26 | BA-40400-02-V14
Two-Channel Controller TOPAX DE
8.3.2 Example of proportional range and reset time
Xp = 50 % (amplification = 2)
Tn = 3min
(sudden change of the actual value by 15%)
After a sudden deviation of the actual value from the setpoint of around
15% (X-W), the control variable Y changes by the same rate as the
control amplification, or twice as much as the Xp value, i.e. 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.
Control variable
Setpoint
Measuring range for free chlorine
1.00 mg/l
X (actual value)
0.15 mg/l
W (Setpoint)
0.30 mg/l
X - W
15 %
Xp (P-range)
50 %
Tn
3 minutes
Y (immediate power output of the controller)
30% through Xp
Y (output power of the automatic controller after
3 minutes)
60% through Tn
8.3.3
Derivative time Tv
(differential action of PID 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 control variable depends on the speed at which the nominal/
actual deviation takes place (i.e. not the actual deviation). The duration
of the correction is determined by the derivative time Tv. If the control
variable does not change, i.e. the speed of change is "0", the correction
factor and the time constants Tv caused by the differential proportion
drop to "0" (even if the actual value consistently deviates from the set-
point). The fact that the regulation leads the actual value to match with
the default one is caused mainly by the integrals portion of the auto-
matic controller. The differential proportion often improves the controller
result because it acts against the trend to deviate.
8.4 Calculation of setable values
In order for the controller to keep actual values of free chlorine and Ph
close to the setpoints within tight limits, e.g. for bathing, the control-
ler must be adjusted to the controlled system. This is achieved via the
control parameters Xp for the proportional area, Tn for the reset time of
the integral range and the derivative time Tv for the differential range.
These settings can be determined by recording the step response of the
controlled system. To do this the actuator must be changed suddenly
by hand from "CLOSED" (0 %) to "OPEN" (100 %) or for example from
30% to 50%.
The following formula can be used for calculating reference values:
Xp ~ 0.83 · ΔX / Δt · Tu
Tn ~ 3,3 · Tu
Variable
Description
Yh
Setting range (e.g. valve fully open or 100% dosing pump
supply)
Xmax
maximum value of the controller variable at 100 % dosing rate
ΔX / Δt
Gradient of the measured curve (see Fig.17)
to
Time of control variable Y change
Tu
lag time (s)
Vmax
maximum increase rate of the measured variable
Vmax
Xmax / Tg = ΔX / Δt
In order to meter chlorine gas, you need accounting for the speed of the
chlorine gas valve. The value of Xp is computed for a drive speed from
0 % through 100 % in 60 seconds. A slower operation would show the
same trend as a bigger proportional range Xp. In order to adjust this,
the Xp value must be first reduced at slower operation and vice versa.
The following formula can be used:
XP new = XP · 60 sec /Ty
Ty = Motor regulation time
As these are approximate values, changing the Xp value may after a cer-
tain time improve the control variable. If the control responds too slowly
or too fast, a smaller Xp and a smaller Tn would result in a faster control
behaviour and a larger Xp and/or Tn would result in slower behaviour.
t
Yh
(open) 100%
(closed) 0%
t
0
Fig.16: State of the control variable, e.g. opening of a valve or dosing rate of a
pump.
Here below, a diagram shows for the controlled variable X over the time
t:
t
X
X
t
0
max
t
X
Tu
Fig.17: Step response of a controller to a change in control variable Y.(X =
actual value; e.g. free chlorine or pH value)
The control parameters can be automatically entered in the TOPAX in
the respective items (see chapter “12.1.13 Menu 5: Service” on page
34).
