square wave). Demodulate the measured feedback with the same signal, the signal and its quadrature, or a properly delayed version of the signal -- the method you choose will depend on the delay characteristics of the plant and their reliability. At any rate, low-pass filter the result. The magnitude of this demodulated signal should correspond well with the degree of saturation you're getting on the output, and the synchronous demodulation will allow you to low-pass filter the signal as low as you wish to reduce noise effects. Finally, servo your input signal to the demodulated output signal so you are getting nearly complete saturation.

Reply to
Tim Wescott

Thanks for the answer!

Yes, the problem I'm working on has an almost monotonic output variable that saturates. Just "almost" because there's some (nonlinear?) unstable term that kicks in at "high" inputs and makes the output to drop very quickly instead of staying at its maximum.

The system is dynamic, and the output increases up to saturation if you keep the input steady. If you increase the input too much, you'll find the output drops.

You'd like to find the maximum input that keeps the output at its maximum, without having the negative term kick in and ruin everything.

I'll study your solution, thank you!

Tim Wescott wrote:

Reply to
metiu uitem

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