Lake Shore Model 340 Temperature Controller User’s Manual
2-8
Cooling System Design
2.5.2 Thermal
Lag
Poor thermal conductivity causes thermal gradients that reduce accuracy but they also cause 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 controllers 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,
degrading 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.
2.5.3 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 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. Many temperature controllers including the Model 340 have two sensor
inputs for this reason.
2.5.4 Thermal
Mass
Cryogenic designers understandably want to keep the thermal mass of the load as small as possible so the
system can cool quickly and improve cycle time. Small mass can also have the advantage of reduced thermal
gradients. Controlling a very small mass is difficult because there is no buffer to adsorb small changes in the
system. Without buffering, small disturbances can very quickly create large temperature changes. There are
systems where it is necessary to add a small amount of thermal mass such as a copper block in order to
improve control stability.
2.5.5 System
Nonlinearity
Because of nonlinearities in the control system, a system controlling well at one temperature may not control
well at another temperature. While nonlinearities exist in all temperature control systems, they are most
evident at cryogenic temperatures. When the operating temperature changes the behavior of the control loop,
the controller must be retuned. As an example, a thermal mass acts differently at different temperatures. The
specific heat of the load material is a major factor in thermal mass and the specific heat of materials like
copper change as much as three orders of magnitude when cooled from 100 K to 10 K. Changes in cooling
power and sensor sensitivity are also sources of nonlinearity.
The cooling power of most cooling sources also changes with load temperature. This is very important when
operating at temperatures near the highest or lowest temperature that a system can reach. Nonlinearities
within a few degrees of these high and low temperatures make it very difficult to configure them for stable
control. If difficulty is encountered, it is recommended to gain experience with the system at temperatures
several degrees away from the limit and gradually approach it in small steps.
Keep an eye on temperature sensitivity. Sensitivity not only affects control stability but it also contributes to
the overall control system gain. The large changes in sensitivity that make some sensors so useful may make
it necessary to retune the control loop more often.