Chapter 2 PID Algorithms
© National Instruments Corporation 2-5 LabWindows/CVI PID Control Toolkit User Manual

Trapezoidal Integration

Trapezoidal integration is used to avoid sharp changes in integral action when there is a
sudden change in the PV or SP. The following formula represents the trapezoidal integration
action for the precise PID algorithm. Use nonlinear adjustment of integral action to counteract
the overshoot. The larger the error, the smaller the integral action, as shown in the following
formula and in Figure 2-1.
Figure 2-1. Nonlinear Multiple for Integral Action (SPrng= 100)
The Autotuning Algorithm
Use autotuning to improve performance. Often, many controllers are poorly tuned. As a
result, some controllers are too aggressive and some controllers are too sluggish. PID
controllers are difficult to tune when you do not know the process dynamics or disturbances.
In this case, use autotuning. Before you begin autotuning, you must establish a stable
controller, even if you cannot properly tune the controller on your own.
uIk()=Kc
Ti
------ ei() ei 1–()+
2
----------------------------------tΔ
i1=
k
∑1
110*ei()
2
SPrng
2
---------------------+
-------------------------------