On-off controller open loop or close loop?
They can be used for either.


A thermostat, such as a bimetallic strip type, is an on-off controller which is used in a closed loop to control room temperature. As the temperature rises above setpoint the heat is turned off. As the temperature falls below setpoint the heat is turned on.
The same heating system could be run from a timer that applies heat for 6 minutes on and 4 minutes off in a repeating pattern. This is open loop. There is no temperature feedback to modify the action of the timer.