2.11.2 Closed Loop PID Control
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2.11.1.5 System Nonlinearity
Because of nonlinearities in the control system, a system controlling well at one tem-
perature 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 con-
troller must be returned. 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 mag-
nitude when cooled from 100 K to 10 K. Changes in cooling power and sensor sensi-
tivity 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 very close to 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
further away from the limit and gradually approach it in small steps.
Keep an eye on temperature sensor sensitivity. Sensitivity not only affects control sta-
bility 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.
2.11.2 Closed Loop PID
Control
Closed loop PID control, often called feedback control, is the control mode most often
associated with temperature controllers. In this mode the controller attempts to keep
the load at exactly the user entered setpoint that can be entered in resistance or
temperature. To do this, it uses feedback from the control sensor to calculate and
actively adjust the control (heater) output. The Model 372 uses a control algorithm
called PID that refers to the three terms used to tune the controller for each unique
system.
The PID control equation has three variable terms: proportional (P), integral (I), and
derivative (D) (FIGURE 2-4). Changing these variables for best control of a system is
called tuning. The PID equation in the Model 372 is:
where the error (e) is defined as: e = Setpoint – Feedback Reading.
2.11.2.1 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 tempera-
tures, to generate the proportional contribution to the output: Output (P) = Pe. If pro-
portional 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 deter-
mined 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.
2.11.2.2 Integral (I)
In the control loop, the integral term, also called reset, looks at error over time to build
the integral contribution to the output: