Chapter 2
PID Algorithms
LabWindows/CVI PID Control Toolkit User Manual
2-6
ni.com
Figure 2-2 illustrates the autotuning procedure excited by the setpoint relay experiment,
which connects a relay and an extra feedback signal with the SP. Notice that the PID Library
autotuning functions directly implement this process. The existing controller remains in
the loop.
Figure 2-2.
Process under PID Control with Setpoint Relay
For most systems, the nonlinear relay characteristic generates a limiting cycle from which the
autotuning algorithm identifies the relevant information needed for PID tuning. If the existing
controller is proportional only, the autotuning algorithm identifies the ultimate gain
K
u
and
ultimate period
T
u
. If the existing model is PI or PID, the autotuning algorithm identifies the
dead time and time constant
T
p
, which are two parameters in the integral-plus-deadtime
model, as follows:
Tuning Formulas
This package uses Ziegler and Nichols’ heuristic methods for determining the parameters of
a PID controller. When you autotune, select one of the following types of loop performance:
fast (1/4 damping ratio), normal (some overshoot), or slow (little overshoot). Refer to the
following tuning formula tables for each type of loop performance.
Table 2-1.
Tuning Formula under P-Only Control (Fast)
Controller
K
c
T
i
T
d
P
0.5
K
u
—
—
PI
0.4
K
u
0.8
T
u
—
PID
0.6
K
u
0.5
T
u
0.12
T
u
SP
e
+
–
P(I) Controller
Process
PV
Relay
+
–
τ
G
P
s
( )
=
e
τ
s
–
T
p
s
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