Filter
Top Products
CNT-APG002-EN 55
®
Appendix A
The math behind PID loops
This appendix presents the mathematical formulas used for PID control
in Tracer MP580/581 controllers, the programmable control module
(PCM), and the universal programmable control module (UPCM).
Velocity model formula
The formula used to calculate the output in the velocity model is shown
below. It uses the integral and proportional gain, but not the derivative
gain. The same formula is used in the PCM and the UPCM.
Where:
K
prop
= proportional gain
K
int
= integral gain
K
diff
= integral gain
c = 2.56 for the PCM and UPCM
c = 1.00 for Tracer MP580/581 controllers
= change in error
= change in the change squared
The factor 2.56 scales the PID output to a range of 0–100% in the PCM
and UPCM.
Proportional control formula
The following formula shows the relationship between the error and the
output in proportional-only control:
The proportional bias calibrates the controller to some known output. So
when the error is zero (which makes the proportional gain zero), the out-
put is equal to the proportional bias.
∆output n()
K
prop
c
--------------
∆error n()×
K
int
error n()×
c
-----------------------------------------
K
diff
c
------------
∆
2
error n()×++=
∆error n()
∆
2
error n()
Output n()
K
prop
c
--------------
error n()× proportional bias+=