Industrial controllers , basic theory
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CONTROLLER RESPONSES
The first and most basic characteristic of the controller response has been
shown to be either direct or reverse action. Once this distinction has been
made, several types of responses are used to control a process. These are:
1. On/off control, or two position control
2. Proportional control
3. Integral (reset)
4. Derivative |
On/off control is illustrated in figure 5
for a reverse acting controller and an air-to-close valve. An on/off
controller only has two outputs, either full maximum or full minimum. For this
system it has been determined that when the measurement falls below the set
point, the valve must be closed to cause it to increase. Thus, whenever the
signal to the automatic controller is below the set point, the controller output
will be 100%. As the measurement crosses the set point the controller output
goes to 0%. This eventually causes the measurement to decrease and as the
measurement crosses the set point again, the output goes to maximum. This cycle
will continue indefinitely, because the controller cannot balance the supply
against the load. This continuous oscillation may, or may not, be acceptable
depending upon the amplitude and length of the cycle. Rapid cycling causes
frequent upsets to the plant supply system and excessive valve wear. The time of
each cycle depends on the dead time in the process because the dead time
determines how long it takes for the measurement signal to reverse its direction
once it crosses the set point and the output of the controller changes. The
amplitude of the signal depends on how rapidly the measurement signal changes
during each cycle. On large capacity process, such as temperature vats, the
large capacity causes a very long time constant. Therefore, the measurement can
change only very slowly.
The result is that the cycle occurs within a very narrow band around the set
point, and this control may be quite acceptable, if the cycle is not too rapid.
By far the most common type of control used in industry is on/off control.
However if the process measurement is more responsive to changes in the supply ,
the amplitude and frequency of the cycle begins to increase. At some point, this
cycle will become unacceptable and some form of proportional control must be
applied.
In order to study the remaining three modes of automatic control open loop
responses will be used. Open loop means that only the response of the controller
will be considered.
Figure 6 shows an automatic controller with an artificial signal from a
manual regulator introduced as the measurement. The set point is introduced
normally and the output is recorded. With this arrangement, the specific
controller responses to any desired change in measurement can be observed.
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Proportional action
Proportional response is the basis for the three mode controller. If the
other two, integral (reset) and derivative, are present, they are added to the
proportional response. "Proportional" means the that the present
change in the output of the controller is some multiple of the percent change in
the measurement
This multiple is called the "gain" of the controller. For some
controllers, proportional action is adjusted by such a "gain"
adjustment, while for others a "proportional band" adjustment is used.
Both have the same purposes and effect.
Figure 7 illustrates the response of a proportional controller
by an input/output pointer pivoting on one oil these positions. With the pivot
in the center between the input and the output graph, 100% change in measurement
is required to obtain 100% change in output, or full valve travel .A controller
adjusted to respond in this way is said to have a 100% proportional band. When
the pivot is moved to the right hand position, the measurement input would have
to change by 200% in order to obtain full output change from 0% to 100%, this is
called a 200% proportional band. Finally, if the pivot were in the left hand
position and if the measurement moved only over 50% of the scale the output
would change over 100% of the scale. This is called a 50% proportional band.
Thus, the smaller the proportional band, the smaller amount the measurement must
change to cause full valve travel. Or, in other words the smaller the
proportional band, the greater the output change for the same size measurement
change. This same relationship is represented by figure 8.
This graph shows how the controller output will respond as a measurement
deviates from set point. Each line on the graph represents a particular
adjustment of the proportional band. Two basic properties of proportional
control can be observed from this graph:
1. For every value of proportional band whenever the measurement
equals the set point, the output is 50%.
2. Each value of the proportional band defines a unique relationship between
measurement and output. For every measurement value there is a specific output
value. For example; using the 100% proportional band line , whenever the
measurement is 25% above the set point, the output from the controller must be
25%. The output from the controller can be 25% only if the measurement is 25%
above setpoint. In the same way, whenever the output from the controller is 25%,
the measurement will be 25% above set point. In other words there is one
specific output value for every measurement value.
For any process control loop only one value of the proportional band is the
best. As the proportional band is reduced, the controller response to any change
in measurement becomes greater and greater. At some point depending upon the
characteristic of each particular process, the response in the controller will
be large enough to drive the measurement back in the opposite direction so far
as to cause constant cycling the measurement. This proportional band value,
known as the ultimate proportional band, is a limit on the adjustment of the
controller in that loop. On the other hand, if too wide a proportional band is
used, the controller response to any change in measurement is too small and the
measurement is not controlled as tightly as possible. The determination of the
proper proportional band for any application is part of the tuning procedure for
that loop. Proper adjustment of the proportional band can be observed by the
response of the measurement to an upset.
Figure 9 shows several examples of varying proportional band for the heat
exchanger.
Ideally, the proper proportional band will produce quarter amplitude damping
in which each half cycle is 1/2 the amplitude of the previous half cycle. The
proportional band which will cause one quarter wave damping will be smaller,
thereby yielding tighter control over the measured variable, as the dead time in
the process decreases and the capacity increases.
One consequence of the application of proportional control to the basic
control loop is offset. Offset means that the controller will maintain the
measurement at a value different from the set point. This is most easily seen by
referring to figure 3. Note that if the load valve is opened, flow will increase
through the valve and the level will begin to fall. In order to maintain the
level, the supply valve would have to open. But note that because of the
proportional action of the linkage the increased open position can only be
achieved at a lowered level. In other words, in order to restore the balance
between the flow in and the flow out, the level must stabilize at a value below
the set point. This difference, which will be maintained by the control loop, is
called offset, and is characteristic of the application of proportional-only
control feedback loops. The acceptability of proportional-only control depends
on whether or not this offset can be tolerated. Since the error necessary to
produce any output decreases with proportional band, the narrower the
proportional band, the less the offset will be. For large capacity, small dead
time applications accepting a very narrow proportional band, proportional-only
control will probably be satisfactory since the measurement will remain within a
small percentage band around the set point.
If it is essential that there be no steady state difference between
measurement and set point under all load conditions, an additional function must
be added to the controller.
