I designed from scratch an analog PID controller to mantain a temperature selected in the range of 60 to 80ºC with a room temp say = 20ºC. The "plant" is a simple 4R7 5 W resistor heated by a PWM-controlled current (100% to 0% range).
For any given setpoint, say 67ºC, I know that room temp is lower, so, if heat is not supplied, the cold source (room) will be pulling the temperature continuously down.
My question: where should I "center" my PWM duty cycle excursion?
If $V_{err}$ = 0, DC = 50%? I heat the resistor with more or less current, pivoting on $V_{err}$ =0
For $V_{err}$ =0, DC = 0% (minimum or null current)? I heat the resistor with a varying current only if Verr is positive
Option 2) seems somewhat reasonable to me, but, at the same time, I see that I am just controlling the heating side of this. Do I leave the room alone doing the cooling with no current supplied by me?