Trane PID Control User Manual

®

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).

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.

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

+

=