So I set it up to dump the parameters so I can visualize the process. Nothing fancy, just CSV out the serial port to a log file, then into Excel so I can see what's going on:
I've run half a dozen trials while I learn how to do PID tuning. That image is from part of the process where I'm looking for a good Kp that doesn't overshoot. After playing with it for a while I decided that I might as well get the rest of the hardware and software done, then play with the fine tuning later.