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What is meant by switching differential/hysteresis?

The switching differential is also referred to as hysteresis and is only relevant for switching controllers with proportional band = 0.
For controllers with inverse operating sense (e.g. heating control), the standard response is as follows:
The switching differential lies below the setpoint. This means that the controller switches off precisely then when the setpoint is exceeded. It only switches on again when the process value has fallen below the switch-on point, which lies below the setpoint by the amount of the switching differential.
On controllers with direct operating sense (e. g. cooling), the switching differential normally lies above the setpoint. As for controllers with inverse operating sense, the switch-off point is precisely at the setpoint. However, it is switched on again above the setpoint, shifted by the amount of the switching differential.

Switching action of a 2-state controller with inverse operating sense:


Switching action of a discontinuous 3-state controller: