BA-40100-0-V04 | Maintenance Instructions TOPAX DX | 5
Chapter 8: Controller
8. Controller
Definitions
Definitions
Actual value (X)
The actual value of X of the measured value for
the respective sensor is constantly indicated.
Default value (W)
The desired value W of a regulation is the value,
which the automatic controller compensates to
keep the process constant.
System deviation (X-W)
The offset X-W arises, if the actual value of X of
the measured variable deviates from the adjusted
default value W. The variable Y results from the
offset and the adjusted control parameters.
Actuating variable (Y)
The correcting variable Y of a regulation is the
value that the automatic controller, accordingly to
its adjusted parameters and the offset (X-W), de-
livers to the actuators (between 0% and 100 %).
8.1 P-controller
Proportional range Xp
(Proportional effect or amplification of the Controller)
The proportional range Xp (p-range) of a proportional controller
indicates by which value the measured variable X must devi-
ate from the default value W, so that the correcting variable is
Y = 100%. If the offset is smaller, then the correcting variable
is proportionally likewise smaller. The correcting variable Y of a
proportional action controller is affected proportionally only by
the offset (X - W). The P - Range is indicated in “%” and always
refers to the measuring range final value. The proportional range
is thus an indirect measure of the controller amplification KR:
K
R
= 100% / Xp %
With a Xp range of 50% the controller amplification is :
100 /50 = -> Controller amplification K
R
=
Xp = 50% means that the disturbance factor Y changes around
100% when the actual value deviates by 50% from the default
value (related to the measuring range final value).
8.2 PI or PID controller
Reset time Tn
(integrals effect)of the PI-automatic controller)
The integral time of a PI- or PID-automatic controller is called
reset time Tn. The integral time is the time required by the ma-
nipulated variable Y in the case of a constant deviation between
default and actual values in order to reach the same change
of the output signal, which is immediately produced by the p-
rate after the jump of the deviation between default and actual
values.
Example:
Xp = 50% (amplification = )
Tn = 3min
(sudden change of the actual value by 15%)
After a sudden deviation of the actual value from the default
value by around 15% (X-to-W), the correcting variable Y changes
by the same rate as the controller amplification, that is twice the
Xp value or by 30%.
Because of the integral behaviour, the manipulated variable
continues to increase as long as the X-to-W deviation remains
present and after a time Tn = 3 minutes reaches once again
30% of correction variable increase.
Correction variable
Value
Measuring range for free chlorine
1,00 mg/l
X (Actual value)
0,15 mg/l
W (Default value)
0,30 mg/l
X - W
15 %
Xp (P-Rate)
50 %
Tn
3 minutes
Y (Immediate power output of the automatic
controller)
30 % through Xp
Y (power output of the automatic controller after
3 minutes)
60 % through Tn
Reproaching time Tv
(differentials effect of the PID automatic controller)
By a differential function a correction factor is entered in the
controlled system when the controlled variable begins to differ
from the default value. The correcting variable depends on the
speed by which the default-to-actual deviation takes place (thus
not the actual deviation). The duration of the correction factor is
determined by the reproaching time Tv. If the controlled variable
does not change, thus the rate of change is “0”, the correction
factor and the time constants Tv caused by the differential rate
drop to “0” (even if the actual value keep deviating away from the
default one). The fact that the regulation leads the actual value to
match with the default one is caused mainly by the integrals por-
tion of the automatic controller. The differential rate often helps
implementing the controller result because it acts against the
trend to deviate.
8.3 Calculation of the setting values
In order for the controller to process actual values of free chlorine
and Ph even in the presence of very slight deviations (almost
close to the default values), it must be adjusted to the control-
led system. This is done via the control parameters Xp for the
proportional area, Tn for the reset time of the integral range and
the reproaching time Tv for the differential range. The determina-
tion of these settings can take place by means of taking up the
step response of the controlled system. In addition the control
members must suddenly and manually change from TO (0%) to
ON (100%) or e.g. from 30% to 50%
All values for the computation of the adjusting parameters can
be obtained.
