CN107271081B - Silicon piezoresistive pressure transmitter temperature compensation method and device based on two-stage least square fitting - Google Patents

Silicon piezoresistive pressure transmitter temperature compensation method and device based on two-stage least square fitting Download PDF

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CN107271081B
CN107271081B CN201710302488.7A CN201710302488A CN107271081B CN 107271081 B CN107271081 B CN 107271081B CN 201710302488 A CN201710302488 A CN 201710302488A CN 107271081 B CN107271081 B CN 107271081B
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李冀
周永宏
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Fujian Wide Plus Precision Instruments Co ltd
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Abstract

The invention belongs to the technical field of pressure transmitters, and particularly relates to a silicon piezoresistive pressure transmitter temperature compensation method and device based on two-stage least square fitting. The invention relates to a silicon piezoresistive pressure transmitter temperature compensation method based on two-stage least square fitting, which comprises the following steps: modeling a temperature compensation model by a two-stage least square method; storing the coefficient matrix of the temperature compensation model into an EPROM of a pressure transmitter; and calculating the pressure value after the output temperature compensation according to the input pressure measurement AD value, the ambient temperature measurement AD value and the coefficient matrix of the temperature compensation model. The temperature compensation method can improve the measurement accuracy of the pressure transmitter, reduce the memory consumption of the pressure transmitter, and improve the operation efficiency of the temperature compensation program.

Description

Silicon piezoresistive pressure transmitter temperature compensation method and device based on two-stage least square fitting
Technical Field
The invention belongs to the technical field of pressure transmitters, and particularly relates to a silicon piezoresistive pressure transmitter temperature compensation method and device based on two-stage least square fitting.
Background
In the manufacturing process of the monocrystalline silicon piezoresistive pressure sensor, the factors such as temperature coefficient difference of resistivity, mismatching of temperature expansion coefficients among packaging materials, temperature influence on the performance of electronic elements and the like are caused by incomplete consistency of ion implantation concentration, so that the change of the ambient temperature can cause zero point offset and sensitivity drift of the sensor, and meanwhile, the output linearity of the sensor is influenced, so that a final measurement result is inaccurate, and therefore, the problem of temperature compensation is not ignored as a key link for improving the overall performance of the sensor.
The current temperature compensation method mainly comprises hardware compensation and software compensation. The hardware compensation carries out optimal configuration on the measurement circuit by changing circuit parameters, but the compensation method has the defects of inconvenient debugging, limited precision, weak process flexibility, increased cost and the like, is unfavorable for production popularization, and the software compensation gradually becomes a focus because the defects can be avoided. The most commonly used software compensation algorithm is a piecewise linear interpolation method, and the method carries out temperature compensation by storing calibration data obtained through experiments into a pressure sensor memory (EPROM) as interpolation points, and has the following main defects: 1. when interpolation points are not more, nonlinear characteristics of the output of the pressure sensor cannot be fully reflected, and measurement accuracy is affected; 2. the data which is needed to be stored in the pressure sensor memory (EPROM) is more, and the hardware cost is increased; 3. when the required compensation accuracy is improved, the compensation calculation operation efficiency is low.
Disclosure of Invention
One of the objectives of the present invention is to overcome the above drawbacks and provide a method for improving the measurement accuracy of a pressure transmitter, reducing the memory consumption of the pressure transmitter, and improving the operating efficiency of a temperature compensation program.
In order to solve the technical problems, the invention provides a silicon piezoresistive pressure transmitter temperature compensation method based on two-stage least squares fitting, which comprises the following steps:
modeling a temperature compensation model by a two-stage least square method;
storing the coefficient matrix of the temperature compensation model into an EPROM of a pressure transmitter;
and calculating the pressure value after the output temperature compensation according to the input pressure measurement AD value, the ambient temperature measurement AD value and the coefficient matrix of the temperature compensation model.
Further, the two-stage least square fitting-based silicon piezoresistive pressure transmitter temperature compensation method is characterized in that the temperature compensation model is as follows:
Figure BDA0001284383250000021
wherein P is a compensation pressure value, and the units Pa and U AD For pressure measurement AD value, C fit Coefficient matrix for temperature compensation model, T AD AD values were measured for temperature.
Further, the "modeling of the temperature compensation model by the two-stage least square method" specifically includes:
respectively collecting pressure measurement AD values under n standard pressure input values under m specified temperature values to obtain m x n pressure measurement AD values;
for each appointed temperature value, carrying out least square fitting with the fitting times of k on n standard pressure input values and n pressure measurement AD values to obtain a polynomial function mapping relation between the standard pressure input values and the pressure measurement AD values under the appointed temperature values and a first-stage coefficient matrix;
and carrying out least square fitting with fitting times of l on m appointed temperature AD values and coefficient row vectors with the length of m in the first-stage coefficient matrix to obtain a polynomial function mapping relation between the temperature AD values and the first-stage coefficient row vectors and the coefficient matrix of the temperature compensation model.
Further, the polynomial function mapping relationship between the standard pressure input value and the pressure measurement AD value at the specified temperature value is:
Figure BDA0001284383250000022
the polynomial function coefficient matrix of the standard pressure input value and the pressure measurement AD value under the specified temperature value is as follows: />
Figure BDA0001284383250000023
Wherein P is an input standard pressure value, and the unit Pa; u (U) AD For pressure measurement AD value, C i，k For the fitting coefficients, i=1, 2, …, m, k is the number of first stage fits.
Further, the polynomial function mapping relationship between the temperature AD value and the first-stage coefficient row vector is as follows:
Figure BDA0001284383250000024
the coefficient matrix of the temperature compensation model is as follows: />
Figure BDA0001284383250000025
Wherein C is k ，C k-1 ，…，C 1 ，C 0 Fitting coefficients for the first stage, C 0，0 ～C k，l For the temperature compensation coefficient, T AD For the temperature AD value, k is the first stage fitting number, and l is the second stage fitting number.
Correspondingly, the invention also provides a silicon piezoresistive pressure transmitter temperature compensation device based on two-stage least square fitting, which comprises:
the first processing module is used for modeling a temperature compensation model through a two-stage least square method;
the second processing module is used for storing the coefficient matrix of the temperature compensation model into an EPROM of the pressure transmitter;
and the third processing module is used for calculating the pressure value after the output temperature compensation according to the input pressure measurement AD value, the ambient temperature measurement AD value and the coefficient matrix of the temperature compensation model.
Further, the temperature compensation model is:
Figure BDA0001284383250000031
wherein P is a compensation pressure value, and the units Pa and U AD For pressure measurement AD value, C fit Coefficient matrix for temperature compensation model, T AD AD values were measured for temperature.
Further, the first processing module includes:
the first processing unit is used for respectively collecting pressure measurement AD values under n standard pressure input values under m appointed temperature values to obtain m x n pressure measurement AD values;
the second processing unit is used for carrying out least square fitting with the fitting times k on n standard pressure input values and n pressure measurement AD values for each appointed temperature value to obtain a polynomial function mapping relation between the standard pressure input values and the pressure measurement AD values under the appointed temperature values and a first-stage coefficient matrix;
and the third processing unit is used for carrying out least square fitting with fitting times of l on m appointed temperature AD values and coefficient row vectors with the length of m in the first-stage coefficient matrix to obtain a polynomial function mapping relation between the temperature AD values and the first-stage coefficient row vectors and a coefficient matrix of the temperature compensation model.
Further, the polynomial function mapping relationship between the standard pressure input value and the pressure measurement AD value at the specified temperature value is:
Figure BDA0001284383250000032
the polynomial function coefficient matrix of the standard pressure input value and the pressure measurement AD value under the specified temperature value is as follows: />
Figure BDA0001284383250000033
Wherein P is an input standard pressure value, and the unit Pa; u (U) AD For pressure measurement AD value, C i，k For the fitting coefficients, i=1, 2, …, m, k is the number of first stage fits.
Further, the polynomial function mapping relationship between the temperature AD value and the first-stage coefficient row vector is as follows:
Figure BDA0001284383250000041
the coefficient matrix of the temperature compensation model is as follows: />
Figure BDA0001284383250000042
Wherein C is k ，C k-1 ，…，C 1 ，C 0 Fitting coefficients for the first stage, C 0，0 ～C k，l For the temperature compensation coefficient, T AD For the temperature AD value, k is the first stage fitting number, and l is the second stage fitting number.
The technical scheme of the invention has the beneficial effects that:
1. the measurement accuracy of the pressure transmitter can be improved.
The technical scheme of the invention considers the nonlinear characteristics of the output of the pressure transmitter, and ensures that all interpolation points reach the lower limit of compensation precision in the whole by introducing a least square method, namely the maximum compensation error can be controlled, thereby solving the problems that the traditional piecewise linear interpolation method cannot embody the nonlinear characteristics of the output of the pressure sensor and cannot ensure higher compensation precision beyond the interpolation points.
2. Memory consumption of the pressure transmitter is reduced.
According to the technical scheme, only the coefficient matrix of the temperature compensation model is needed to be stored in the memory of the pressure transmitter, and all sampling interpolation data are not needed to be stored in the memory like a piecewise linear interpolation method, so that the needed memory space is greatly reduced, and the hardware cost can be reduced.
3. The operating efficiency of the temperature compensation program can be improved.
According to the technical scheme, the pressure value after temperature compensation can be calculated and output once only by inputting the pressure measurement AD value, the ambient temperature measurement AD value and the coefficient matrix of the temperature compensation model, a linear section where a measured working point is located is obtained without carrying out lookup for a plurality of times like a piecewise linear interpolation algorithm, and measured data is substituted as input into the linear section to calculate corresponding pressure output.
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FIG. 1 is a flow chart of the steps of a method for temperature compensation of a silicon piezoresistive pressure transmitter based on a two-stage least squares fit.
FIG. 2 is a flow chart of a temperature compensation model modeling step by a two-stage least squares method of the present invention.
FIG. 3 is a block diagram of a temperature compensation device for a silicon piezoresistive pressure transmitter based on a two-stage least squares fit according to the present invention.
Fig. 4 is a block diagram of a first process module according to the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In electronic components, under the condition that other conditions are unchanged, the output signals drift along with the change of temperature, in order to reduce the phenomenon, a certain algorithm is generally adopted to correct the output results, the purpose of eliminating the influence of the temperature change on the output signals of the components in a certain range is achieved, and the processing mode is called temperature compensation of the electronic components.
The silicon piezoresistive pressure transmitter is a pressure sensor manufactured according to the piezoresistive effect principle of monocrystalline silicon, and receives external pressure and converts the external pressure into a standard output signal in proportion, and the signal output by the silicon piezoresistive pressure transmitter is also affected by the ambient temperature, so that the temperature compensation problem is not ignored as a key link for improving the overall performance of the sensor.
FIG. 1 is a flow chart of the steps of a method for temperature compensation of a silicon piezoresistive pressure transmitter based on two-stage least squares fitting according to the present invention, comprising the steps of:
step 1, modeling a temperature compensation model by a two-stage least square method;
when the ambient temperature remains unchanged, the pressure AD value measured by the silicon piezoresistive pressure transmitter and the pressure value input by the silicon piezoresistive pressure transmitter are not necessarily the same due to the disturbance of some manufacturing processes, and a certain nonlinear mapping relation which can be expressed as a polynomial function exists between the pressure AD value and the pressure AD value. Along with the change of the environmental temperature, the temperature can be considered to actually influence each coefficient of the polynomial function in the nonlinear mapping, so that different nonlinear mapping relations under different temperature conditions are formed.
Based on the principle, the temperature compensation model adopted by the technical scheme of the invention is as follows:
Figure BDA0001284383250000051
wherein P is the compensated pressure value, i.e. taking into account the current ambient temperaturePressure value after element correction, unit Pa, U AD For pressure measurement of AD value, i.e. pressure value not taking into account ambient temperature factors, C fit Coefficient matrix for temperature compensation model, T AD For temperature measurement AD values, the AD values of the invention refer to digital signals output after analog-to-digital conversion.
Therefore, the key point of the technical scheme of the invention is how to calculate the coefficient matrix C of the temperature compensation model fit FIG. 2 is a flow chart of a temperature compensation model modeling step by a two-stage least squares method according to the present invention, comprising the steps of:
step 101, respectively collecting pressure measurement AD values under n standard pressure input values under m appointed temperature values to obtain m times n pressure measurement AD values;
in order to calculate the coefficient matrix of the temperature compensation model, data needs to be sampled first, for example, pressure values of 1000, 0 and 1000 (unit, pa) are respectively input at the ambient temperatures of 20, 0 and 20 (unit, celsius), and the pressure AD value measured by the silicon piezoresistive pressure transmitter is read out to obtain 9 sampling values in total. The ambient temperature and the input pressure values mentioned here must be within the permissible operating range of a silicon piezoresistive pressure transmitter.
102, for each appointed temperature value, carrying out least square fitting with the fitting times of k on n standard pressure input values and n pressure measurement AD values to obtain a polynomial function mapping relation between the standard pressure input values and the pressure measurement AD values under the appointed temperature values and a first-stage coefficient matrix;
at any given temperature value, consider the functional relationship between the pressure input value and the pressure measurement AD value as:
Figure BDA0001284383250000061
the polynomial function mapping relationship between the standard pressure input value and the pressure measurement AD value at the m specified temperature values is: />
Figure BDA0001284383250000062
Wherein P is an input standard pressure value, and the unit Pa; u (U) AD For pressure measurement AD value, C i，k For the fitting coefficients, i=1, 2, …, m, k is the number of first stage fits. At this time, a polynomial function coefficient matrix of the standard pressure input value and the pressure measurement AD value at the specified temperature value can be calculated by using a least squares fitting function in MATLAB, where the polynomial function coefficient matrix is:
Figure BDA0001284383250000063
and 103, carrying out least square fitting with fitting times of l on m appointed temperature AD values and coefficient row vectors with the length of m in the first-stage coefficient matrix to obtain a polynomial function mapping relation between the temperature AD values and the first-stage coefficient row vectors and a coefficient matrix of the temperature compensation model.
If the coefficients of order Guan Nige in the first-stage coefficient matrix are expressed in vector form, the coefficient matrix may also be expressed in vector form as c= [ C (k), C (k-1), …, C (1), C (0)]Wherein vector C (k) = [ C 1，k ，…C i，k ，…，C m，k ] T Representing the coefficient before the kth term when the temperature level is m.
Since each coefficient vector C (k) has m elements and the temperature calibration points are also m, the least square fitting can be used again to establish the polynomial relationship of degree l (l.ltoreq.m) between the first-stage coefficient row vector and the temperature AD value:
Figure BDA0001284383250000064
wherein C is k ，C k-1 ，…，C 1 ，C 0 Fitting coefficients for the first stage, C 0，0 ～C k，l For the temperature compensation coefficient, T AD For the temperature AD value, k is the first stage fitting frequency, l is the second stage fitting frequency, and then the coefficient matrix of the temperature compensation model is calculated by adopting the least square fitting function in MATLAB, wherein the coefficient matrix is as follows: />
Figure BDA0001284383250000071
Step 2, the coefficient matrix of the temperature compensation model is stored in an EPROM of the pressure transmitter, and the coefficient matrix of the temperature compensation model is usually stored in the EPROM of the pressure transmitter in a 16-system form as a double-precision floating point number;
and step 3, calculating the pressure value after the output temperature compensation according to the AD value measured by the input pressure, the AD value measured by the ambient temperature and the coefficient matrix of the temperature compensation model.
In the actual measurement process of the silicon piezoresistive pressure transmitter, firstly, the AD value of the ambient temperature and the AD value of the pressure (the pressure value which is not influenced by the ambient temperature factor) are measured, and then the coefficient matrix of the temperature compensation model in the EPROM is read, and the method comprises the following steps of
Figure BDA0001284383250000072
And calculating and outputting the corrected pressure value.
The following describes the steps of the temperature compensation method of the silicon piezoresistive pressure transmitter based on the two-stage least squares fitting according to a specific embodiment:
step 1, modeling a temperature compensation model of a monocrystalline silicon piezoresistive pressure transmitter with a measurement range of-40 KPa-40KPa and a working temperature range of-20 ℃ to 70 ℃, wherein the method comprises the following steps:
step 101, placing a monocrystalline silicon piezoresistive pressure transmitter in a high-low temperature box, connecting a pressure air source with an air pipe, providing stable pressure input through a pressure regulating device, taking 17 pressure measurement points (n=17) with 5KPa as a step distance, namely P cal Taking 5 temperature points (m=5) of-20deg.C, 0deg.C, 25deg.C, 50deg.C, 70deg.C, etc., namely T cal A total of 17 x 5 total of 85 pressure transmitter measurement outputs AD, U cal Wherein each output sampling point is measured three times and averaged to obtain the sampling data shown in the following table.
Step 102, setting a first-stage fitting coefficient as 3, and calculating to obtain a first-stage coefficient matrix by using a least squares fitting function for 5 calibration temperature points and sampling data by using MATLAB mathematical software, wherein the first-stage coefficient matrix is as follows:
Figure BDA0001284383250000073
step 103, setting the fitting coefficient of the second stage as 2, and according to the coefficient matrix C of the first stage UP And 5 temperature calibration temperature AD data, and calculating to obtain coefficient matrix C of the monocrystalline silicon piezoresistive pressure transmitter temperature compensation model by using least square fitting function fit The method comprises the following steps:
Figure BDA0001284383250000074
step 2, storing the coefficient matrix of the temperature compensation model into an EPROM of the monocrystalline silicon piezoresistive pressure transmitter;
and step 3, calculating the pressure value after the output temperature compensation according to the AD value measured by the input pressure, the AD value measured by the ambient temperature and the coefficient matrix of the temperature compensation model.
In the actual measurement process of the silicon piezoresistive pressure transmitter, firstly, the AD value of the ambient temperature and the AD value of the pressure (the pressure value which is not influenced by the ambient temperature factor) are measured, and then the coefficient matrix of the temperature compensation model in the EPROM is read, and the method comprises the following steps of
Figure BDA0001284383250000081
And calculating and outputting the corrected pressure value.
The technical scheme of the invention considers the nonlinear characteristics of the output of the pressure transmitter, and ensures that all interpolation points reach the lower limit of compensation precision in the whole by introducing a least square method, namely the maximum compensation error can be controlled, thereby solving the problems that the traditional piecewise linear interpolation method cannot embody the nonlinear characteristics of the output of the pressure sensor and cannot ensure higher compensation precision beyond the interpolation points.
In the above embodiment, if the piecewise linear interpolation method is adopted, 85 sets of values are formed by corresponding outputs (U) measured at 5 temperature points (T) and 17 pressure points (P) through experiments, and the values of each set of values are stored in the memory, where P, T are inputs and U is an output. Each data is stored in the memory as 16-ary single precision floating point numbers, each single precision data occupies 4 bytes, and a total of 4×3×85=1020 bytes are required. The technical scheme of the invention only needs to store 12 coefficient values related to the memory polynomial, each coefficient is represented by a double-precision 16-system number, each double-precision data occupies 8 bytes, the total occupied memory size is 8 x 12 = 96 bytes, and the memory occupation is greatly reduced.
The compensation precision of the existing piecewise linear interpolation algorithm is in a direct proportion relation with the obtained interpolation point, when the compensation precision requirement is high, a large number of calibration experiments are needed, and the calibration cost is too high. The interpolation method essentially carries out table lookup, when the accuracy is improved after compensation, table lookup calculation is carried out many times, the straight line section where the working point of actual measurement is located is obtained after table lookup is completed, and the measured data is substituted as input into the pressure output corresponding to the straight line calculation of the section, so that compensation can be completed. The technical scheme of the invention can calculate the pressure value after temperature compensation once only by inputting the pressure measurement AD value, the ambient temperature measurement AD value and the coefficient matrix of the temperature compensation model, thereby greatly improving the temperature compensation calculation efficiency.
FIG. 3 is a block diagram of a temperature compensation device for a silicon piezoresistive pressure transmitter based on two-stage least squares fitting according to the present invention, comprising:
the first processing module is used for modeling a temperature compensation model through a two-stage least square method;
wherein, the temperature compensation model is:
Figure BDA0001284383250000082
wherein P is a compensation pressure value, and the units Pa and U AD For pressure measurement AD value, C fit Coefficient matrix for temperature compensation model, T AD AD values were measured for temperature.
The second processing module is used for storing the coefficient matrix of the temperature compensation model into an EPROM of the pressure transmitter;
and the third processing module is used for calculating the pressure value after the output temperature compensation according to the input pressure measurement AD value, the ambient temperature measurement AD value and the coefficient matrix of the temperature compensation model.
Fig. 4 is a block diagram of a first processing module according to the present invention, including:
the first processing unit is used for respectively collecting pressure measurement AD values under n standard pressure input values under m appointed temperature values to obtain m x n pressure measurement AD values; the present processing unit is used to collect sample data in order to calculate a coefficient matrix of the temperature compensation model.
The second processing unit is used for carrying out least square fitting with the fitting times k on n standard pressure input values and n pressure measurement AD values for each appointed temperature value to obtain a polynomial function mapping relation between the standard pressure input values and the pressure measurement AD values under the appointed temperature values and a first-stage coefficient matrix;
when the ambient temperature remains unchanged, the pressure AD value measured by the silicon piezoresistive pressure transmitter and the pressure AD value input by the silicon piezoresistive pressure transmitter are not necessarily the same due to the disturbance of some manufacturing processes, and a certain nonlinear mapping relation which can be expressed as a polynomial function exists between the pressure AD value measured by the silicon piezoresistive pressure transmitter and the pressure AD value, and the functional relation between the pressure AD value and the pressure AD value is considered as follows:
Figure BDA0001284383250000091
the polynomial function mapping relationship between the standard pressure input value and the pressure measurement AD value at the m specified temperature values is: />
Figure BDA0001284383250000092
Wherein P is an input standard pressure value, and the unit Pa; u (U) AD For pressure measurement AD value, C i，k For the fitting coefficients, i=1, 2, …, m, k is the number of first stage fits. At this time, a polynomial function coefficient matrix of the standard pressure input value and the pressure measurement AD value at the specified temperature value can be calculated by using a least squares fitting function in a MATLAB mathematical calculation library, and is as follows: />
Figure BDA0001284383250000093
And the third processing unit is used for carrying out least square fitting with fitting times of l on m appointed temperature AD values and coefficient row vectors with the length of m in the first-stage coefficient matrix to obtain a polynomial function mapping relation between the temperature AD values and the first-stage coefficient row vectors and a coefficient matrix of the temperature compensation model.
If the Guan Nige order coefficients in the first-stage coefficient matrix are expressed in vector form, the first-stage coefficient matrix may also be expressed in vector form as c= [ C (k), C (k-1), …, C (1), C (0)]Wherein vector C (k) = [ C 1，k ，…C i，k ，…，C m，k ] T Representing the coefficient before the kth term when the temperature level is m.
Again establishing the polynomial relation of degree l (l.ltoreq.m) between the first-stage coefficient row vector and the temperature AD value:
Figure BDA0001284383250000101
wherein C is k ，C k-1 ，…，C 1 ，C 0 Fitting coefficients for the first stage, C 0，0 ～C k，l For the temperature compensation coefficient, T AD For the temperature AD value, k is the first stage fitting frequency, l is the second stage fitting frequency, and then the coefficient matrix of the temperature compensation model is calculated by adopting the least square fitting function in MATLAB, wherein the coefficient matrix is as follows: />
Figure BDA0001284383250000102
The foregoing detailed description will be given for the purpose of illustration only, and the invention is not limited to the above-described embodiments, but is to be construed as merely illustrative of the principles of the invention, as long as they are within the scope of the invention.

Claims (7)

1. The temperature compensation method of the silicon piezoresistive pressure transmitter based on the two-stage least square fitting is characterized by comprising the following steps:
modeling a temperature compensation model by a two-stage least square method; respectively collecting pressure measurement AD values under n standard pressure input values under m specified temperature values to obtain m x n pressure measurement AD values;
for each appointed temperature value, carrying out least square fitting with the fitting times of k on n standard pressure input values and n pressure measurement AD values to obtain a polynomial function mapping relation between the standard pressure input values and the pressure measurement AD values under the appointed temperature values and a first-stage coefficient matrix;
performing least square fitting with fitting times of l on m appointed temperature AD values and coefficient row vectors with length of m in the first-stage coefficient matrix to obtain a polynomial function mapping relation between the temperature AD values and the first-stage coefficient row vectors and a coefficient matrix of the temperature compensation model;
storing the coefficient matrix of the temperature compensation model into an EPROM of a pressure transmitter;
calculating a pressure value after output temperature compensation according to an input pressure measurement AD value, an ambient temperature measurement AD value and a coefficient matrix of the temperature compensation model;
the polynomial function mapping relation between the standard pressure input value and the pressure measurement AD value under the specified temperature value is as follows:
Figure FDA0004231898830000011
the polynomial function coefficient matrix of the standard pressure input value and the pressure measurement AD value under the specified temperature value is as follows: />
Figure FDA0004231898830000012
Wherein P is an input standard pressure value, and the unit Pa; u (U) AD For pressure measurement AD value, C i,k For the fitting coefficients, i=1, 2, …, m, k is the first stage fitting number;
the polynomial function mapping relation between the temperature AD value and the first-stage coefficient row vector is as follows:
Figure FDA0004231898830000013
the coefficient matrix of the temperature compensation model is as follows: />
Figure FDA0004231898830000014
Wherein C is k ，C k-1 ，…，C 1 ，C 0 Fitting coefficients for the first stage, C 0,0 ～C k,l For the temperature compensation coefficient, T AD For the temperature AD value, k is the first stage fitting number, and l is the second stage fitting number.
2. The method for temperature compensation of a silicon piezoresistive pressure transmitter based on two-stage least squares fitting according to claim 1, wherein the temperature compensation model is:
Figure FDA0004231898830000021
wherein P is a compensation pressure value, and the units Pa and U AD For pressure measurement AD value, C fit Coefficient matrix for temperature compensation model, T AD AD values were measured for temperature.
3. A silicon piezoresistive pressure transmitter temperature compensation device based on two-stage least squares fitting, adopting the silicon piezoresistive pressure transmitter temperature compensation method based on two-stage least squares fitting as set forth in any one of claims 1-2, comprising:
the first processing module is used for modeling a temperature compensation model through a two-stage least square method;
the second processing module is used for storing the coefficient matrix of the temperature compensation model into an EPROM of the pressure transmitter;
and the third processing module is used for calculating the pressure value after the output temperature compensation according to the input pressure measurement AD value, the ambient temperature measurement AD value and the coefficient matrix of the temperature compensation model.
4. The two-stage least squares fitting based silicon piezoresistive pressure transmitter temperature of claim 3The temperature compensation device is characterized in that the temperature compensation model is as follows:
Figure FDA0004231898830000022
wherein P is a compensation pressure value, and the units Pa and U AD For pressure measurement AD value, C fit Coefficient matrix for temperature compensation model, T AD AD values were measured for temperature.
5. The two-stage least squares fitting based silicon piezoresistive pressure transmitter temperature compensation device according to claim 3, wherein the first processing module comprises:
the first processing unit is used for respectively collecting pressure measurement AD values under n standard pressure input values under m appointed temperature values to obtain m x n pressure measurement AD values;
the second processing unit is used for carrying out least square fitting with the fitting times k on n standard pressure input values and n pressure measurement AD values for each appointed temperature value to obtain a polynomial function mapping relation between the standard pressure input values and the pressure measurement AD values under the appointed temperature values and a first-stage coefficient matrix;
and the third processing unit is used for carrying out least square fitting with fitting times of l on m appointed temperature AD values and coefficient row vectors with the length of m in the first-stage coefficient matrix to obtain a polynomial function mapping relation between the temperature AD values and the first-stage coefficient row vectors and a coefficient matrix of the temperature compensation model.
6. The device of claim 5, wherein the polynomial function mapping between the standard pressure input value and the pressure measurement AD value at the specified temperature value is:
Figure FDA0004231898830000023
standard pressure input value and pressure measurement AD value at the specified temperature valueThe polynomial function coefficient matrix is: />
Figure FDA0004231898830000031
Wherein P is an input standard pressure value, and the unit Pa; u (U) AD For pressure measurement AD value, C i,k For the fitting coefficients, i=1, 2, …, m, k is the number of first stage fits.
7. The two-stage least squares fitting based temperature compensation device of a silicon piezoresistive pressure transmitter according to claim 5, wherein the polynomial function mapping relationship of the temperature AD value and the first stage coefficient row vector is:
Figure FDA0004231898830000032
the coefficient matrix of the temperature compensation model is as follows: />
Figure FDA0004231898830000033
Wherein C is K ，C k-1 ，…，C 1 ，C 0 Fitting coefficients for the first stage, C 0,0 ～C k,l For the temperature compensation coefficient, T AD For the temperature AD value, k is the first stage fitting number, and l is the second stage fitting number.
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