2.2 Ziegler-Nichols’ Tuning
2 – 5
2.2
Ziegler-Nichols’ Tuning
For many applications, a good starting point for tuning is one of
the two classic Ziegler-Nichols methods
2
. These two methods are
briefly described below; for more details, see, for example, Åstr ¨om
& H¨agglund,
PID Controllers: Theory, Design, and Tuning
, Instru-
ment Society of America (1995).
2.2.1
Open-loop tuning
The open-loop Ziegler-Nichols method involves introducing a small
step change to the process under control, and making a few mea-
surements from the response. The procedure is:
•
Switch the SIM960 into
Manual
mode, and then adjust until
the process is stable and near the desired operating point.
•
Now make a small, sudden step change,
Δ
, in the control signal.
Call this time
t
=
0.
•
Record the process response in the
Measure
signal. Define the
(dimensionless) process step-response function:
h
(
t
)
=
Measure
(
t
)
−
Measure
(0)
Δ
•
Observe the point of maximum slope in
h
. Extend a straight
line through this point, tangent to
h
, downward (see Figure 2.2).
•
Let
L
be the time coordinate where the straight line crosses
h
=
0; and let
a
be the negative of the
h
–intercept (i. e.,
a
>
0 in
Figure 2.2).
•
Note that it is
not
necessary to wait for the process to completely
settle following the step change
Δ
—it is su
ffi
cient to simply wait
until the maximum slope is observed in
Measure
.
From
a
and
L
, Ziegler and Nichols suggest tuning for
P
,
PI
, and
PID
control as shown in Table 2.1
Control
P
I
D
P
1
/
a
PI
0
.
9
/
a
1
/
(3
L
)
PID
1
.
2
/
a
1
/
(2
L
)
L
/
2
Table 2.1: Ziegler-Nichols open-loop tuning parameters
2
Ziegler, J. G., & Nichols, N. B. 1942, Trans. ASME, 64, 759
SIM960 Analog PID Controller
