National Instruments 371685C-01 用户手册

This section describes how the PID Control Toolkit functions implement the precise PID 
algorithm.

The current error used in calculating integral action for the precise PID algorithm is shown in 
the following formula:

where SP

 is the range of the SP and L is the linearity factor that produces a nonlinear gain 

term in which the controller gain increases with the magnitude of the error. If L is 1, the 
controller is linear. A value of 0.1 makes the minimum gain of the controller 10% K

. Use of 

a nonlinear gain term is referred to as a precise PID algorithm. 

The error for calculating proportional action for the precise PID algorithm is shown in the 
following formula:

where 

β is the setpoint factor for the Two Degree of Freedom PID algorithm described in the 

 section. The formula used to calculate derivative action for the precise 

PID algorithm is the same formula used to calculate derivative action for the fast PID 
algorithm.

In applications, SP changes are usually larger and faster than load disturbances, while load 

disturbances appear as a slow departure of the controlled variable from the SP. PID tuning for 
good load-disturbance responses often results in SP responses with unacceptable oscillation. 
However, tuning for good SP responses often yields sluggish load-disturbance responses. 
β, when set to less than one, reduces the SP response overshoot without affecting the 
load-disturbance response, indicating the use of a Two Degree of Freedom PID algorithm. 
β is an index of the SP response importance, from zero to one. For example, if you consider 
load response the most important loop performance, set 

β to 0.0. Conversely, if you want the 

PV to quickly follow the SP change, set 

β to 1.0.

e(k) = (SP PV

)(L+ 1 L

–

(

)*

–

-------------------------

) 

–

( )

(

β* SP PV

)(L+ 1 L

–

(

)*

βSP PV

–

----------------------------

) 

–

=

( )= K

* eb k

( )

(

)