U.S. patent number 3,771,167 [Application Number 05/111,894] was granted by the patent office on 1973-11-06 for method for calculating the average value of a noise corrupted signal.
This patent grant is currently assigned to Leeds & Northrup Company. Invention is credited to Charles W. Ross.
United States Patent |
3,771,167 |
Ross |
November 6, 1973 |
**Please see images for:
( Certificate of Correction ) ** |
METHOD FOR CALCULATING THE AVERAGE VALUE OF A NOISE CORRUPTED
SIGNAL
Abstract
A method for determining the average load provided by a steel
refining furnace so that the control signal for controlling the
power distribution system including the furnace load can be
modified to avoid response of the control system when there is a
loss of arc in the furnace. An average load is calculated for the
furnace with that average being maintained until a predetermined
period of time has elapsed after a sudden drop in load before the
average is modified. As a result, sudden drops in load due to loss
of arc are effectively rejected in establishing the average load
value and the control signal is modified in accordance with the
change in furnace load so that unwanted control is not effected in
response to a loss of arc.
Inventors: |
Ross; Charles W. (Hatboro,
PA) |
Assignee: |
Leeds & Northrup Company
(Philadelphia, PA)
|
Family
ID: |
22341006 |
Appl.
No.: |
05/111,894 |
Filed: |
February 2, 1971 |
Current U.S.
Class: |
700/297; 700/209;
708/445; 700/89 |
Current CPC
Class: |
F27D
19/00 (20130101); Y02P 10/216 (20151101); Y02P
10/286 (20151101); C21C 2300/06 (20130101); C21C
2005/5288 (20130101); Y02P 10/20 (20151101); Y02P
10/25 (20151101) |
Current International
Class: |
G06f 015/56 () |
Field of
Search: |
;328/151 ;444/1
;235/151.21 |
Primary Examiner: Botz; Eugene G.
Claims
What is claimed is:
1. In a sampled data system the method for automatically modifying
the control signal for a power distribution system which includes
an electric steel refining furnace as part of its load so that the
control signal will not change significantly as a result of loss of
arc in the furnace, comprising the steps of:
automatically computing the average value of the furnace load as a
linear average of the sampled furnace load measurements after the
sampled value deviates from the previously calculated average by an
amount which is greater than a preset meximum representing the
expected maximum value from furnace melting noise,
automatically computing the average as an exponential average of
the values of the furnace load after said linear average attains a
value substantially equal to the value which would be computed as
the exponential average for the last sampled value and the
previously calculated average so long as the deviation of the value
from the previously calculated average is less than said preset
maximum, and
automatically maintaining the average at its last value and
changing the value of the control signal by a weighted value
directly related to the difference between the last sampled furnace
load measurement and the previous average value of the furnace load
so as to modify said control signal in magnitude and polarity so
that the change in furnace load, due to the loss of arc, will not
produce a comparable change in the control signal, said maintenance
of the average and changing of the value of the control signal
being carried out during a preset maximum time period representing
the expected maximum time duration of a loss of arc when that
period follows a deviation of the sampled value of the furnace load
beyond a preset maximum and so long as that deviation exceeds said
preset maximum.
2. The method for automatically modifying the control signal for a
power distribution system which includes an electric steel refining
furnace as a part of its load so that the control signal will not
change significantly as a result of loss of arc in the furnace,
comprising the steps of:
automatically comparing a previous average value for periodic
samples of the furnace load with the presently sampled value for
the furnace load;
automatically incrementing a timer when said comparison indicates
that the change in the furnace load from its previous average
constitutes a decrease beyond that preset deviation limit which
when exceeded indicates a loss of arc in the furnace;
automatically setting the average at the present sampled value of
load when,
said comparison indicates a change in furnace load from the
previous average of magnitude sufficient to constitute an increase
beyond a deviation limit set to be comparable to the change in load
expected from furnace melting noise, and
said timer has incremented to a preset value representing the
expected maximum time duration of a loss of arc;
automatically averaging the furnace load values sampled since
restarting the average at the sampled value when said comparison
indicates that the change in the furnace load from its previous
average constitutes a change of insufficient magnitude to exceed
either said increase or decrease limit; and
automatically holding the average at the previous average and
changing the value of the control signal by a weighted value
directly related to the difference between the presently sampled
furnace load and the previous average value of the furnace load so
as to modify said control signal in magnitude and polarity so that
the change in furnace load due to the loss of arc will not produce
a comparable change in the control signal when said timer has not
incremented to said preset value.
Description
BACKGROUND OF THE INVENTION
This invention relates to a method for determining the average of
sampled values of a noise corrupted process measurement so that
sudden changes in the value are followed. More particularly, the
invention relates to the determination of the average load on an
electric arc furnace in which case it is desirable that sudden
drops in load due to a loss of arc in the furnace should be ignored
and the control signal for the power distribution system supplying
the furnace should not be modified in accordance with the extent of
the load change during the loss of arc so as to prevent a
correspondingly large control response to that transient
condition.
In the normal control system, a simple filtering of the noise would
be all that would be necessary; however, when the measured value is
subject to wide fluctuations, an intolerable delay, in response to
such fluctuations, would occur using a simple filtering technique.
In order to provide a control response to sudden changes in the
measured value, means must be provided for recognizing those sudden
changes so that the filtering may be modified whereby the delay in
responding to such a change can be minimized.
In the case of the arc furnace, special situations arise which make
it desirable to delay the response to sudden changes in furnace
load. For example, during the loss of arc in an electric steel
refining furnace, control response would be disadvantageous in that
the very large load drop usually associated with a loss of arc is a
transient condition which lasts only for a short time relative to
the system response time and is therefore not amenable to
correction by the usual control systems wherein the governor
adjustments on the generators are modified in response to load
changes in the system as evidenced by the deviation of the area
control error from zero. The control systems for load distribution
may, for example, be of the type shown in my U.S. Pat. No.
3,510,637 which issued May 5, 1970.
It is therefore an object of this invention to provide a method for
determining the average of a sample value of a noise corrupted
measurement so that the calculation of the average is subject to
modification in response to large changes in the value
measured.
It is a further object of this invention to provide a method for
determining the average load on an arc furnace so that the
calculation of the average is not subject to modification in
response to the transient load change which occurs due to a loss of
arc in the furnace.
It is still a further object of this invention to provide means for
modifying the control signal for the power distribution system
which includes the electric furnace so as to prevent the control
system from attempting to change the generation in the system in
response to the load change resulting from the loss of arc, unless
the load change is of a greater duration than expected.
SUMMARY OF THE INVENTION
This invention provides a method for determining at the end of each
sampling period in a sampled data system an average for a noise
corrupted process measurement subject to changes in value which are
large compared with the magnitude of the noise. The steps of the
method include the computation of the average as an exponential
average of the sampled values and the restarting of that average at
a value corresponding with the sampled value after the sampled
value has deviated from the previously calculated average by an
amount which is greater than a maximum value preset to represent
the expected maximum value for the noise.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a representative load profile for an electric arc
furnace.
FIG. 2 is an algorithm setting forth the steps which can be
programmed on a general purpose digital computer to carry out the
novel method of this invention.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring to FIG. 1, there is shown a load profile for an electric
steel refining furnace which has, for purposes of this description,
been exaggerated amd simplified. That load profile is shown as the
continuous line 10 while the average values of the furnace load
calculated in accordance with the method of this invention is shown
by the dotted line 12, with each dot representing the value
established as a result of a particular sample of the existing
furnace load.
At time T.sub.1 the furnace load FL comes on. It would normally be
measured on a line connected to the furnace itself or on a tie line
to a group of leads which includes the furnace. As will be evident
from FIG. 1, previous to the time T.sub.1 the average value of the
furnace load and the sampled value of the furnace load are both
zero. When the furnace load increases beyond the average AFL by an
amount greater than DFLR, as at T.sub.2, the average is updated to
the current value of the furnace load.
Between the times T.sub.2 and T.sub.3 the load fluctuates rapidly
over a relatively small range as a result of arcing. During that
time period the average remains substantially constant at its new
value, namely the average value of the load between T.sub.2 and
T.sub.3.
At the time T.sub.3 the furnace is turned off for the addition of
scrap and the furnace remains off until the time T.sub.4 ; however,
as shown by FIG. 1, the average value which is calculated by the
method of the present invention remains at the value it had just
prior to the time T.sub.3 until a particular time period after the
drop in the load. That time period is adjusted to be sufficient so
that any drop in load due to a loss of arc would have recovered by
a reforming of the arc prior to the expiration of that period.
Thus, that time period can be considered as a rejection period
during which a drop in load is not taken into account in the
computation of the average load. It will be noted, however, that
after that period has expired, the average load then becomes the
existing furnace load, for the load drop is assumed to be such that
its duration will make control response feasible. For example, just
prior to the time T.sub.4, the computer average becomes zero.
When the furnace comes back on at the time T.sub.4 at a higher load
level, the average again follows tha existing value of the load
since, as the load changes by a sufficient amount DFLR, the average
is restarted with the current value.
As shown during the period between T.sub.4 and T.sub.5, the
computed average generally follows the average of the noisy signal
representing the furnace load during that part of the melting
period in the furnace.
At the time T.sub.5 the load on the furnace decreases rapidly as a
result of a loss of arc in the furnace and then it recovers as the
arc is reestablished so that the duration of the load drop after
the time T.sub.5 is less than that period assigned as the rejection
period, and therefore the calculated average is not modified in
response to the load drop, as shown.
After the time T.sub.5, the melting phase continues until just
prior to the time T.sub.6 at which time a tap change occurs so that
the refining of the furnace batch may begin at the time T.sub.6 at
a reduced load level. Associated with the tap change is a load drop
greater than the value DFLL, which represents the change limit in
the decrease direction which must be exceeded to indicate a loss of
arc, and thus the rejection period is started. Since the rejection
period does not elapse before the time T.sub.6, the average load
takes on the value of the sampled load after the time T.sub.6 ;
thus, the average continues at the value calculated before the tap
change until the end of the rejection period. Then during that part
of the refining period up to the load drop just prior to the time
T.sub.7 which represents another tap change, the average remains at
the constant refining level. After the second tap change, which is
similarly accomplished before the rejection period elapses, the new
average is established at the furnace load FL sampled just after
T.sub.7.
Between the time T.sub.7 and T.sub.8, the furnace load remains
constant as does the average value computed for the furnace load
except that just prior to T.sub.8 the furnace load is reduced to
zero by furnace shut-down for the end of the heat. As noted in FIG.
1, the average remains at its previous value until the rejection
period has elapsed following the drop in load at shut-down. The
average is then calculated as zero just after the time T.sub.8.
In order to provide for a computer average furnace load which will
be modified only in response to load changes which do not represent
arcing noise or a loss of arc in the furnace as shown in FIG. 1,
the method illustrated by the algorithm of FIG. 2 may be followed
in the programming of a general purpose digital computer. By using
that method there will also be provided a modification of the
control error for the load distribution system which includes the
furnace so as to take into account the fact that control action is
not desired during a loss of arc since the expected quick recovery
makes it undesirable to provide control response prior to arc
recovery. Control is, however, allowed where load changes have
occurred which persist beyond the period established as the
rejection period; for example, between T.sub.3 and T.sub.4 in FIG.
1.
The first step in the algorithm of FIG. 2 involves the introduction
of a lag factor in connection with the sampled values of the
furnace load. It is necessary to introduce this lag in order to
coordinate the furnace load measurement with the normal tie line
load measurements which are incorporated into the computation of
the control error for the particular load distribution area in
which the furnace is located, since the normal measurements made
from the tie line inherently involve a lag because of the type of
apparatus used. Therefore, the lagged furnace load LFL, as a result
of the present sample of the furnace load FL, is calculated as
shown in the block 20. By adding to the previous lagged furnace
load LFL, the product of the lag factor KLAG and the quantity FL -
LFL, representing the difference between the sampled load and the
previous value for the lagged furnace load.
Utilizing the computed value LFL, the change in furnace load DFL is
computed as shown in block 22 by subtracting from LFL the average
furnace load AFL, calculated as a result of the computation of the
average furnace load based on the previous sample of FL.
After computing DFL, the value DFL is then examined for polarity as
shown in block 24. If DFL is greater than zero, the program then
proceeds to the step described in block 26 whereas if the value DFL
is not greater than zero, as would be the case for a decreasing
load from the furnace, the program would proceed to the step
described in block 28 where the value DFL is examined to see if it
is less than -DFLL which represents that limit value established
for a decreasing load which would normally be exceeded by a loss of
arc in the furnace but which would not be exceeded by the normal
noise in the load profile during the melting period.
If the change in the furnace load DFL indicates a decreased furnace
load which exceeds the deviation limit DFLL, then the step shown in
block 30 is carried out, namely, the incrementing of the rejection
timer by 1, so as to obtain a new value for SPKRT which represents
the time elapsed following a large load drop. After incrementing
that timer, the program proceeds to the step described in block 32
wherein the value established for the timer is examined to see if
it equals SPKRW, which represents the rejection time period
established for large downward load drops and is thus the time
period during which any loss of arc is expected to have been
reestablished.
If SPKRT does not equal SPKRW, the load drop which occurred has not
existed for a sufficient duration of time so as to give assurance
that it is not caused by a loss of arc in the furnace and therefore
it must be assumed that it could have resulted from an arc loss and
therefore that a control response to the load decrease should not
be made in accordance with the magnitude of the load drop. It
might, however, be advantageous to modify to a moderate extent the
control error for the area, namely ACE, so that the additive
effects of random load changes by the system load and by the
furnace melt noise are not ignored. Thus, as shown in block 34, the
area control error ACE is modified by subtracting the product of a
wieghting factor FLRW and the load drop DFL. Normally, the
weighting factor FLRW would be in the range of 0.8 to 1, depending
upon the relative magnitude of the load drop to be rejected as
compared with the magnitude of the noise.
By modifying the area control error so that the full effect of the
load drop is not evidenced by a change in value of the control
error, ineffective control can be prevented as previously pointed
out. After the modification of the area control error, the program
then proceeds to the step described in block 36 which indicated
that the average furnace load AFL, which had been previously
calculated, is maintained and the program then exists.
Considering the other alternative paths in the program illustrated
by the algorithm of FIG, 2, we can examine the result of the change
in furnace load DFL being positive so as to indicate an increase
and cause the program to proceed to the step described in block 26.
As shown in block 26, the change in load DFL is examined to see if
it exceeds the increase limit DLFR, which has a value established
to be comparable to the change in load expected from the noise;
thus, if DFL is greater than DFLR indicating that there has been a
load increase which is beyond that expected as a result of the melt
noise, that the program proceeds to the step shown in block 40
where it is indicated that the average is restarted. As indicated,
the value AFL is reset to be equal to the presently sampled furnace
load FL and at the same time a zero is put into the memory position
reserved for the signal RAC, which represents the count of the
Restart Average Counter which counts the number of samples which
are being used in establishing the average furnace load AFL
following its being reset to a value FL.
After the location of the average and the zeroing of the Restart
Average Counter, the program then proceeds to carry out the step
described in block 42 by resetting the spike rejector. A zero is
placed into the memory loaction reserved for the value SPKRT,
representing the timer whose value is incremented as set forth
previously in the block 30. In other words, the time accumulated by
the timer which establishes the rejection period is replaced by
zero and any rejection period which was in the process of being
timed out is terminated.
After setting a zero in the memory location for SPKRT, the program
proceeds to the step of block 44 which indicates that the next step
is a restarting of the average. As shown in this block, the value
RAC is examined to see if it exceeds a value representing 1/.alpha.
represented by the mnemonic IALP.
In the algorithm of FIG. 2, upon the establishment of a new value
for the average furnace load, as for example in the step of block
40, the consecutive samples are averaged on a linear or equally
weighted basis until the number of samples equals IALP after which
the averaging is done on an exponential basis in order to remove as
much as possible from the average value the effect of the noise.
The .alpha. factor is related to the size of the lag introduced in
the exponential averaging by the equation .alpha. = - .epsilon.
.sup..sup.-T
where: T.sub.s is the sample period in seconds and
.tau. is the time constant of the lag in seconds.
Typical values for .tau. in this application are 1- 3 minutes which
corresponds to an .alpha. between 0.33 and 0.011. When the ratio of
.sup.T s/.tau. is small, .alpha. can be approximated by that ratio.
Therefore, for this application the approximation IALP = 1/.alpha.
.congruent. .tau./T.sub.s and greatly simplifies the tuning
required to adapt the algorithm to a particular system.
It will be evident from the algorithm of FIG. 2 that if RAC is not
greater than IALP, the linear averaging is carried out by following
the steps of the program which first include that shown in block
48; namely, an incrementing of RAC by 1 to give a new value of RAC.
The program then proceeds to the step of block 50 where the
reciprocal of the new value RAC is calculated and is identified as
FAW, which represents the furnace average weighting factor. From
the block 50 the program then proceeds to the step of block 52
where the new value for the average furnace load is computed as the
sum of the previous value for the average furnace load plus the
product of FAW and the quantity FL - AFL which is the present
sampled furnace load minus the previous average furnace load. From
the step of block 52 the program then exists.
* * * * *