I'll answer what I can, but I would consider myself a PID "dabbler". There are others around here who are more proficient, so don't take my answers as a final word on things. Just an attempt to help.
1. Always think about your units! Always! Really!
The first place this comes into play is your error term (SP - PV). Be sure that SP and PV are expressed in the same units before you do the subtraction.
2. The output of the PID calculation is a "control effort". It will vary with both your instantaneous error (the Proportional term) and different aspects of your error *history* (the Integral and Derivative terms). You may need to further scale or transform this number into the right form / units for your actuator.
In your system, you'll have an error term in units of force. The "control effort" you want to give to your actuator will be in terms of "incremental displacement". A larger force error will require a larger adjustment in incremental position.
Note: many real-world systems can be controlled with just PI. Not all need the D term.
3. It's actually normal, not unusual, that the feedback sensor is distinct from the actuator or "plant" and just keeps measuring no matter what the plant is doing. Part of the beauty of a feedback loop is that once set up correctly, it keeps automatically making the right thing happen.
4. A dynamic model of your plant would be vital if you wanted to *simulate* the behavior of your control system. But you should *not* insert that model into your PID calculations when you're controlling the real system.
Two notes. One, the plant model can be useful to PID wizards (I'm not one), who can derive near-optimal PID gains using that knowledge. Two, there are *other* control methods (such as feed-forward, state space control, probably others) that *would* insert the plant model knowledge into the calculations. But for regular, "simple" PID control, leave it out.
Actually here's a third note. It *can* be helpful to use your knowledge of the relationship between force and incremental displacement (for example, a scaling factor like 2.0 cm/N). It'll give you a rough order of magnitude of where to start with your P gain as you start tuning your parameters. Again, I'm not a PID wizard, but I might start with P value that's somewhere around 1/4 of that or less. Specifically, if you had an instantaneous error of 1.0 N, the 2.0 cm/N relationship might seem to suggest you'd want to apply a "control effort" of 2 cm incremental motion. I'd be inclined to start with a P value more like 0.5 cm/N or less.
5. All this discussion so far has conveniently ignored an important factor -- the likely latency between delivering a command to the motion stage and the time it takes to finish obeying that command and producing the corresponding force feedback. Simple PID can have trouble with time delays, though I expect yours won't be so severe as to prevent you from getting decent behavior with "mere" PID.
A simple strategy that could help you is to reduce the rate of your control loop. You'll probably reduce your difficulties if the loop interval is a little but not an awful lot faster than your actuator response time. (For example, if response time is ~250 msec for modest incremental motions, a 50 msec loop rate is probably more appropriate than a 5 msec loop rate.)
-Kevin P
CAUTION! New LabVIEW adopters -- it's too late for me, but you *can* save yourself. The new subscription policy for LabVIEW puts NI's hand in your wallet for the rest of your working life. Are you sure you're *that* dedicated to LabVIEW? (Summary of my reasons in this post, part of a voluminous thread of mostly complaints starting here).
