I recently figured out something about my PID that allowed me to autotune it much more precisely. I'm not sure if every PID has this feature, but if, like me, your PID tended to overshoot a degree or two after autotuning it, this might help.
It turns out my PID, Auberins Sy-2362 has a setting in one of the menus called the "atdu." This is an autotune offset setting and the default on my PID is 10. So whenever I went to autotune, the PID offset the set value by 10 degrees. If, like me, you typically tried to autotune by setting the set value to about five or ten degrees higher than the initial water temp, well, the PID will struggle to figure out the proper settings because of the atdu.
I used think that the trouble with my autotuning was that I always did it with just water, not grain and water which would have more mass. But I recently waited until after a brew day and then autotuned with the spent grain still in the mash tun. The result? I was still overshooting by a degree or two.
Eventually, I figured out the atdu offset and set it to zero. After autotuning, the system is spot on, mine maybe overshoots a tenth or two tenths of a degree, but I have it set to maximum accuracy and have the temp filter at zero. So it's pretty much right there.
On my PID, to get to the atdu I have to enter 0089 in the settings password. Yours may be different.
Anyway, I hope that helps anyone who, like me, was having trouble tuning their PID. Maybe I'm the last to know this, but it took me quite a while to figure out.