-3640 The Magical Mystery Solved

I found out the mystery behind -3640 offset. You see, the PID loop has a default out put of 50%. And the output limits do not change the output; it just clamps the normally 0-100% to the limits settings. So, with a proportional band of 8000 and limits of 3.5-5.5%, it takes an error of -3540 to bring the output to 4.5. So, what I had to do was remove the limits and set the proportional band to 80. Now the output of 0-100% is unacceptable for the pressure setpoint. So I have to scale it to 3.5-5.5 Bar.

So, thus the question is this, how did it work in the first place?