He might black-box those from the same supplier that Ricochet Rabbit gets his bullets from.
This kit has most of the data collection components (including software package) you need included
Make a stable rig to hold the strain gauge in place. Attach the data collecting strain gauge to the bowstring using the hook or some other attachment you design.
Attach some kind of stable, non-damaging clamp (approximating a human hand grip) to the bow handle. Have the bow handle pulled forward at a speed approximating a normal bow draw by some pulling device. You could even do this manually with a big lever for simplicity though using a piston or electric screw or ram or similar pulling method would be more accurate. You would need to be able to easily adjust the draw length somehow as I assume different bows will have different draw geometries. Record data values as a clamp arrangement pulls the bow forward the desired distance.
Thats an interesting twist, move the bow instead of the string. I use homemade shooting machines now. The way I draw them is with a foot stirrup running over a pulley so it leaves both my hands free. Up to a 100# draw is almost effortless with a foot stirrup. I could easily apply that to drawing the bow instead of the string and all my data collecting instruments would remain stable. Great suggestion.
Have you ever visited any of the major bow manufacturers to see what kind of equipment their R&D departments are using?
A guy built one a few years ago with high speed photography and sank a ton of money into it. I think he was a bit bitter as he could not demand the prices he needed for testing to pay for his machine. He put something like $125,000 into it. Much heavier than it needed to be and overly engineered and built in my eyes. I made my shooting machine from scrap lumber and used it for 10 years.
Good post - brought back a lot of memories. Have tuned lot of loops in chemical plants in my lifetime. But back to the OP - most software or hardware implementations of the PID controller nowadays have auto tuning in-built - so it will do it for you. Also, unless you need very fast controls and the sensors have good accuracy and frequency response, I’ll skip the D in the PID.