4.4.7 Optimisation of the Process Regulator
The basic settings have now been made; all that needs to
be done is to optimise the proportional gain, the
integration time and the differentiation time (
7-33 Process
PID Proportional Gain
,
7-34 Process PID Integral Time
,
7-35 Process PID Differentiation Time
). In most processes,
this can be done by following these guidelines:
1.
Start the motor
2.
Set
7-33 Process PID Proportional Gain
to 0.3 and
increase it until the feedback signal again begins
to vary continuously. Then reduce the value until
the feedback signal has stabilised. Now lower the
proportional gain by 40-60%.
3.
Set
7-34 Process PID Integral Time
to 20 s and
reduce the value until the feedback signal again
begins to vary continuously. Increase the
integration time until the feedback signal
stabilises, followed by an increase of 15-50%.
4.
Only use
7-35 Process PID Differentiation Time
for
very fast-acting systems only (differentiation
time). The typical value is four times the set
integration time. The differentiator should only be
used when the setting of the proportional gain
and the integration time has been fully
optimised. Make sure that oscillations on the
feedback signal is sufficiently dampened by the
lowpass filter on the feedback signal.
NOTE
If necessary, start/stop can be activated a number of times
in order to provoke a variation of the feedback signal.
4.4.8 Ziegler Nichols Tuning Method
In order to tune the PID controls of the frequency
converter, several tuning methods can be used. One
approach is to use a technique which was developed in
the 1950s but which has stood the test of time and is still
used today. This method is known as the Ziegler Nichols
tuning method.
NOTE
The method described must not be used on applications
that could be damaged by the oscillations created by
marginally stable control settings.
The criteria for adjusting the parameters are based on
evaluating the system at the limit of stability rather than
on taking a step response. The proportional gain is
increased until continuous oscillations are observed (as
measured on the feedback), that is, until the system
becomes marginally stable. The corresponding gain
(K
u
)
is
called the ultimate gain. The period of the oscillation
(P
u
)
(called the ultimate period) is determined as shown in
130BA183.10
y(t)
t
Pu
Illustration 4.12 Marginally Stable System
Measure
P
u
when the amplitude of oscillation is quite
small. Then “back off” from this gain again, as shown in
K
u
is the gain at which the oscillation is obtained.
Type of
Control
Proportional
Gain
Integral Time
Differentiation
Time
PI-control
0.45 *
K
u
0.833 *
P
u
-
PID tight
control
0.6 *
K
u
0.5 *
P
u
0.125 *
P
u
PID some
overshoot
0.33 *
K
u
0.5 *
P
u
0.33 *
P
u
Table 4.23 Ziegler Nichols Tuning for Regulator, based on a
Stability Boundary.
Experience has shown that the control setting according to
Ziegler Nichols rule provides a good closed loop response
for many systems. The process operator can do the final
tuning of the control iteratively to yield satisfactory
control.
Step-by-step Description
Step 1: Select only proportional control, meaning that the
Integral time is selected to the maximum value, while the
differentiation time is selected to zero.
Step 2: Increase the value of the proportional gain until
the point of instability is reached (sustained oscillations)
and the critical value of gain,
K
u
, is reached.
Step 3: Measure the period of oscillation to obtain the
critical time constant,
P
u
.
Application Examples
VLT
®
Decentral Drive FCD 302
60
MG04H102 - VLT
®
is a registered Danfoss trademark
4
4