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WEM.017 US
Method and Apparatus for Statistical Set Point Bias
Control
S
Technical Field
The present invention relates to feedback control
devices, and in particular to feedback control
devices employing a numerically calculated set point.
Background Art
Industrial process controllers are commonly tuned
to control an output to meet a particular output
specification. Where the features of the system
function ideally, setting the control to the ideal
specification then produces the specified output with
no variation. Material handling systems do not work
ideally for numerous reasons, and as a result there
is frequently a statistical distribution in the out-
put from the system. Where there is no functional
difference between the high side and the low side
results of the statistical distribution, setting the
control to meet the center of the statistical dis-
tribution is a correct choice.
Functional differences may exist between the high
and low sides of the distribution. One side of the
distribution is then acceptable, while the other is
not. For example, a chemical reaction may occur on
the high side of the distribution that produces a
pollutant thereby spoiling the output, or the mater-
- ial or energy investment may exceed what is necessary
thereby wasting resources. In the cases where an
important difference esists in the output distribu-
tion, the process needs to be controlled so the dis-
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65859-98
trlbution ls on the preferred slde of the speclflcatlon and then
to be withln a measure of closeness to the speclficatlon.
Where the dlstrlbutlon ls known and has a fixed value, a
slmple solutlon ls to tune the process to a level offset from the
speciflcation by an amount sufflcient to locate the distrlbution
center in the preferred zone, but close enough to the
speclflcatlon so the amount of output falllng ln the unacceptable
zone ls tolerable. Unfortunately, an output distrlbutlon is
generally not known, and is likely to change ln tlme. Further,
the feature lmportant to control may not be the center of the
distribution, which may not be symmetrlc, but the amount of
product, or the exlstence of any product occurring in the
unacceptable zone.
Summary of the Inventlon
The lnventlon provldes a process control devlce for set
polnt bias control comprislng:
a) a process control devlce responsive to a set polnt
condltlon and a measured amount condltion to produce a control
signal used to affect a process havlng a feature measured to
produce the measured amount,
b) means for generatlng a set polnt blas, and
c) means for offsettlng a speclficatlon llmlt by the set
polnt blas ln a preferred dlrectlon to produce the set polnt
condltlon.
The lnventlon also provldes a method for set polnt blas
control of a process wlth a controller recelvlng a set polnt value
to operate on the process produclng a measured amount comprlslng
B~
1 ~ 3~ ~ 7 65859-98
the steps of:
a) recelvlng a speclflcatlon llmlt,
b) offsettlng the speclflcatlon llmlt ln a preferred
dlrectlon wlth a blas amount to produce a set polnt amount,
c) generatlng an error slgnal amount from the set polnt
amount and the measured amount,
d) controlllng a process accordlng to the error slgnal
amount,
e) measurlng a process feature to produce the measured
0 amount, and
f) performlng a blas computatlon on the measured amount to
generate the blas amount.
The lnventlon further provldes a process control devlce
for set polnt blas control comprlslng:
a) a process control devlce responslve to a set polnt
amount and a measured amount to produce a control slgnal used to
affect a process havlng a feature measured to produce the measured
amount,
b) means for produclng the set polnt amount offset by a
blas amount from a speclflcatlon llmlt on a preferred slde of the
speclflcatlon llmlt, and
c) means for generatlng a control slgnal from the set polnt
amount and the measured amount.
The lnventlon stlll further provldes a method for set
polnt blas control of a process wlth a controller recelvlng a set
polnt value to operate on the process produclng a measured amount
comprlslng the steps of:
2a
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65859-98
a) recelvlng a speclflcation llmlt,
b) produclng a set polnt amount from a dlfference between
the speclflcatlon llmlt and the measured amount, a duratlon of the
dlfference, and a flrst galn whlle the measured amount ls on a
preferred slde of the speclflcatlon limlt and a second galn whlle
the measured amount ls not on the preferred slde of the
speclflcatlon llmlt,
c) generatlng an error slgnal amount ln response to the set
polnt amount and the measured amount,
d) controlllng the process accordlng to the error slgnal
amount, and
e) measurlng a process feature to produce the measured
amount.
Blasing the set polnt of a controller to the preferred
slde of a speclflcatlon llmlt ln relatlon to the standard
devlatlons or varlatlon ln the controlled varlable keeps most of
the excurslons ln the controlled varlable on the acceptable slde
of the speclflcatlon llmlt. The speclflcatlon llmlt may then be
approached as closely as observed varlatlon allows. The
controlled process may then be maxlmlzed for proflt or quallty by
keeplng the controlled varlable close to the speclflcatlon llmlt,
but wlthout exceedlng the llmlt.
Brlef DescrlPtlon of the Drawlnqs
FIG. 1 shows a schematlc dlagram of a statlstlcal
control process.
FIG. 2 shows a schematlc dlagram of a preferred control
process.
2b
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Best Mode for Making the Invention
FIG. 1 shows a schematic diagram of a control
process employing a statistical control process. A
specification limit 30 is received defining the pre-
ferred output condition. The specification limit 30is then augmented or diminished by a bias amount 40
in a summation block 50 depending on whether errors
in the process output are preferred on the high side
or low side of the specification limit 30. The
specification limit 30 offset by the bias amount 40
is then the set point 60 for a controller 70.
The controller 70 affects a process 80 having a
measured feature called a measured variable 90. The
goai of the controller 70 is to bring the process 80
to a state where the measured variable equals the set
point 60, or in the present case, where the distribu-
tion of the measured variable 90 values is offset on
the preferred side of the specification limit 30.
The set point 60 and measured variable 90 are used
to produce a control signal affecting the controller.
Commonly, the difference between the set point 60 and
the measured variable 90 is computed in a difference
block 100 as an error signal 110 used as the control
signal. The error signal 110 is supplied to the
2S controller 70 to direct the direction and size of the
controller's response in affecting the process 80 and
correspondingly the measured variable 90. The pro-
cess 80 is sensed to produce the measured variable
go which is returned to the difference block 100 to
generate the error signal 110.
Applicant additionally supplies the measured
variable 90 to a bias calculating block 120. The
bias calculating block 120 calculates a statistical
measure of the distribution in the measured variable
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90, for esample, the standard deviation. The statis-
tical measure is then appropriately scaled to produce
the bias amount 40.
Numerous statistical measures may be made. The
standard deviation is a familiar and preferred
measure by the applicant. To compute the standard
deviation of the measured variable 90, an average
value of the measured variable 90 is computed for a
sample period. The length of the sample period is
determined by the user in accordance with the nature
- of the process 80, the sampling rate of the measured
variable 90, and the level of confidence sought.
Where the specification limit 30 has a fixed value,
and the process 80 is slow moving in comparison to
the sampling rate, good statistics may generally be
taken under all conditions. Where the distribution
is changing, the statistic needs to be normalized by
the distribution trend, and compensated for the
delay in the process 80.
The average sample value of the measured variable
90 may be computed as a running average of a number
of sample values. A number ns is selected by the
user which is the number of samples to be averaged.
The number ns times the sample rate tr gives an
effective sample period, which in the preferred form
esceeds the closed loop period of the measured
signal, and in further preference is set to corres-
pond to the capacity of the process 80.
The sample average, save, may be computed in
several ways. A running average may be computed by
summing the ns most recent sample values si and
dividing the sum by the sample count ns. With each
additional sample, the oldest sample value
S(i ns 1) is removed, while the newest sample value
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Si is included in the sum. The sum is divided by
the sample count ns.
Alternatively, a weighted time series sum may be
computed, for example, save ~sie ti/~,
where all sample values si are included but given
less weight as the sample ages. The time ti is the
age of the sample si. The factor ~ is a- time
constant similar to the sample count ns selected
by the user to correspond to the process 80, sampling
rate and other process 80 features. The weighted
time series is conveniently computed as a percentage
of the previous weighted average plus the remaining
percentage times the current sample value, save =
(X %) (sold) ~ (100 - X %) (Si) -
Alternatively a block average, although not a
preferred average, may be computed where ns samples
are taken, and averaged as a block. The next ns
values are used as a block for the next average cal-
culation. Applicant prefers a running average.
The average value, save, is subtracted from the
current sample value, si, and the result squared,
(Si ~ Save) The squared value is then
averaged over a number of samples. Again the average
of the squared values may be computed in the several
ways listed. Averaging the sum of the squares in the
same fashion as the sample average is convenient.
Again a running average is preferred. The square
root of the result is the standard deviation. The
standard deviation is then scaled according to the
degree of quality assurance required in measured
variable 90. For a normal distribution and an offset
of one standard deviation, only 15.87 percent of the
measured variable 90 samples should be in the unac-
ceptable zone, for an offset of two standard devia-
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tions only 2.28 percent of the output should be inthe unacceptable zone, and for three standard
deviations, only 0.14 percent.
To enhance the uniformity of the distribution in
S the measured variable 90 a subgrouping procedure may
be performed. A subgroup of nS samples, four or
more, may be averaged as a group to form a subgroup
sample value sgj. The statistical analysis is per-
formed on the subgroup sample values sgj. Thus,10 the standard deviation calculated is for the subgroup
values sgj which may then be converted to the
standard deviation of the individual samples si by
multiplying by the square root of the number of
samples in the subgroup.
The statistically calculated bias operates with
the assumption that the set point is at the mean of
the distribution. If the process is nonlinear, dis-
tribution of the controlled variable tends to be
skewed leading to a statistically inaccurate result.
Compensation may be applied to the set point 60 and
measurement variable 90 signals to linearize the
signals, and as a result, to linearize the error
signal 110 and the response of the controller. The
distribution in the measured variable 90 is then
forced to become more uniform. However, the mean of
measured variable 90 distribution curve may no longer
coincide with the set point 60 of the controller 70.
Setting the bias 40 as function of the standard devi-
ation is then not completely accurate, and fails
according to the degree of skewness in the measured
variable 90.
An alternative method and apparatus uses an
integrator to position the set point so no more than
a selected percentage of the integrated area between
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the measured variable and the specification limit
lies on the unacceptable side of the specification
limit. An integrator gain is weighted so a higher
gain is applied when the measurement is on the un-
acceptable side of the specification limit than whenthe measurement is on the acceptable side of the
specification. The gains are weighted in portion to
the ratio of the desired integrated areas.
FIG. 2 shows a schematic diagragm of a preferred
controlled area biasing control process. A specifi-
cation limit 210 is received by an integrator block
220. Broadly, the integrator block 220 responds to
the difference between the specification limit 210
and a measurment signal 230. As the difference
lS increases, the response of the integrator block 220
increases. The integrator block 220 also responds
to the duration of the difference. As the duration
of the difference increases, the response of the
integrator block also increases.
The integrator block 220 also responds to a gain
factor. A separate gain block may be used, operating
with the measurement signal 230, and providing a gain
signal to the integrator block 220. Applicant pre-
fers including the gain generating process in the
integrator block 220. The gain producing means in a
simple and preferred form examines the measurement
signal 230 for one of two conditions. Where the
measurement signal 230 is on the preferred side of
the measurement distribution, the gain signal is low.
Where the measurement signal 230 is on the unaccept-
able side of the specification limit 210 the gain
signal is high. Preferrably, the product of the low
gain and the portion of the output sought to be on
the preferred side of the specification limit eguals
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the product of the high gain and the portion of the
output allowed in the unacceptable side of the dis-
tribution. For example, where 97 percent of the
distribution is sought to be in the acceptable
region, and 3 percent is allowed in the unacceptable
region, the low qain signal times 97 should equal 3
times the high gain signal. Conceptually the pre-
ferred integrator block 220 integrates the area
between the specification and measurement amounts,
and weights the result so the area on the unaccept-
able side appears large. The preferred integrator
block 220 integrates the difference between the
specification limit 210 and the measurement signal
230 according to a two state (high low) gain func-
tion. The integrator block 220 then outputs a setpoint signal 240.
The set point signal 240 may optionally be lin-
earized in a set point function block 250 to produce
a linearized set point signal 260. The set point
signal 240, or linearized set point signal 260, as
the case may be, is combined in a difference block
270 with the measurement signal 230 to produce an
error signal 280. The error signal 280 is supplied
to a controller 290 operating on a process 300 having
a measured feature to produce the measured signal
230. The measured signal 230 may optionally be
li-nearized in a measurement function block 310 to
produce a linearized measurement signal 320. In most
instances, where the set point 240 is linearized in
a function block 250, the measurement signal 230 is
linearized correspondingly so the two signals com-
bined in the difference block 270 are comparable.
While there have been shown and described what
are at present considered to be the preferred embodi-
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ments of the invention, it will be apparent to thoseskilled in the art that various changes and modifi-
cations can be made herein without departing from the
scope of the invention defined by the appended
claims. For example, numerous combinations and
formulations of statistical measures are possible.
Different statistical moments, cubic or higher
orders, may be made, or corresponding roots of higher
order moments may be made. Different distributions
in the measured variable other than a normal dis-
- tribution may be used or assumed. The calculation
and signal processes may be performed by digital or
analog equipment, or may be implemented directly in
hardware as is within the scope of those skilled in
the art.
