TECHNICAL FIELD

This relates to the compensation of electrical devices for changes in their resistance, capacitance or inductance due to one or more environmental factors. More particularly, it relates to a computer simulated bridge circuit which compensates for such factors in the operatio of electrical devices. Because the electrical devices of primary -interest are semiconductor strain gauges, the invention will be described in terms of such application. It will be recognized, ^' however, that the principles disclosed have application to other devices as well.

BACKGROUND ART

Metallic strain gauges have been used as transduce for many years. More recently, semiconductor strain gauge have come into use having sensitivities that are hundreds of times greater than that of their metallic counterparts.

A strain gauge is typically used by bonding it to a flexible object and measuring the change in voltage across the gauge or the change in gauge resistance as different loads are applied to the object to vary the stress on the gauge. It is particularly advantageous to use a Wheatstone bridge in which two strain gauges are connected in series in one half of the bridge and two resistors are connected in series in the other half. Each of these four elements is in a separate arm of the bridge with the supply voltage applied to the noαes between the two halves and the output voltage measured between the node between the two resistors and the node between the two strain gauges. If the gauges are mounteα

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on opposite sides of the object so that bending of the object applies a tensile loading (or stress) to one gauge and a compressive loading to the other, the ratio of the resistance of the two strain gauges is a function of the amount of deflection in the object. Hence, the output voltage from the bridge circuit can be related to the. amount of deflection in the object. In a pressure-to- displacement transducer such as that shown in Birger B. Gabrielson's U.S. Patent 4,172,388, which is incorporated herein by reference, this provides a convenient means of producing an output electrical signal which is a function of the pressure exerted by a fluid.

Ideally, a strain gauge should have the same resistance at any constant stress throughout its operating temperature range and its resistance should vary linearly with the stress that is applied. Thus, as shown in Fig. 1, a plot of strain gauge resistance (or voltage drop) versus temperature and stress is ideally a flat rectilin- ear surface 10. In practice, however, the resistance of a semiconductor strain gauge is a function of both stress and temperature and the plot of strain gauge resistance versus temperature and stress is neither flat nor recti¬ linear.

Practical semiconductor strain gauges are very sensitive to variations in temperature. For example, the resistance of a strain gauge at 180°F (82 ^β C) may be twice that of a strain gauge at 0°F (-18 ^β C) at the same pressure Moreover, strain gauges have both a temperature coefficien of resistance and a temperature coefficient of gauge factor or sensitivity. Thus, both their resistance and their rate of change of resistance with applied stress vary with temperature. Even worse, the magnitude of both coefficients varies randomly from one-gauge to the next; and the process of bonding the gauges is very likely to

modify both the resistance and the temperature coeffici¬ ents of the gauges. Thus, while..it is possible to select matched pairs of semiconductor strain gauges whose temper ature coefficients are approximately the same and to use such matched pairs in a bridge circuit to cancel out some errors due to variations in temperature, temperature effects still remain which will produce significant error in the signal produced by the bridge circuit.

A plot of actual strain gauge resistance versus temperature and stress is typically a curved non-recti¬ linear surface such as a surface 15 of Fig. 1. As shown by surface 15, there are three types of error associated with the semiconductor strain gauge. First is the error in zero point, i.e., the variation A with temperature in the resistance of the strain gauge when the strain gauge is in the unstrained state. This error is random i both polarity and magnitude from one gauge to another. Second is the error in span, i.e., the variation B - (C-A) with temperature in the difference between the resistance of the strain gauge at maximum loading and its resistance in the unloaded, zero-point-corrected state. This error is uniform in polarity but random in magnitude from one gauge to another. The third error depicted by surface 15 i non-linearity of response with stress. As will be apparent, these variations in strain gauge resistance also lead to variations in the output voltage from the strain gauge bridge circuit.

Corrections are made for this variation in output voltage because of changes in resistance with temperature by measuring the resistance of the gauges under zero stress at two temperatures and selecting a series/parallel network of resistance for one gauge which offsets the effects of its temperature coefficient of

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resistance enough that the ratio of the resistance in the two strain gauge arms at the two compensation temperatures is identical. As a result, the output of the bridge circuit at zero stress is the same for both temperatures. This process is called two-point temperature compensation. It is also called zero or initial value ^" compensation. Obviously, such compensation could be made ^" instead at any other value of stress and accordingly this technique will be referred to generically as constant value compensation. As disclosed in my U.S. Patent 4,172,389, which is incorpor¬ ated hereby by reference, this technique can be extended so that ^' the ratio of the resistances in the two strain gauge arms is substantially the same at three different temperatures, thereby providing three-point temperature (or constant value) compensation.

While such temperature compensation does improve the performance of the circuit as a measuring device, it does not guarantee that the resistance ratios are the same at any other temperature because of the complex effects of the temperature induced strain in the gauges. Moreover, temperature compensation alone makes no correction for the variation in output voltage because of change in."sensitivity with temperature.

The variation in output voltage because of change in sensitivity with temperature may be compensated by the use of a span compensation resistance. The value o this resistance is selected to balance the temperature coefficient of sensitivity. More particularly, in one method, once the bridge is temperature compensated at its two compensation temperatures, its output voltage is measured at these two temperatures with maximum deflection being applied to the object on which the gauges are mounted. A resistor is then selected so that the output

voltage under maximum stress is the same at both compensa¬ tion temperatures. Alternatively, as shown in my U.S. Patent 4,172,389, a value for the span compensation resistance can be determined from a series of measurements performed on the strain gauges when connected in series with an arbitrary resistance. .These techniques generally are referred to as span compensation.

These techniques provide for span compensation at only two values of temperatures. Span compensation at other temperatures can be approximated by the use of a resistor-thermistor network as disclosed in John Raven's ϋ. S. Patent 4,174,639, which is incorporated herein by reference.

Despite the improvements in accuracy that can be achieved by two- and three-point temperature compensation and by span compensation, there is still substantial residual error at temperatures other than those where the compensation was made. The major causes of these errors are the non-tracking of the compensated gauges at tempera¬ tures other than the compensation temperatures, the inaccuracies in resistance of the compensation resistors, and the temperature coefficient of the resistors used for compensation as well as for the other elements in the bridge circuit. Other sources of error are the mismatch in the temperature offsets in the amplification of the output signal from the bridge, the temperature coefficient of the voltage source applied to the bridge, the mismatch between the true span error curve and the variable voltage provided by the resistor-thermistor network, and the temperature coefficients and inaccuracies in many other less critical components. For example, the cumulative effect of these errors may result in an error of 1/2% of full scale per 10Q ^β F (56°C) in tne output of the bridge

circuit under zero stress and up to 1% of full scale under other stresses. Moreover, as is apparent from the '389 and '639 patents, the improvements in accuracy that are achieved are won only at the cost of custom-tailoring the various compensation resistances to the idiosyncracies of individual strain gauges.

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DISCLOSURE OF INVENTION

I have devised a method and apparatus for compensating for the foregoing errors in the operation ₀ f s rain gauge transducers. Moreover, the method and apparatus I have devised are generally applicable to the compensation of all types of devices for deviations from ideal performances over their operating ranges.

In a preferred embodiment of my invention the apparatus comprises a semiconductor strain gauge transducer with a quasi-stable voltage supply, two strain gauges and two precision resistors which form a voltage divider network; a scanner for scanning the strain gauges and precision resistors; an analog-to-digital converter for digitizing the output of the scanner; and a micropro¬ cessor for calculating a corrected output representing the phenomenon that is monitored by the strain gauge transduce Alternatively, one of the precision resistors may be a short circuit. Advantageously, the gauges are mounted in customary fashion on opposite sϊdes of a flexible object which is bent as a function of the parameter being measured When the gauges are so mounted in opposition, flexing of the object puts one gauge into compression thereby decreasing its resistance and puts the other gauge into tension thereby increasing its resistance. Since these changes in resistance are approximately equal, the sum of the resistances of the two gauges is relatively insensitive to stress while being highly sensitive to 'temperature. The scanner successively reads the voltage drops across the two strain gauges and the two precision resistors. These analog signals are then converted to digital form by the A/D converter and entered into the microcomputer for calculation of the output.

The microcomputer contains substantial memory

in which are stored a set of bridge completion constants, a table of correction constants and a set of temperature compensation and signal conditioning algorithms. The bridge completion constants are a set of values represen¬ tative of the bridge supply voltage and the resistances of a set of bridge completion resistors which are selected durin factory calibration to provide two point temperature and two point span compensation for the pair of strain gauges used in the transducer. The table of correction constants is likewise determined during factory calibration. One group of these constants provides for zero point compensation over the operating temperature range of the transducer, ^• a second group provides for span compensation over the operating temperature range of the transducer, and a third group compensates for other input to output non-lineari¬ ties over the operating range of the transducer. The constants stored in each of these groups are the slopes and intercepts of the appropriate compensation curves at several discrete points over the operating temperature or stress range. Pursuant to the temperature compensation and signal conditioning algorithms stored in the microcomputer, the microcomputer uses the signals from the A/D converter, the bridge completion constants and the correction con¬ stants to calculate a corrected output signal representa¬ tive of what is measured by the strain gauge transducer.

In accordance with my invention, the digital signals applied to the microcomputer are corrected for voltage offsets and temperature related errors in the scanner and A/D circuit by measuring the voltages across the precision resistors, determining the voltage offset from the output signals from the A/D circuit and subtrac¬ ting this voltage error from the voltage measurements across the strain gauges. Alternatively, where one of the precision resistors is replaced by a short circuit, the voltage offset is simply the output of the A/D circuit

when the scanner's inputs are shorted. Since the resistanc of the precision rejsistor is accurately known, the ratios of the voltage drops across the strain gauges to the vol¬ tage drop across the precision resistor are. then used to determine the resistance values of the two strain gauges.

After the resistance values are calculated, they are used with the bridge completion constants to calculate the output voltage that would be observed from a Wheatstone strain gauge bridge that used the two strain gauges of the sensor together with the bridge completion ' resistors and the bridge supply voltage having the values specified by the bridge completion constants. This process may be termed primary temperature compensation. As indicated above, the values of these bridge completion constants are selected during factory calibration so that the output of this bridge circuit is -temperature compensated at two points and is also span compensated at two points. The selection of appropriate bridge resistance values to provide for two point temperature and two point span compensation is well within the skill of the art.

After this primary temperature compensation procedure is carried out, a secondary process is implemented to compensate for temperature effects using the first two groups of correction constants stored in the memory of the microprocessor. This process is essentially a search and interpolation routine to locate the proper slope and intercept to use for correction and then calculate the precise correction factor. However, since the output signal from the primary temperature compensation process is not a onotonic function of temperature, some other signal must be used to select a unique set of correction constants. One possibility is to measure directly the operating temperature of the strain gauges and select the appropriate correction factors accordingly. This, however.

^*• ■ requires the use of separate temperature sensors and accom panying circuitry. Since the sum of the resistances of th two strain gauges mounted in opposition is a highly sensi¬ tive monotonic function of temperature that is .substan- tially independent of stress, I prefer to relate the correction factors to this sum, thereby, eliminating the need to make any measurement of temperature. After the appropriate constants are selected in accordance with the sum of the resistances of the two strain gauges, this sum and the selected correction constants are used to calcu¬ late a temperature compensated output voltage.

Finally, the temperature compensated output signal is corrected for non-linearity of output as a func- tion of an input such as the stress applied to the trans¬ ducer. Since the temperature compensated output signal is a monotonic function of the applied stress, the correction constants may be related directly to this output signal. Thus the appropriate slope and intercept correction constants are selected in accordance with the value of the temperature compensated output signal; and this value and the correction constants are used to calculate an output signal that has been corrected for non-linearities due to both temperature and stress.

The foregoing method and apparatus offers many distinct advantages over a conventional Wheatstone bridge strain gauge sensor. Since the fully compensated output voltage is calculated from the voltage drops read by the scanner, it is only necessary that the supply voltage be stable for the relatively short period required to scan the precision resistors and strain gauges. Thus, fluctuations or temperature related changes in the supply voltage do not affect the

accuracy of measurement. Moreover, the use of resistance values in calculating the output signals makes the calcul tions independent of the voltage applied to the digital network. This permits the voltage level applied to my strain gauge sensor to be signi icantly lower than that for systems which utilize a conventional Wheatstone bridge circuit.

Furthermore, the fully compensated output signal is far more accurate than that which can be produced by the equivalent hard-wired Wheatstone bridge. Unlike actual resistors and supply voltages whose values change as a function of temperature, the values of the bridge completion constants and the compensation constants used in the practice of my invention do not change with tempera ture. As a result, all the temperature errors of a heat¬ stone bridge .that are not directly associated with the strain gauges are eliminated. Second, the gain constant, which is equivalent to the excitation voltage in a hard¬ wired bridge, can be chosen to provide any output range without the constraints imposed on a hardware bridge by the maximum excitation voltage that can be tolerated by the gauges or by the signal conditioning electronics without degradation in performance. In particular, the bridge compensation constants and gain constant can be selected during the factory calibration procedure to provide a standard zero and full scale signal regardless of the stress range over which the individual device will be operated. Since all of this can be achieved simply by altering the constants stored in the microprocessor, the strain gauge sensors of my invention may readily be customized for individual application. As a result, the preferred embodiment of my invention is an extremely accurate, highly versatile strain gauge transducer.

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BRIEF DESCRIPTION OF THE DRAWINGS

These and other objects, features, elements and advantages of my invention will be readily apparent ^ from the following description in which:

Fig. 1 is a plot of the resistance of a strain gauge sensor as a function of stress and temperature;

Fig. 2 is a schematic diagram of an illustrati embodiment of my invention;

Fig. 3 is a schematic diagram of a bridge circuit useful in understanding my invention;

Fig. 4 is a plot of the typical error in zero point when compensated at two points; Fig. 5 is a plot of the typical, error in zero point when compensated in accordance with my invention;

Fig. 6 is a plot of the typical error in span when compensated at two points;

Fig. 7 is a plot of the typical error in span when compensated in accordance with my invention;

Fig. 8 is a plot of output error versus applie stress;

Fig. 9 is a plot of the typical output error versus applied stress when compensated in accordance wit my invention;

Fig. 10 is a flow chart of an illustrative embodiment of the method used in practicing ray invention and Figs. 1 and 12 are flow charts of subroutine that may be used ^* in the practice of my invention.

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BEST MODE OF CARRYING OUT THE INVENTION

As shown in Fig. 2, preferred apparatus 20 for carrying out my invention comprises a semiconductor strai gauge sensor 30, a scanner 40, an A/D converter 50, a microcomputer 60 and an output circuit- 80. Strain gauge sensor 30 further comprises a quasi-stable voltage supply 32, first and second precision resistors 34, 35, and firs and second strain gauges 36, 37. If desired, the second precision resistor may be a short circuit. Strain gauges 36, 37 are preferably mounted on opposite sides of. a cantilever beam (not shown) so that one gauge is com¬ pressed and the other is tensed when the beam moves in response to the phenomenon being measured. An example of such a mounting, which is commercially available, is disclosed on the aforementioned patent of Berger B. Gabrielson. Scanner 40 successively reads. the voltage drops V1 , V2, V3, V4, across precision resistor 34, the two strain gauges 36, 37 and precision resistor 35, respectively. The analog signals so read by scanner 40 are converted to digital form by A/D converter 50 and entered into microcomputer 60 for calculation of the output. As will be apparent to those skilled in the art, any number of techniques may be used for analog-to-digital conversion. The output calculated by microcomputer 60. may be used to drive a display, run a strip-chart recorder or control any number of other well known output devices represented schematically by output circuit 80.

Microcomputer 60 comprises a central processing unit 62, a memory 64, an I/O bus 66 and an internal bus 68. Memory 64 preferably includes a random access memory (RAM) 71, a read only memory (ROM) 72 and a programmable read only memory (PROM) 73. A program for operation of the microcomputer is stored in read only memory 72. This program includes temperature compensation and signal

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conditioπing algorithms used to calculate the output signal. A set of bridge completion constants and a table of correction constants are stored in programmable read only memory 73. These constants are determined during factory calibration of strain gauges 36, 37 and are a unique set of values intended to correct the output of that particular pair of strain gauges in order to compensa for temperature effects, as well as non-linearity of the transducer with the applied input. In addition, the bridge completion constants may be selected so as to provide a standard zero and full scale signal regardless of the.stress range for which the particular unit of apparatus will be used.

To determine the bridge completion constants and the table of correction constants for each strain gauge transducer, the voltage drops across precision resistors 3 35 and strain gauges 36, 37 are measured at several dif¬ ferent temperatures for both zero and maximum stress as well as at several different stresses and minimum temper¬ ature. These measurements are typically made at five to seven values over the range of interest. The measured voltage drops are corrected for voltage offsets and temperature related errors by subtracting from these values an error voltage, EV. The corrected values are:

VR = VI - EV ^■ VGA = V2 - EV ( 1 )

VGB = V3 - EV

where V1 , V2, and V3 are the signals defined above as received by microcomputer 60, VR is the corrected value of the voltage drop across resistor 34 and VGA and VGB are the corrected values of the voltage drops across gauges 36, 37. The error voltage may be determined in many ways.

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In the case where the resistance of precision resistor 34 is twice that of precision resistor 35, the error voltage EV is given by EV = 2V4 - V1 where VI and V4 are the signals representative of the voltage drops across the precision resistors as received by microcomputer 60. Where the second precision resistor is replaced by a shor circuit, EV ^~~ V4 , where V4 is the signal received by the microcomputer when the inputs to the scanner are shorted. Since the resistance R of precision resistor 34 is known, the resistance of gauges 36, 37 can be calculated as follow

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GA = (VGA/VR) • R

GB = (VGB/VR) • R (2)

where VGA, VGB, VR, and R are as defined above.

Using the gauge resistance values so calculated for the minimum and maximum temperatures for both zero and maximum stress, appropriate bridge completion constants are first calculated for two point temperature compensa¬ tion and two point span compensation. Using these bridge completion constants and the gauge resistance values cal¬ culated for the intermediate temperatures and zero stress, a piece-wise linear approximation to the zero point tem¬ perature compensation curve is then calculated for the operating temperature range of the sensor. The slopes and intercepts of the piece-wise linear components provide the correction constants for temperature compensation. Once these correction constants are calculated, a piece-wise linear approximation to the compensation curve for span error is calculated. Again the slopes and intercepts of the piece-wise linear components constitute the correction constants for span error. Finally, using the calculated gauge resistances for several different stress levels between zero and maximum a piece-wise linear approximation

is calculated to the compensation curve for non-linearity of the transducer in response to the applied input. Again the slopes and intercepts of the piece-wise linear compo- . nents constitute the correction constants for this non- linearity.

This procedure is carried out for each strain gauge transducer made in accordance with my invention. Advantageously, the scanner and A/D converter used in measuring the voltage drops across the precision resistors 34, 35 and strain gauges 36, 37 should ^' be the same- scanner 40 and A/D converter 50 that are connected, to sensor 30 in the device as finally shipped. The calculations that are performed to determine the bridge completion constants and the table of correction constants may be performed by microcomputer 60 that is shipped as part of the final product. Alternatively, they may be performed by separate calibration equipment (not shown).

Numerous techniques are available to compensate strain gauge bridges at two points for errors in zero point and/or span. My invention may be practiced using any of these techniques. I prefer to select the bridge completion constants in the following fashion. For calculation purposes, the calibration equipment simulates a conventional strain gauge bridge 110 as shown in Fig. 3. This bridge comprises four resistors 111, 112, 113, 114 and the two strain gauges 36, 37. Resistors 111, 112 and strain gauges 36, 37 are connected in series in the active half of the bridge. Resistors 113, 114 are connected in series to form the reference half of the bridge. An input (or supply, or excitation) voltage VI is applied to the nodes between the two halves of the bridge; and the output voltage VO is measured between the node between

resistors 113, .114 and the node between strain gauges 36, 37. It can readily be shown that

where GA and GB are the resistances of strain gauges 36, 37 and A, B, C and D are the resistances of resistors 111, 112, -113, and 114, respectively. Two point temperature and span compensation can be achieved by appropriate selection of the resistance of resistors 111, 112.

In particula ^' r, it can be shown that span compens tion can be achieved for two temperatures L, H if the sum of the resistance of resistors 111, 112 is given by:

_A+B = VG(H,M)-VG(L,M) (V0(H)/V0(L) )

(VR(L,M)/R) (V0(H)/V0(L) )-VR(H,M)/R ( where

VG(H,M)=VG (H,M)+VGB(H,M) VG(L,M)=VGA(L,M)+VGB(L,M) V0(H)=(R+GA(H,Z) ) VR(H,Z)/R

-(R+GA(H,M)) VR(H,M)/R VO(L)=(R+GA(L,Z) ) VR(L,Z)/R

-(R+GA(L,M) ) VR(L,M)/R H = the upper temperature ^• L = the lower temperature Z = zero stress M = maximum stress

R, VR, VGA and VGB are as defined in equations (1) and (2) and GA(T,S) is the resistance of gauge 36 at the tempera¬ tures T and stresses S indicated. For the value of A + B determined by equation (4), the output voltage VO of

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the bridge circuit is the same at maximum stress at both the lower and upper temperatures L, H.

For two point temperature compensation it can b shown that the total resistance A + B should be distribut between resistors 111 and 112 so that:

GA(H,Z)÷A GA(L,Z)+A (5) GB(H,Z)+B ⁼ GB(L,Z)+B

where GA(T,S) and GB(T,S) are the resistances of gauges 36, 37 at the temperatures T and stresses S indicated. Accordingly, specific- values of A and B are determined by the calibration equipment by solution of equations (4) an (5). For these specific values of A and B, the output voltage VO of the bridge circuit is the same at zero stress at both the lower and upper temperatures L, H.

It is not necessary to determine discrete values for the resistances C, D of resistors 113, 114. Instead, the value of the ratio D/(C + D) is calculated b the calibration equipment from equation (3) so that the output voltage VO has a desired value at zero stress. Typically, the desired output voltage at zero stress is zero so

GB(Z)+B (6)

D/ ⁽ C+D ⁾ = _{GB(Z)+B+GA(Z)+A}

Finally, a suitable excitation voltage VI is chosen, preferably one which produces a full scale output signal VO at maximum stress. The values A, B _r D/(C÷D), and VI are the bridge completion constants for the pair of strain gauges 36, 37 for which they are calculated. These

values are stored in PROM 73 of the microcomputer that is part of the same apparatus as these gauges.

Once the bridge completion constants are determined the calibration equipment calculates the table of correctio constants which likewise is eventually stored in PROM 73 of the microcomputer associated with the strain gauges

36, 37 for which these correction constants are calculate First the calibration equipment calculates the magnitude

VOzi. of the output of the bridge circuit at several intermediate temperatures and zero stress. The difference /\ zi between each of these values and the output value VO determined by equation (3) for the minimum and maximum temperatures at zero stress is then calculated:

As shown in Fig. 4, these differences may be linked together by straight lines to form a piece-wise linear approximation to the curve of zero point error versus temperature.. The calibration equipment calculates the slopes zi. ^" and intercepts bzi. of each of these p ^~ iece- wise linear components and retains this information and the temperature ranges for which each slope and intercept are used for inclusion in the table of correction constants. Use of these correction•constants will reduce the zero point error to a curve such as that shown in Fig. 5. In practice, the use of a five to seven intermediate te pera- ture values i has given satisfactory results. Obviously greater accuracy can be achieved by using even more values and fewer values may be used if the loss in accuracy is acceptable.

Next, the calibration equipment calculates the magnitude VO . of the output of the bridge circuit

at the same intermediate temperatures (i _. = 1, 2, ...) and maximum stress- using equation (3), the bridge com¬ pletion constants and the values GA, GB of the strain gauge resistances at these intermediate temperatures and maximum stress. The difference or span _* _ ._. between each of these values VO . and the uncompensated output VO . of the bridge circuit at the same temperature and zero stress is then determined:

^• ssii . - VOsi - VO Zl (i * 1, 2 (8)

^• The calibration equipment then calculates the ratio R SI of the span, VO - VO , in the output values of the bridge circuit as determined by equation (3) for maximum stress and zero stress at either the minimum or the w_ ^~~ -t-i-- temperatures to the span _.. for each intermediate temperature:

^R si " ^VO s " ^VO z - ^ _{s i} ⁽ i - 1 , 2. . . ^{) (} 9 ⁾

As will be apparent, ea .ch value Rsi. is a correction factor for span error. As shown in Fig. 6, the span correction factors may be linked together by straight lines to form a piece-wise linear approximation to the span error correction curve versus<temperature. The calibration equipment calculates the slopes m . and intercepts b . of each of these piece-wise linear com¬ ponents .and retains this information and the temperature ranges for which each slope and intercept are used for th table of correction constants. Use of these correction constants will reduce the span error to a curve such as that shown in Fig. 7.

As indicated above, the correction factors may be related directly to temperature if separate temperatur

sensors and accompanying circuitry are used. I prefer, however, to relate the correction factors to the sum, GA + GB, of the corrected values of the resistances of strain gauges 36, 37. When these gauges are mounted in opposition, the sum of their resistances is a highly sensitive monotonic function of temperature that is sub¬ stantially independent of stress. Since the values of the resistances GA and GB are available in the microcom¬ puter, the sum of these resistances SUM = GA+GB is- readily-^calculated at each intermediate temperature (i = 1, 2,...). Each slope and intercept m _* _.., b2 _~ .m and m ., b . defining "the piece-wise linear approxi- ation to the error correction curve between successive intermediate temperatures can therefore be associated with a range of the resistance SUM rather than an actual temperature range.

To linearize the output with respect to an input such as applied stress, the calibration equipment calcu¬ lates the output VO, that should be observed from the bridge at minimum temperature at several values of stress (n = 1, 2,...) between zero and maximum assuming the output is a linear function of stress from zero to maximum. The calibration equipment also calculates the magnitude VO of the output of the bridge circuit at minimum temperature and the same values of stress using equation (3), the bridge completion constants and the values GA, GB of the strain gauge resistances at these values of stress and temperature. For each value n of stress, the differ- - enceΔn is determined between the value VO,t _. en and the calculated linearized value VO I,n:

Δ _n = VO _{t cn} - V0 _{l n} ( n = 1 , 2 , . . . ) ( 1 0 )

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As shown in Fig. 8 these differences may be linked togeth by straight lines to form a piece-wise linear approximati to the non-linearity compensation curve versus the values of VO _^ for n = 1, 2,... The calibration equipment cal- tcn culates the slopes . and intercepts b. of each of thes piece-wise linear components and retains this information and the ranges of for which each slope and inter- cept is used for inclusion in the table of correction constants. Use of these correction constants will reduce the linearity error to a curve such as that shown in Fig. 9. Again the use .of five to seven intermediate values n has given satisfactory results but fewer or more values may be used as accuracy requires.

As will be apparent, this use of a table of correc tion factors which associates ranges of VOt.en with set of linearity correction factors assumes that the values o the temperature compensated output VO of the bridge circuit are monotonic with applied stress and substantial ly independent of temperature. Within the range of accuracy otherwise achievable with my invention, these conditions are attainable.

The bridge completion constants and the table of correction constants are then stored in programmable read only memory 73 of the microcomputer that is connecte to the pair of strain gauges for which these constants we calculated. The four bridge completion constants provide the constants needed to calculate equation (3). One grou of correction constants associates a set of slopes and intercepts for a piece-wise linear approximation to a zer error correction curve with the resistance values SUM ove which the individual approximations are to be used. A second group associates a set of slopes and intercepts fo

a piece-wise linear, approximation to a span error correction curve with the resistance values SUM over which the individual approximations are to be used. A third group associates a set of slopes and intercepts, for a piece-wise linear approximation to' a linearity correction curve with the bridge output values over which the individual approxi¬ mations are to be used.

. After the constants are stored in its memory, apparatus 20 may be used like any strain gauge sensor in the myriad applications to which strain gauges are applied. Once the gauges are connected so as to monitor the pheno¬ menon of interest, scanner 40 may be operated in endless cycles in which it successively ^" reads the voltage drops VI, V2, V3, V4 across precision resistor 34, strain gauge 36, 37 and precision resistor 35, respectively. The analog signals read by scanner 40 are converted to digital form by A/D converter 50 and entered into microcomputer 60 fo calculation of the output.

As enumerated in Fig. 10, microcomputer 60. receive - the measured voltage drops and corrects them for voltage offset and temperature related errors in accordance with equation (1). The resistances GA, GB of gauges 36, 37 are then calculated in accordance with equation (2); and from these values the total gauge resistance, SUM, is calculated.

Next, the output VO of the bridge for two point temperature and span compensation is calculated using equation (3) and the four bridge completion constants stored in memory 73 of microcomputer 60.

To perform secondary temperature compensation the resistance value SUM is used to select appropriate

slopes and intercepts for calculating zero point compensa tion at that resistance value. These values are then use to calculate the temperature compensated output VO as follows:

VO _fcc - (VO - (b _zi + _zi SUM)) • (b _si + m _si SUM) (11

where the terms are as defined above and bzi. , mzi. ,

. _Q b . and m . are the slopes and intercepts for tempera¬ ture and span compensation at the value of SUM.

Finally, the temperature compensated output is corrected for non-linearity with stress by selecting - _j g from the table of correction constants the appropriate slope and intercept for correction for non-linearity at that value of stress. These values are then used to calculate the linearized output VO, as follows:

0 ^V0 1 = ^VO tc ^{" (} ln ^{+ m} ln ^VO tc> - ^{■ (}

where the terms are as defined above and b. and m.

In In are the slope and intercept for linearity compensation at the value of VOt,c ^* 5

If desired, the output VO- may then be filtered and/or processed in any number of special function routine Illustrative special functions shown in Fig. 10 include span scaling, zero scaling and square root. Others will 0 be evident to those skilled in the art. Finally, the out¬ put from microcomputer 60 is updated and the appropriate signal applied to output circuits 80. Microcomputer 60 then recycles, reads another set of voltages VI through V4 and commences anew the process of calculating the output. 5

Nu erous methods may be used for filtering the output signal VO.. The filtering step is used to cope with the inherent granularity in the digital represen- 5 tation of the analog continuum. The magnitude of this granularity is a function of the resolution and repeata¬ bility of the A/D converter. The granularity constitutes "digital noise" which is random in nature and distributed about the mean process variable. This noise can be ■JO reduced by use of various averaging techniques. ^" One common technique is exponential filtering which produces filtered output voltage signal, VO _f as follows:

VO = A (vo _α ) + (1-A) VO _f ' (13)

15 where A is a number between 0 and 1 and VO _f ' is the immed ately previous filter output. Alternatively, the filtere output voltage signal may be a running average in which the means value of the last N measurements of the process 0 variable is used as the output. However, since the outpu is the mean value of N measurements, the response to a step change in the process variable requires N + 1 measure ment updates.

5 In order to improve the response time to changes in the process variable while minimizing the effects of random noise, I prefer to test each newly calculated value VO, to determine if it is sufficiently different from the previous values that it is likely to represent a 0 new process value. Where the test is satisfied, the newly calculated value is accepted as the new process value. Otherwise, it is merely added to the running average.

There are numerous routines for performing such a test. In one such technique depicted in Fig. 11 , the routine is entered with the linearized value VO-, and

previously calculated values of the average output AVE an the number N of the values in this average. The new valu VO. is tested against the average value AVE to determine if the absolute value of the difference is less than a noise constant which is equal to three standard deviation of the measured noise. If it is not, the previous averag value is replaced by the new value VO, and this new average value becomes the output. Otherwise the running average is updated and the updated average value is supplied as the output.

- •

The number ϊtf of values used in the running average can vary from two to some predetermined limit; an the more values used in the average the better the filter ing. In practice, I have set. the maximum value of N at 10 since this provides about a 3 to 1 reduction in random noise while permitting a reasonable response time to changes in the process variable that are smaller than the noise constant. If desired, this technique can be extended so that the response o the output varies in accordance-wit ^' the magnitude of the difference between VO, and AVE. For example, the number _ of values used in calculating the ^' new value of AVE can vary inversely with the magnitude of the difference between VO, and AVE.

Another problem that occurs in digital systems using A/D converters is associated with occasional noise spikes. If such a spike occurs during a data scan by εcanner^O, the calculated output will not represent' the process variable. If the difference between the calculated output and the average value exceeds the noise constant, the filtering process of Fig. 11 will discard the running average of good data in favor of the noise spike.

To minimize the likelihood of such an event, I prefer to make an additional logical test as shown in the flow chart of Pig. ^" 12. When the new value VO. exceeds the average value AVE by the noise constant, this new val is held out of the calculation of the average and the pre vious value of the running average is used as the output. If the next data scan results in an output within the predetermined limit, the previous reading is considered t be bad data and is discarded. If, however, the second da scan also exceeds the noise limit, both outputs are.considere to be good data and the output follows the last data scan.

Illustrative resistance values for the strain gauges 36, 37 used in the practice of my invention are about 750 ohms + 20% at 0 ^β F (-18 ^β C) and about 1500 ohms + 20% at 180 ^β F (82 ^β C). The resistances of the precision resistors may be about 1000 ohms; and their change in resistance with respect to temperature should be relativel constant at least when compared to the change in resis- tance of the strain gauges. The lower the temperature coefficient of resistance of the precision resistors, the more accurate will be ^' the transducer; and in practicing the invention, I prefer to use _t 1% wire-wound resistors having a change in resistance of 5 parts per million (ppm) per ^* C. Obviously larger temperature coefficients can be used in the practice of the invention with attendant loss in accuracy. Conceivably, even carbon resistors could be used in practicing the invention although it is doubtful at present price levels that- such a device would be accurate enough to justify the added costs of the micro¬ processor. The values A and B determined by equations (4) and (5) are each about 350 — 50 ohms. The values D/(C+D) and VI vary with the particular application.

My invention may be implemented in all manner of devices. In one embodiment, the sensor is a diffused

diaphragm strain gauge; and the analog inputs from the precision resistor and the strain gauges are multiplexed by an Intel 4052 analog multiplexer and amplified by a conventional instrumentation amplifier circuit. These voltages are sequentially converted to digital signals b a single Intersil 7104-1 16 bit integrating A/D converte An Intel 8039 microprocessor with a 2716 EPROM is used t calculate the output. The standard output is a five digi display of pressure scaled to a selectable engineering unit. Alternatively, set point alarms, peak detection an BCD or IEEE-488 interfaces can be provided by the micro¬ computer. An Intel 8049 microprocessor with 2K masked R is a likely replacement for the 8039 microprocessor and EPBOM

In another eπbodimant sensor 30 is a SIGNATURE (R.T.M.) strain gauge transducer manufactured by Bristol-Babcock Inc. and the microprocessor is a CMOS microprocessor with associated CMOS memory which emulates a 1804 micro¬ computer. In this embodiment the voltages from the 4052 analog multiplexer are converted to frequencies by a voltage- to- frequency converter. These frequency signals are used as control signals for a pair of 8 bit counters which count the constant clock frequency of the microcom¬ puter. The resulting 16 bit count is proportional to the period of the control frequency and therefore inversely proportional to the analog input voltages. From these values the microprocessor calculates the resistance of th strain gauges. The output of the microprocessor is a standard 4-20 milliamp industrial signal. Optional outputs may include a square root output' ^* option for flow applications, pulse duration modulation, and frequency and/or other serial asynchronous communication schemes.

As will be apparent from the foregoing, the invention broadly comprises a computer simulated bridge circuit which compensates for the effects of one or πiore

environmental variables. -In the preferred embodiment of the invention, the bridge is a strain gauge heatstone bridge and the computer stores a table of bridge completio constants which are used by the computer for zero point an span' compensation at two temperatures.. Further, the computer stores tables of correction constants which provide for zero point and span compensation at inter¬ mediate temperature values as well as correction of non-linearities in the response of the circuit to the applied input. As will be apparent to those skilled in the art, however, numerous variations may be made in the above described device within the scope of my invention.

While I pref-er to calculate the bridge constants in accordance with equations (3), (4), and (5), it is possible to practice the invention using nominal values for these constants. Obviously, in such case more of the burden of compensation is shifted to the error correction curves of Figs. 4, 6, and 8. Similarly, it is possible to practice the invention without even using the span and ^' temperature compensation resistances 111, 112. Likewise other bridge configurations may be used in place of the Wheatstone bridge configuration disclosed above. As will be apparent, precision resistors 34, 35 are used in part to obtain an accurate measure of the current through the strain gauges. Alternatively, a precision current source could be used in place of the ^' voltage supply and precision resistors although such alternative is likely to be more expensive and less accurate. „ ^•

While it is preferable and simpler to use the sum of the gauge resistances as a measure of temperature,indepen dent temperature sensors can be used in the practice of the invention. Moreover, the invention may also be used to co pensate for temperature and stress effects where the pair of strain gauges are not mounted in opposition. In such a case the use of an independent temperature sensor will be- a necessity.

As another alternative it is possible to practice my invention using no bridge at all. In ^' this case correction ^' curves must be established which relate the voltage drops across the precision resistor and the strain gauges directl to corrected output values. In essence, in the practice of this alternative what is recorded in the memory of the micro¬ computer is a set of piece-wise linear approximations to compensation curves which relate the measured output of the resistor and gauges to the correct output at several discrete values of applied stress at several values of temperature. To calculate the corrected output, the microcomputer uses the compensation curve for the closest temperature in excess of that of the strain gauges and the compensation curve for the closest temperature below that of the strain gauges. By interpolation between these compensation curves, a piece-wise linear approximation to a new compensation curve is constructed for the actual temperature of the strain gauges. A correction factor for the measured output of the strain gauges is then determined from the new compensation curve by interpolation _^ on that piece of the linear approximation which corresponds to the measured output of the strain gauges. The corrected output is then obtained by modifying the measured output by the correction factor. While this alternative avoids the use of any bridge, it does so only at the cost of considerable additional memory for storage of the approximations to the curves.

While the invention has been described in terms of compensation for temperature and stress effects on the resistance of strain gauges, it will be recognized that the invention may be practiced on all manner of devices that are affected by all manner of environmental variables. One class of such devices are those which use surrogate values for tem¬ perature and/or stress. One example is the use of the sum of the resistances of strain gauges 36, 37 as a measure of temperature. . Another example is the case where the stress in the strain gauges is generated by displacement of _ device

coupled to a cantnevered beam on which the gauges ^' are mounted. There, the displacement of the device may be used as a surrogate for stress since the stress applied is a function of displacement. In such an instance, the correc- tion constants used for span compensation and linearization may be calculated with respect to physical displacements instead of applied stress, thereby providing compensation for non-linearity between the applied displacement and the output signal. The invention may also be used to compensate for zero point (or constant) value errors, span errors, and non- linearities in the response of all types of resistive devices and not just strain gauges. The techniques detailed above can be used in compensating the errors in any resistive device whose resistance varies as a function -of two environ¬ mental variables. With, suitable modi ications the same techniques may be used to compensate for the errors in the resistance of a device whose resistance varies as a func¬ tion of only one environmental variable. Illustrative resistive devices with which the invention may be prac¬ ticed include resistance temperature devices, thermistors, potentiometrie sensors and Foxboro pressure sensors such as those described in U.S. Patent 4,172,387.

Likewise the same techniques may be applied to cora- pensate for errors in the inductance or capacitance of inductive or capacitive devices whose inductance or cap¬ acitance is a function of one or more environmental variables. Obviously, .the scanner in such an apparatus would have to be able to read some parameter of the inductive or capaci- tive device which is related to its inductance orcapacitance. Depending on what parameter is read, it may be advantageous to use devices different from the voltage source and precision resistors used in Fig.3 to obtain a precise measurement of current through the strain gauge. The application of my techniques to such inductive and capacitive devices will be apparent to those skilled in the art in view of the fore¬ going disclosure.