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48 c
HAPTER
2: Cooling System Design and Temperature Control
Model 372 AC Resistance Bridge and Temperature Controller
2.11 Temperature
Control The Model 372 includes a dedicated control input to perform closed-loop tempera-
ture control in a dilution refrigerator or other low power cryogenic cooling system.
The load must be equipped with a temperature sensor for feedback and a resistive
heater to add heating power into the system. The instrument, sensor, and heater play
important roles in establishing stable temperature control.
2.11.1 Considerations
For Good Control Most of the techniques discussed above to improve cryogenic temperature measure-
ment apply to control as well. There is an obvious exception in sensor location and a
compromise is suggested in section 2.11.3.
2.11.1.1 Thermal Conductivity
Good thermal conductivity is important in any part of a cryogenic system that is
intended to be at the same temperature. Most systems begin with materials that
have good conductivity themselves, but as sensors, heaters, sample holders, etc., are
added to an ever more crowded space, the junctions between parts are often over-
looked. In order for control to work well, junctions between the elements of the con-
trol loop must be in close thermal contact and have good thermal conductivity.
Gasket materials should always be used along with reasonable pressure.
2.11.1.2 Thermal Lag
Poor thermal conductivity causes thermal gradients that reduce accuracy and also
causes thermal lag that make it difficult for controllers to do their job. Thermal lag is
the time it takes for a change in heating or cooling power to propagate through the
load and get to the feedback sensor. Because the feedback sensor is the only thing
that lets the controller know what is happening in the system, slow information to
the sensor slows the response time. For example, if the temperature at the load drops
slightly below the setpoint, the controller gradually increases heating power. If the
feedback information is slow, the controller puts too much heat into the system
before it is told to reduce heat. The excess heat causes a temperature overshoot,
which degrades control stability. The best way to improve thermal lag is to pay close
attention to thermal conductivity both in the parts used and their junctions.
2.11.1.3 Two-Sensor Approach
There is a conflict between the best sensor location for measurement accuracy and
the best sensor location for control. For measurement accuracy the sensor should be
very near the sample being measured, which is away from the heating and cooling
sources to reduce heat flow across the sample and therefore thermal gradients. The
best control stability is achieved when the feedback sensor is near both the heater
and cooling source to reduce thermal lag. If both control stability and measurement
accuracy are critical it may be necessary to use two sensors, one for each function.
Another reason to use a separate control sensor is that a dedicated control sensor can
be run with higher excitation power. The additional power will reduce the accuracy of
the feedback sensor but create a larger signal for better control stability. Accuracy of
the control sensor is not important if the temperature sample is measured with a dif-
ferent sensor.
2.11.1.4 Thermal Mass
Cryogenic designers understandably want to keep the thermal mass of the load as
small as possible. Small mass can have the advantage of reduced thermal gradients
but controlling a very small mass is difficult because there is no buffer to adsorb
changes in cooling power. Without buffering, small disturbances can very quickly cre-
ate large temperature changes. In some systems it is necessary to add a small amount
of thermal mass in order to improve control stability.