Note: Descriptions are shown in the official language in which they were submitted.
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Method of And System For Controlling The Ratio of A Variable Lead Parameter
And
An Adjustable Lag Parameter For A Lag-lead Process
The present invention relates to a method of and system for controlling the
ratio of a variable
lead parameter and an adjustable lag parameter for a lag-lead process and
particularly, but
not exclusively, to apparatus for controlling the aix/gas ratio iri a~gas
combustion plant.
It is known that the air/gas ratio (AGR) in a gas combustion plant should be
maintained
substantially constant to achieve optimum combustion efficiency of the plant.
Air/gas ratio
controllers are used in the plant to maintain the air/gas ratio when the gas
flow rate is
increased or decreased. To achieve this, the air/gas ratio controller monitors
the gas flow rate
and adjusts the air flow rate accordingly, usually by adjusting a valve in an
air supply line.
A problem with existing air/gas ratio control is the difficulty in adjusting
the air flow rate to
match accurately the gas flow rate. The present invention aims to provide an
improved
method and system for air/gas ratio control.
Accordingly, the present invention provides a method of controlling the ratio
of a variable
lead parameter and an adjustable lag parameter for a lag-lead process, the
method
comprising: monitoring said lead parameter and providing a lead signal
representative of the
value of said lead parameter; monitoring said lag parameter and providing a
lag signal
representative of the value of said lag parameter; comparing said lead and lag
signals and
providing an error signal representative of the deviation of the ratio of said
lead and lag
parameters from apreselected ratio; and adjusting said lag parameter to reduce
said deviation
in response to said deviation exceeding a preselected deviation.
In a preferred form of the invention said error signal is compared with a
preselected threshold
value and said lag parameter is adjusted in response to said error signal
exceeding said
preselected threshold value. Advantageously, the error signal is compared with
an error
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range defined by a first, upper preselected threshold value and a second,
lower preselected
threshold value and said lag parameter is adjusted in response to said error
signal falling
outside said error range.
The present invention also provides a control system for providing lag-lead
control of a
process having a variable lead parameter and an adjustable lag parameter, the
system
comprising: lead monitoring means for monitoring said lead parameter and
providing a lead
signal representative of the value of said lead parameter; lag monitoring
means for
monitoring said lag parameter and providing a lag signal representative of the
value of said
lag parameter; comparator means for comparing said lead and lag signals and
providing an
error signal representative of the deviation of the ratio of said lead and lag
parameters from
a preselected ratio; and adjusting means for adjusting said lag parameter to
reduce said
deviation in response to said deviation exceeding a preselected deviation.
Advantageously, the system fwther comprises threshold value means for
providing a
preselectable threshold value and comparator means for comparing said error
signal with said
preselectable threshold value. The adjusting means is operable to adjust said
lag parameter
in response to said error signal exceeding said preselectable threshold value.
Preferably, said threshold value means comprises a first, upper threshold
value means for
providing a first, upper preselected threshold value and a second, lower
threshold value
means for providing a second, lower preselectable threshold value, thereby to
define an error
range; said compaxator means is operable to compare said~error signal with
said upper and
lower preselectable threshold values; and said adjusting means is operable to
adjust said lag
parameter in response to said error signal falling outside said error range.
The present invention will now be described, by way of example only, with
reference to the
accompanying drawings in which:
Figure 1 is a schematic block diagram showing a typical gas combustion plant;
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Figure 2 is a schematic block diagram of an air/gas ratio controller used in
the plant of Figure
1;
Figure 3 is a schematic block diagram of a control system having a preferred
form of air/gas
ratio controller according to one aspect of the present invention;
Figure 4 is a schematic block diagram of a preferred form of air/gas ratio
controller according
to another aspect of the present invention;
Figure 5 is a schematic~block diagram of a modification to the controller of
fig. 4;
Figure 6 is a graph showing the change in valve position with applied control
voltage;
Figure 7 is a graph showing the derivative of the valve characteristic of
Figure,6; and
Figure 8 is a graph showing the relationship between the valve derivative and
total deadband
value.
A typical gas combustion plant 10 is shown in Figure 1. The plant 10 consists
of three main
parts, a temperature controller 12, an air/gas ratio control system 20 and a
burner 40 within,
for example, a kiln or furnace 41.
The temperature controller 12 is able to control the temperature of the
furnace 41, either by
following a predetermined temperature profile or by allowing a user to define
the desired
temperature profile. To increase the temperature of the fiunace, for example,
the controller
12 adjusts the valve in the gas supply line to increase the flow rate of the
gas supplied to the
burner and the air/gas ratio control system 20 adjusts the air flow rate to
attempt to maintain
the ratio between the flow rates of the air and the gas supplied to the burner
substantially
constant. A typical configuration for an air/gas ratio control system is shown
in Figure 2.
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The system 20 includes a gas valve 22 connected to the gas supply line 24 for
varying the gas
flow rate along the line. A gas flow measurement sensor 26 is positioned
downstream of the
gas valve 22 for monitoring the gas flow rate along the line. Similarly, an
air valve 28 is
positioned at a point in the air supply line 30 for varying the air flow rate
along the line and
an air flow measurement sensor 32 is positioned downstream of the air valve 28
for
monitoring the air flow rate along the air line. -
The gas valve 22 is connected to receive an input signal from the temperature
controller 12
to adjust the flow rate of the gas: The air valve 28 is connected to receive
an input from an
air/gas ratio controller 34 to adjust the flow rate of the air in dependence
on the gas flow rate.
The air/gas ratio controller 34 receives an input from both of the gas and air
measurement
sensors 26, 32 and compares the flow rates of the gas and the air and adjusts
the air valve to
maintain the required air/gas ratio.
It can be seen that if the combustion process is to function with the maximum
possible
efficiency, the air/gas ratio controller 34 must control the air valve to
follow changes in the
gas valve as closely as possible.
Such a system is commonly l~nown as a lag-lead system. In a lag-lead system
when a lead
parameter (the gas flow rate) varies, a lag parameter (in this case the air
flow rate) is adjusted
to maintain the ratio of the parameters substantially constant.
The flow rate of the air and the gas axe monitored by the measurement sensors
of the air/gas
ratio control system 20. These preferably sample the flow rate at a
predetermined samplilig
rate. The lead parameter (here the gas flow rate) and the lag parameter (here
the air flow
rate) are sampled at regular time intervals. The lead parameter is sampled
usually at a faster
rate than the lag parameter and can be sampled as fast as once every 20ms. The
sample rate
of the lag parameter would be adjusted to suit the lead parameter sample rate
and in tlus
instance would be typically once every 120ms. A typical sample range for the
lag parameter
would be between 100ms and SOOms. In a natural gas combustion system the
air/gas ratio
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is typically required to be maintained in the order of 10:1, known as the
stoichiometric/gas
ratio. Changes in the temperature reference signal result in the gas valve
being adjusted by
the temperature controller 12. This changes the gas flow rate and thus the
air/gas ratio from
the desired value. This change in the gas flow rate is monitored by the
controller 34 which
acts to~adjust the air valve 28 to return the air/gas ratio to the desired
value.
If a change in the air/gas ratio is detected (i.e. the a3r/gas ratio moves
away from the desired
value) by the air/gas ratio controller during a particular sampling of the air
and gas flow the
controller will move the air valve in the required direction (either towards
its fully open or
fully closed position) until the next sample is taken.
However, if the error in the air/gas ratio is smaller than the change in the
air/gas ratio effected
by the air valve movement over one sample interval (the period between one
sample time and
the next) the valve will overshoot the desired position and the desired air
flow rate will not
be achieved. At the next sampling, the controller 34 will detect a reverse
error and will move
the valve in the opposite direction i.e. it will move the valve towards its
closed position if the
previous error caused the valve to be moved towards its open position, and
vice versa.
Again, the valve will be moved too far in the reverse direction during the
sample interval and
will stop at or close to its initial position i.e. the position from which it
was first moved in
response to the originally monitored error in the air/gas ratio. This opening
and closing of
the valve, known as hunting, will repeat for as long as the error in the
air/gas ratio remains
substantially the same as or smaller than the change effected by movement of
the air valve
over one sampling interval. The air valve and consequently the air flow rate
will thus
oscillate about the level required to achieve the desired air/gas ratio. These
oscillations are
known as limit cycles.
It can be seen that if the error in the air/gas ratio exceeds a particular
threshold level (being
defined by the change in the air/gas ratio effected by the air valve movement
over one sample
interval) then no limit cycling will occur. However, if the error lies below
the threshold level
then limit cycling will occur. For valves with linear characteristics i.e.
wluch exhibit a linear
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response, the threshold level is constant throughout the valve's operating
range. However,
many electromagnetically operated valves exhibit a non-linear response where
the air flow
rate through the valve varies non-linearly in relation to the applied control
signal. Thus, the
change in the air flow through the valve during movement of the valve towards
its fully open
or fully closed position over a single sample interval will be different
depending on the
position of the valve within its operating range (Figure 6). Consequently, the
threshold level
defining the area value below which limit cycling occurs will vary over the
operating range
of the valve.
Since the motor driving the valve acts as an integrator, the change in flow
over one sampling
interval can be found by differentiating the valve characteristic (Figure 7).
The differential
curve of the valve characteristic shows how much the valve moves (and thus by
how much
the air flow rate will alter) during one sample interval, depending on the
initial position of
the valve in the valve operating range. Since errors in the air/gas ratio can
have negative as
well as positive values, it is necessary to establish both positive and
negative derivative
curves centred around a zero value in order to establish the threshold level.
As shown in
Figure 8, this effectively produces an "error envelope" within which limit
cycling occurs
(Figure 8). Thus limit cycling will occur where:
E(Ts, u) ~ ~ I s(tt) I .........................................(1)
where:
8(u) is the derivative of the valve characteristic at any given valve position
(u) and
2*8(u) represents the deadband value;
Ts is the sample time; and
a is the valve position.
Conversely, limit cycling will not occur where:
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E(Ts, u) ~ Z ~ S~u~ I ........................................~2~
In order to reduce or substantially eliminate limit cycling in the air/gas
ratio controller, it is
therefore desirable to ensure that the air valve is not adjusted when the
error lies within the
error envelope of the valve. In other words when equation 1 applies. In a
preferred form of
the invention, this is achieved by implementing a so-called "deadband" as
described below.
Fig. 3 is a schematic block diagram of part of a control system 90 having a
preferred form
of air/gas ratio controller 100. The controller 100 has a first comparator 102
which is
connected to receive two input signals, the first from the gas flow sensor 26
being connected
to a non-inverting input of the comparator 102 and the second from the air
flow sensor 32
connected to an inverting input. An output of the first comparator 102 is
connected firstly
to a non-inverting input of a second comparator 104 and secondly to an
inverting input of a
third comparator 106.
Positive and negative fixed threshold value circuits 108, 110; the purpose of
which is
described below, are connected to non-inverting and inverting inputs of the
second acid third
comparators 104, 106 respectively. An output of each of the second and third
comparators
104, 106 is connected to a respective operational amplifier 112, 114. An
output of each
operational amplifier is connected to a respective relay 116, 118 which
actuate movement
of the air valve 28.
During operation of the combustion plant 10, the flow rates of the gas and the
air supplied
to the burner 40 are measured by the flow sensors 26, 32 each of which
generates a signal S~,
Sa corresponding to the respective flow rate and sends the signal to the
air/gas ratio controller
'100.
The gas flow signal Sg and the air flow signal Sa are fed to the first
comparator 102, the gas
flow signal Sg to the non-inverting input and the air flow signal Sa to the
inverting input. The
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comparator 102 compares the two signals and generates an error signal E as a
function of the
comparison.
The error signal E represents the difference between the actual air flow
measured by the
sensor 32 and the desired air flow to produce a stoichiometric air/gas ratio
with the current
gas flow rate. Since the sensor 32 would normally produce an air signal Sa
which is a
magnitude of 10 greater than the gas signal Sg produced by the gas sensor 26
for a
stoichiometric ratio (i.e. an air flow rate which is a magnitude of 10 greater
than the gas flow
rate) the value of the air signal Sa is adjusted to the same level as the gas
signal Sg for a
stoichiornetric ratio. This can be effected by a simple voltage divider in the
air flow sensor
32.
The error signal E is fed to the non-inverting input of the second comparator
104 and to the
inverting input of the third comparator 106, each of which compares the error
signal E value
with fixed positive and negative threshold values generated by the positive
and negative
threshold value circuits 108, 110 respectively.
If the error signal value is greater than or equal to the positive threshold
value, then the
comparator 104 applies an actuation signal through the first operational
amplifier 112 to the
first relay 116 which energises the air valve 28 to move in a first direction,
towards its fully
closed position. Similarly, if the error signal value is less than or equal to
the negative
threshold value, the comparator 106 applies an actuation signal through the
second
operational amplifier 114 to the second relay 116 which energises the air
valve 28 to move
in the opposite direction towards its fully open position.
If, however, the error signal value is less than the positive threshold value
and greater than
the negative threshold value, the second and third comparators are unaffected
and the air
valve is not adjusted.
The threshold value circuits 108,110 set an error signal range within which
the controller 100
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takes no corrective action. Thus, if the gas flow rate is changed in order to
increase or
decrease the temperature of the burner 40 this will 'result in an air/gas
ratio which moves
away from the desired value. This will result in an error signal being
generated by the
comparator 102, the error signal representing the difference between the
actual air/gas ratio
and the desired airlgas ratio. It will therefore be appreciated that if the
change in the air flow
rate which is required to return the air/gas ratio to the desired level is
less than the change
represented by the error signal range set by the threshold value circuits 108,
110 then the
error signal E will fall within this range and the air valve 28 will remain
unactuated. The
error is in effect deemed to be zero and the air valve is not adjusted. The
threshold range set
by the threshold circuits 108, 110 is termed a "deadband". In practice, this
reduces the
occurrence of limit cycling in the air flow and allows the desired air/gas
ratio to be
maintained more closely.
The value of the deadband affects the performance of the air/gas ratio
controller 100 which
in turn affects the efficiency of the combustion plant. Selection of the
correct value for the
deadband is therefore important. By malting the deadband value high, limit
cycle oscillations
are reduced, but the accuracy of control of the air valve to provide the
desired air/gas ratio
is reduced. Conversely, a low threshold value gives good accuracy but
increases the
occurrence of limit cycling. It is preferable, therefore to malce the deadband
as small as
possible, without causing limit cycling.
It is apparent from the above description that if the deadband value
represents a change in air
flow rate which is slightly larger than the movement of the air valve (change
in air flow rate)
in a single sample interval, then adjustment of the valve can be made without
limit cycling
occurring. A constant deadband value can therefore be used for valves with
linear
characteristics. However, for non-linear valves having an error envelope such
as that shown
iri Figure 8, the use of a constant deadband value is ineffective since limit
cycling may occur
in some parts of the~operating range of the valve even though a deadband is
used.
A solution is to vary the value of the deadband according to the valve
characteristic over the
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valve's operating range. It is found that the optimum deadband value for a
given valve
position is equal to twice the value of the differential of the valve
characteristic at that
position. Since the deadband is centred around a zero value the upper and
lower threshold
levels of the deadband (set by the positive and negative threshold circuits
108, 110)
correspond to the positive and negative derivative curves of the valve. Thus,
the deadband
is chosen to map exactly the error envelope of the valve. Thus, the controller
will adjust the
air valve in the instance where:
E(Ts, u) ( Z D a
2
where D(u) = 8 (u) and represents the deadband value defined by the error
envelope at a
given valve position (u) which is the region within which limit cycling does
not occur even
in the absence of a deadband since the value of an error within which region
is greater than
or equal to the change in flow caused by adjustment of the valve during one
sample interval.
Conversely,'the controller will not adjust the air valve in the instance
where:
I E(Ts, u) ~ ~ D a
2
In this case, the error lies within the deadband which is the region in which
limit cycling
would occur if the air valve were adjusted and the deadband were not present.
A solution is to vary the value of the deadband in dependence on the valve
characteristic over
the operating range of the valve.
Figure 4 shows a second embodiment of air/gas ratio controller 200 as part of
a control
system 190. In figures, 3, 4 and 5 like reference numerals indicate like
parts. As can be seen,
the controller 200 is similar in form to the controller 100 of Figure 3 but
with the fixed
threshold value circuits replaced by variable threshold value circuits 208,
210 each of which
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comprises a look-up table. The variable threshold value circuits 208, 210 are
connected to
receive a signal from an air valve position sensor 222 via an operational
amplifier 220. The
valve position sensor 222 can be of the form which simply monitors the voltage
applied to
the valve to drive the valve bettveen its open and closed positions.
Before the control system is put into operation the characteristic of the air
valve is measured
and the differential curve shown in Figure 7 determined for the valve in order
to provide the
error envelope shown in Figure 8. A number of different threshold values or
levels are then
taken from the envelope of Figure 8, a positive and a negative value for
selected valve
positions. The positive values are stored in the look-up table of the
threshold value circuit
208 and the negative values are stored in the look-up table of the threshold
value circuit 210.
During operation, as the valve position changes, the threshold value in the
look-up table
which is compared with the error signal is selected according to the position
signal from the
air valve position sensor.
The value generated by each variable threshold value circuit 208, 210 is thus
a function of
the position of the air valve 28 and thus of the air flow rate. As the
position of the air valve
varies, the change in the air flow rate which occurs during each sample
interval also varies.
The air valve characteristics are effectively stored in the look-up table in
each threshold
circuit 208, 210. The look-up table therefore gives the characteristic at a
given valve position
and thus determines the deadband value for that position. The deadband is thus
varied
according to the instantaneous position of the air valve 28.
As in the previous embodiment, if the error signal E calculated by cornparator
202, lies
within the range defined by the instantaneous positive and negative threshold
values
generated by the threshold circuits 208, 210, then the error is deemed to be
zero and no
corrective action is made to air valve 28.
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If, however, the error value.lies on or outside the error envelope, the air
valve 28 is adjusted
as described previously.
Since the deadband value is always greater than the change in air flow
effected by movement
of the air valve during one sample interval, the occurrence of limit cycling
is 'minimised. In
addition, the accuracy of the air/gas ratio controller 200 is increased. This
results in a
significant improvement in combustion efficiency of the gas combustion plant
since the
airlgas ratio is maintained at an optimum.
It will be apparent that various modifications and improvements can be made to
the present
invention.
The present invention may be modified such that the movement of the air valve
28 is
continuously monitored to determine whether the characteristics of the valve
have changed
owing to wear, for example. If the valve characteristics have changed, this
information can
be fed to the variable threshold value circuits to modify the deadband value
fox each position
of the valve. An example of such a modification to the present invention is
shown in fig.
5 in which like reference numerals indicate like parts.
In Figure 5 one of the relays, in this case relay 116 which actuates the valve
towards its fully
closed position, is connected to an input of a multiplexer 300. An output of
the air flow
sensor 32 and the valve position sensor 222 are also connected to the
multiplexer 300.
The output from the multiplexer 300 is connected to aparameter estimator 302
whose output
in turn is connected to the variable threshold value circuits 208, 210.
The parameter estimator 302 may be a microprocessor running, for example,
MATLAB.
Before the control system is put into operation the characteristic of the air
valve is measured
and the response curve shown in Figure 6 is stored in a store in the parameter
estimator 302.
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This can be effected by moving the valve from one of a fully open and closed
position to the
other and monitoring the signals from the valve position sensor 222 and the
air flow rate
sensor 32 which are then stored in the parameter estimator 302 as continuously
variable
values or discrete values.
When relay 116 is actuated to move the air flow valve 28 towards its fully
closed position
the parameter estimator 302 is also enabled. During closing of the valve 28
the parameter
estimator 302 processes the outputs from the air flow rate and position
sensors 32, 222 and
compares the monitored flow rate with the previously stored flow rate. If
there is a deviation
between the monitored flow rate with the previously stored flow rate this
would suggest, for
example, wear in the valve mechanism. The parameter estimator 302 then adjusts
the
threshold values in the look up tables in the threshold value circuits 208,
210 which relate
to the monitored valve position to take account of changes in the valve
characteristics which
have occurred. It will be appreciated that equally the movement of the valve
towards its fully
open position may be used to update the look up tables to take account of
wear, in which case
the estimator 302 would be enabled with relay 118.
Whilst the above description is made with reference to a lag-lead control
system wherein the
lead parameter is the gas flow rate and the lag parameter is the air flow
rate, it will be
appreciated that the invention is equally applicable to systems wherein the
lead parameter is
the air flow rate and the lag parameter is the gas flow rate, or any other lag-
lead system.
It Will also be appreciated that whilst the preferred form of the invention
has been described
with reference to an air/gas combustion plant or fiunace, the invention is
equally applicable
to lag-lead control systems for controlling the ratio of two fluids where the
fluids may be in
gas or liquid form.
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