Tuning PID for an exponential control

I suppose it could go either way. I figured valve position is the controlled variable, x, and flow is the result, y.

This would be a good time to mention that the curve is only good for one set of conditions. Specifically if fluid density, viscosity, upstream pressure, or downstream pressure vary then the curve will not be accurate. That is why a feedback loop is necessary.

How about creating a curve that is valve command vs position

Your PID loop would be outputing 0-100% of "requested flow".
If your PID was at 50%, you want 50% flow or 50% position of the valve. You could then use equeation with 50 as the input and come out with 80% command.

But like tom said, you must have a feedback loop.
 

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