Lake Shore Model 331 Temperature Controller User’s Manual
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 331 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. In some systems 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.
2.6 PID CONTROL
For closed-loop operation, the Model 331 temperature controller uses a algorithm called PID control.
The control equation for the PID algorithm has three variable terms: proportional (P), integral (I), and
derivative (D). See Figure 2-3. Changing these variables for best control of a system is called tuning.
The PID equation in the Model 331 is:
Heater Output =+ +
L
N
M
O
Q
P
z
Pe I edt D
de
dt
af
where the error (e) is defined as: e = Setpoint – Feedback Reading.
Proportional is discussed in Paragraph 2.6.1. Integral is discussed in Paragraph 2.6.2. Derivative is
discussed in Paragraph 2.6.3. Finally, the manual heater output is discussed in Paragraph 2.6.4.
Cooling System Design 2-9
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