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Calculating the gains
CNT-APG002-EN 11
®
Calculating the gains
Table 1 shows recommended initial values for the proportional and inte-
gral gains for several applications. Most applications do not require a
derivative contribution, so the derivative gain is not shown. We recom-
mend using a ratio of 4:1 between the proportional and integral gains, so
the proportional gain should be four times as large as the integral gain.
You may need to modify the values shown in Table 1 when tuning a PID
loop, but try to maintain the 4:1 ratio.
You can also calculate proportional and integral gains using the following
calculations:
The proportional gain is scaled by a factor of 0.80, so it contributes 80% of
the final output. The integral gain contributes 20% of the final output.
Example
In a duct static pressure system, an actuator can move the inlet guide
vanes of an air handler from 0–100%, so the output range is 100. We want
a throttling range of 2.0 in. wc (so a change in pressure of 2.0 in. wc or
more will drive the output from 0–100% or vice versa). The calculations
look like this:
So based on the desired throttling range of 2.0 in. wc, the initial propor-
tional gain is 40 and the integral gain is 10.
Table 1: Starting gain values for applications
Application Output Throttling range
Proportional
gain
Integral
gain
Discharge-air cooling Valve position 0–100% 20.0°F (11.1°C) 4.0 (8.0) 1.0 (2.0)
Discharge-air heating Valve position 0–100% 40.0°F (22.2°C) 2.0 (4.0) 0.5 (1.0)
Space temperature Discharge setpoint
50–100°F (10–37.8°C)
2.0°F (1.1°C) 20.0 (20.0) 5.0 (5.0)
Duct static pressure Inlet guide vane or variable-frequency
drive (VFD) position 0–100%
2.0 in. wc (0.5 kPa) 40.0 (160) 10.0 (40.0)
Building static
pressure
Inlet guide vane or variable-frequency
drive (VFD) position 0–100%
20.0 in. wc (5.0 kPa) 4.0 (8.0) 1.0 (2.0)
Discharge-air cooling Electric/pneumatic
5.0–15.0 psi (34–103 kPa)
20.0°F (11.1°C) 0.4 (4.0) 0.1 (1.0)
Proportional gain
0.80 output range×
throttling range
--------------------------------------------------------=
Integral gain
0.20 output range×
throttling range
--------------------------------------------------------=
Proportional gain
0.80 output range×
throttling range
------------------------------------------------------
0.80 100×
2.0 in. wc
----------------------------
40===
Integral gain
0.20 output range×
throttling range
------------------------------------------------------
0.20 100×
2.0 in. wc
----------------------------
10===