Pid Algorithms; The Pid Algorithm - National Instruments PID Control Toolkit 371685C-01 User Manual

PID Algorithms

This chapter explains the fast PID, precise PID, and autotuning algorithms.

The PID Algorithm

The PID controller compares the setpoint (SP) to the process variable (PV) to obtain the error
(e), as follows:
Then the PID controller calculates the controller action, u(t), as follows. In this equation, K
is the controller gain.
If the error and the controller output have the same range, –100% to 100%, controller gain is
the reciprocal of proportional band. T
time, and T is the derivative time in minutes, also called the rate time. The following formula
d
represents the proportional action.
The following formula represents the integral action.
The following formula represents the derivative action.
© National Instruments Corporation
e = SP – PV
⎛
t
1
⎜
∫
u t ( )
K e --- - e t d
= +
⎜
c
T
i
⎝
0
is the integral time in minutes, also called the reset
i
t ( )
u K e
=
p c
t
K
∫
c
t ( ) =
u ------- e t d
I
T
i
0
de
t ( )
u K T
-------
=
D c d
dt
2-1
⎞
de
⎟
T
----- -
+
⎟
d
dt
⎠
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