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Activity 36-1—ON/OFF Control The initial slope of a first-order response curve intersects the final value line at a time equal to the time constant of the first-order response. This means that, for a process with a first-order response that is forced to change at a defined rate from an initial measurement to a final measurement, the process time constant can be determined by knowing the final possible high and low values. An ON/OFF heating system provides hot air at a temperature of 100°F when the heating system is ON. With the heating system OFF, the minimum temperature is 40°F. The setpoint is 70°F. The heating time constant is the amount of time required to heat the process from the setpoint to the maximum possible temperature when heated at the initial rate of change. The cooling time constant is the time required for the process to cool down from the setpoint to the minimum temperature when the heating system is OFF and cooled at the initial rate of change. The process has a 1°F deadband and stays ON for 2 min and stays OFF for 5 min. 1. What is the heating time constant? 2. What is the cooling time constant? The process has a 2°F deadband, a dead time of 2 min, a heating time of 4 min to move through the dead- band, and a cooling time of 8 min to move through the deadband. 3. Draw the heating and cooling response curves on the graph paper on the back of this page. 4. What is the heating time constant? 5. What is the cooling time constant? 6. What is the amount of overshoot during the heating cycle? 7. What is the amount of undershoot during the cooling cycle? Technical Publishers

Activity 36-1—ON/OFF Control
The initial slope of a first-order response curve intersects the final value line at a time equal to the time constant
of the first-order response. This means that, for a process with a first-order response that is forced to change at
a defined rate from an initial measurement to a final measurement, the process time constant can be determined
by knowing the final possible high and low values.
An ON/OFF heating system provides hot air at a temperature of 100°F when the heating system is ON. With
the heating system OFF, the minimum temperature is 40°F. The setpoint is 70°F. The heating time constant is the
amount of time required to heat the process from the setpoint to the maximum possible temperature when heated
at the initial rate of change. The cooling time constant is the time required for the process to cool down from the
setpoint to the minimum temperature when the heating system is OFF and cooled at the initial rate of change.
The process has a 1°F deadband and stays ON for
2 min and stays OFF for 5 min.
1. What is the heating time constant?
2. What is the cooling time constant?
The process has a 2°F deadband, a dead time of 2 min, a heating time of 4 min to move through the dead-
band, and a cooling time of 8 min to move through the deadband.
3. Draw the heating and cooling response curves on the graph paper on the back of this page.
4. What is the heating time constant?
5. What is the cooling time constant?
6. What is the amount of overshoot during the heating cycle?
7. What is the amount of undershoot during the cooling cycle?
Technical Publishers

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