I disagree. Getting inductive elements that are accurate to 10% is hard.
Getting 1% resistors is easy. I strongly suspect that using feedback
would allow a wider range of mechanical parts.
---
Hmmm... You're arguing, so I guess I was right. Anyway, take a look
at the last two sentences in your post.

Unless you're using actual
physical position as as feedback, I don't think using 1% resistors
will make much difference if the characteristics of the magnetic
structure are as variable as you seem to think they are.
How about it? Have you got any data to supprt your claim?
---
Yes but .... "crank up the current" while monitoring the voltage. The
inward motion of the plunger causes the voltage to rise abruptly.
---
So what? Whether you crank either the current or the voltage the
other will follow and the plunger will move. The voltage will settle
in a few milliseconds or so, and when it does and the solenoid plunger
is where you want it to be, _that's_ when you measure the voltage.
There's really no reason to monitor it while the plunger is being
moved, since what's important is what the voltage across the solenoid
happens to be when the plunger is positioned properly, not what it's
doing while it's getting there.
---
If you digitized that curve, and applied that voltage profile, your idea may work
well enough.
---
"If"? Did you miss this part?:
"burn that data into ROM, hook a DAC to the data outputs of the ROM
and a counter to the address inputs and count through them so that the
time from start to finish is as long as you want the plunger to be
moving, and you're done."
---
We are just talking about getting a "quality feel" out of
some "cheap junk" parts here. We are not launching a space probe.
---
Seems like, for some reason, you always have to follow grudging
acceptance with a reprimand. NIH envy or something like that,
perhaps?
In any case, continuing along the open-ended digital path, it's a
small jump from
[COUNTER]--[ROM LUT]--[DAC]--[DC AMP]--[SOLENOID]
to
[µC]--[R-2R]--[DC AMP]--[SOLENOID]
Which would certainly be cheap, (even for a one-off) but hardly junk
or rocket science.
BTW, perhaps a way to even out the differences between the
electrical/mechanical transfer functions in the solenoids would be to
implement a mechanical 'spring stretcher' which would allow the center
position of the solenoid to be adjusted mechanically with a given,
empirically derived current flowing through the winding.
Or perhaps (even simpler) a spring of fixed length and spring rate,
and offset and span adjustments on the amp?