The ON/OFF control (two-position ) controller operates only when the measurement crosses the set point.
In on/off control ,a valve would have only two positions fully opened or fully closed .As a result the output measurement always cycles above and below the set point.
Application of On/Off control
ON-OFF control is best applied to a large capacitance process that has essentially no dead time . Eg : large tank or bath
A system where dead time is short and rate of rise is slow can be handled adequately by ON/OFF control