I have seen other attempts at performing adaptive gain. One such attempt is to limit the authority of the tension regulator output (maximum output or Control Variable) to vary speed to achieve tension. In a PID tension controller, this is done by adjusting a PID regulator parameter called PID MAXCV. I saw a case where the MAXCV was set to a minimum value of 50% and maximum value of 100%. The MAXCV was programmed to change between the minimum and maximum settings based on a limited speed range of the line.
Changing the MAXCV does not change the gain of the regulator, but does limit the authority of the speed regulator to make speed changes.
This method seemed very complicated. I did not have opportunity to compare the tension regulator response using this method with other methods of adaptive control. Tension control was adequate.
Another method of adaptive control for a center wind spindle tension regulator through speed was to adapt the PID gain by the ratio of diameter, not speed. This also produced stable tension regulation at all diameters and speeds. It should be noted that the tension regulator was less responsive at large diameters.