CN116358741A - Temperature resolving method for platinum resistance temperature measuring system - Google Patents
Temperature resolving method for platinum resistance temperature measuring system Download PDFInfo
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- CN116358741A CN116358741A CN202310328025.3A CN202310328025A CN116358741A CN 116358741 A CN116358741 A CN 116358741A CN 202310328025 A CN202310328025 A CN 202310328025A CN 116358741 A CN116358741 A CN 116358741A
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- G01K—MEASURING TEMPERATURE; MEASURING QUANTITY OF HEAT; THERMALLY-SENSITIVE ELEMENTS NOT OTHERWISE PROVIDED FOR
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- G01K7/00—Measuring temperature based on the use of electric or magnetic elements directly sensitive to heat ; Power supply therefor, e.g. using thermoelectric elements
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- G01K7/18—Measuring temperature based on the use of electric or magnetic elements directly sensitive to heat ; Power supply therefor, e.g. using thermoelectric elements using resistive elements the element being a linear resistance, e.g. platinum resistance thermometer
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Abstract
The invention discloses a temperature resolving method for a platinum resistance temperature measuring system, which is used for resolving the temperature by using two-point calibration, linear interpolation and nonlinear regression correction modes based on the characteristics of nonlinear change of platinum resistance along with the temperature and nonlinear change of output voltage of the temperature measuring system; compared with the current general multipoint calibration and piecewise interpolation temperature calculation method, the temperature measurement method has the advantages that only the boundary point of the temperature measurement region needs to be calibrated in a wider temperature measurement region, the problem that the resistance value of the platinum resistor changes along with the temperature nonlinearity and the output voltage of the temperature measurement circuit changes nonlinearity can be overcome by carrying out nonlinear regression correction on the theoretical resistance value calculated by interpolation, the temperature measurement precision of the temperature measurement system is not limited by the hardware condition of the temperature measurement system, the requirement of high-precision temperature measurement can be met by using few hardware resources, a platinum resistance value and temperature regression relation is established according to the resistance value-temperature dividing table of the platinum resistor, and the temperature can be directly solved by the relation according to the platinum resistance value after regression correction.
Description
Technical Field
The invention belongs to the technical field of platinum resistance temperature measurement, and relates to a temperature resolving method for a platinum resistance temperature measurement system.
Background
The temperature measurement is used as a general measurement technology, has very wide effect, and particularly has extremely high requirements on the accuracy of the temperature measurement in the fields of material science, aerospace and industrial control. Among the temperature sensors, platinum resistance type temperature sensors are widely used in their relatively more stable and linear characteristics. In a temperature measurement system, a two-wire system, three-wire system or four-wire system temperature measurement circuit is generally used for converting a platinum resistance value R, a voltage value corresponding to the platinum resistance value R is obtained after conversion, then an A/D conversion is carried out to obtain a sampling value, generally, in an environment with a narrow temperature measurement interval range, the interval boundary value resistance value R, A/D sampling value is calibrated, and then the temperature can be approximately obtained through an interpolation calculation mode. However, in an environment with a wider temperature measurement range, the method of calculating the temperature by matching the linear interpolation with the simple two-point calibration becomes not applicable any more due to the nonlinear characteristics of the resistance value of the platinum resistor along with the temperature change and the nonlinear characteristics of the resistance-voltage conversion of the two-wire system, three-wire system and four-wire system platinum resistor temperature measuring circuit disclosed at present, and the solution error of a medium temperature area is greatly increased under the wide temperature measurement environment, so that the requirement of high-precision temperature measurement is not met.
In order to solve the above problems, the temperature is calculated by adopting a mode of multi-point calibration and collocation with piecewise interpolation calculation, and the relationship between all related quantities is linear in a range by default, and the method can theoretically improve the measurement precision of a medium temperature zone, but has the following defects:
1. multiple calibrations are needed and calibration data are stored to improve the resolving precision, and a large amount of hardware storage resources are consumed.
2. A large amount of memory space is required in the thermometry system for storing the platinum resistance index table.
3. The temperature measurement precision of the temperature measurement system is completely limited by hardware resources of the temperature measurement system, and the wide-range and high-precision temperature measurement cannot be performed under the condition of limited hardware resources.
Disclosure of Invention
The invention aims to provide a temperature resolving method for a platinum resistance temperature measuring system, which can resolve a temperature value with high precision by only storing a calibration value twice by the temperature measuring system on the premise of extremely few required hardware storage resources.
The invention is realized by the following technical scheme:
the temperature resolving method for the platinum resistance temperature measuring system is realized based on the platinum resistance temperature measuring system and comprises the following steps:
step 1, determining that the platinum resistance graduation meter is in a temperature measuring interval [ T ] 0 ，T M ]Corresponding resistance value interval R 0 ，R M ]；
Step 2, the resistance value is R 0 And R is M The fixed resistor of the (C) is connected with a platinum resistance temperature measuring system for calibration to obtain a sampling value interval S 0 ，S M ]；
Step 3, according to the resistance value interval [ R ] 0 ，R M ]And sampling value interval S 0 ，S M ]The linear proportion relation of the medium temperature T is calculated by adopting a linear interpolation formula t Theoretical resistance value R corresponding to the condition t And recording an arbitrary medium temperature T t Under the condition of replacing the platinum resistor, accessing the resistance Zt of a real resistor in the specific resistance temperature measurement system;
step 4, using theoretical resistance value R t As independent variable, with the resistance Z of the real resistor t Carrying out nonlinear regression on the dependent variable to obtain a resistance value correction formula;
step 5, adopting a resistance value correction formula to calculate the theoretical resistance value R obtained in the step 3 t Correcting to obtain a corrected theoretical resistance value R t ’；
Step 6, using the resistance Z of the real resistor t As independent variable, at any medium temperature T t Carrying out nonlinear regression on the dependent variable to obtain a temperature correction formula;
step 7, correcting the theoretical resistance value R calculated in the step 5 t ' bring in the temperature correction formula to obtain the corrected medium temperature T t ’。
The platinum resistance temperature measuring system is the prior art and is not an improvement point of the invention, and the specific structure and the use method thereof are not described herein.
In order to better implement the present invention, further, the linear interpolation formula in the step 3 is specifically:
wherein: r is R t For platinum resistance at any medium temperature T t The theoretical resistance value corresponding to the condition; r is R 0 For platinum resistance graduation table at T 0 Reading the corresponding resistance value at temperature; r is R M For platinum resistance graduation table at T M Reading the corresponding resistance value at temperature; s is S 0 Has a resistance value of R 0 The fixed resistor of the (C) is connected with a calibration value measured by a platinum resistance temperature measuring system; s is S M Has a resistance value of R M The fixed resistor of the (C) is connected with a calibration value measured by a platinum resistance temperature measuring system; s is S t For platinum resistance at any medium temperature T t And under the condition, sampling values are output through a platinum resistance temperature measurement system.
In order to better implement the present invention, further, the resistance value correction formula in the step 4 is specifically:
Z t ＝a n ×R t n +a n-1 ×R t n-1 ...+a 3 ×R t 3 +a 2 ×R t 2 +a 1 ×R t +a 0 ；
wherein: z is Z t The resistance value of a real resistor in a specific resistance temperature measurement system is accessed to replace a platinum resistor; r is R t For platinum resistance at any medium temperature T t The theoretical resistance value corresponding to the condition; a, a 0 -a n Is a correction coefficient.
In order to better implement the present invention, further, the temperature correction formula in step 6 is specifically:
T t ＝A n ×Z t n +A n-1 ×Z t n-1 ...+A 3 ×Z t 3 +A 2 ×Z t 2 +A 1 ×Z t +A 0 ；
wherein: t (T) t Is any medium temperature; z is Z t To replace platinum resistor to access the resistance value of a real resistor in a specific resistance temperature measurement system；A 0 -A n Is a correction coefficient.
In order to better implement the invention, further, the medium temperature T is corrected in the step 7 t The' calculation formula is specifically:
wherein: t (T) t ' is the correction medium temperature; z is Z t ' is to correct the resistance of the real resistor; r is R t ' is the corrected theoretical resistance value.
Compared with the prior art, the invention has the following advantages:
based on the characteristics that the platinum resistance varies nonlinearly with the temperature and the output voltage of the temperature measuring system varies nonlinearly, the temperature is calculated by using two-point calibration, linear interpolation and nonlinear regression correction modes; compared with the current general multipoint calibration and piecewise interpolation temperature calculation method, the temperature measurement method has the advantages that only the boundary point of the temperature measurement region needs to be calibrated in a wider temperature measurement region, the problem that the resistance value of the platinum resistor changes along with the temperature nonlinearity and the output voltage of the temperature measurement circuit changes nonlinearity can be overcome by carrying out nonlinear regression correction on the theoretical resistance value calculated by interpolation, the temperature measurement precision of the temperature measurement system is not limited by the hardware condition of the temperature measurement system, the requirement of high-precision temperature measurement can be met by using few hardware resources, a platinum resistance value and temperature regression relation is established according to the resistance value-temperature dividing table of the platinum resistor, and the temperature can be directly solved by the relation according to the platinum resistance value after regression correction.
Drawings
FIG. 1 is a schematic diagram of the steps in the process of the present invention.
Detailed Description
Example 1:
the temperature resolving method for the platinum resistance temperature measuring system of the embodiment is realized based on the platinum resistance temperature measuring system, as shown in fig. 1, and comprises the following steps:
step 1, determining that the platinum resistance graduation meter is in a temperature measuring interval [ T ] 0 ，T M ]Corresponding resistance value interval R 0 ，R M ]；
Step 2, the resistance value is R 0 And R is M The fixed resistor of the (C) is connected with a platinum resistance temperature measuring system for calibration to obtain a sampling value interval S 0 ，S M ]；
Step 3, according to the resistance value interval [ R ] 0 ，R M ]And sampling value interval S 0 ，S M ]The linear proportion relation of the medium temperature T is calculated by adopting a linear interpolation formula t Theoretical resistance value R corresponding to the condition t And recording an arbitrary medium temperature T t Under the condition of replacing the platinum resistor, accessing the resistance Zt of a real resistor in the specific resistance temperature measurement system;
step 4, using theoretical resistance value R t As independent variable, with the resistance Z of the real resistor t Carrying out nonlinear regression on the dependent variable to obtain a resistance value correction formula;
step 5, adopting a resistance value correction formula to calculate the theoretical resistance value R obtained in the step 3 t Correcting to obtain a corrected theoretical resistance value R t ’；
Step 6, using the resistance Z of the real resistor t As independent variable, at any medium temperature T t Carrying out nonlinear regression on the dependent variable to obtain a temperature correction formula;
step 7, correcting the theoretical resistance value R calculated in the step 5 t ' bring in the temperature correction formula to obtain the corrected medium temperature T t ’。
The linear interpolation formula in the step 3 is specifically:
wherein: r is R t For platinum resistance at any medium temperature T t The theoretical resistance value corresponding to the condition; r is R 0 For platinum resistance graduation table at T 0 Reading the corresponding resistance value at temperature; r is R M For platinum resistance graduation table at T M Reading the corresponding resistance value at temperature; s is S 0 Has a resistance value of R 0 The fixed resistor of the (C) is connected with a calibration value measured by a platinum resistance temperature measuring system; s is S M Has a resistance value of R M The fixed resistor of the (C) is connected with a calibration value measured by a platinum resistance temperature measuring system; s is S t For platinum resistance at any medium temperature T t And under the condition, sampling values are output through a platinum resistance temperature measurement system.
The resistance value correction formula in the step 4 specifically includes:
Z t ＝a n ×R t n +a n-1 ×R t n-1 ...+a 3 ×R t 3 +a 2 ×R t 2 +a 1 ×R t +a 0 ；
wherein: z is Z t The resistance value of a real resistor in a specific resistance temperature measurement system is accessed to replace a platinum resistor; r is R t For platinum resistance at any medium temperature T t The theoretical resistance value corresponding to the condition; a, a 0 -a n Is a correction coefficient.
The temperature correction formula in the step 6 specifically includes:
T t ＝A n ×Z t n +A n-1 ×Z t n-1 ...+A 3 ×Z t 3 +A 2 ×Z t 2 +A 1 ×Z t +A 0 ；
wherein: t (T) t Is any medium temperature; z is Z t The resistance value of a real resistor in a specific resistance temperature measurement system is accessed to replace a platinum resistor; a is that 0 -A n Is a correction coefficient.
The medium temperature T is corrected in the step 7 t The' calculation formula is specifically:
wherein: t (T) t ' is the correction medium temperature; z is Z t ' is to correct the resistance of the real resistor; r is R t ' is the corrected theoretical resistance value.
Example 2:
the temperature resolving method for platinum resistance temperature measuring system of the embodiment takes a three-wire constant current temperature measuring system for measuring PT1000 type platinum resistance as an example, and the temperature measuring interval [ T ] 0 ，T M ]Is at-100deg.C, 100deg.C]。
According to the required temperature measuring range of minus 100 ℃ and 100 DEG C]Inquiring the graduation table of PT1000 type platinum resistor to obtain the corresponding resistance values of 602.56 omega and 1385.06 omega respectively when the boundary temperature value of the temperature measuring area is obtained, thus obtaining the resistance value interval [ R ] 0 ，R M ]Is [602.56 omega, 1385.06 omega ]]。
To obtain R 0 ＝602.56Ω、R M The method comprises the steps of (1) taking 1385.06 omega as a calibration point, and respectively connecting fixed resistors with resistance values of 602.56 omega and 1385.06 omega into a three-wire constant-current temperature measurement system for calibration: the sampling values obtained after 16-bit A/D conversion of the temperature measuring system are respectively S 0 =100 and S M =65500 and stores R by the memory of the thermometry system 0 ＝602.56Ω、R M ＝1385.06Ω、S 0 ＝100、S M ＝65500、T 0 ＝-100℃、T M Several data at 100 ℃;
the data in the resistance value interval [602.56 omega, 1385.06 omega ] and the data in the sampling value interval [100, 65500] are in linear proportion relation, and can be according to a linear interpolation formula:
the corresponding data are carried in:
R t ＝602.56+(S t -100) x (1385.06-602.56)/(65500-100) to calculate the arbitrary medium temperature T t Corresponding theoretical resistance value R t Here, the temperature measurement range is minus 100 ℃ and 100 DEG C]Dividing the temperature measuring region into 11 groups at equal intervals for 10 sections to obtain 11 groups of temperatures T in the temperature measuring region t Theoretical resistance value R under the condition t And record the temperature T t Resistance Z of 11 sets of real resistors correspondingly connected under the condition t 。
11 groups of theoretical resistance values R t ＝{602.56Ω，683.75Ω，764.16ΩThe resistance Z of the real resistors corresponding to 843.85, 923.22, 1003.24, 1080.94, 1159.51, 1235.27, 1310.14, 1385.06 respectively t＝ {602.56 Ω,683.25 Ω,763.28 Ω,842.71 Ω,921.6Ω,1000 Ω,1077.94 Ω,1155.41 Ω,1232.42 Ω,1308.97 Ω,1385.06 Ω }, as R t As an independent variable, Z t For the dependent variables, a unitary cubic polynomial regression was performed, and the regressed relationship was as follows:
Z t ＝0.0000000568×R t 3 +0.0001510067×R t 2 +1.1236307962×R t -32.29(1)
the regressed equation (1) is used as the platinum resistance measured by the temperature measuring system at any medium temperature T t Corresponding theoretical resistance value R under condition t The theoretical resistance value R obtained by calculation is calculated according to the correction calculation formula of (2) t Carrying out equation (1) to calculate a corrected theoretical resistance value R t ′＝{602.36Ω，683.54Ω，763.50Ω，842.48Ω，921.05Ω，1000.34Ω，1077.58Ω，1156.09Ω，1232.33Ω，1308.35Ω，1385.23Ω}。
The resistance value interval R can be calculated according to the graduation table of PT1000 platinum resistance 0 ，R M ]Internal data and temperature measurement interval [ T ] 0 ，T M ]Data were subjected to a one-dimensional cubic polynomial regression with Z t As an independent variable, T t For the dependent variables to participate in regression for 202 sets of data, the regressed relationship is as follows:
T t ＝1.04952×10 -9 ×Z t 3 -1.34185×10 -5 ×Z t 2 +2.32198×10 -1 ×Z t -244.575(2)
equation (2) is used as arbitrary medium temperature T t R is calculated according to the calculation formula of (2) t ' = {602.36 Ω,683.54 Ω,763.50 Ω,842.48 Ω,921.05 Ω,1000.34 Ω,1077.58 Ω,1156.09 Ω,1232.33 Ω,1308.35 Ω,1385.23 Ω }, and the correction medium temperature T can be calculated by introducing into equation (2) t ’＝{-100.07℃，-79.92℃，-59.94℃，-40.06℃，-20.14℃，0.08℃，19.9℃，40.18℃，59.98℃，79.84℃，100.03℃}。
The maximum error of the final calculated corrected medium temperature from the actual medium temperature was 0.18 ℃ and the average error was 0.09 ℃. If higher resolving precision is required, the system resolving precision can be effectively improved by increasing the powers of the equation (1) and the equation (2) and increasing the data sample size involved in the model derivation.
In the following, only raised power is taken as an example, and the data sample size of the participation model derivation is unchanged.
The regression power was set to 5 times, and there were:
Z t ＝-6.02855×10 -13 ×R t 5 +3.011624×10 -9 ×R t 4 -5.844019×10 -6 ×R t 3 +5.509965×10 -3 ×R t 2 -1.532333×R t +454.7904
calculating a correction theoretical resistance value R t ′＝{602.607Ω，683.083Ω，763.431Ω，842.791Ω，921.368Ω，1000.370Ω，1077.340Ω，1155.860Ω，1232.440Ω，1308.791Ω，1385.120Ω}。
Calculating the temperature T of the correction medium t ' = { -100.008 ℃, -80.038 ℃, -59.954 ℃, -39.978 ℃, -20.065 ℃,0.080 ℃,19.850 ℃,40.120 ℃,60.010 ℃,79.962 ℃,100.002 ℃ }. The maximum error between the final calculated temperature value and the actual temperature value is 0.158 ℃, and the average error is only 0.055 ℃.
After the power of the correction model is raised, the temperature resolving precision of the temperature measuring system is obviously improved.
Other portions of this embodiment are the same as those of embodiment 1, and thus will not be described in detail.
The foregoing description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and any simple modification, equivalent variation, etc. of the above embodiment according to the technical matter of the present invention fall within the scope of the present invention.
Claims (5)
1. The temperature resolving method for the platinum resistance temperature measuring system is realized based on the platinum resistance temperature measuring system and is characterized by comprising the following steps of:
step 1, determining that the platinum resistance graduation meter is in a temperature measuring interval [ T ] 0 ，T M ]Corresponding resistance value interval R 0 ，R M ]；
Step 2, the resistance value is R 0 And R is M The fixed resistor of the (C) is connected with a platinum resistance temperature measuring system for calibration to obtain a sampling value interval S 0 ，S M ]；
Step 3, according to the resistance value interval [ R ] 0 ，R M ]And sampling value interval S 0 ，S M ]The linear proportion relation of the medium temperature T is calculated by adopting a linear interpolation formula t Theoretical resistance value R corresponding to the condition t And recording an arbitrary medium temperature T t Under the condition of replacing platinum resistor, the resistance Z of a real resistor in a specific resistance temperature measurement system is accessed t ；
Step 4, using theoretical resistance value R t As independent variable, with the resistance Z of the real resistor t Carrying out nonlinear regression on the dependent variable to obtain a resistance value correction formula;
step 5, adopting a resistance value correction formula to calculate the theoretical resistance value R obtained in the step 3 t Correcting to obtain a corrected theoretical resistance value R t ’；
Step 6, using the resistance Z of the real resistor t As independent variable, at any medium temperature T t Carrying out nonlinear regression on the dependent variable to obtain a temperature correction formula;
step 7, correcting the theoretical resistance value R calculated in the step 5 t ' bring in the temperature correction formula to obtain the corrected medium temperature T t ’。
2. The method for temperature calculation of platinum resistance temperature measurement system according to claim 1, wherein the linear interpolation formula in step 3 is specifically:
wherein: r is R t For platinum resistance in any mediumTemperature T t The theoretical resistance value corresponding to the condition; r is R 0 For platinum resistance graduation table at T 0 Reading the corresponding resistance value at temperature; r is R M For platinum resistance graduation table at T M Reading the corresponding resistance value at temperature; s is S 0 Has a resistance value of R 0 The fixed resistor of the (C) is connected with a calibration value measured by a platinum resistance temperature measuring system; s is S M Has a resistance value of R M The fixed resistor of the (C) is connected with a calibration value measured by a platinum resistance temperature measuring system; s is S t For platinum resistance at any medium temperature T t And under the condition, sampling values are output through a platinum resistance temperature measurement system.
3. The method for temperature calculation of platinum resistance temperature measurement system according to claim 2, wherein the resistance value correction formula in step 4 is specifically:
Z t ＝a n ×R t n +a n-1 ×R t n-1 …+a 3 ×R t 3 +a 2 ×R t 2 +a 1 ×R t +a 0 ；
wherein: z is Z t The resistance value of a real resistor in a specific resistance temperature measurement system is accessed to replace a platinum resistor; r is R t For platinum resistance at any medium temperature T t The theoretical resistance value corresponding to the condition; a, a 0 -a n Is a correction coefficient.
4. A temperature calculation method for a platinum resistance temperature measurement system according to claim 3, wherein the temperature correction formula in step 6 specifically comprises:
T t ＝A n ×Z t n +A n-1 ×Z t n-1 ...+A 3 ×Z t 3 +A 2 ×Z t 2 +A 1 ×Z t +A 0 ；
wherein: t (T) t Is any medium temperature; z is Z t The resistance value of a real resistor in a specific resistance temperature measurement system is accessed to replace a platinum resistor; a is that 0 -A n To correct the systemA number.
5. The method for temperature resolution of platinum resistance temperature measurement system according to claim 4, wherein said step 7 is performed by correcting said medium temperature T t The' calculation formula is specifically:
wherein: t (T) t ' is the correction medium temperature; z is Z t ' is to correct the resistance of the real resistor; r is R t ' is the corrected theoretical resistance value.
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