CN112902818A - Method for calibrating magnetic linear position sensor - Google Patents
Method for calibrating magnetic linear position sensor Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B7/00—Measuring arrangements characterised by the use of electric or magnetic techniques
- G01B7/003—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring position, not involving coordinate determination
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B7/00—Measuring arrangements characterised by the use of electric or magnetic techniques
- G01B7/02—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring length, width or thickness
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Abstract
The invention provides a correction method of a magnetic linear position sensor, which comprises the following steps: the magnet is enabled to move along the linear stroke, and meanwhile, a processing unit in the sensor is enabled to require the magnetic angle type sensing element to periodically return a currently generated sine signal and a currently generated cosine signal until the magnet finishes the linear stroke; the signal processing device receives the digitized sine signal and the digitized cosine signal transmitted by the processing unit, and performs second derivative operation of an arctan function on the sine signal value subtracted by the first preset value and the cosine signal value subtracted by the second preset value to obtain a curvature curve, and determines the effective detection distance and the corresponding curvature value range of the induction element by taking an effective line segment in the curvature curve as a characteristic curve, and obtains a polynomial equation fitting the characteristic curve, and writes the polynomial equation and the curvature value range into the processing unit as a mathematical model of the induction element. Therefore, the detection distance of the sensing element can be increased, and the use number of the sensing element is reduced.
Description
Technical Field
The present invention relates to a method for calibrating a position sensor, and more particularly, to a method for calibrating a magnetic linear position sensor.
Background
Referring to fig. 1, one conventional way to obtain the detection distance of a magnetic angle type sensing element S (e.g., AMR, Hall, TMR …) is to make the magnetic angle type sensing element S sense the magnetic field of a magnet M moving along a linear stroke P1, so as to generate a sine wave signal and a cosine wave signal related to a moving distance of the magnet M and output them to a signal processor 10, the signal processor 10 digitizes the sine wave signal and the cosine wave signal into a digitized sine wave signal sin formed of a plurality of sine signal values Usin as shown in fig. 1 and a digitized cosine wave signal cos formed of a plurality of cosine signal values Ucos as shown in fig. 1, and performs a second derivative (atan2) operation of an ARCTAN function (ARCTAN) on the sine signal values Usin and the cosine signal values Ucos, i.e., atan2(Usin/Ucos), to obtain a plurality of curvature values, and the curvature values form a curvature curve C1 as shown in fig. 1, the curvature value of each point on a valid line segment L1 in the curvature curve C1 corresponds to a detection distance, and since the curvature value of the valid line segment L1 only ranges from 0.2 to 1.2, it means that an effective detection distance of the magnetic angle sensor S is not long, for example, the detection distance shown in fig. 1 is only 6mm, and therefore, assuming that the length to be detected is 6 times of 6mm, at least 6 magnetic angle sensors S need to be arranged in parallel for detection at the same time.
Disclosure of Invention
The present invention is directed to a calibration method for a magnetic linear position sensor, which can increase the detection distance of a magnetic angle sensor in the magnetic linear position sensor, thereby reducing the number of magnetic angle sensors.
The invention provides a correction method of a magnetic linear position sensor, wherein the magnetic linear position sensor is arranged on one side of a linear stroke to detect the position of a magnet which reciprocates along the linear stroke, and comprises a magnetic angle type sensing element and a processing unit; the correction method comprises the following steps: (A) the magnet is moved along the linear stroke, and a signal processing device processes the linear strokeThe unit requests the magnetic angle type sensing element to transmit back a currently generated sine signal and a currently generated cosine signal at a sampling frequency until the magnet finishes the linear stroke; (B) the processing unit digitalizes the sine signals and the cosine signals continuously transmitted by the magnetic angle type sensing element and outputs the signals to the signal processing device; (C) the signal processing device obtains the corresponding relation between the position of each sampling point of the magnet in the linear stroke and the digitized sine signal value and cosine signal value according to the length of the linear stroke and the sampling frequency, subtracts a first preset value from the sine signal value, and subtracts a second preset value from the cosine signal value; (D) the signal processing device performs second derivative (atan2) operation of an arc tangent function on the sine signal values subtracted by the first preset value and the cosine signal values subtracted by the second preset value, namely atan2 (subtracting the sine signal values of the first preset value/subtracting the cosine signal values of the second preset value) to obtain a plurality of corresponding curvature values, and the curvature values form a curvature curve; (E) the signal processing device takes an effective line segment in the curvature curve as a characteristic curve of the magnetic angle type sensing element, and determines an effective detection distance and a corresponding curvature value range of the magnetic angle type sensing element according to the characteristic curve; (F) the signal processing device determines a polynomial equation fitting the characteristic curve according to the effective detection distance and the curvature value range by curve fitting and linear regression analysis
M and beta of0～βmWherein i is 1,2,3 … n, yiRepresenting a relative distance, x, between the magnetic angle type sensing element and the magnetiRepresents the curvature value, beta0～βmIs a coefficient of the magnetic angle type induction element; and (G) the signal processing device writes the polynomial equation into the processing unit as a mathematical model of the magnetic angle type sensing element.
In some embodiments of the present invention, the first predetermined value is one of a maximum value and a minimum value of the sinusoidal signal values; the second predetermined value is one of two of the combinations of the maximum value and the minimum value of the cosine signal values.
In some embodiments of the invention, m is 6.
In some embodiments of the present invention, the magnetic angle sensing element has two magnetoresistive bridges 45 ° apart, wherein one of the magnetoresistive bridges senses the magnetic field of the magnet and generates a sine wave signal, and wherein the other magnetoresistive bridge senses the magnetic field of the magnet and generates a cosine wave signal 45 ° apart from the sine wave signal.
In some embodiments of the invention, the range of curvature values is-pi to pi.
The invention has the beneficial effects that: in the calibration procedure, the effective detection distance of the magnetic angle type sensing element can be increased by properly translating the sine signal values and the cosine signals obtained by sensing the magnetic angle type sensing element and then performing the second derivative (atan2) operation of the ARCTAN function (ARCTAN), thereby achieving the effects and purposes of reducing the number of the magnetic angle type sensing element and increasing the detection distance of the magnetic linear position sensor 2.
Drawings
Fig. 1 illustrates a conventional method for obtaining the detection distance of a magnetic angle sensor.
FIG. 2 is a flow chart of an embodiment of a calibration method for a magnetic linear position sensor according to the present invention.
FIG. 3 illustrates the components and arrangement of the magnetic linear position sensor to be calibrated in this embodiment.
Fig. 4 is a detailed circuit diagram of a magnetic angle-type sensing element included in the magnetic linear position sensor of the present embodiment.
Fig. 5 is a schematic waveform diagram of the digitized sine wave signal sin and the digitized cosine wave signal cos digitized by the processing unit of the present embodiment.
Fig. 6 illustrates the digitized sine wave signal sin and the digitized cosine wave signal cos of fig. 5 being shifted down by a first preset value and a second preset value, respectively.
Fig. 7 illustrates the second derivative of the ARCTAN function (atan2) of the sine wave signal sin 'and the cosine wave signal cos' shown in fig. 6 to obtain corresponding curvature values, which constitute a curvature curve C2.
Fig. 8 illustrates that the X-axis data and the Y-axis data of the effective line segment L2 of the curvature curve C2 shown in fig. 7 are replaced with each other to become a replaced effective line segment L2'.
Detailed Description
The invention is described in detail below with reference to the following figures and examples:
before the present invention is described in detail, it should be noted that in the following description, like elements are represented by like reference numerals.
Referring to fig. 2, which is a main flow of a calibration method of a magnetic linear position sensor according to an embodiment of the present invention, and as shown in fig. 3, the magnetic linear position sensor 2 to be calibrated is disposed at one side of a linear stroke P2 to detect a position of a magnet M reciprocating along the linear stroke P2, for example, the magnet M is a piston disposed in a cylinder 1, and the linear stroke P2 is a piston stroke of the piston reciprocating in the cylinder 1. The magnetic linear position sensor 2 mainly includes a magnetic angle type sensing element 21 and a processing unit 22, such as a microprocessor or a Micro Controller Unit (MCU). The magnetic angle type sensing element 21 is disposed at one side of the linear stroke P2, for example, an outer wall surface of the cylinder 1, to sense the magnetic field of the magnet M and output an analog sine signal and a cosine signal; the processing unit 22 is electrically connected to the magnetic angle sensor 21 to receive the sine signal and the cosine signal.
Since the characteristics of the magnetic angle-type sensing element 21 in each magnetic linear position sensor 2 are different, before the magnetic linear position sensor 2 leaves the factory, the magnetic linear position sensor 2 needs to go through a calibration procedure to find the mathematical model corresponding to the characteristics of the magnetic angle-type sensing element 21; and as shown in fig. 4, the magnetic angle type sensing element 21 (e.g., AMR, Hall, TMR …) has two magnetoresistive bridges (bridges) 211, 212 with a 45 ° phase difference (i.e., a 45 ° angle included); therefore, in the calibration method of the present embodiment, as shown in step S1 of fig. 2, first, the magnet M is moved from the end of the linear stroke P2 away from the magnetic angle-type sensing element 21 toward the magnetic angle-type sensing element 21, and after passing through the magnetic angle-type sensing element 21, the magnet M is moved away from the magnetic angle-type sensing element 21 to the other end of the linear stroke P2, in the process, the two magnetoresistive bridges 211 and 212 continuously sense the magnetic field of the magnet M to generate a sine wave signal SIN and a cosine wave signal COS with a phase difference of 45 °.
Meanwhile, a signal processing device 3, such as but not limited to a personal computer, enables the processing unit 22 to request the magnetic angle sensor 21 to transmit back the sine signal (i.e. the value of a certain point of the sine wave signal SIN, the analog voltage value) and the cosine signal (i.e. the value of a certain point of the cosine wave signal COS, the analog voltage value) generated at present at a sampling frequency (e.g. 10 times/second) until the magnet M has finished the linear stroke P2, so that the magnetic angle sensor 21 transmits back 10 sine signals and 10 cosine signals to the processing unit 22 every second, and then, as shown in step S2 of fig. 2, the processing unit 22 digitizes and outputs the received sine signals and cosine signals to the signal processing device 3. The digitized values of the sine signal values Usin and the cosine signal values Ucos may be compared to the values indicated by the left vertical axis of fig. 5.
Therefore, the signal processing device 3 can obtain the corresponding relationship between the position of the magnet M at each sampling point in the linear stroke P2 and the digitized sine signal values Usin and the digitized cosine signal values Ucos, such as the digitized sine signal sin composed of the digitized sine signal values Usin shown in fig. 5 and the digitized cosine signal cos composed of the digitized cosine signal values Ucos shown in fig. 5, according to the moving distance of the magnet M (i.e. the length of the linear stroke P2) and the sampling frequency.
Then, as shown in step S3 of fig. 2, the signal processing apparatus 3 subtracts a first preset value from the sine signal values Usin to obtain Usin ', as shown in fig. 6, which is equivalent to shift down (offset) the digitized sine signal sin by the first preset value to obtain a shifted digitized sine signal sin', and the signal processing apparatus 3 subtracts a second preset value from the cosine signal values Ucos to obtain Ucos ', as shown in fig. 6, which is equivalent to shift down (offset) the digitized cosine signal cos by the second preset value to obtain a shifted digitized cosine signal cos'; in this embodiment, the first predetermined value is one half of a sum of a maximum value and a minimum value of the plurality of sinusoidal signal values Usin, but not limited thereto; the second predetermined value is one half of a sum of a maximum value and a minimum value of the plurality of cosine signal values Ucos, but not limited thereto.
Next, as shown in step S4 of fig. 2, the signal processing device 3 performs a second derivative (atan2) operation of an ARCTAN function (ARCTAN) on the sine signal values Usin '(i.e., the translated digitized sine wave signal sin') subtracted by the first predetermined value and the cosine signal values Ucos '(i.e., the translated digitized cosine wave signal cos') subtracted by the second predetermined value to obtain corresponding curvature values, which can be compared with the values marked by the right vertical axis of fig. 7, and constitute a curvature curve C2 shown in fig. 7, and an effective line segment L2 of the curvature curve C2 represents a characteristic curve of the magnetic angle sensor 21, and determines an effective detection distance of the magnetic angle sensor 21 and a corresponding curvature value range.
For example, when the curvature value is-1, it can be known that the distance value is-2 mm from the effective line segment L2 (the characteristic curve), which can represent the position of the magnet M located at the left side of the magnetic angle type sensing element 21 and at a distance of about 2mm from the magnetic angle type sensing element 21 when viewing fig. 3. Similarly, when the curvature value is 2, it can be known that the distance value is 2.6mm, which represents that the magnet M is located at the right side of the magnetic angle type sensing element 21 and is spaced from the magnetic angle type sensing element 21 by about 2.6 mm. As shown in fig. 7, in the present embodiment, since the curvature value range can reach-pi, the corresponding effective detection distance can be increased to 14mm, and thus, the detection distance (14mm) of the magnetic angle type sensing element 21 can be increased to more than twice of the detection distance (6mm) of the known art by performing the second derivative (atan2) operation of the ARCTAN function (ARCTAN) after translating the signal value obtained by the magnetic angle type sensing element 21, and therefore, assuming that the required detection length is 6 times of 6mm, only 3 magnetic angle type sensing elements 21 need to be arranged in parallel for simultaneous detection, and the number of the magnetic angle type sensing elements 21 can be reduced.
Then, as shown in step S6 of fig. 2, the signal processing device 3 determines the effective detection distance of the magnetic angle sensor 21 and the corresponding curvature value range by using the effective line segment L2 (i.e., the effective detection distance and the corresponding curvature value range) as the characteristic curve of the magnetic angle sensor 21, and the signal processing device 3 determines a polynomial equation fitting the characteristic curve by curve fitting and linear regression analysis according to the effective detection distance and the curvature value range
M and beta of0～βmWherein i is 1,2,3 … n, yiRepresents a relative distance, x, between the magnetic angle type sensing element 21 and the magnet MiRepresents the curvature value, beta0～βmIs a coefficient of the magnetic angle type inductance element 21.
Specifically, as shown in fig. 8 a, assuming that the effective line segment L2 (the characteristic curve) is composed of 100 curvature values (the curvature value range) corresponding to 100 positions (i.e., the distance values between the 100 magnets M and the magnetic angle sensor 21, i.e., the effective detection distance), in the present embodiment, the signal processing device 3 first replaces the data of the X-axis and the Y-axis of the effective line segment L2, so that the X-axis represents the curvature values and the Y-axis represents the corresponding distance values, and the effective line segment L2 becomes the replaced effective line segment L2', as shown in fig. 8B. Then, the signal processing device 3 determines a polynomial equation most suitable for the replaced effective line segment L2
For example, by using Polynomial Fitting (Polynomial Fitting), regression equation using univariate m-degree Polynomial
The permuted valid line segment L2' is fitted and the polynomial regression equation is solved with a matrix as shown below:
wherein y is1～ynRepresents the 100 distance values, x1～xnRepresents the 100 curvature values, beta0～βmIs a coefficient, and since the characteristics of each of the magnetic angle type induction elements 21 are different, the coefficient β thereof0～βmSo that the coefficients β of the magnetic angle-type inductive element 21 can be found by the matrix operation0～βmAnd a polynomial equation that determines the fit to be used for the displaced valid line segment L2'. For example, the embodiment may use the polyfit instruction provided by MATLAB to find the optimal coefficients (parameters) of the unary mth degree polynomial equation and the polynomial equation that best fits the replaced valid line segment L2'.
For example, the above-mentioned known 100 curvature value (x) is indicated by the polyfit instruction1～xn) Corresponding to the 100 distance values (y)1～yn) When the optimal coefficients of the 8 polynomial equations and the fitting result of the optimal coefficients with the replaced effective line segment L2 ' are obtained by respectively substituting the optimal coefficients into 8 polynomial equations of 1-membered 1-th order to 1-membered 8-th order, and the result of fitting the unary 6-th order polynomial equation to the replaced effective line segment L2 ' is found to be optimal (i.e., the unary 6-th order polynomial equation is closest to and most representative of the replaced effective line segment L2 ') from the 8 polynomial equations, the signal processing device 3 uses the unary 6-th order polynomial equation having the optimal fitting result, and the equation is, for example, y 2.4431x6-8.2418x5+15.967x4-10.349x3+7.6091x2+1.567x +1.0009, wherein y represents a relative distance (i.e. the distance value) between the magnet M and the magnetic angle sensor 21, and x represents a curvature value. Then, in step S7 of fig. 2, the signal processing apparatus 3 writes the unary 6 th-order polynomial equation and the curvature value range into the processing unit 22 as a mathematical model of the characteristic curve of the magnetic angle sensor 21, thereby completing the calibration process.
Thereby, when the magnetic linear position sensor 2 is practically applied to the cylinder 1 such as shown in FIG. 3 to detect the position of the piston (i.e., the magnet M) in the cylinder 1, when the processing unit 22 receives the simulated sine signal and the simulated cosine signal transmitted from the magnetic angle sensor 21, the processing unit 22 digitizes the sine signal and the cosine signal into a sine signal value and a cosine signal value, and subtracting the first preset value from the sine signal value and subtracting the second preset value from the cosine signal value, performing an second derivative (atan2) operation of an ARCTAN function (ARCTAN 2) on the sine signal value subtracted by the first preset value and the cosine signal value subtracted by the second preset value, i.e., atan2 (the sine signal value subtracted by the first preset value/the cosine signal value subtracted by the second preset value) to obtain a curvature value; then, when the processing unit 22 determines that the curvature value is within the curvature value range, the processing unit substitutes the curvature value into the mathematical model, so as to obtain a distance value by using the 6 th-order polynomial equation, where the distance value represents the relative distance between the magnetic angle type sensing element 21 and the magnet M; then, the processing unit 22 can directly output the distance value for the back-end application, or convert the distance value into a corresponding analog signal, such as an analog voltage (e.g., a voltage value of 1-5V) or an analog current (e.g., a current value of 4-20 mA), and output the analog voltage or the analog current to the back-end application.
To sum up, in the calibration procedure of the above embodiment, the second derivative (atan2) of the ARCTAN function (ARCTAN) is calculated after the sine signal value and the cosine signal obtained by the magnetic angle sensor 21 are properly translated, so that the effective detection distance of the magnetic angle sensor 21 can be increased, and the effects and purposes of reducing the number of the magnetic angle sensor 21 and increasing the detection distance of the magnetic linear position sensor 2 can be achieved; furthermore, by means of a calibration procedure, the mathematical model in the processing unit 22 of the magnetic linear position sensor 2 is made to fit the characteristic curve of the magnetic angular sensing element 21, and an effective detection distance and a corresponding curvature value range of the magnetic angular sensing element 21 are determined; therefore, the processing unit 22 only needs to digitize the sine signal and the cosine signal transmitted from the magnetic angle sensing element 21, then performs atan2 (subtracting the sine signal value of the first preset value/subtracting the cosine signal value of the second preset value) operation on the sine signal value subtracted by the first preset value and the cosine signal value subtracted by the second preset value to obtain a corresponding curvature value, and then inputs the curvature value into the mathematical model for calculating the distance, so as to quickly obtain a relative distance between the magnetic angle sensing element 21 and the magnet M by using an easily calculated unary M-th order polynomial equation.
The above description is only for the preferred embodiment of the present invention, and it is not intended to limit the scope of the present invention, and any person skilled in the art can make further modifications and variations without departing from the spirit and scope of the present invention, therefore, the scope of the present invention should be determined by the claims of the present application.
Claims (5)
1. A method for calibrating a magnetic linear position sensor disposed on one side of a linear path to detect a position of a magnet reciprocating along the linear path, the magnetic linear position sensor comprising a magnetic angle-type sensing element and a processing unit, the method comprising:
a: the magnet is made to move along the linear stroke, and simultaneously, the signal processing device makes the processing unit request the magnetic angle type sensing element to transmit back the currently generated sine signal and cosine signal at the sampling frequency until the magnet finishes the linear stroke;
b: the processing unit digitizes and outputs a plurality of sine signals and a plurality of cosine signals continuously transmitted by the magnetic angle type sensing element to the signal processing device;
c: the signal processing device obtains the corresponding relation between the position of each sampling point of the magnet in the linear stroke and a digitized sine signal value and a digitized cosine signal value according to the length of the linear stroke and the sampling frequency, subtracts a first preset value from the sine signal value, and subtracts a second preset value from the cosine signal value;
d: the signal processing device carries out second derivative operation of an arc tangent function on the sine signal value subtracted by the first preset value and the cosine signal value subtracted by the second preset value to obtain a plurality of corresponding curvature values, and the curvature values form a curvature curve;
e: the signal processing device takes an effective line segment in the curvature curve as a characteristic curve of the magnetic angle type sensing element, and determines an effective detection distance and a corresponding curvature value range of the magnetic angle type sensing element according to the characteristic curve;
f: the signal processing device determines a polynomial equation fitting the characteristic curve according to the effective detection distance and the curvature value range by curve fitting and linear regression analysis
M and beta of0～βmWherein i is 1,2,3 … n, yiRepresenting the relative distance, x, between the magnetic angle type sensing element and the magnetiRepresents the curvature value, beta0～βmIs a coefficient of the magnetic angle type induction element; and
g: the signal processing device writes the polynomial equation and the curvature value range into the processing unit as a mathematical model of the characteristic curve of the magnetic angle type inductive element.
2. The method of claim 1, wherein the first predetermined value is one half of a sum of a maximum value and a minimum value of the sine signal values, and the second predetermined value is one half of a sum of a maximum value and a minimum value of the cosine signal values.
3. The method of calibrating a magnetic linear position sensor according to claim 1 or 2, wherein m is 6.
4. The method of calibrating a magnetic linear position sensor according to claim 1 or 2, wherein the magnetic angle type sensing element has two magnetoresistive bridges which are different by 45 °, one of the two magnetoresistive bridges sensing the magnetic field of the magnet and generating a sine wave signal, and the other magnetoresistive bridge sensing the magnetic field of the magnet and generating a cosine wave signal which is different by 45 ° from the sine wave signal.
5. The method of calibrating a magnetic linear position sensor according to claim 1 or 2, wherein the curvature value ranges from-pi to pi.
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