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19.1.3
Derivative Action
The derivative action sets a control action based on the prediction of what will happen in the future. The value of this action is
proportional to the error trend (increase or decrease).
This action helps to improve dynamic performance, while maintaining the high value of the proportional action, but is less simple
to adjust. It is useful in that, if the output deviates too quickly from the setpoint value, the error derivative and, therefore, the
derivative action, can be significant.
This action is defined using the derivative constant K
Where T
is the value of the derivative time defined by one of the following parameters:
d
•
P20.07 (for the adjustment of direct expansion units with inverter compressor).
•
P20.23 (for humidifier adjustment).
•
P20.96 (for the adjustment of direct expansion units with compressors with delivery air adjustment active and Free
Cooling).
The T
time defines the projected time horizon: If too small, it will not have a good anticipatory effect; if too large, its forecast
d
may be completely wide of the mark.
The following table shows the reactions on the system caused by the increase of the derivative time and resulting increase of
the derivative constant.
Parameter
Constant
(Increases)
(Increases)
T
K
d
d
The derivative action can be disabled by setting the derivative time to 0.
19.1.4
The combined effect of the three actions
The control action of the system is, therefore, calculated, one moment at a time, as the sum of the three contributions
(Proportional, Integral and Derivative).
The Proportional Action represents the component most sensitive to the current value of the error:
•
High K
values entail a significant reaction also for slight error variations.
p
•
Reduced values transfer on the control variable limited variations also in case of significant errors.
The Integral action varies in a linear manner following the action of proportionality coefficient K
takes the past trend of the error into account:
•
Reduced T
values lend greater importance to past system history.
i
•
High values decrease the weight of the integral action by transferring to the control variable variations that are more
dependent on the current error value.
The Derivative action varies in a linear manner with the error derivative following the action of proportionality coefficient K
and, as mentioned before, takes the current trend of the error into account:
•
High T
values place greater importance on what may be the future trend of the error, with greater reliance on the
d
algorithm
•
Lower values transfer to the control variable variations that are less dependent on future trends.
The image below illustrates what has been said above:
Version 38
(also known as derivative gain) calculated with this formula:
d
��
��
Promptness
Overshoot
of response
Increases
Decreases
(slightly)
= ��
∗ ��
��
��
Balancing time
Decreases (slightly)
Error at full
Stability
power
Does not change
Improves
/T
and, as mentioned above,
p
i
*T
p
d
229
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