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What is meant by 2-state controller?

The 2-state controller (ON/OFF controller) switches the output when the setpoint is reached. If the value falls below the setpoint by a certain adjustable tolerance (xsd, switching differential, hysteresis), then the output is switched on again. It therefore only has two switching states. It is used in temperature control applications where the heating or cooling is only switched on or off.
A 2-state controller with dynamics can, however, also operate with a P, I, or D component.