You probably won't be constucting a model in the classical sense bit the effect will be the same.
It sounds like you are generating the rewind speed refewrence completely out of the plc. For the purpose of what we are doing here we will asume the rewind is doing what you tell it to do.
In the perfect world you wouldn't need a PID loop to do this. If you knew the unwind and rewind roll diameters and the motor to spindle gear ratio for the unwind and rewind you could calculate the exact speed command for the rewind spindle to get the unwind and rewind roll surface speeds to exactly match. You want to get as close to that as you can.
I have seen two relatively stable ways of calculating roll diameter that are pretty easy to implement. In your case you aren't shooting for an exact roll diameter. All you want is a ratio of the unwind diameter to the rewind diameter.
This description assumes you can get both the unwind and rewind speed feedback or the unwind and rewind speed command. The command would probably be better in your case. Let's assume the PID block is controlling the dancer reasonably well; that is, the dancer is stable and not on either mechanical end of travel. The rewind to unwind speed ratio is:
Command Ratio = Rewind Speed Command / Unwind Speed Command
or you can use the speed feedback and get:
Feedback Ratio = Rewind Speed Feedback / Unwind Speed Feedback
Keep in mind the rewind speed command listed above is the total speed command for the rewind, both the PID and anything else we throw in. Ideally both calculations woild yield the same ratio. However in practice the feedback ratio will bounce around more. You could use this ratio directly to develop a rewind speed command:
Rewind Speed Command = Unwind Speed Command * Ratio
You can probably tell that this method results in positive feedback for the rewind speed command. The faster you tell the rewind to go, the bigger the ratio, which tells the rewind to go faster, which results in a bigger ratio, which tells.... The PID function is what keeps this from happening. If you drive the rewind speed command too far one way or another with the ratio the PID will detect the dancer displacement and respond to bring the dancer back to the right spot.
I wouldn't directly use the ratio calculation as the speed multiplier. I have seen too many cases where a bad calculation can push the speed command past where the PID can correct for it and you do run away. Instead, compare the calculated ratio to the ratio you use as your speed multiplier. If the calculated value is greater than the speed multiplier, add some small value to the speed multiplier. If calculated is less than the speed multiplier, subtract the small value from the speed multiplier. And only do the add/subtract thing if you are above some minimum speed. Do the comparison and the add or subtract every 500 msec or so as a start. Do it more often if your speed multiplier changes too slowly. You will know you are fast enough if the speed ratio bounces up and down just a little bit all the time. If it is constantly going in one direction the compare rate is too slow or the amount you are adding/subtracting is too small.
Now multiply your unwind speed times the speed multiplier to get a baseline rewind speed command. Then add in the PID output to get a total speed command for the drive. You will notice that the PID output will be much smaller with this method. And you will accel and decel with much better dancer stability.
When you reset, just set you speed multiplier (ratio) to the full roll to empty core ratio and you will be good to go.
Good luck.
Keith