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130BA183.10
y(t)
t
Pu
Illustration 16.5 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 x
K
u
0.833 x
P
u
–
PID tight
control
0.6 x
K
u
0.5 x
P
u
0.125 x
P
u
PID some
overshoot
0.33 x
K
u
0.5 x
P
u
0.33 x
P
u
Table 16.7 Ziegler Nichols Tuning for Regulator,
Based on a Stability Boundary
Use the control settings described below for initial tuning.
The process operator can then fine-tune the control as
necessary.
Step-by-step description
1.
Select only proportional control (integral time is
selected to the maximum value, while the differ-
entiation time is selected to 0).
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.
3.
To obtain the critical time constant, measure the
period of oscillation:
P
u
.
4.
To calculate the necessary PID control parameters,
use
.
PID Controls
Design Guide
MG37N102
Danfoss A/S © 6/2016 All rights reserved.
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