How does proportional band work in temperature control?

[TSN79]

I've always struggled with understanding proportional band - even after watching a number of videos trying to explain it. Now I've got a fan regulator that has a temperature sensor and a potentiometer. It works by sending a signal (0-10V) to the fan if the ambient temperature drops below a certain value. It also has a knob where the temperature proportional band can be set between 1-8°C. I think it means how much the temperature is allowed to drift past the set point before the fan starts or stops. Is that about right...?

 

[jrmichler]

The fan speed signal (controller output) is proportional to the difference between the setpoint (what you want) and the measured (what you have) signals. Example: Setpoint is 30 deg C and proportional band is 5 deg C. Then output could be fan 0% speed at 30 deg C, 20% speed at 29 deg C, and 100% speed at 25 deg C.

Deadband is different. The thermostat in my house has deadband control. It turns the heater on at 70 deg F, and off at 71.5 deg F. Below 70 deg F, the heater is always on. Above 71.5 deg F, the heater is always off. In between, the heater could be either on or off.