Chapter 2 PID Algorithms
LabWindows/CVI PID Control Toolkit User Manual 2-2 ni.com

Implementing the PID Algorithm with the PID Functions

This section describes how the PID Control Toolkit functions implement the fast (positional)
PID algorithm. The fast PID algorithm is the default algorithm used in the PID Control
Toolkit.

Error Calculation

The following formula represents the current error used in calculating proportional, integral,
and derivative action, where PVf is the filtered process variable.

Proportional Action

Proportional action is the controller gain times the error, as shown in the following formula:

Trapezoidal Integration

Trapezoidal integration is used to avoid sharp changes in integral action when there is a
sudden change in the PV or SP. Use nonlinear adjustment of the integral action to counteract
overshoot. The following formula represents the trapezoidal integration action.

Partial Derivative Action

Because of abrupt changes in the SP, apply derivative action to only the PV, not to the error
(e), to avoid derivativekick. The following formula represents the partial derivative action.

Controller Output

Controller output is the summation of the proportional, integral, and derivative action,
asshown in the following formula:
e(k) = (SP PVf)–
uPk()=Kc*ek()()
uIk()=Kc
Ti
------ ei() ei 1–()+
2
----------------------------------tΔ
i1=
k
∑
uDk() = Kc Td
Δt
----- PV
fk()PV
fk1–()–()–
uk() uPk() uIk() u+Dk()+=