22
c
HAPTER
2:
Cooling System Design and Temperature Control
Model 335 Temperature Controller
2.6.4 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 absorb 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.
2.6.5 System
Non-Linearity
Because of nonlinearities, a system controlling well at one temperature may not con-
trol well at another temperature. While nonlinearities exist in all temperature control
systems, they are most evident at cryogenic temperatures. When the operating tem-
perature 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. 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 tem-
perature 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 dif-
ficulty is encountered, it is recommended to gain experience with the system at tem-
peratures 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 sensi-
tivity that make some sensors so useful may make it necessary to retune the control
loop more often.
2.7 PID Control
For closed-loop operation, the Model 335 temperature controller uses an algorithm
called PID control. The control equation for the PID algorithm has three variable
terms: proportional (P), integral (I), and derivative (D). See FIGURE 2-2. Changing
these variables for best control of a system is called tuning. The PID equation in the
Model 335 is:
Heater output =
P e I e
+
dt D
+
de
dt
------
where the error (e) is defined as: e = setpoint – feedback reading.
Proportional is discussed in section 2.7.1. Integral is discussed in section 2.7.2. Deriv-
ative is discussed in section 2.7.3. Finally, the manual heater output is discussed in
section 2.7.4.
