CA2178809A1 - Transmitter with improved compensation - Google Patents
Transmitter with improved compensationInfo
- Publication number
- CA2178809A1 CA2178809A1 CA002178809A CA2178809A CA2178809A1 CA 2178809 A1 CA2178809 A1 CA 2178809A1 CA 002178809 A CA002178809 A CA 002178809A CA 2178809 A CA2178809 A CA 2178809A CA 2178809 A1 CA2178809 A1 CA 2178809A1
- Authority
- CA
- Canada
- Prior art keywords
- transmitter
- membership
- value
- span
- compensation
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Abandoned
Links
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
- G01D3/00—Indicating or recording apparatus with provision for the special purposes referred to in the subgroups
- G01D3/028—Indicating or recording apparatus with provision for the special purposes referred to in the subgroups mitigating undesired influences, e.g. temperature, pressure
- G01D3/036—Indicating or recording apparatus with provision for the special purposes referred to in the subgroups mitigating undesired influences, e.g. temperature, pressure on measuring arrangements themselves
- G01D3/0365—Indicating or recording apparatus with provision for the special purposes referred to in the subgroups mitigating undesired influences, e.g. temperature, pressure on measuring arrangements themselves the undesired influence being measured using a separate sensor, which produces an influence related signal
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
- G01D18/00—Testing or calibrating apparatus or arrangements provided for in groups G01D1/00 - G01D15/00
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
- G01D3/00—Indicating or recording apparatus with provision for the special purposes referred to in the subgroups
- G01D3/02—Indicating or recording apparatus with provision for the special purposes referred to in the subgroups with provision for altering or correcting the law of variation
- G01D3/022—Indicating or recording apparatus with provision for the special purposes referred to in the subgroups with provision for altering or correcting the law of variation having an ideal characteristic, map or correction data stored in a digital memory
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10S706/00—Data processing: artificial intelligence
- Y10S706/90—Fuzzy logic
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10S706/00—Data processing: artificial intelligence
- Y10S706/902—Application using ai with detail of the ai system
- Y10S706/903—Control
- Y10S706/906—Process plant
Abstract
A circuit (58) for compensating variables in a measurement transmitter (2). Within the transmitter, a sensor (54) senses a primary process variable such as differential pressure and a converter (56) digitizes the sensed process variable. The sensor (54) senses pressures within a span of pressures values. A memory (68) inside the transmitter stores at least two membership functions. The memory (68) also stores a set of compensation formulas, each formula corresponding to a membership function. A selection circuit (64) in the transmitter (2) selects those membership functions which have a non-zero value at the digitized PV, and a correction circuit (66) provides at least one correction value calculated from a compensation formula corresponding to a selected membership function. A weighting circuit (70) multiplies each correction value by its corresponding selected membership function, and combines the multiplicands to provide a compensated PV. The compensated PV is coupled to a control circuit (6) connecting the transmitter (2) to a control system (4).
Description
~WO 95120141 2 l 7 8 8 ~ 9 , ; ~, ~
T~ .n WITH 11~.. - .~ . ~ATION
BAC~GROUND OF T~P' INVENTION
This invention relates to a technique for compensating a sensed variable, where the variable can 5 be representative of position as in a process automation application, or representative of some other physical variable such as pressure, t~ _ ~LuLe, pE~, optical intensity as in a process control industry application.
~ore particularly, the invention applies to devices, 10 such as transmitters, actuators and positioners, which ate a sensed variable to provide an output representative of the variable.
There is a need to improve the accuracy with which measurement transmitters and devices with actuated 15 outputs, such as a positioner, ~~ate outputs representative of process variables. ~easurement transmitters sense process variables such as pressure j temperature, flow, p~, position, displacement, velocity znd the like in a process control or process automation 20 installation. Transmitters have analog-to-digital (A/D) converters for digitizing sensor outputs representative of sensed process variable and a ~ ~ation circuit for compensating the repeatable errors in the digitized process variable outputs. Temperature is one of the 25 main sources of the error. The P~tion circuit typically comprises a microprocessor which calculates the, PAted process variable output with long polynomial functions selected to fit the error characteristics of the sensor over a span of pressures.
30 Constants in the long polynomial function are individually selected to each sensor. During manufacture, individual testing of each sensor generates A. set o characterization constants related to the sensor errors which is later stored in a transmitter Wo 95/20141 ~`` ` 21 78809 EEPRO~. Using this cation scheme, process veriables can typically be corrected to an accur~cy of .05% over the span of the primary proce66 variable which the transmitter measures. For example, known pressure 5 transmitters having a span of O to 150 inches of water provide corrected pressures within . 05% accuracy.
Limited electrical power and limited time to compute the output m~lke it ~; f f; C" 1 t to complete more complex computation needed to improve accuracy.
Errors in the operating characteristic o~ the sensor cen be a complex, sometimes non-linear function of many variables . The primary variable ( the variable which is _ cated), contributes directly to the error, while secondary process variables (which affect 15 the measurement of the primary process variables ) contribute indirectly to the error. As the need for accuracy increases, contributions of secondary variables become si~n i f i ~nt . Current approaches solve this quandary with high order polynomials in multiple process 20 variables, but the resulting equation is arithmeticaily ill-conditioned and sensitive to the manner in which the polynomial i5 computed, in that overflows may occur.
One transmitter compensation equation is an eleventh order polynomial with approximately lOO terms in three 25 variables, which must be calculated each time the transmitter outputs a process variable. Gener~ting characterization constants for these high order polynomials is costly and time consuming. Furthermore, this approach cannot optimally capture the real behavior 30 of the non-linear process variables, which interact nr~nl inP;lrly.
In addition to concerns of software and computational complexity, power consumption is critical for transmitters which receive all their operating powe~
T~ .n WITH 11~.. - .~ . ~ATION
BAC~GROUND OF T~P' INVENTION
This invention relates to a technique for compensating a sensed variable, where the variable can 5 be representative of position as in a process automation application, or representative of some other physical variable such as pressure, t~ _ ~LuLe, pE~, optical intensity as in a process control industry application.
~ore particularly, the invention applies to devices, 10 such as transmitters, actuators and positioners, which ate a sensed variable to provide an output representative of the variable.
There is a need to improve the accuracy with which measurement transmitters and devices with actuated 15 outputs, such as a positioner, ~~ate outputs representative of process variables. ~easurement transmitters sense process variables such as pressure j temperature, flow, p~, position, displacement, velocity znd the like in a process control or process automation 20 installation. Transmitters have analog-to-digital (A/D) converters for digitizing sensor outputs representative of sensed process variable and a ~ ~ation circuit for compensating the repeatable errors in the digitized process variable outputs. Temperature is one of the 25 main sources of the error. The P~tion circuit typically comprises a microprocessor which calculates the, PAted process variable output with long polynomial functions selected to fit the error characteristics of the sensor over a span of pressures.
30 Constants in the long polynomial function are individually selected to each sensor. During manufacture, individual testing of each sensor generates A. set o characterization constants related to the sensor errors which is later stored in a transmitter Wo 95/20141 ~`` ` 21 78809 EEPRO~. Using this cation scheme, process veriables can typically be corrected to an accur~cy of .05% over the span of the primary proce66 variable which the transmitter measures. For example, known pressure 5 transmitters having a span of O to 150 inches of water provide corrected pressures within . 05% accuracy.
Limited electrical power and limited time to compute the output m~lke it ~; f f; C" 1 t to complete more complex computation needed to improve accuracy.
Errors in the operating characteristic o~ the sensor cen be a complex, sometimes non-linear function of many variables . The primary variable ( the variable which is _ cated), contributes directly to the error, while secondary process variables (which affect 15 the measurement of the primary process variables ) contribute indirectly to the error. As the need for accuracy increases, contributions of secondary variables become si~n i f i ~nt . Current approaches solve this quandary with high order polynomials in multiple process 20 variables, but the resulting equation is arithmeticaily ill-conditioned and sensitive to the manner in which the polynomial i5 computed, in that overflows may occur.
One transmitter compensation equation is an eleventh order polynomial with approximately lOO terms in three 25 variables, which must be calculated each time the transmitter outputs a process variable. Gener~ting characterization constants for these high order polynomials is costly and time consuming. Furthermore, this approach cannot optimally capture the real behavior 30 of the non-linear process variables, which interact nr~nl inP;lrly.
In addition to concerns of software and computational complexity, power consumption is critical for transmitters which receive all their operating powe~
2 ~ 78809 _WO 9~/201~
over the same wire6 used for communication.
Furthermore, some "intrinsically safe" areas where transmitters are installed limit the transmitter ~ s available power . The f inite current budget not only limits the number and complexity of the calculations, but impacts the functionality able to be incorporated in the transmitter. For example, A/D converters could convert digitized sensor outputs more rapidly if more power were available, thereby increasing the transmitter update rate. An EEP~OM large enough to acc~ te all the characterization constant6 also consume6 power which would otherwise provide additional functionality.
There i8 thus a need for an accurate method for compensating process variables which is computationally simple and requires small numbers of stored characterization constants, so as to consume a reduced amount of power and provide excess power for additional functionality and increased update rates in the transmitter.
STTMM~T~Y OF 'rT-TT` INVENTION
In an: ' ~'; t, a measurement transmitter has a sensor for sensing a process variable (PV) such as pressure and digitizing means for digitizing an output representatiYe of the sen6ed PV. The sensor senses the PV within a span of PV values. A memory inside the transmitter stores at least two membership functions, each membership function having a non-zero value over a predetermined region of the PV span and a substantially zero value over the L- i nd~r of the 6pan . The memory also stores a set of compensation f~rr-~ , each formula corresponding to a membership f unction . A selection circuit in the transmitter selects those membership functions which have a non-zero ordinate at the value of the digitized PV and a correction circuit provides at Wo95120141 l~11u~ l 2 1 78809 ~
least one correction value, each correction value calculated from a _ ~ation formula corresponding to a selected membership function. A weighting circuit weights each correction value by the ordinate of the corresponding selected membership function, and 1n~c the multiplicands to provide a compensated PV. The compensated PV is coupled to a control circuit connecting the transmitter to a control system.
A second . ' ~; L includes a sensor for sensing a primary PV such as differential pressure, ~nd other sensors for sensing secondary PVs such as line pressure and t ~ aLul~. A set of converters digitize the sensed PVs. Each of the variables is elssigned at least one membership function, with at least one of the variables having assigned at least two single dimen~ional membership functions. The membership functions having a substantially non-zero ordinate at the digitized PV values are selected, and compensation ~ormulas corresponding to the selected membership functions are retrieved from a memory. An FAND circuit forms all unique three element combinations o~ the ordinates and provides the "rule strength" or minimum of the each of the combinations. A weighting circuit function perform in substantially the same way as described above to provide a compensated primary PV, which is formatted and coupled to a two wire circuit.
RRTF~F' DESCRIPTION OF THE DR~WINGS
FIG . l is a sketch of a f ield mounted transmitter shown i~ a process control installation;
FIG. 2 is a block diagram of a transmitter made according to the present invention;
FIGS. 3A-C are plots of the three membership functions A-C respectively and FIG. 3D is a plot o~ the -0 95/2nl4l 2 1 7 ~ 8 ~ 9 A ~
'` '~ ` J ~ ! '.
. , , j ; ~ ,,.
all three membership functions A-C, all shown as a function of llnl ,~~Aated norr~ ed pressure;
FIG. 4 is a flowchart of, ~~Aat;n~ circuit 58 in FIG. 2;
FIG. 5 is a block diagram of ~ Aation circuit 58 with an alternative ~ t of membership function selection circuit 64;
FIG. 6 is a plot of a mul~ ciona membership functions;
FIG. 7 is a plot of the error as a function of pres6ure for two differential pressure sensors A and B.
TABLE l shows constants Rl through Rlo for each of the three regions.
DETATT~n DEsrRTpTIo~ OF TTTF pRP~ RRFn ~MR~nTM~NTs In FIG. 1, a pressure transmitter shown generally at 2 transmits an output representative of pressure to a digital control system ~DCS) 4 via a two wire current loop shown generally at 6. A fluid 8 in a tank 10 flows through pipe 12 irto a series of other pipes 14, 16 and 18, all containing fluid 8.
Measurement transmitter 2 senses the pressure difference across an orifice plate 20 situated in the flow of fluid 8. The pressure difference is representative of the f low rate of f luid 8 in pipe 12 . A valve 22 located downstream from transmitter 2 controls the flow in pipe 12 as a function of _ ~nrlA received from DCS unit 4 over another two wire loop 24. DCS unit 4 is typically located in a control room away from the process control field installation and in an explosic,l. pLoof and intrinsically safe area, whereas transmitter 2 and valve 22 are mounted directly onto pipe 12 in the field.
In FIG. 2, transmitter 2 is shown with two t~rm;n;llA 50, 52 which are couplable to two ttrm;n~lA of DCS 4 over twisted wire pair 6. DCS 4 is modeled as a W0 95120141 ` ~ i . r~ C
resistance and a power supply in serie6 and is shown generally at 4. Transmitter 2 h~s a sensor section 54 including a capacitance based differential pressure sensor 54A, an absolute pressure sensor 54B and a 5 temperature sensor 54C. Transmitter 2 senses differentiaI pressures between 0 and 250 inches of water. However, the types of process variable6 which transmitter 2 mea6ures may include ones representative of position, volumetric flow, mass flow, temperature, 10 level, density, disp~ , pH, turbidity, dissolved oxygen and ion concentration. Analog output from sensors 54A-C is coupled to converter circuit 56, which includes voltage or capacitance based analog-to-digital (A/D~ converters which can be of the type disclosed in ~.S. Patents 4,878,012, 5,083,091, 5,11g,033 and 5,155,455, assigned to the same assignee as the present invention. Each of converters 56A-C generates a serial bitstream of 10 to 16 bits representative of the corresponding digitized process variable (PV) onto a bus 20 connected to compensation circuit 58.
r t~ation circuit 58 uses fuzzy logic to provide an output representing a compensated PV and typically comprises a microprocessor such as a Motorola 68HC05 with integrated memory. Circuit 58 compensates 25 the errors in the digitized signal representing differential pressure with the r~;q;t;7~r3~ signals representing absolute pressure, temperature and differential pressure. C _ ~ation circuit 58 is based on the premise that compensation is most ~ccurately 30 modelled by segmenting the variables to be ~ ~Ated into multiple regions which overlap each other, where each region has assigned to it a simplified compensation formula optimized for that region and a membership function which can be multidimensional. The "strength"
-~Wo 95/20141 ; ~ 2 1 7 8 8 0 9 P~l/u~ ~
of the formula in the region is variable throughout the region and is described by the ordinate of the membership function at the value of the vari~ble to be --2cated. The ordinate of the member6hip function i5 5 typically a number between 0 and lO0 percent, indicating the extent to which the value of the variable to be RAted can be modeled by the Ration formula assigned to the selected region. Compensation is determined by first selecting the regions which include lO the value of the variable to be ~ ,-~Rated, and selecting the membership functions and ~nRation formulas corresponding to each selected region. The next step is to provide a set of correction values, by calculating each of the - - Ration L~ R at the 15 value of the variable to be ~ ~~Rated, and det~rm;ninq the strength of each correction value from the corresponding membership function. Finally, a , cation value is provided by combining the correction values, as weighted by the strength of the 20 membership function at the variable value to be compensated .
A member6hip function selection circuit 64 selects which membership function is non-zero at the digitized P,T,L value and outputs signals representative 25 of the selected membership functions on bus 64B.
Circuit 64 also outputs ordinates of the selected membership functions at the digitized P,T,L values (the ~rule strengths" ) at bus 64A. As a general rule, compensation circuit 58 includes at least two single 30 dimensional membership functions for differential pressure, each overlapping the other. If more than one varia~le i5 used for compensation, there ~as to be at least two membership functions for one of the variables.
FIGS. 3A-C show differential pressure membership Wo 95/20141 ~ 8- ~ 1 7 8 8 0 9 functions A, B and C, each of which have a non-zero value over a different prede~orm;n~d range of uncompensated pressures within the span. The variable to be compensated (differential pressure) is compensated 5 by the all three variables (P, T and ~), but only P is assigned membership functions . ( In the most general case, each variable i6 assigned multiple membership functions. ) Membership function A, shown as a solid line in FIG. 3A, has a non-zero value between 0 and 50%
lO span and a zero value thereafter. Membership function B, shown as a dotted line in FIG. 3B, has a non-zero value between 0 and 100% span and a zero value elsewhere. Membership function C, shown as a solid line in FIG. 3C, has a non-zero value between 50% and 100%
15 span and a zero elsewhere. FIG. 3D shows membership functions A, B and C plotted as a function of normalized pressure span. The non--zero segments of membership functions A, B and C define Regions l, 2 and 3, respectively. The form of the equations need not be the 20 same for each of the regions. The preferred form of the -nF:~tion formula for Regions 1--3 to meet the required accuracy with the metal cell DP sensor is given by Equ~tion l, which has a second order term as its highest term and requires no more that ten 25 characterization constants.
PCOR~ (P, ~,L~--Kl+K2P+K,l'+K,L+K5P2+K6:r (1) +K7L2+K~PL+Kg ~P+KloL~
Compensation formula evaluation circuit 66 evaluates and provides a correction value for each of the compensation formulas corresponding to the selected membership functions. The set of characterization constants for .. .. . .
g each of Regions 1-3 2re stored in memory 68 and given below in TA3LE 1.
K1 -2 . 5152 --3 . 4206 -7 .1604 5K2 278.5154 283.4241 293.4994 K3 --4 .1357 -2 . 3884 --0 . 3094 K4 2 . 4908 2 . 5038 2 . 7488 }t5 -3 . 4611 -lO . 5786 -17 . 4490 K6 ~4 .1901 --5 . 6594 -6 . 9354 K7 -0.1319 --0.1589 --0.2082 K8 11.9573 11.8335 11.4431 Kg --9 . 3189 --10 . 3664 --11. 5712 K1o 1.1318 1.2281 1.3502 15 Memory 68 i8 a non-volatile memory containing membership ~unctions, _^n~ation formulas and characterization constants for the r , ~ation f~ c. Combining ~unction circuit 70 receives the correction values and the rule strengt~s and provide6 a compensated P process 20 variable according to the equation given by:
21 ~wlfp~ (P, ~r, L) Pc2~p 21-1Wl ( 2 ) where N is the number of selected regions, Wi is the rule strength for the ith region, fi(P,T,1,) i 6 the correction value from the compensation ~ormula corresponding to the ith region and PComp represent6 the 2 5 compen s ated di f f ere~tial pre 5 5 ure .
WO 95/20141 ~ s 2 ~ 78809 Output circuit 62 receives and formats the compensated difierential pressure PV and couples it to r~rin~l~ 50, 52 for transmis6ion over process control loop 6. Output circuit 62 may be realized in several ways . A f irst alternative is a digital-to-analog circuit where the compensated PV is converted to an analog current representative of the, -n~ated PV and is thereafter coupled onto current loop 6. A second alternative is e fully digital transmission, such as Fieldbus, of the . ~ated PV onto loop 6. A third implementation superimposes a digital signal representative of the PV on an analog current also representative of the PV, such as in the HART0 protocol.
The number and the functional form of the membership functions are detPrminPd by the compensation accuracy required (e.g. .059~ accuracy) and the sensor's operating characteristics. For example, a sensor with a significant amount of error which must be compensated requires more membership f unctions than does a sensor which substantially meets the required amount of accuracy. Membership functions for the sensor which needs more ~ inn may each have a different functional form (e.g. exponential, gaussian, polynomial, constant, cubic spline, gaussian and logarithmic).
Consider a pressure of ~pproximately 30% of span, corresponding to an applied pressure of 75 . 0 inches of water, indicated on FIG. 3D by a solid vertical line and included in the non-zero segments of membership function A and s. Membership functions A and B, corresponding to Regions l and 2 are the "selected membership functions". The values of the two membership functions at 30~ of span are .359 and .641, respectively. The compensation formulas for Region l and 2 are given by Equation 3 and 5:
~W ~ ; 2 1 7 8 8 0 9 fp (P,T,L)--2.512+278.5154P-4.137T+2.4908L-3.4611P~
-4.1901T2-0.1319L**2+11.9573PL-9.3189~P+1.1318LT
fP2 (P, T~ ~) --3 4206+283 .4241P-2 . 3884T+2 . 5038L-10 5786p2 ~5) -5.694T**2-0.1589L~*2+11.8335PL-10.3664TP+1.2281LT
Correction values from Equation 3 and 5 are 75.188 and 75 . 070 inches of water, respectively. The compensated pressure is provided by a combining function, given by Equation 2 above, and is 75.112 inches of water, 5 simplified from:
.359 (75 .188) +.641 (75 . 070) (7) Pcoll~p . 3 5 9 1 . 6 4 1 The T and L values substituted into the above equation correspond to room temperature and atmospheric line pres sure .
Rather than executing a single eleventh order 10 polynomial as in the prior art, only two second order polynomials are computed. The resulting correction value from the second order function is insensitive to the manner in which computation takes place ( e . g. no overflows), requires less execution time, takes fewer 15 characterization constants and provides more space in memory for additional software functionality in transmitter 2. Another benefit of a fuzzy logic implementation of ~ation circuit 58 is to capture the effect of non-linear interaction between variables, 20 which is .iiffic~llt to model in a prior art single polynomial compensation scheme. The types of variables adapted for use in the disclosed, ~ation scheme are not limited to sensed PV8. The variable may be a time dependent variable, such as the first or second 25 derivative, or the integral, of the variable. In thi6 case, the corr~sp~n~lin~ membership function would be WO 95/20141 1 ~111 ~'0~ - ~
2 ~ 78~09 arranged to provide minimal ~-nRation when the derivative is large ( i . e . the magnitude of the compensation is insignificant compared to the magnitude of the pres6ure change, so it is adequate to 5 approximately compensate the primary PV). Optimal value stem actuation by a positioner or actuator, such as in a pick and place machine, requires a sensed position and may include a velocity and an acceleration. Another type of variable is a "history rlPron~l~nt variable, lO where effects of hysteresis are taken into account.
History de~e~,del~L PVs include information about the previous measurements taken with the specific sensor in transmitter 2. For example, extreme overpressurization of a capacitive based pressure sensor modifies its 1~ capacitance as a function of pressure in subsequent measurements. Different compensation formulas apply depending on the severity and frequency of the overpressurization. Another type of variable is a 'position ~l~rRn~ t" variable, where the value of the 20 variable changes with position, such as in a diaphragm having one stiffness when bowed and another stiffness in the absence of applied pressure. Another type of variable is a "device tl~p~n~ nt" variable, where the membership functions and compensation formulas change 25 with the materials used to manufacture transmitter 2.
For example, a sensor sensing pressure within a low pressure range has different compensation requirements than does a high range pressure sensor. Similarly, a pressure sensor with a diaphragm made of HASTELLOY0 has 30 different error characteristics, and hence requires different compensation, than does one made of D~ONEL0.
The present invention solves inaccuracies in 2 prior art ~ Ration technique called piecewise linear fitting. In piecewise linear fitting, the span ~O 95/20141 , ~ 2 1 7 ~ 8 0 9 ; ., , ~, ~ , ,, of the variable of interest is segmented into two or more ranges, and a linear equation is selected for each range which optimally f its each of the ranges .
Unfortunately, there are typically small 5 discontinuities, or mismatches, at the boundaries between the separately _ -Rated ranges. The present Ancation scheme, with the overlapping membership functions, provides a smooth transition between ranges of the variable of interest.
In FIG. 4, a flowchart of the functions in compensation circuit 58 is disclosed. The process variables P,T,L are sensed and digitized in blocks 200 and 202 respectively. A counter for counting the number of regions i5 inir;Al;7ed in block 204. A decision 15 block 206 retrieves the ith membership function from a memory block 208 and determines whether the digitized P,T,L value is in the ith region described by the ith membership function. If the digitized point is included in the region, a computation block 210 retrieves 20 appropriate Ration formulas and characterization constants from memory 208 to compute the ordinate value of a membership function fmi(P,T,L) and a correction value fCi(P,T,L) computed from the ith -nRation formula, or otherwise increments the region counter i.
25 Decision block 212 causes the loop to re-execute until all the regions which include the digitized P,T,L point are selected. Then block 214 computes the compensated dif ferential pressure as indicated.
FIG. 5 details an alternative ~ i nt of 30 membership function selection circuit 64. Exactly as in FIG. 2, ~uzzy Ration circuit 58 receives digitized differential pressure (P), digitized absolute linç
pressure (L) and digitized temperature (T), and uses those three variables to provide a ~: -AAted WO 95/20141 F~ 3'' 2 1 78~09 differential pres6ure. The three main furlctional blocks are a rule strength clrcuit 302, a ~ _ Aation formula evaluation circuit 304 and a ;nin~ circuit 306.
However, in this alternative: ~ _rli t, all of the 5 three variables (P,T,L) are assigned multiple membership functions. In particular, differential pressure is assigned four membership functions defined a8 fp1, fp2, fp3 and fp4; temperature is assigned three membership functions defined as ft1, ft2, and ft3; and absolute 10 pressure is assigned two membership functions defined as fll and fl2- Circuit 58 is preferably implemented in a C~105 microprocessor (with adequate on-chip memory), so as to conserve power in the transmitter, which receives power solely from the current loop.
Circuit 310 receives the digitized P value and selects those member~hip functions which have a non-zero ordinate at t~te digitized P value. secause the non-zero portions of the membership functions may overlap, there is usually more that one selected membership function 20 for each digitized PV. When the membership functions overlap each other by 509~, 2N equations are computed where N is the number of variables which are divided into more than one membership function. The output o~
circuit 310 i6 the ordinate of each of the selected 25 membership functions corresponding to the digitized P
value, and is lAhellPd at 310A. Por example, if the digitized P value were inr~lt~ d in the non-zero portion of three of the four P membership functions, then circ~lit 310 outputs three values, each value being an 30 ordinate o~ the three selected membership function6 corresponding to the digitized P value. Specifically for P = pO, bus 310A include5 the ordinate8: [ fp2(Po) ~
fp3~po)~ fp4(po) ]. At about the same time so as to be effectiv~ly simultaneous, circuit 312 receive6 the o 95/20141 r~
~w ; i `~ i ` 2 1 7880~
digitized T value and selects temperature membership functions having a non-zero value at the digitized T
value. If the digitized T value were included in the non-zero portion of two of the three T membership f unctions, then circuit 312 outputs two values on bus 312A, each value being an ordinate of a selected membership function. Specifically for T = tor bus 312A
includes the ordinates: [ ft2~to), ft3(to) ]. In similar fashion, circuit 314 receives the digitized L
value and selects absolute pressure membership functions having a non-zero value at the digitized L value. If the digitized L value were included in both of the two L membership functions, then circuit 314 outputs two values on bus 314A, each value being an ordinate of a selected membership fu~ction. Spe~ if ir~l ly for L = lo~
bus 314A includes the ordinate5: [ f ll ( lo ) ~ f 12 ( lo ) ] -Fuzzy AND circuit 316 forms all unique three element combinations of the ordinates it receives from circuits 310-314 (where each combination includes one value from each of the three busses 310A, 312A and 314A) and outputs the fuzzy AND (the minimum) of each of the unique combinations on a bus 31 6A . For the set of P, T
and L values from the eYample above, the set of unique membership function ordinate combinations is:
[ fp2(Po) ft2(to) fll(lO) ]
[ fp2(Po) ft2(to) f12(10) ]
[ fp2(Po) ft3(to) fll(10) ]
[ fp2(Po) ft3(to) fl2(l0) ]
[ fp3(P0) ft2(to) fll(lO) ]
[ fp3(Po) ft2(to) fl2(lo) ]
[ fp3(P0) ft3(to) fll(lO) ]
[ fp3(Po) ft3(to) fl2(10) ]
[ fp4(Po) ft2(to~ fll(lO) ]
[ fp4(Po) ft2(to) fl2(l0) ]
[ fp4(Po) ft3(to) fll(lO) ]
[ fp4(P0) ft3(to) fl2(l0) ]
Wo 95120141 I ~
~; ~ 2178809 The effect of the fuzzy AND circuit 316 i6 to take single variable membership function~ for P, T and and create multivariable membership function6 in P-T-I, sp~ce. Although it canno~ be rendered gr~phically, 5 circuit 316 creates in P-T-L space a set of 24 three-variable membership functions from the four P, three T
and two L single-~ ionA1 membership functions.
There are 24 compensation formulas corresponding to the 24 membership functions. In general, the number of 10 multivariable membership ~unctions created i6 equal to the product of the number of membership f unctions defined for each individual variable. FIG. 6 gives an example of multivariable membership functions in two variables, P and T. Twelve overlapping pe~t~hefirally 15 shaped two-variable membership functions are defined in P-T space from four triangularly shaped P membership functions nnd three triangularly T membership functions.
Each multivariable membership function ~ oLLe~L,onds to a compensation formula, and the ordinate of the 20 multivariable membership function (the output of the fuzzy A~D) is called a "rule strength" which describes the extent to which the compensated pressure can be modelled with the ~o-L~ .vllding, -n~tion formula.
Circuit 316 selects those compensation 25 formulas ~l~LL~yollding to each "rule strength" output on bus 316B. Bus 316B ha6 as many signals in it as there are compensation formulas. A "one" value corresponding to a specific ~ ~a~;nn formula indicates that it is selected for use in compensation formula evaluation 30 circuit 304. In our specific example, each of the twelve rule strengths defines a point on the surface of twelve separate pentahedron6, 80 that twelve compensation formulas (out o~ a total of 24) are selected .
0 95/20141 r ~ ~
~w 21 7~09 ~ emory 308 store6 the form and the characterization constants for each of the ~ -n~ation formulas. C~ ,-n~ation formula evaluation circuit 304 retrieves the constants for the selected ~, %ation formula6 indicated via bus 316B from memory 308, and calculates a correction value corresponding to each of the selected , ~ation formulas. Combining circuit 306 receives the correction values and the rule strengths for each of the selected regions and weights the correction values by the appropriate rule strength.
The weighted average is given by Equation 4. The characterization constants stored in memory 308 are the result of a weighted least squares f it between the actual operating characteristics of the sensor and the chosen form of the compensation formula for that ~, ~ation formula. (The weighted least squares fit is performed during --nllfact~re, rather than operation of the unit. ) The weighted least s~auares fit is given by:
~_p~ ( 8 ) where b is a nxl vector of calculated characterization coefficients, P is the nxn weighted covariance matrix of the input data matrix X and ~ is the nxl weighted covariance vector of X with y. The data matrix X is of dimension mxn where each row is one of m data vectors representing one of the m (P,T,L) characterization points .
In an alternate embodiment of compensation circuit 58 shown in FIG. 5, FA~D circuit 316 is obviated and membership function circuits 310-314 are replaced by three explicitly defined three dimensional membership functions having the form of a radial basis function given generally by:
Wo 95/20 14 1 P ~ ~
2 1 7 8 8 0 q R~ exp [ ~ ] ( 9 ) In the radial basis function, X i8 a three dimensional vcctor who6e components are the digitized P, T 2nd L
values, Xi is a three dimensional vector d~f i n i ns the center of the function in P-T-L space, and c~ controls 5 the width of the function. A set of multidimensional membership functions, such as with radial basis functions, effectively replaces the function of FAND
circuit 316, since the FAND circuit provides a set of multidimensional membership functions from sets of 10 single ~l;r~ Al membership functions.
The present invention is particularly suitable when used in a transmitter with dual differential pressure sensors. FIG. 7 shows the sensor error on the respective y axes 400,402 plotted as a function of sensed differential pressure on x axes 404,406 for two pressure sensors A and B (labelled), each connected as shown for pressure sensor 54A in FIG. 2. Sensor A
senses a wide range of pressure6 between 0 and lO00 PSI, while sensor B senses pressure over a tenth of the other 20 sensor~s span; from 0 to 100 PSI. The error for sensor A is greater at any given pressure than the error for sensor B at the same pressure. A dual sensor transmitter as described here has an output representative of the converted output ~rom sensor B at 25 low pressures, but switches to an output representatiVe of the converted output ~rom sensor A over higher pressures. The present compensation scheme provides a smooth transmitter output when the transmitter switches between the sensors A and B. In the same fashion as 30 disclosed in FIG3A-D, the output from sensor A is treated as one process variable and output ~rom sensor B is treated as ~nother process variable. As disclosed, o ~5120141 P~
~w 2 1 7 8 8 0 9 each process variable has ~ ne~l to it a membership function and a --~ation formula, which indicate the extent to which the process variable can be modelled by the compensation f ormula . A correction value is provided from computing each of the two compensation formulas, and a ~ in;ng function weights the correction values and provides a compensated pressure.
This is a preferred ~ -- RAtion scheme for dual sensor transmitters in that output from both sensors is used throughout a switchover range of pressures, (i.e. no data is discarded for pressures measured within the switchover range ) with the relative weighting of the output from each sensor defined by each sensor's membership function. This ~rplicAhility of the present ~ation scheme to dual sensors applies equally well to transmitters having multiple sensors sensing the same process variable, and to transmitters with redundant sensors where each sensor senses a range of PVs substantially the same as the other.
Although the present invention has been described with reference to preferred embodiments, workers skilled in the art will recognize that changes may be made in f orm and detail without departing f rom the spirit and scope of the invention. The present invention can be applied to devices outside of the process control and process automation industry, and for example could be used to compensate control surface position in an airplane. The type of variables used in the compensation circuit can be other than PVs, the ^n~ation formulas and membership functions can be of forms other than poly ;.ql~, and the combining function can be ~ non li=e~r ~veraging function.
over the same wire6 used for communication.
Furthermore, some "intrinsically safe" areas where transmitters are installed limit the transmitter ~ s available power . The f inite current budget not only limits the number and complexity of the calculations, but impacts the functionality able to be incorporated in the transmitter. For example, A/D converters could convert digitized sensor outputs more rapidly if more power were available, thereby increasing the transmitter update rate. An EEP~OM large enough to acc~ te all the characterization constant6 also consume6 power which would otherwise provide additional functionality.
There i8 thus a need for an accurate method for compensating process variables which is computationally simple and requires small numbers of stored characterization constants, so as to consume a reduced amount of power and provide excess power for additional functionality and increased update rates in the transmitter.
STTMM~T~Y OF 'rT-TT` INVENTION
In an: ' ~'; t, a measurement transmitter has a sensor for sensing a process variable (PV) such as pressure and digitizing means for digitizing an output representatiYe of the sen6ed PV. The sensor senses the PV within a span of PV values. A memory inside the transmitter stores at least two membership functions, each membership function having a non-zero value over a predetermined region of the PV span and a substantially zero value over the L- i nd~r of the 6pan . The memory also stores a set of compensation f~rr-~ , each formula corresponding to a membership f unction . A selection circuit in the transmitter selects those membership functions which have a non-zero ordinate at the value of the digitized PV and a correction circuit provides at Wo95120141 l~11u~ l 2 1 78809 ~
least one correction value, each correction value calculated from a _ ~ation formula corresponding to a selected membership function. A weighting circuit weights each correction value by the ordinate of the corresponding selected membership function, and 1n~c the multiplicands to provide a compensated PV. The compensated PV is coupled to a control circuit connecting the transmitter to a control system.
A second . ' ~; L includes a sensor for sensing a primary PV such as differential pressure, ~nd other sensors for sensing secondary PVs such as line pressure and t ~ aLul~. A set of converters digitize the sensed PVs. Each of the variables is elssigned at least one membership function, with at least one of the variables having assigned at least two single dimen~ional membership functions. The membership functions having a substantially non-zero ordinate at the digitized PV values are selected, and compensation ~ormulas corresponding to the selected membership functions are retrieved from a memory. An FAND circuit forms all unique three element combinations o~ the ordinates and provides the "rule strength" or minimum of the each of the combinations. A weighting circuit function perform in substantially the same way as described above to provide a compensated primary PV, which is formatted and coupled to a two wire circuit.
RRTF~F' DESCRIPTION OF THE DR~WINGS
FIG . l is a sketch of a f ield mounted transmitter shown i~ a process control installation;
FIG. 2 is a block diagram of a transmitter made according to the present invention;
FIGS. 3A-C are plots of the three membership functions A-C respectively and FIG. 3D is a plot o~ the -0 95/2nl4l 2 1 7 ~ 8 ~ 9 A ~
'` '~ ` J ~ ! '.
. , , j ; ~ ,,.
all three membership functions A-C, all shown as a function of llnl ,~~Aated norr~ ed pressure;
FIG. 4 is a flowchart of, ~~Aat;n~ circuit 58 in FIG. 2;
FIG. 5 is a block diagram of ~ Aation circuit 58 with an alternative ~ t of membership function selection circuit 64;
FIG. 6 is a plot of a mul~ ciona membership functions;
FIG. 7 is a plot of the error as a function of pres6ure for two differential pressure sensors A and B.
TABLE l shows constants Rl through Rlo for each of the three regions.
DETATT~n DEsrRTpTIo~ OF TTTF pRP~ RRFn ~MR~nTM~NTs In FIG. 1, a pressure transmitter shown generally at 2 transmits an output representative of pressure to a digital control system ~DCS) 4 via a two wire current loop shown generally at 6. A fluid 8 in a tank 10 flows through pipe 12 irto a series of other pipes 14, 16 and 18, all containing fluid 8.
Measurement transmitter 2 senses the pressure difference across an orifice plate 20 situated in the flow of fluid 8. The pressure difference is representative of the f low rate of f luid 8 in pipe 12 . A valve 22 located downstream from transmitter 2 controls the flow in pipe 12 as a function of _ ~nrlA received from DCS unit 4 over another two wire loop 24. DCS unit 4 is typically located in a control room away from the process control field installation and in an explosic,l. pLoof and intrinsically safe area, whereas transmitter 2 and valve 22 are mounted directly onto pipe 12 in the field.
In FIG. 2, transmitter 2 is shown with two t~rm;n;llA 50, 52 which are couplable to two ttrm;n~lA of DCS 4 over twisted wire pair 6. DCS 4 is modeled as a W0 95120141 ` ~ i . r~ C
resistance and a power supply in serie6 and is shown generally at 4. Transmitter 2 h~s a sensor section 54 including a capacitance based differential pressure sensor 54A, an absolute pressure sensor 54B and a 5 temperature sensor 54C. Transmitter 2 senses differentiaI pressures between 0 and 250 inches of water. However, the types of process variable6 which transmitter 2 mea6ures may include ones representative of position, volumetric flow, mass flow, temperature, 10 level, density, disp~ , pH, turbidity, dissolved oxygen and ion concentration. Analog output from sensors 54A-C is coupled to converter circuit 56, which includes voltage or capacitance based analog-to-digital (A/D~ converters which can be of the type disclosed in ~.S. Patents 4,878,012, 5,083,091, 5,11g,033 and 5,155,455, assigned to the same assignee as the present invention. Each of converters 56A-C generates a serial bitstream of 10 to 16 bits representative of the corresponding digitized process variable (PV) onto a bus 20 connected to compensation circuit 58.
r t~ation circuit 58 uses fuzzy logic to provide an output representing a compensated PV and typically comprises a microprocessor such as a Motorola 68HC05 with integrated memory. Circuit 58 compensates 25 the errors in the digitized signal representing differential pressure with the r~;q;t;7~r3~ signals representing absolute pressure, temperature and differential pressure. C _ ~ation circuit 58 is based on the premise that compensation is most ~ccurately 30 modelled by segmenting the variables to be ~ ~Ated into multiple regions which overlap each other, where each region has assigned to it a simplified compensation formula optimized for that region and a membership function which can be multidimensional. The "strength"
-~Wo 95/20141 ; ~ 2 1 7 8 8 0 9 P~l/u~ ~
of the formula in the region is variable throughout the region and is described by the ordinate of the membership function at the value of the vari~ble to be --2cated. The ordinate of the member6hip function i5 5 typically a number between 0 and lO0 percent, indicating the extent to which the value of the variable to be RAted can be modeled by the Ration formula assigned to the selected region. Compensation is determined by first selecting the regions which include lO the value of the variable to be ~ ,-~Rated, and selecting the membership functions and ~nRation formulas corresponding to each selected region. The next step is to provide a set of correction values, by calculating each of the - - Ration L~ R at the 15 value of the variable to be ~ ~~Rated, and det~rm;ninq the strength of each correction value from the corresponding membership function. Finally, a , cation value is provided by combining the correction values, as weighted by the strength of the 20 membership function at the variable value to be compensated .
A member6hip function selection circuit 64 selects which membership function is non-zero at the digitized P,T,L value and outputs signals representative 25 of the selected membership functions on bus 64B.
Circuit 64 also outputs ordinates of the selected membership functions at the digitized P,T,L values (the ~rule strengths" ) at bus 64A. As a general rule, compensation circuit 58 includes at least two single 30 dimensional membership functions for differential pressure, each overlapping the other. If more than one varia~le i5 used for compensation, there ~as to be at least two membership functions for one of the variables.
FIGS. 3A-C show differential pressure membership Wo 95/20141 ~ 8- ~ 1 7 8 8 0 9 functions A, B and C, each of which have a non-zero value over a different prede~orm;n~d range of uncompensated pressures within the span. The variable to be compensated (differential pressure) is compensated 5 by the all three variables (P, T and ~), but only P is assigned membership functions . ( In the most general case, each variable i6 assigned multiple membership functions. ) Membership function A, shown as a solid line in FIG. 3A, has a non-zero value between 0 and 50%
lO span and a zero value thereafter. Membership function B, shown as a dotted line in FIG. 3B, has a non-zero value between 0 and 100% span and a zero value elsewhere. Membership function C, shown as a solid line in FIG. 3C, has a non-zero value between 50% and 100%
15 span and a zero elsewhere. FIG. 3D shows membership functions A, B and C plotted as a function of normalized pressure span. The non--zero segments of membership functions A, B and C define Regions l, 2 and 3, respectively. The form of the equations need not be the 20 same for each of the regions. The preferred form of the -nF:~tion formula for Regions 1--3 to meet the required accuracy with the metal cell DP sensor is given by Equ~tion l, which has a second order term as its highest term and requires no more that ten 25 characterization constants.
PCOR~ (P, ~,L~--Kl+K2P+K,l'+K,L+K5P2+K6:r (1) +K7L2+K~PL+Kg ~P+KloL~
Compensation formula evaluation circuit 66 evaluates and provides a correction value for each of the compensation formulas corresponding to the selected membership functions. The set of characterization constants for .. .. . .
g each of Regions 1-3 2re stored in memory 68 and given below in TA3LE 1.
K1 -2 . 5152 --3 . 4206 -7 .1604 5K2 278.5154 283.4241 293.4994 K3 --4 .1357 -2 . 3884 --0 . 3094 K4 2 . 4908 2 . 5038 2 . 7488 }t5 -3 . 4611 -lO . 5786 -17 . 4490 K6 ~4 .1901 --5 . 6594 -6 . 9354 K7 -0.1319 --0.1589 --0.2082 K8 11.9573 11.8335 11.4431 Kg --9 . 3189 --10 . 3664 --11. 5712 K1o 1.1318 1.2281 1.3502 15 Memory 68 i8 a non-volatile memory containing membership ~unctions, _^n~ation formulas and characterization constants for the r , ~ation f~ c. Combining ~unction circuit 70 receives the correction values and the rule strengt~s and provide6 a compensated P process 20 variable according to the equation given by:
21 ~wlfp~ (P, ~r, L) Pc2~p 21-1Wl ( 2 ) where N is the number of selected regions, Wi is the rule strength for the ith region, fi(P,T,1,) i 6 the correction value from the compensation ~ormula corresponding to the ith region and PComp represent6 the 2 5 compen s ated di f f ere~tial pre 5 5 ure .
WO 95/20141 ~ s 2 ~ 78809 Output circuit 62 receives and formats the compensated difierential pressure PV and couples it to r~rin~l~ 50, 52 for transmis6ion over process control loop 6. Output circuit 62 may be realized in several ways . A f irst alternative is a digital-to-analog circuit where the compensated PV is converted to an analog current representative of the, -n~ated PV and is thereafter coupled onto current loop 6. A second alternative is e fully digital transmission, such as Fieldbus, of the . ~ated PV onto loop 6. A third implementation superimposes a digital signal representative of the PV on an analog current also representative of the PV, such as in the HART0 protocol.
The number and the functional form of the membership functions are detPrminPd by the compensation accuracy required (e.g. .059~ accuracy) and the sensor's operating characteristics. For example, a sensor with a significant amount of error which must be compensated requires more membership f unctions than does a sensor which substantially meets the required amount of accuracy. Membership functions for the sensor which needs more ~ inn may each have a different functional form (e.g. exponential, gaussian, polynomial, constant, cubic spline, gaussian and logarithmic).
Consider a pressure of ~pproximately 30% of span, corresponding to an applied pressure of 75 . 0 inches of water, indicated on FIG. 3D by a solid vertical line and included in the non-zero segments of membership function A and s. Membership functions A and B, corresponding to Regions l and 2 are the "selected membership functions". The values of the two membership functions at 30~ of span are .359 and .641, respectively. The compensation formulas for Region l and 2 are given by Equation 3 and 5:
~W ~ ; 2 1 7 8 8 0 9 fp (P,T,L)--2.512+278.5154P-4.137T+2.4908L-3.4611P~
-4.1901T2-0.1319L**2+11.9573PL-9.3189~P+1.1318LT
fP2 (P, T~ ~) --3 4206+283 .4241P-2 . 3884T+2 . 5038L-10 5786p2 ~5) -5.694T**2-0.1589L~*2+11.8335PL-10.3664TP+1.2281LT
Correction values from Equation 3 and 5 are 75.188 and 75 . 070 inches of water, respectively. The compensated pressure is provided by a combining function, given by Equation 2 above, and is 75.112 inches of water, 5 simplified from:
.359 (75 .188) +.641 (75 . 070) (7) Pcoll~p . 3 5 9 1 . 6 4 1 The T and L values substituted into the above equation correspond to room temperature and atmospheric line pres sure .
Rather than executing a single eleventh order 10 polynomial as in the prior art, only two second order polynomials are computed. The resulting correction value from the second order function is insensitive to the manner in which computation takes place ( e . g. no overflows), requires less execution time, takes fewer 15 characterization constants and provides more space in memory for additional software functionality in transmitter 2. Another benefit of a fuzzy logic implementation of ~ation circuit 58 is to capture the effect of non-linear interaction between variables, 20 which is .iiffic~llt to model in a prior art single polynomial compensation scheme. The types of variables adapted for use in the disclosed, ~ation scheme are not limited to sensed PV8. The variable may be a time dependent variable, such as the first or second 25 derivative, or the integral, of the variable. In thi6 case, the corr~sp~n~lin~ membership function would be WO 95/20141 1 ~111 ~'0~ - ~
2 ~ 78~09 arranged to provide minimal ~-nRation when the derivative is large ( i . e . the magnitude of the compensation is insignificant compared to the magnitude of the pres6ure change, so it is adequate to 5 approximately compensate the primary PV). Optimal value stem actuation by a positioner or actuator, such as in a pick and place machine, requires a sensed position and may include a velocity and an acceleration. Another type of variable is a "history rlPron~l~nt variable, lO where effects of hysteresis are taken into account.
History de~e~,del~L PVs include information about the previous measurements taken with the specific sensor in transmitter 2. For example, extreme overpressurization of a capacitive based pressure sensor modifies its 1~ capacitance as a function of pressure in subsequent measurements. Different compensation formulas apply depending on the severity and frequency of the overpressurization. Another type of variable is a 'position ~l~rRn~ t" variable, where the value of the 20 variable changes with position, such as in a diaphragm having one stiffness when bowed and another stiffness in the absence of applied pressure. Another type of variable is a "device tl~p~n~ nt" variable, where the membership functions and compensation formulas change 25 with the materials used to manufacture transmitter 2.
For example, a sensor sensing pressure within a low pressure range has different compensation requirements than does a high range pressure sensor. Similarly, a pressure sensor with a diaphragm made of HASTELLOY0 has 30 different error characteristics, and hence requires different compensation, than does one made of D~ONEL0.
The present invention solves inaccuracies in 2 prior art ~ Ration technique called piecewise linear fitting. In piecewise linear fitting, the span ~O 95/20141 , ~ 2 1 7 ~ 8 0 9 ; ., , ~, ~ , ,, of the variable of interest is segmented into two or more ranges, and a linear equation is selected for each range which optimally f its each of the ranges .
Unfortunately, there are typically small 5 discontinuities, or mismatches, at the boundaries between the separately _ -Rated ranges. The present Ancation scheme, with the overlapping membership functions, provides a smooth transition between ranges of the variable of interest.
In FIG. 4, a flowchart of the functions in compensation circuit 58 is disclosed. The process variables P,T,L are sensed and digitized in blocks 200 and 202 respectively. A counter for counting the number of regions i5 inir;Al;7ed in block 204. A decision 15 block 206 retrieves the ith membership function from a memory block 208 and determines whether the digitized P,T,L value is in the ith region described by the ith membership function. If the digitized point is included in the region, a computation block 210 retrieves 20 appropriate Ration formulas and characterization constants from memory 208 to compute the ordinate value of a membership function fmi(P,T,L) and a correction value fCi(P,T,L) computed from the ith -nRation formula, or otherwise increments the region counter i.
25 Decision block 212 causes the loop to re-execute until all the regions which include the digitized P,T,L point are selected. Then block 214 computes the compensated dif ferential pressure as indicated.
FIG. 5 details an alternative ~ i nt of 30 membership function selection circuit 64. Exactly as in FIG. 2, ~uzzy Ration circuit 58 receives digitized differential pressure (P), digitized absolute linç
pressure (L) and digitized temperature (T), and uses those three variables to provide a ~: -AAted WO 95/20141 F~ 3'' 2 1 78~09 differential pres6ure. The three main furlctional blocks are a rule strength clrcuit 302, a ~ _ Aation formula evaluation circuit 304 and a ;nin~ circuit 306.
However, in this alternative: ~ _rli t, all of the 5 three variables (P,T,L) are assigned multiple membership functions. In particular, differential pressure is assigned four membership functions defined a8 fp1, fp2, fp3 and fp4; temperature is assigned three membership functions defined as ft1, ft2, and ft3; and absolute 10 pressure is assigned two membership functions defined as fll and fl2- Circuit 58 is preferably implemented in a C~105 microprocessor (with adequate on-chip memory), so as to conserve power in the transmitter, which receives power solely from the current loop.
Circuit 310 receives the digitized P value and selects those member~hip functions which have a non-zero ordinate at t~te digitized P value. secause the non-zero portions of the membership functions may overlap, there is usually more that one selected membership function 20 for each digitized PV. When the membership functions overlap each other by 509~, 2N equations are computed where N is the number of variables which are divided into more than one membership function. The output o~
circuit 310 i6 the ordinate of each of the selected 25 membership functions corresponding to the digitized P
value, and is lAhellPd at 310A. Por example, if the digitized P value were inr~lt~ d in the non-zero portion of three of the four P membership functions, then circ~lit 310 outputs three values, each value being an 30 ordinate o~ the three selected membership function6 corresponding to the digitized P value. Specifically for P = pO, bus 310A include5 the ordinate8: [ fp2(Po) ~
fp3~po)~ fp4(po) ]. At about the same time so as to be effectiv~ly simultaneous, circuit 312 receive6 the o 95/20141 r~
~w ; i `~ i ` 2 1 7880~
digitized T value and selects temperature membership functions having a non-zero value at the digitized T
value. If the digitized T value were included in the non-zero portion of two of the three T membership f unctions, then circuit 312 outputs two values on bus 312A, each value being an ordinate of a selected membership function. Specifically for T = tor bus 312A
includes the ordinates: [ ft2~to), ft3(to) ]. In similar fashion, circuit 314 receives the digitized L
value and selects absolute pressure membership functions having a non-zero value at the digitized L value. If the digitized L value were included in both of the two L membership functions, then circuit 314 outputs two values on bus 314A, each value being an ordinate of a selected membership fu~ction. Spe~ if ir~l ly for L = lo~
bus 314A includes the ordinate5: [ f ll ( lo ) ~ f 12 ( lo ) ] -Fuzzy AND circuit 316 forms all unique three element combinations of the ordinates it receives from circuits 310-314 (where each combination includes one value from each of the three busses 310A, 312A and 314A) and outputs the fuzzy AND (the minimum) of each of the unique combinations on a bus 31 6A . For the set of P, T
and L values from the eYample above, the set of unique membership function ordinate combinations is:
[ fp2(Po) ft2(to) fll(lO) ]
[ fp2(Po) ft2(to) f12(10) ]
[ fp2(Po) ft3(to) fll(10) ]
[ fp2(Po) ft3(to) fl2(l0) ]
[ fp3(P0) ft2(to) fll(lO) ]
[ fp3(Po) ft2(to) fl2(lo) ]
[ fp3(P0) ft3(to) fll(lO) ]
[ fp3(Po) ft3(to) fl2(10) ]
[ fp4(Po) ft2(to~ fll(lO) ]
[ fp4(Po) ft2(to) fl2(l0) ]
[ fp4(Po) ft3(to) fll(lO) ]
[ fp4(P0) ft3(to) fl2(l0) ]
Wo 95120141 I ~
~; ~ 2178809 The effect of the fuzzy AND circuit 316 i6 to take single variable membership function~ for P, T and and create multivariable membership function6 in P-T-I, sp~ce. Although it canno~ be rendered gr~phically, 5 circuit 316 creates in P-T-L space a set of 24 three-variable membership functions from the four P, three T
and two L single-~ ionA1 membership functions.
There are 24 compensation formulas corresponding to the 24 membership functions. In general, the number of 10 multivariable membership ~unctions created i6 equal to the product of the number of membership f unctions defined for each individual variable. FIG. 6 gives an example of multivariable membership functions in two variables, P and T. Twelve overlapping pe~t~hefirally 15 shaped two-variable membership functions are defined in P-T space from four triangularly shaped P membership functions nnd three triangularly T membership functions.
Each multivariable membership function ~ oLLe~L,onds to a compensation formula, and the ordinate of the 20 multivariable membership function (the output of the fuzzy A~D) is called a "rule strength" which describes the extent to which the compensated pressure can be modelled with the ~o-L~ .vllding, -n~tion formula.
Circuit 316 selects those compensation 25 formulas ~l~LL~yollding to each "rule strength" output on bus 316B. Bus 316B ha6 as many signals in it as there are compensation formulas. A "one" value corresponding to a specific ~ ~a~;nn formula indicates that it is selected for use in compensation formula evaluation 30 circuit 304. In our specific example, each of the twelve rule strengths defines a point on the surface of twelve separate pentahedron6, 80 that twelve compensation formulas (out o~ a total of 24) are selected .
0 95/20141 r ~ ~
~w 21 7~09 ~ emory 308 store6 the form and the characterization constants for each of the ~ -n~ation formulas. C~ ,-n~ation formula evaluation circuit 304 retrieves the constants for the selected ~, %ation formula6 indicated via bus 316B from memory 308, and calculates a correction value corresponding to each of the selected , ~ation formulas. Combining circuit 306 receives the correction values and the rule strengths for each of the selected regions and weights the correction values by the appropriate rule strength.
The weighted average is given by Equation 4. The characterization constants stored in memory 308 are the result of a weighted least squares f it between the actual operating characteristics of the sensor and the chosen form of the compensation formula for that ~, ~ation formula. (The weighted least squares fit is performed during --nllfact~re, rather than operation of the unit. ) The weighted least s~auares fit is given by:
~_p~ ( 8 ) where b is a nxl vector of calculated characterization coefficients, P is the nxn weighted covariance matrix of the input data matrix X and ~ is the nxl weighted covariance vector of X with y. The data matrix X is of dimension mxn where each row is one of m data vectors representing one of the m (P,T,L) characterization points .
In an alternate embodiment of compensation circuit 58 shown in FIG. 5, FA~D circuit 316 is obviated and membership function circuits 310-314 are replaced by three explicitly defined three dimensional membership functions having the form of a radial basis function given generally by:
Wo 95/20 14 1 P ~ ~
2 1 7 8 8 0 q R~ exp [ ~ ] ( 9 ) In the radial basis function, X i8 a three dimensional vcctor who6e components are the digitized P, T 2nd L
values, Xi is a three dimensional vector d~f i n i ns the center of the function in P-T-L space, and c~ controls 5 the width of the function. A set of multidimensional membership functions, such as with radial basis functions, effectively replaces the function of FAND
circuit 316, since the FAND circuit provides a set of multidimensional membership functions from sets of 10 single ~l;r~ Al membership functions.
The present invention is particularly suitable when used in a transmitter with dual differential pressure sensors. FIG. 7 shows the sensor error on the respective y axes 400,402 plotted as a function of sensed differential pressure on x axes 404,406 for two pressure sensors A and B (labelled), each connected as shown for pressure sensor 54A in FIG. 2. Sensor A
senses a wide range of pressure6 between 0 and lO00 PSI, while sensor B senses pressure over a tenth of the other 20 sensor~s span; from 0 to 100 PSI. The error for sensor A is greater at any given pressure than the error for sensor B at the same pressure. A dual sensor transmitter as described here has an output representative of the converted output ~rom sensor B at 25 low pressures, but switches to an output representatiVe of the converted output ~rom sensor A over higher pressures. The present compensation scheme provides a smooth transmitter output when the transmitter switches between the sensors A and B. In the same fashion as 30 disclosed in FIG3A-D, the output from sensor A is treated as one process variable and output ~rom sensor B is treated as ~nother process variable. As disclosed, o ~5120141 P~
~w 2 1 7 8 8 0 9 each process variable has ~ ne~l to it a membership function and a --~ation formula, which indicate the extent to which the process variable can be modelled by the compensation f ormula . A correction value is provided from computing each of the two compensation formulas, and a ~ in;ng function weights the correction values and provides a compensated pressure.
This is a preferred ~ -- RAtion scheme for dual sensor transmitters in that output from both sensors is used throughout a switchover range of pressures, (i.e. no data is discarded for pressures measured within the switchover range ) with the relative weighting of the output from each sensor defined by each sensor's membership function. This ~rplicAhility of the present ~ation scheme to dual sensors applies equally well to transmitters having multiple sensors sensing the same process variable, and to transmitters with redundant sensors where each sensor senses a range of PVs substantially the same as the other.
Although the present invention has been described with reference to preferred embodiments, workers skilled in the art will recognize that changes may be made in f orm and detail without departing f rom the spirit and scope of the invention. The present invention can be applied to devices outside of the process control and process automation industry, and for example could be used to compensate control surface position in an airplane. The type of variables used in the compensation circuit can be other than PVs, the ^n~ation formulas and membership functions can be of forms other than poly ;.ql~, and the combining function can be ~ non li=e~r ~veraging function.
Claims (17)
1. A measurement device related to controlling a process, comprising:
sensing means for sensing a PV within a span of PV values and for providing a signal representative of the sensed PV;
storing means for storing at least two membership functions, each membership function having a non-zero value over a predetermined region of the PV span and a substantially zero value over a remainder of the span, each membership function having a compensation formula corresponding thereto;
compensation means for calculating correction values according to the compensation formula for those membership functions which are non-zero at the value of the sensed PV, the compensation means adjusting each correction value by the corresponding membership function value to provide a weighted correction value and combining the weighted correction values to provide a compensated PV; and an output circuit for coupling the compensated PV to a loop circuit.
sensing means for sensing a PV within a span of PV values and for providing a signal representative of the sensed PV;
storing means for storing at least two membership functions, each membership function having a non-zero value over a predetermined region of the PV span and a substantially zero value over a remainder of the span, each membership function having a compensation formula corresponding thereto;
compensation means for calculating correction values according to the compensation formula for those membership functions which are non-zero at the value of the sensed PV, the compensation means adjusting each correction value by the corresponding membership function value to provide a weighted correction value and combining the weighted correction values to provide a compensated PV; and an output circuit for coupling the compensated PV to a loop circuit.
2. A measurement transmitter, comprising:
conversion means for sensing a PV within a span of PV values and for providing a digitized output representative of the sensed PV;
a memory for storing at least two membership functions, each membership function having a non-zero value over a predetermined region of the PV span and a substantially zero value over the remainder of the span, and for storing a set of compensation formulas, each formula corresponding to a membership function;
selection means for selecting those membership functions which have a non-zero value at the digitized PV;
correction means for providing at least one correction value, each correction value calculated from a compensation formula corresponding to a selected membership function;
weighting means for weighting each correction value by its corresponding selected membership function, and for combining the weighted correction values to provide a compensated PV; and an output circuit for coupling the compensated PV to a control circuit.
conversion means for sensing a PV within a span of PV values and for providing a digitized output representative of the sensed PV;
a memory for storing at least two membership functions, each membership function having a non-zero value over a predetermined region of the PV span and a substantially zero value over the remainder of the span, and for storing a set of compensation formulas, each formula corresponding to a membership function;
selection means for selecting those membership functions which have a non-zero value at the digitized PV;
correction means for providing at least one correction value, each correction value calculated from a compensation formula corresponding to a selected membership function;
weighting means for weighting each correction value by its corresponding selected membership function, and for combining the weighted correction values to provide a compensated PV; and an output circuit for coupling the compensated PV to a control circuit.
3. The transmitter of claim 2 where the non-zero regions of two of the membership functions overlap each other.
4. The transmitter of claim 2 where at least one membership function is triangularly shaped.
5. The transmitter of claim 2 where at least one membership function is a gaussian function.
6. The transmitter of claim 2 where the weighting means combine the correction values according to a weighted average.
7. The transmitter of claim 2 where at least one of the compensation formulas is a polynomial function.
8. The transmitter of claim 2 where the PV is one of a set of PVs representative of differential pressure, position, volumetric flow, mass flow, temperature, level, density, displacement, pH, turbidity, dissolved oxygen and ion concentration.
9. The transmitter of claim 8 where there are three membership functions for the differential pressure, the membership functions each having a center point corresponding to a maximum value of the membership function, where the center points are evenly spaced along the span of PV values.
10. The transmitter of claim 8 where there are three membership functions each overlapping at least one other membership function by 50%.
11. A method for calculating compensated process variables, comprising:
sensing a PV representative of a process, the PV taking on values within a predetermined span of PV values;
converting the sensed PV to a digitized PV;
storing at least two membership functions, each membership function having a non-zero value over a predetermined region of the PV span and a substantially zero value over the remainder of the span;
storing a set of compensation formulas, each formula corresponding to a membership function;
selecting those membership functions which have a non-zero value at the digitized PV;
providing at least one correction value, each correction value calculated from a compensation formula corresponding to a selected membership function;
weighting each correction value by its corresponding selected membership function, and combining the weighted correction values to provide a compensated PV; and coupling the compensated PV to a control circuit.
sensing a PV representative of a process, the PV taking on values within a predetermined span of PV values;
converting the sensed PV to a digitized PV;
storing at least two membership functions, each membership function having a non-zero value over a predetermined region of the PV span and a substantially zero value over the remainder of the span;
storing a set of compensation formulas, each formula corresponding to a membership function;
selecting those membership functions which have a non-zero value at the digitized PV;
providing at least one correction value, each correction value calculated from a compensation formula corresponding to a selected membership function;
weighting each correction value by its corresponding selected membership function, and combining the weighted correction values to provide a compensated PV; and coupling the compensated PV to a control circuit.
12. A method for calculating a compensated variable related to an automated process, comprising:
sensing a PV representative of the process, the PV taking on values within a predetermined span of PV values;
converting the sensed PV to a digitized PV;
storing at least two membership functions, each membership function having a non-zero value over a predetermined region of the PV span and a substantially zero value over the remainder of the span;
storing a set of compensation formulas, each formula corresponding to a membership function;
selecting those membership functions which have a non-zero value at the digitized PV;
providing at least one correction value, each correction value calculated from a compensation formula corresponding to a selected membership function;
weighting each correction value by its corresponding selected membership function, and combining the weighted correction values to provide a compensated PV; and coupling the compensated PV to a control circuit.
sensing a PV representative of the process, the PV taking on values within a predetermined span of PV values;
converting the sensed PV to a digitized PV;
storing at least two membership functions, each membership function having a non-zero value over a predetermined region of the PV span and a substantially zero value over the remainder of the span;
storing a set of compensation formulas, each formula corresponding to a membership function;
selecting those membership functions which have a non-zero value at the digitized PV;
providing at least one correction value, each correction value calculated from a compensation formula corresponding to a selected membership function;
weighting each correction value by its corresponding selected membership function, and combining the weighted correction values to provide a compensated PV; and coupling the compensated PV to a control circuit.
13. A transmitter in a process control system comprising:
a sensor for sensing a physical variable in the system, the physical variable taking on values within a span of values, the sensor having an output representative of the physical variable within the span;
digitizing means for digitizing the sensor output;
selection and storing means for selecting a region from a set of regions, each region related to a different portion of the span, a region becoming selected when the sensor output is included within the region, each region having a compensation formula and a membership function corresponding thereto;
computation means for retrieving the membership functions and the compensation formulas corresponding to the selected regions, and for providing the ordinates of the membership functions at the value of the sensor output and for providing the value of the compensation formulas at the value of the sensor output; and compensation means for weighting the value of the compensation formulas by the ordinate of the corresponding membership functions so as to provide a compensated transmitter output.
a sensor for sensing a physical variable in the system, the physical variable taking on values within a span of values, the sensor having an output representative of the physical variable within the span;
digitizing means for digitizing the sensor output;
selection and storing means for selecting a region from a set of regions, each region related to a different portion of the span, a region becoming selected when the sensor output is included within the region, each region having a compensation formula and a membership function corresponding thereto;
computation means for retrieving the membership functions and the compensation formulas corresponding to the selected regions, and for providing the ordinates of the membership functions at the value of the sensor output and for providing the value of the compensation formulas at the value of the sensor output; and compensation means for weighting the value of the compensation formulas by the ordinate of the corresponding membership functions so as to provide a compensated transmitter output.
14. The transmitter of claim 13 where each variable is assigned at least one membership function and the weighting means further comprise:
forming means for forming a combination of the ordinates of each of the selected membership functions, each combination comprising one ordinate related to each variable;
an FAND circuit for selecting the minimum value in each of the combinations;
where the weighting means weight each correction value by the ordinate of the corresponding membership functions to provide a compensated transmitter output.
forming means for forming a combination of the ordinates of each of the selected membership functions, each combination comprising one ordinate related to each variable;
an FAND circuit for selecting the minimum value in each of the combinations;
where the weighting means weight each correction value by the ordinate of the corresponding membership functions to provide a compensated transmitter output.
15. A measurement transmitter, comprising:
sensing means comprising at least two sensors, one sensor adapted to sense PVs within a first range of PVs and the other sensor adapted to sense PVs within a second range of PV values, each sensor providing an output signal representative of the sensed PV, the ranges including a maximum and a minimum PV value, the minimum and the maximum defining a transmitter span;
storing means for storing at least two membership functions, each membership function having a non-zero value over a predetermined region of the transmitter span and a substantially zero value over a remainder of the transmitter span, each membership function having a compensation formula corresponding thereto;
compensation means for calculating correction values according to the compensation formula for those membership functions which are non-zero at the value of the sensed PV, the compensation means adjusting each correction value by the corresponding membership function value to provide a weighted correction value and combining the weighted correction values to provide a compensated PV; and an output circuit for coupling the compensated PV to a loop circuit.
sensing means comprising at least two sensors, one sensor adapted to sense PVs within a first range of PVs and the other sensor adapted to sense PVs within a second range of PV values, each sensor providing an output signal representative of the sensed PV, the ranges including a maximum and a minimum PV value, the minimum and the maximum defining a transmitter span;
storing means for storing at least two membership functions, each membership function having a non-zero value over a predetermined region of the transmitter span and a substantially zero value over a remainder of the transmitter span, each membership function having a compensation formula corresponding thereto;
compensation means for calculating correction values according to the compensation formula for those membership functions which are non-zero at the value of the sensed PV, the compensation means adjusting each correction value by the corresponding membership function value to provide a weighted correction value and combining the weighted correction values to provide a compensated PV; and an output circuit for coupling the compensated PV to a loop circuit.
16. The measurement transmitter of claim 15 where the first range is substantially the same as the second range.
17. The measurement transmitter of claim 15 where the first range is larger than the second range.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US08/186,288 US5642301A (en) | 1994-01-25 | 1994-01-25 | Transmitter with improved compensation |
| US08/186,288 | 1994-01-25 |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA2178809A1 true CA2178809A1 (en) | 1995-07-27 |
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|---|---|---|---|
| CA002178809A Abandoned CA2178809A1 (en) | 1994-01-25 | 1995-01-17 | Transmitter with improved compensation |
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| EP (1) | EP0741858B1 (en) |
| JP (1) | JP3557213B2 (en) |
| CN (1) | CN1139483A (en) |
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| RU (1) | RU2138781C1 (en) |
| SG (1) | SG44457A1 (en) |
| WO (1) | WO1995020141A1 (en) |
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-
1995
- 1995-01-17 JP JP51969195A patent/JP3557213B2/en not_active Expired - Fee Related
- 1995-01-17 DE DE69504036T patent/DE69504036T2/en not_active Expired - Lifetime
- 1995-01-17 BR BR9506548A patent/BR9506548A/en not_active Application Discontinuation
- 1995-01-17 CN CN95191314A patent/CN1139483A/en active Pending
- 1995-01-17 RU RU96116924A patent/RU2138781C1/en active
- 1995-01-17 EP EP95908616A patent/EP0741858B1/en not_active Expired - Lifetime
- 1995-01-17 MX MX9602017A patent/MX9602017A/en not_active Application Discontinuation
- 1995-01-17 CA CA002178809A patent/CA2178809A1/en not_active Abandoned
- 1995-01-17 SG SG1996000573A patent/SG44457A1/en unknown
- 1995-01-17 WO PCT/US1995/000835 patent/WO1995020141A1/en active IP Right Grant
-
1997
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| JP3557213B2 (en) | 2004-08-25 |
| US5960375A (en) | 1999-09-28 |
| EP0741858B1 (en) | 1998-08-12 |
| DE69504036D1 (en) | 1998-09-17 |
| US5642301A (en) | 1997-06-24 |
| RU2138781C1 (en) | 1999-09-27 |
| JPH09508210A (en) | 1997-08-19 |
| MX9602017A (en) | 1997-05-31 |
| WO1995020141A1 (en) | 1995-07-27 |
| BR9506548A (en) | 1997-08-19 |
| EP0741858A1 (en) | 1996-11-13 |
| DE69504036T2 (en) | 1999-04-15 |
| CN1139483A (en) | 1997-01-01 |
| SG44457A1 (en) | 1997-12-19 |
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Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| FZDE | Discontinued |