Watlow Electric Revision 5 - Manual (Page 51)

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Kp is the proportional gain, and FSR/Kp is referred to as the
proportional band PB. The gain can be set from 0 to 255 for the
SYSTEM 32. Note that when gain is specified in the control equation
the output would be different for the same error if a different full scale is
used. If PB is used the FSR cancels out and the PB is independent of
the input range.
TI is the integral or reset time, and 1/TI is referred to as the reset rate.
For the SYSTEM 32, the integral or reset time can be set from 0 [off] to
1020 seconds with 4 second resolution. This corresponds to a reset rate
of 0.05 to 15 repeats per minute.
TD is the derivative time and the range for the SYSTEM 32 is 0 [off] to
255 seconds or 0.01 to 4.25 minutes.
8.1.5 PROPORTIONAL CONTROL [P]
Proportional control is when the control output signal is linearly
proportional to the error. In the above equation the integral and derivative
effects are zero. For the SYSTEM 32 this is accomplished by setting the
integral and derivative constants to zero. The proportional constant is also
known as gain.
As the gain of the controller is increased a small increase in error will cause
a large change in the control output. Since cycling of the PV can result
from high gain, reducing the gain is one way to improve stability.
In the control equation, once the error times the gain divided by the full
scale range reaches 100% [full control output] additional error cannot
increase the control output. If the error is less than this value a control
response proportional to the error is made. Thus if the error is less than
FSR/Kp it is said to be within the PROPORTIONAL BAND (PB). The PB
is equal to the full scale of the controller input divided by the gain. Thus a
gain of 100, for a thermocouple with a range of 0 to 1400 oF, results in a
proportional band of 140 oF.
Using ANASOFT-32 for the SYSTEM 32 allows the a choice of displays
for the proportional function. This function can be shown and entered as
either Gain or Proportional Band. If proportional band is selected, the
values can be entered IN THE ACTUAL ENGINEERING UNITS OF THE
INPUT regardless of the span of the instrument. Thus, a PB of 30 represents
30 oF for any thermocouple input range in the SYSTEM 32.
Gain may also be used, but once again the input span of the controller
becomes critical. For the SYSTEM 32, a gain of 30 represents 48 oF PB for
a Type J T/C, 87 oF for a Type K T/C, and 29 oF for a Type T T/C. To
obtain PB divide the span by the gain setting.