would you like to see what a heating system looks like when it only has a bi-metal thermostat and what it looks like after a PID is applied? I built the BBCC system and plotted an espresso pull without the PID enabled and a pull with the PID enabled.
Check out these images:
without the PID enabled:
http://picasaweb.google.com/lh/photo/x68EzW2yrshM0udw0MJfKw
with the PID enabled:
http://picasaweb.google.com/lh/photo/cHzCR15XaT0FJJZeoWLevw
note: I have two heat settings(brew/steam) and in the test run, the temp rises to the first/brew temp and then a short while later I push the button to set the temp to the higher/steam temp. After a short period on steam, I then set the target temp back to the brew temp.
You can see that with the standard bimetal thermostat, the temp swings all over the place around the target temp but with the PID control enabled, there's a small overshoot and a quick recovery and much more stable and steady temperature held.
Doug