Lake Shore Model 321 Autotuning Temperature Controller User’s Manual
D-2
Application Notes
III PROPORTIONAL CONTROL
The block diagram in Figure 1 shows a systems in which
only proportional control is being used. In this system,
the desired control temperature setting (set point) is
being compared to the sensor signal and the difference,
or error signal (including polarity), is amplified within the
controller. When the sensor temperature corresponds to
the set point temperature (in voltage for a diode or
resistance for a resistor), the sensor signal will be equal
to, but opposite in polarity to the set point signal and the
error signal will be zero. In older instruments, the set
point is normally calibrated in millivolts or volts or
resistance, corresponding to the sensor output signal.
Most modern controllers have stored within them the
appropriate voltage-temperature or resistance-
temperature sensor characteristic so that the set point
can be calibrated directly in temperature. However, as
discussed in Section VII, this convenience feature can
compromise the resolution and accuracy of the
controller.
The output of the controller is dc power to a resistive
heater, the output magnitude of which depends on the
size and sign of the error signal, as well as on the gain
of the deviation amplifier and the output power supply.
Since the controller's power output state tracks the
deviation amplifier output, it is evident that the power
output is proportional to the magnitude of the error
signal. In process control nomenclature, this response is
described in terms of "proportional control".
Let us examine the behavior of the sensor signal—set
point—deviation circuit in a modern cryogenic controller,
the Lake Shore Cryotronics Model DRC-82C. In figure
2, the amplifier output (deviation gain times error) is
plotted against the error signal for two amplifier gains:
A
v
= 100 and A
v
= 1000. "Gain" in this closed loop
system refers not to the power gain, as in an audio
amplifier, but is related to the maximum amount of error
signal allowed before the controller is directed to
produce full output power. The DRC-82C requires a 0 to
8 volt signal from the deviation amplifier to drive the
power output stage from zero-to-maximum. In Figure 2,
For Av = 1000, there is a narrow band of error signals (0
to -8 mV) within which the proportional action occurs.
This "proportional band" expands tenfold for A
v
= 100,
and so on for lower gains; obviously, gain and
proportional band are inversely related. Proportional
band is expressed as a percentage of full scale range.
Note that the proportional band in mV can be converted
to temperature in kelvins if the sensitivity of the sensor
in mV/K is known. As an example, suppose the sensor producing the error signal in Figure 2 had a sensitivity of 1 mV/K
and the set point full scale range was 100 mV = 100 K. The proportional band would then be 8% (or 8 K) and 80% (or 80
K) for A
v
= 1000 and 100, respectively. In cryogenic applications, this terminology is less significant; gain, which is
multiplicative, is usually more useful, since it is more easily understood by the user.
The power output stage of a cryogenic controller may or may not have variable gain associated with it. If the controller has
several output power stage ranged for example, 5, covering 5 orders of magnitude in power) as does the DRC-82C, then
the controller output into a 50 ohm load and with a gain of 200 for 5 watts and 50 watts would have the response shown in
figure 3. Note that the
overall
voltage and power gain of the controller is modified by changing the output power settings.
FIGURE 1.
Block diagram of Cryogenic Temperature Controller. A
v
is
amplifier voltage gain.
FIGURE 2.
Output plot of the deviation amplifier showing Proportional
Bands for gain settings of 100 and 1000. For the DRC-82C, the
maximum available gain is 1000.
FIGURE 3.
Output Power versus error signal in voltage or equivalent
temperature of sensor for two different power settings: (A) corresponds
to a sensor sensitivity of -50 mV/K; (B) corresponds to a sensor
sensitivity of -2.5 mV/K. Note that the curves are linear in voltage,
not
power.
