The Pid Equation - Allen-Bradley SLC 500 Series Reference Manual
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9-2
Proportional Integral Derivative Instruction
The PID Equation
Publication 1747-RM001G-EN-P - November 2008
The PID equation controls the process by sending an output signal to the
control valve. The greater the error between the setpoint and process variable
input, the greater the output signal, and vice versa. An additional value (feed
forward/bias) can be added to the control output as an offset. The result of
PID calculation (control variable) drives the process variable you are
controlling toward the set point.
The PID instruction uses the following algorithm:
Standard equation with dependent gains is shown below.
E ( )
Output
K
=
+
C
Standard Gains constants are listed in the following table.
Table 9.1 Standard Gain Constants
Term
Controller Gain K
C
Reset Term 1/T
I
Rate Term T
D
(1)
SLC 5/02 processors.
(2)
Applies to SLC 5/03 and higher processors PID ranges when bit Reset and Gain Range (RG) bit is set to 1.
The derivative term (rate) provides smoothing by means of a low-pass filter.
The cutoff frequency of the filter is 16 times greater than the corner frequency
of the derivative term.
(
)
1
D PV
∫
E ( ) t d
⋅
---- -
---------------- -
T
+
+
D
T
df
I
Range (Low to High)
(1)
0.1 to 25.5 (dimensionless)
(2)
0.01 to 327.67 (dimensionless)
25.5 to 0.1 (minutes per repeat)
327.67 to 0.01 (minutes per repeat
(1)
0.1 to 25.5 (minutes)
(2)
0.01 to 327.67 (minutes)
Feed Forward/Bias
Reference
Proportional
(1)
Integral
(2)
)
Derivative
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