Jesco EASYPOOL SMART 02, Руководство по эксплуатации

Страница: 23 / 44

EASYPOOL SMART 0 Operating Manual | 3
Controller
4.8.2 Proportional integral (differential) controller, PI(D)
controller
Reset time Tn
(integral effect of PI 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 of proportional range and reset time
Xp = 50 % (amplification = )
Tn = 3 min
(sudden change of the actual value by 15%)
After a sudden deviation of the actual value from the default val-
ue 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 pattern, the control variable continues to
increase provided the (X-W) deviation remains, and after a time
Tn = 3 minutes reaches again 30% of the control variable.
Control variable Set value
Measuring range for free chlorine 1.00 mg/l
X (actual value) 0.15 mg/l
Set point (W) 0.30 mg/l
X - W 15 %
Xp (P-range) 50 %
Tn 3 minutes
Y (Immediate power output of the automatic
controller) 30 % by Xp
Y (output power of the controller after 3 minutes) 60 % through Tn
Derivative time Tv
(differential effect of PID controller)
With the 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 control causes the actual value
to match the default one is caused mainly by the integral por-
tion of the automatic controller. The differential rate often helps
implementing the controller result because it acts against the
trend to deviate.
4.8.3 Calculating the control parameters
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 controlled
system. This is done via the control parameters Xp for the pro-
portional area, Tn for the reset time of the integral range and the
reproaching time Tv for the differential range.
The determination 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
"CLOSE" (0 %) to "OPEN" (100 %) or e.g. from 30 % to 50 %.
The following formula can be used for calculating reference val-
ues:
Xp ≈ 0.83 · ΔX / Δt · Tu
Tn ≈ 3.3 · Tu
Variable Description
Yh setting range (e.g. valve fully up or 100% of the dosing pump
delivery)
Xmax maximum control variable at 100% dosing rate
ΔX / Δt Gradient of the measured curve (see Fig. 4.8.3.)
to Time of change of control variable Y
Tu lag time (s)
As we are dealing here with approximate values, a certain im-
provement of the controlled variable can sometimes be obtained
by changing the Xp value after certain time. If the regulation
should react too slowly or on the contrary too fast, smaller Xp and
smaller Tn would result into a faster automatic controller action
and in a larger Xp and/or Tn slower-acting settings.
t
Yh
100%
0%
t
0
Fig. 4.8.3.1.: Status of the control variable, e.g. valve opening (0% = closed,
100% = open) or dosing rate of a dosing pump.
The following diagram shows the control variable X over time t
(see Fig. 4.8.3.):
t
X
X
t
0
max
t
X
Tu
Fig. 4.8.3..: Step response of a controller to a change in control variable Y.
(X = actual value; e.g. free chlorine or pH value)