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10. Principles of regulatory function
Freely selectable control functions mean that the
®
Conex
DIS-C controller can be adapted to a wide
variety of closed-loop control systems.
10.1 Regulatory behaviour
10.1.1 P regulation behaviour
The P controller has a static characteristic curve.
The characteristic proportional band for the P
controller is Xp. Within this range, which is limited to
a maximum or minimum depending on the control
direction, there is a proportional correlation between
the input and output quantities of the controller.
The lower limit is the response threshold of the
controller. This is the smallest regulatory deviation
that leads to a measurable control variable.
The upper limit separates the proportional band from
saturation. Above this limit, no further increase in
output signal is possible, regardless of increases in
the input signal. This range is called the control
range of the controller, and the control variable can
have any value within this range.
Due to the static characteristic curve, the P controller
cannot reach the setpoint in a stationary state.
This results in a consistent regulatory deviation,
which can be reduced by decreasing Xp, but which
cannot be completely eliminated using a P controller.
The controller reacts quicker with small Xp values.
The Xp value cannot, however, be reduced
arbitrarily, as this causes the controller to become
unstable.
10.1.2 I regulation behaviour
The non-delayed relationship between the regulatory
deviation and the control variable in a P controller
results in an undesirable persistent regulatory
deviation. However, if the regulatory deviation is
controlled directly by the regulating speed instead of
the control variable, this fixed assignment of the two
variables no longer applies. The result is an
integrated controller.
With a regulatory deviation of zero, i.e. when the
setpoint is equal to the actual value, the regulating
speed is also zero. Both positive and negative
regulatory deviations can be influenced by positive
or negative regulating speeds. The control variable
covers the whole control range. The control range of
the I controller is the range in which the regulatory
deviation controls the regulating speed in a linear
fashion.
The characteristic value of the I controller is the reset
time Tn. The reset time is the time that must elapse,
due to the integrated mode of action, for the step
response to reach the value that a P controller would
reach immediately.
16
The control circuit reacts slowly. If a regulatory
deviation results, an I controller can only react by
constantly changing its control variable. For this
reason, regulation with I controllers is always slower
than with controllers that act proportionally. If the
speed of the controller is increased by decreasing
the integration constant, the control circuit has a
slight tendency towards instability.
At Tn = 0, the controller has no I proportion.
In the absence of external influences, a control
circuit with an I controller therefore has no residual
regulatory deviation in a stationary state when the
control variable is constant.
10.2 Limit values
Note
Setting for a limit value: Xp = O.
In principle, the limit value only has two switching
states; ON and OFF. Depending on the set control
direction, the controller is deactivated when the
setpoint value is exceeded, or when the value drops
below the setpoint.
10.2.1 Limit values with hysteresis
To prevent constant switching when the setpoint
value is reached, it is possible to specify a hysteresis
for the controller.
Example:
setpoint 600 μS/cm
•
hysteresis 10 μS/cm.
•
The hysteresis band is arranged symmetrically
around the switching point.
•
Switch-off point = measured value + hysteresis / 2
•
Switch-on point = measured value - hysteresis / 2.
μS/cm
605 μS/cm
605
µS/cm
600 μS/cm
600
µS/cm
595 μS/cm
595
µS/cm
Relay
1
0
Limit values with hysteresis
Fig. 12
t
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