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Lake Shore Model 325 Temperature Controller User’s Manual
2-8 Cooling System Design
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 325 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 325 is:
where the error (e) is defined as: e = Setpoint – Feedback Reading.
Proportional is discussed in Section 2.6.1. Integral is discussed in Section 2.6.2. Derivative is discussed in Section 2.6.3.
Finally, the manual heater output is discussed in Section 2.6.4.
2.6.1 Proportional (P)
The Proportional term, also called gain, must have a value greater than zero for the control loop to operate. The value of
the proportional term is multiplied by the error (e) which is defined as the difference between the setpoint and feedback
temperatures, to generate the proportional contribution to the output: Output (P) = Pe. If proportional is acting alone,
with no integral, there must always be an error or the output will go to zero. A great deal must be known about the load,
sensor, and controller to compute a proportional setting (P). Most often, the proportional setting is determined by trial
and error. The proportional setting is part of the overall control loop gain, and so are the heater range and cooling power.
The proportional setting will need to change if either of these change.