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Back to [Frequently
Asked Questions]
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FAQs:
Control Engineering |
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For additional details, request the book: "Control
Engineering."
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What
is meant by proportional band (Xp1, Xp2)?
In a purely
proportional controller (P controller) the manipulating
variable (controller output Y) is proportional to the
control deviation within the proportional band (Xp). The
gain of the controller can be matched to the process by
altering the proportional band. If a narrow proportional
band is chosen, a small deviation is sufficient to achieve a
100 % output, i.e. the gain increases as the proportional
band (Xp) is reduced. The reaction of the controller to a
narrow proportional band is faster and more pronounced. A
proportional band that is too narrow will cause the control
loop to oscillate. Any alteration of the proportional band
will also affect the I and D action of a PID controller to
the same extent.
If the proportional band is set to zero, the controller
action is ineffective. This means that the controller
operates solely as a limit contact. The selected hysteresis
or switching differential is effective, the settings for the
derivative time and the reset time, however, are not taken
into account.
For all controller types, except for the 3-state (double-setpoint)
controller, only the proportional band Xp1 is relevant. With
3-state controllers only, separate settings for the
proportional band (for both operating senses) are necessary
(e. g. Xp1 for heating and Xp2 for cooling).
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What
is meant by derivative time?
The intensity of
the D component (differential component) can be set via the
derivative time. The D component of a controller with PID or
PD action reacts to the rate of change of the process value.
When the setpoint is approached, the D component acts as a
brake, thereby preventing the control variable from
overshooting the setpoint.
Basically, the D component has the following effects:
As soon as the control variable changes, the D component
reacts against this change.
For a controller with an inverse operating sense (i.e. for
heating) this would mean, for example:
-
if
the control variable decreases as a result of a
disturbance in the process, the D component forms a
positive manipulating variable, which counteracts the
reduction in control variable.
-
if
the control variable increases as a result of a
disturbance in the process, the D component forms a
negative manipulating variable, which counteracts the
increase in control variable.
The damping action increases with the size of the
setting for the derivative time (value in seconds).
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What
is meant by reset time?
The
I component of the controller output signal has the effect
of continuously altering the manipulating variable, until
the process value has reached the setpoint.
As long as the control deviation is present, the
manipulating variable is integrated upwards or downwards.
The longer the control deviation continues to be present in
a controller, the larger the integral effect on the
manipulating variable. The larger the control deviation and
the smaller the reset time, the more pronounced (faster) the
effect of the I component.
The I component ensures stabilization of the control loop
without permanent control deviation. The reset time is a
measure of the effect the control deviation duration has on
the control action. A larger reset time means that the
I component is less effective and vice versa. Within the
specified time Tn (in sec.), the change in the manipulating
variable that is produced by the P component (xp or pb), is
added once more. Accordingly, there is a fixed relationship
between the P and the I component. A change in the P
component (xp) also means a changed time response, at a
constant value for Tn.
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What
is meant by switching differential/hysteresis?
The switching differential is also referred to as
hysteresis and is only relevant for switching controllers
with proportional band = 0.
For controllers with inverse operating sense (e.g. heating
control), the standard response is as follows:
The switching differential lies below the setpoint. This
means that the controller switches off precisely then when
the setpoint is exceeded. It only switches on again when the
process value has fallen below the switch-on point, which
lies below the setpoint by the amount of the switching
differential.
On controllers with direct operating sense (e. g. cooling),
the switching differential normally lies above the setpoint.
As for controllers with inverse operating sense, the
switch-off point is precisely at the setpoint. However, it
is switched on again above the setpoint, shifted by the
amount of the switching differential.
Switching action of a 2-state controller with inverse
operating sense:
Switching
action of a discontinuous 3-state controller:
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What
is meant by contact spacing?
If
the process variable varies within a fixed interval about
the setpoint - the contact spacing Xsh - then neither of the
outputs is active. Exception: 3-state controllers with I and
D components. Within the contact spacing, only the
proportional component is inactive.
This contact spacing is necessary to prevent continual
switching between the two manipulating variables, e.g.
heating and cooling registers, when the control variable is
unsteady. The contact spacing is also commonly called the
dead band. Too small a dead band can lead to a pointless
waste of energy in a plant.
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What
is meant by cycle time (Cy)?
The
switching cycle time is quoted in seconds and defines the
period during which a full switching cycle consisting of
switch-on and switch-off times takes place.
Generally,
the cycle time should be selected so that the actual control
process can still be smoothed out. At the same time, the
switching frequency must always be taken into account.
The response can best be reset in manual mode so that the
direct influence of the manipulating variable on the cycle
time can be monitored. With a manipulating variable of 50 %,
"Ton" and "Toff" are equal. If the
manipulating variable is altered, this ratio alters
accordingly.
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What
is meant by actuator stroke time (tt)?
The actuator
stroke time is a variable provided by the actuator drive and
is therefore only relevant for modulating controllers or
proportional (continuous) controllers with integral actuator
driver.
The time that the actuator drive takes to travel once across
the full usable manipulation range is set under actuator
stroke time.
The actuator stroke time cannot be determined by
self-optimization (auto-tuning). It must always be set before
the optimization.
The actuator stroke time provides the controller with
information about the effect of the actuating pulses. At an
actuator stroke time of 20 seconds, for example, the
percentage change in manipulating variable, at the same
actuating pulse, is significantly larger than for an
actuator with 100 seconds stroke time, for example.
When selecting or dimensioning actuator drives, it must be
taken into account that a short stroke time of, say, less
than 10 seconds will result in large steps of the
manipulating variable, and consequently to a reduced control
accuracy. If, for example, we assume that 0.5 seconds is the
shortest actuating pulse time, a stroke time of 10 seconds
would result in only 20 actuating steps. This would mean
that the manipulating variable can only be changed in 5 %
steps.
Actuator drives with a very long stroke time can, however,
be disadvantageous as far as the dynamics is concerned,
because the manipulating variable can only be changed
relatively slowly by the control action. In actual
operation, however, problems arising from stroke times that
are too short occur more frequently than those caused by
stroke times that are too long.
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What
is meant by digital input filter (dF)?
The
digital input filter (dF) serves to dampen the input signals
and affects both indication and controller. The larger the
value for "dF", the larger the damping of the
input signal. An extremely high or low value can have a
negative influence on the control quality. In most cases,
the default setting for "dF" can be used for
operation.
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Why
is a 3-state controller unsuitable for actuator drives?
The modulating
controller, like the 3-state controller, has two switching
control outputs, which are, however, designed especially for
motorized actuator drives, e.g. for opening or closing. If a
continuous output signal is required for the 3-state
controller in order to maintain a certain output level, we
can see that, in the case of the modulating controller, the
electrical actuator drive will remain in the position
reached when there is no further signal from the controller.
Accordingly, the actuator drive can remain 60 % open, for
example, although it is not operated by the controller at
this instant.
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General
note on optimization
Controller
optimization (or tuning) is the adjustment of the controller
to a given process or control loop. The control parameters
have to be selected such that the most favorable response of
the control loop is achieved under the given operating
conditions. However, this optimum response can be defined in
different ways, such as reaching the setpoint quickly, with
a small overshoot, or a somewhat longer stabilization time
with no overshoot. If all that is expected of the controller
is a response such as for a limit contact (without pulsed
operation), there is no need to find the optimum settings
for proportional band, derivative time or reset time. Only
the switching differential has to be predefined.
In most cases, the controller can itself determine the
control parameters through the self-optimization
(auto-tuning)
facility, if the process permits self-optimization.
Alternatively, the optimum parameter setting can be
determined "manually", through experiments and
empirical equations (see formulae in the appendix).
When controllers are swapped, or with identical control
installations, control parameters can also be directly
accepted or entered.
After a manual parameter setting, auto-tuning may no longer
be started, since this would overwrite the settings.
Formulae
for setting according to the oscillation method:
| Controller
action |
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| P |
XP
= XPk / 0,5 |
| PI |
XP
= XPk / 0,45
TP = 0,85 ·TK |
| PID |
XP
= XPk / 0,6
Tn = 0,5 · TK
Tv = 0,12 · TK |
Formulae
for setting according to the step response:
| Controller
action |
Control
loop |
Error |
| P |
XP
= 3,3 · KS · (Tu/Tg)
· 100 % |
XP
= 3,3 · KS · (Tu/Tg)
· 100 % |
| PI |
XP
= 2,86 · KS · (Tu/Tg)
· 100 %
Tn = 1,2 · Tg |
XP
= 1,66 · KS · (Tu/Tg)
· 100 %
Tn = 4 · Tu |
| PID |
XP
= 1,66 · KS · (Tu/Tg)
· 100 %
Tn = 1 · Tg
Tv = 0,5 · Tu |
XP
= 1,05 · KS · (Tu/Tg)
· 100 %
Tn = 2,4 · Tu
Tv = 0,42 · Tu |
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Controller
characteristic/operating sense (definitions/selection
criteria)
inverse:
The controller output Y is larger than 0, or the relay is
energized, when the process value is smaller than the
setpoint (e. g. heating).
direct:
The controller output Y is larger than 0, or the relay is
energized, when the process value is larger than the
setpoint (e. g. cooling).
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What
is meant by 2-state controller?
The
2-state controller (ON/OFF controller) switches the output
when the setpoint is reached. If the value falls below the
setpoint by a certain adjustable tolerance (xsd, switching
differential, hysteresis), then the output is switched on
again. It therefore only has two switching states. It is
used in temperature control applications where the heating
or cooling is only switched on or off.
A 2-state controller with dynamics can, however, also
operate with a P, I, or D component.
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What
is meant by 3-state controller?
3-state
controllers have two outputs which may be either switching
or continuous (relay contact or e.g. 4 - 20 mA). 3-state
controllers are used if the control variable has to be or
can be influenced through two actuators with opposing
action.
This may be a climatic cabinet with a thyristor power unit
for the electric heating and a solenoid valve for cooling.
In this example, a 3-state controller with a continuous
(analog) output for the heating function (controller output
1) and a switching output for the cooling function
(controller output 2) would be the best choice.
On 3-state controllers, the parameters proportional band,
reset time, derivative time and hysteresis, familiar from
2-state controllers, can often be set separately for both
operating senses. The 3-state controller additionally
features the parameter contact spacing.
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What
is meant by modulating controller?
Modulating
controllers have two switching outputs and are especially
designed for operating actuator drives which can, for
instance, open or close a flap valve.
Actuators/actuator drives that can be operated:
AC motor actuators, DC motors, 3-phase motor actuators,
hydraulic cylinders with solenoid valves etc.
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What
is meant by proportional controller with integral actuator
driver?
The
short form "actuating controller" is used to
describe a "proportional controller with integral
actuator driver". In contrast to the modulating
controller, an actuator feedback signal is essential for the
actuating controller.
The actuating controller controls the clockwise or
anticlockwise movement of the motorized actuator via 2
switching outputs.
The position of the motorized actuator is registered and
compared with the manipulating variable (yR) of the
proportional controller.
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| What
is meant by cascade control? |
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Cascade
control can significantly improve the control quality. This
applies in particular to the dynamic action of the control
loop, in other words, the transition of the process variable
following setpoint changes or disturbances.
Example
1: schematic construction of a cascade
Chocolate has to be heated to vs = 40 °C for
processing. The chocolate temperature must nowhere exceed 50
°C (even close to the heater). It is therefore heated on a
water bath.
Cascade control is used in order to achieve rapid
stabilization.
Controller 1 is always the master controller, controller 2
always the slave.
The setpoint for the slave controller is produced by output
conversion. The control output y1 is converted to a
setpoint using the unit of the process value x2
(here: 0 - 100 % = 0 - 50 °C).
| List
of symbols |
| C1 |
-
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Controller
1 |
| C2 |
-
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Controller
2 |
| I1 |
-
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Analogue
input 1 |
| I2 |
-
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Analogue
input 2 |
| O2 |
-
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Output
2 |
| w1 |
-
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Setpoint
controller 1 |
| w2 |
-
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Setpoint
controller 2 |
| x1 |
-
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Process
value controller 1 |
| x2 |
-
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Process
value controller 2 |
| xw1 |
-
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Deviation
controller 1 |
| xw2 |
-
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Deviation
controller 2 |
| y1 |
-
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Control
output 1 |
| y2 |
-
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Control
output 2; output 1 of controller 2 |
| vs |
-
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Chocolate
temperature |
| vw |
-
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Water
bath temperature |
Example 2: construction of a trimming cascade
Two
charges of chocolate have to be heated to 40 °C and 50 °C.
The chocolate temperature must nowhere (not even close to a
heater) exceed the setpoint by more than 10 °C. It is
therefore heated on a water bath.
Trim cascade control is used to achieve rapid stabilization
without overshoot and without altering the controller
configuration (output conversion) at a change of setpoint
(batch change).
Controller 1 is always the master controller, controller 2
always the slave controller.
The setpoint for the slave controller is produced by output
conversion and the addition of the master controller setpoint
(w1).
In setpoint conversion, the control output y1 is
converted to a value with the unit of the process value w2.
It corresponds to the maximum permitted temperature difference
(± | x1 - w1
|; here: 0 - 100 % = -10 to +10 °C).
| List
of symbols |
| C1 |
-
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Controller
1 |
| C2 |
-
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Controller
2 |
| I1 |
-
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Analogue
input 1 |
| I2 |
-
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Analogue
input 2 |
| O2 |
-
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Output
2 |
| w1 |
-
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Setpoint
controller 1 |
| x1 |
-
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Process
value controller 1 |
| x2 |
-
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Process
value controller 2 |
| xw1 |
-
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Deviation
controller 1 |
| xw2 |
-
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Deviation
controller 2 |
| y1 |
-
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Control
output 1 |
| y2 |
-
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Control
output 2; output 1 o controller 2 |
| Yn |
-
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Converted
control output 1 |
| vs |
-
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Chocolate
temperature |
| vw |
-
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Water
bath temperature |
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