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Transfer element with dead time
If the output variable follows the input variable, resulting in a time offset, this is termed a
dead time response.
The time constant T
t
is the dead time.
You can image the dead-time element as composed of an infinite number of 1st-order lags.
If the dead time is sufficiently small, it can be treated like a first-order lag element for
calculation purposes.
Let us take the current converter as an example because the output for a control voltage U
st
on the trigger set can only have a delaying effect depending on the trigger delay angle on the
output depending on the instantaneous phase angle of the line voltage. The signal for a
phase angle change is only acted upon after a dead time of the output voltage U
a
.
Integral-action transfer element
Example: Speed ramp-up of a motor with a constant motor and load torque in the armature
setting range.
Proportional-plus-integral controller; PI controller
Frequency response: G
R
= Kp * (1 + p * Tn) / (p * Tn)
With the factor (1 + p * Tn) it is possible to compensate for a time constant of the control loop
here. This always compensates for the greatest time constant.
Kp: gain; Tn: reset time; Xe: input variable; Xa: output variable
The output initially responds with a step change in voltage corresponding the the factor Kp
and then with integration of the input voltage over time.
Tn: Time required to reach a magnitude of change corresponding to the Xe *Kp.
x
t
x
a
x
e
T
t
t
Ti
Xe
Xa
Xe: input variable; Xa: output variable
Transfer function: f(t) = Xa(t) / Xe = t / Ti
Frequency response: F(p) = 1 / (p * Ti)
In the case of a step change in the input
variable, the output variable increases
linearly. Ti = integral-action time
Dynamic response:
x
a
(t) = x
e
(t -T
t
)
Frequency response:
F (p) = e
-pTt