DE102022122599B3 - Method for detecting a position of a target using a linear magnetic position sensor - Google Patents

Abstract

The invention relates to a method for detecting a position (x) of a target (T) using a linear magnetic position sensor with at least two sensor elements (E1, E2) which are set up to measure a magnetic field vector of the target (T). The magnetic field vector of the target (T) is measured by at least one sensor element (E1, E2). A tangent function of half the vector angle is calculated from the magnetic field vector. Finally, the position of the target (T) is determined using a linear function from the tangent function of half the vector angle and the position (x1, x2) of the at least one sensor element (E1, E2).

Description

The present invention lies in the field of magnetic position sensors, which detect the position of a target by measuring a magnetic field vector of the target. The target is either magnetic itself or a magnetic field transmitter is arranged on the target. Linear magnetic position sensors typically have several sensor elements that are arranged along a straight line parallel to the direction of movement of the target and at the same distance from one another. The sensor elements measure the magnetic field vector - i.e. the magnetic flux density vector - of the target.

State of the art

Conventionally, to detect the position of the target, the vector angle of the target - i.e. the angle between the location vector of the target and the direction vector of the straight line in which the sensor elements are arranged (hence the direction vector between two adjacent sensor elements) - is calculated. For this purpose, the “arctan2” function of the axial component of the magnetic field vector - i.e. the component of the magnetic flux density vector that points in the direction of the straight line of the sensor elements - and the radial component of the magnetic field vector - i.e. the component of the magnetic flux density vector perpendicular to the axial component - used.

However, the precise determination of the position is difficult due to the course of the arctan2 function. There are known approaches to detecting the position that only use relatively linear parts of the asymmetric magnetic field vector or the arctan2 function. Due to the inaccurate determination of the position, the linear magnetic position sensor is limited in terms of the detection range and the minimum number of sensor elements per unit length.

The DE 10 2020 134 217 A1 discloses a small sensor device whose dimensions approximately correspond to its measuring range. It has a coil arrangement and sensor electronics. The coil arrangement is a planar excitation coil, by means of which a changing magnetic field can be generated to induce eddy currents and/or magnetic polarization in a target. A first planar reception coil is arranged parallel to and overlapping with the excitation coil, the excitation coil and the first reception coil being arranged parallel to the end face of the sensor device. The sensor electronics is set up to determine a parameter of an electrical signal of the excitation coil, which can be changed due to a feedback effect of the object, and a parameter of a voltage that can be induced in the first receiving coil due to the feedback effect of the object, and from the determined parameter of the inducible electrical signal Excitation coil and the determined at least one parameter of the inducible voltage of the first receiving coil to determine the longitudinal position of the target.

The DE 10 2016 102 978 A1 describes a magnetic position sensor with a permanent magnetic material that extends along a path. A first angle magnetic field sensor is set up to output a first signal. It is arranged at a distance from the material. A second angle magnetic field sensor is set up to output a second signal. It is arranged at a distance from the material and from the first angle magnetic field sensor. An evaluation unit is set up to determine a relative positioning of the angle magnetic field sensors relative to the material parallel to the path based on the signals. The magnetization of the material has a period length that varies along the path.

The DE 10 2018 203 884 A1 shows a position determination device comprising a displacement body which can be displaced along a displacement path and has a magnet arrangement and a sensor arrangement which comprises a plurality of magnetic field sensors which are arranged along the displacement path and are used to detect the magnetic field provided by the magnet arrangement. The position determination device is suitable for providing a respective measured value with each magnetic field sensor. The position determination device is designed to provide a position value that indicates a position of the displacement body based on a provided measured value and a sensor parameter and to carry out a calibration procedure for automatically determining the sensor parameter.

The DE 10 2016 124 952 A1 discloses a magnetic angle detection system for detecting a rotation angle of a magnetic field source rotatable about an axis of rotation. Several magnetic field detection elements are located in/on one plane and are not arranged on a single straight line through the axis of rotation. They provide output signals that are functions of the same magnetic field component located parallel to the axis of rotation. A processing unit is arranged to determine the angle of rotation from an angle between a pointer and a reference direction. The pointer is determined based on the output signals.

It is the object of the present invention to improve the detection of the position and to increase the accuracy of the position determination.

Disclosure of the invention

• Ein Magnetfeldvektor des Ziels, dessen Position erfasst werden soll, wird durch zumindest ein Sensorelement des linearen magnetischen Positionssensors gemessen. Insbesondere misst jedes Sensorelement jeweils den Magnetfeldvektor des Ziels. Bei den meisten Anwendungen ist das Ziel in einer axialen Anordnung, bei der sein magnetisches Dipolmoment (oder das magnetische Dipolmoment des am Ziel angeordneten Magnetfeldgebers) nur in Bewegungsrichtung des Ziels oder entgegen der Bewegungsrichtung ausgerichtet ist, und in einer radialen Anordnung, bei der das Dipolmoment in einer senkrechten Richtung zur Bewegung des Ziels oder entgegen dieser ausgerichtet ist. Aufgrund der bekannten Symmetrie der axialen und der radialen Anordnung, reicht es bei den meisten Anwendungen aus, den Magnetfeldvektor in zwei Dimensionen zu messen. Die erste Dimension ist parallel zur Bewegungsrichtung und zumindest zwei Sensorelemente sind in dieser Richtung in bekannten Abständen, insbesondere äquidistant angeordnet und weisen eine sensitive Achse in Richtung dieser ersten Dimension auf. Eine zweite Dimension verläuft senkrecht zur ersten Dimension durch das geometrische Zentrum des Ziels. Die Anordnungslinie der Sensorelemente weist eine weitere sensitive Achse in Richtung dieser zweiten Dimension auf.

The invention relates to a method with the following steps:

• A magnetic field vector of the target whose position is to be detected is measured by at least one sensor element of the linear magnetic position sensor. In particular, each sensor element measures the magnetic field vector of the target. In most applications, the target is in an axial arrangement in which its magnetic dipole moment (or the magnetic dipole moment of the magnetic field transmitter located at the target) is oriented only in the direction of movement of the target or against the direction of movement, and in a radial arrangement in which the dipole moment is oriented in a direction perpendicular to or counter to the movement of the target. Due to the known symmetry of the axial and radial arrangement, in most applications it is sufficient to measure the magnetic field vector in two dimensions. The first dimension is parallel to the direction of movement and at least two sensor elements are arranged in this direction at known distances, in particular equidistantly, and have a sensitive axis in the direction of this first dimension. A second dimension runs perpendicular to the first dimension through the geometric center of the target. The arrangement line of the sensor elements has a further sensitive axis in the direction of this second dimension.

A value of a tangent function of half the vector angle is determined from the measured magnetic field vector. This function is hereinafter referred to as the “retan” function and is calculated according to Formula 1: $$\text{retan}\left(b_x,b_{\mathrm{e.g}},{\phi }_{+}\right)=\text{tan}\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\left(\text{arctan2}\left(b_x,b_{\mathrm{e.g}}\right)+{\phi }_{+}\right)\right)$$

B _x denotes the axial component and B _z the radial component of the magnetic field vector. arctan2(B _x , B _z ) gives the vector angle of the magnetic field vector. φ ₊ is an optional quantity that indicates the orientation of the target's magnetic dipole. The value of φ ₊ is known in advance or can be determined independently of the method at hand.

wobei die Vektorkomponenten $b_x^A$

und $b_z^A$

gemäß Formel 3 berechnet werden können: $$\begin{array}{c}{b}_x^A=-\frac{3}{2}\text{cos}\left(2\alpha \right)-\frac{1}{2}\\ b_z^A=-\frac{3}{2}\text{sin}\left(2\alpha \right)\end{array}$$

α bezeichnet den Ortsvektor-Winkel.The half vector angle α _B of these vectors can be calculated using formula 2: $${\mathrm{\alpha }}_b=\text{arctan2}\left(b_x^A,b_{\mathrm{e.g}}^A\right)$$

where the vector components $b_x^A$

and $b_{\mathrm{e.g}}^A$

can be calculated according to formula 3: $$\begin{array}{c}{b}_x^A=-\frac{3}{2}\text{cos}\left(2\alpha \right)-\frac{1}{2}\\ b_{\mathrm{e.g}}^A=-\frac{3}{2}\text{sin}\left(2\alpha \right)\end{array}$$

α denotes the position vector angle.

x bezeichnet die Position des Ziels, x₁ bezeichnet die Position eines Sensorelements, R₁ bezeichnet den Wert der retan-Funktion, der aus der Messung dieses Sensorelements erhalten wird - also R₁ = retan(B_x1 B_z1, φ₊) - und m bezeichnet die Steigung. Die Steigung ist ein Koeffizient für die Korrelation der relativen longitudinalen Position (also in Bewegungsrichtung des Ziels) des Sensorelements und der Position des Ziels und hängt von gegenwärtigen geometrischen Faktoren ab. Dieser Koeffizient wird vorzugsweise mittels einer Kalibrierung bestimmt. Hierfür wird vorteilhaft die später beschriebene Selbst-Kalibrierung verwendet.The retan function is a relatively linear function of the position of the target and, especially compared to the arctan2 function of the corresponding magnetic field components, has a significantly higher linearity over the entire relevant measurement range. Due to the linear relationship between the position of the target and the retan function, a linear function can be established for the position of the target and the retan function, which is expressed in Formula 4: $$x=\mathrm{<figure-callout\; id="1"\; label="m\; R"\; filenames="DE102022122599B3\_0029.png,DE102022122599B3\_0032.png"\; state="\{\{state\}\}">m</figure-callout>}{R}_{}{}_1+x_1$$

x denotes the position of the target, x ₁ denotes the position of a sensor element, R ₁ denotes the value of the retan function obtained from the measurement of this sensor element - i.e. R ₁ = retan(B _x1 B _z1 , φ ₊ ) - and m denotes the slope. The slope is a coefficient for the correlation of the relative longitudinal position (i.e. in the direction of movement of the target) of the sensor element and the position of the target and depends on current geometric factors. This coefficient is preferably determined by means of a calibration. The self-calibration described later is advantageously used for this.

Further measurements can be carried out with other sensor elements and corresponding linear functions can be set up. The same value can be assumed for the slope.

Using the linear function for the retan function and the relative longitudinal position of the at least one sensor element, the position of the target is finally calculated according to Formula 4.

As a result, the position of the target is determined using the retan function, which is highly linear. The linearity is also given for large distances between the sensor elements, so that fewer sensor elements are used per unit length can be det, which leads to a cost reduction in the production of the position sensor. In addition, the detection range of the position sensor extends beyond the sensor elements, so that measurements can also be carried out outside a sensor housing in which the sensor elements are arranged. This means that even a short sensor can cover a relatively large detection range. Finally, due to the linearity, the detection areas of different position sensors can be combined to form even larger detection areas.

A preferred way to carry out the calibration in order to determine the slope of the linear function is self-calibration using the at least two sensor elements, in which the following steps are carried out. Two sensor elements each measure a magnetic field vector of the target - a total of two magnetic field vectors - with the target located at an arbitrary position within the detection range. For each magnetic field vector, the retan function is calculated according to Formula 1. The optional quantity φ ₊ , which indicates the orientation of the target's magnetic dipole, can be omitted since this corresponds for both measurements and is eliminated in the subsequent calculation. Then for each retan function the value at the position of the target is calculated.

The difference is calculated from the two values of the retan functions and finally the ratio between the distance between the two sensor elements, which is determined by the structure of the position sensor and is therefore known, and the difference between the two values of the retan function at the position of the Target formed. As shown below, this ratio corresponds to the slope of the linear function described above for both sensor elements.

The linear function for the first sensor element is expressed by Formula 4 as described above: $$x=m{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="DE102022122599B3\_0029.png,DE102022122599B3\_0032.png"\; state="\{\{state\}\}">R</figure-callout>}}_1+x_1$$

Analogously, a linear function can be set up for the second sensor element, which is expressed by the formula 4*: $$x=m{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="DE102022122599B3\_0028.png,DE102022122599B3\_0029.png"\; state="\{\{state\}\}">R</figure-callout>}}_2+x_2$$

Here, x further denotes the position of the target, x ₂ denotes the position of the second sensor element, R ₂ denotes the value of the retan function for the measurement with the second sensor element - i.e. R ₂ = retan(B _x2 ,B _z2 ,φ ₊ ) - and m denotes the same slope as in Formula 4 for the first sensor element.

By subtracting the two equations 4 and 4* you get the following equation: $$\begin{array}{l}0=m\left({\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="DE102022122599B3\_0029.png,DE102022122599B3\_0032.png"\; state="\{\{state\}\}">R</figure-callout>}}_1-R_2\right)+\left(x_1-x_2\right)\\ <=>m=\left(x_2-x_1\right)/\left({\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="DE102022122599B3\_0029.png,DE102022122599B3\_0032.png"\; state="\{\{state\}\}">R</figure-callout>}}_1-R_2\right)\end{array}$$

This means that a self-calibration can be carried out using just two sensor elements to determine a value for the gradient. Due to the linearity, only the measured values for the two retan functions R ₁ and R ₂ and the distance x ₂ - x ₁ of the two sensor elements, which is known from the structure of the position sensor, are used for calibration. To self-calibrate, the target only needs to travel a short distance within the sensor's detection range or can even stand still.

In general, the linear magnetic position sensor can have a plurality of sensor elements and the method according to the invention can be extended to the plurality of sensor elements.

In practice, with multiple sensor elements, deviations in the ideal structure of the linear magnetic position sensor and/or the orientation of the magnetic field with respect to the sensor elements can occur. These arise, for example, from misalignments, offsets and/or measurement/evaluation errors of the sensor elements. As a result, the characteristic of the retan function may deviate from the linear dependence of the position. As a result, the difference in retan function values calculated during self-calibration depends on the current position of the target. Especially when the target is located at a great distance from the sensor elements and this makes the target's magnetic field comparable to, for example, background magnetism or an offset, or when small alignment errors from the ideal axis of the sensor elements or the radial orientation lead to errors in linearity , irrelevant values may occur, both for the retan function and for the relative position calculated from it. As a further result, the multiple sensor elements may provide ambiguous results for the location of the target.

In the case of three or more sensor elements, it can therefore be provided that, during self-calibration, two calculated slopes of the linear functions for the at least three sensor elements are merged with one another in pairs - i.e. for two of the sensor elements each - in order to determine a general slope. Preferably, a weighted arithmetic mean can be used to fuse the slopes slopes calculated in pairs can be calculated. The weightings can be determined arithmetically from values that are relevant for the signal-to-noise ratio or for the signal-offset ratio, for example the magnitude of the magnetic field vectors that are measured by the sensor elements working in pairs. Values for the slope that were obtained in unreliable measurement situations, for example when the target is on the edge of the detection ranges of the sensor elements, can also be suppressed or excluded during fusion.

Alternatively or additionally, provision can be made to compare the calculated values of the slope for the plurality of sensor elements with one another. During the comparison, contradictory values that do not fit with the other values can be identified and excluded. In addition, a range can be specified for the respective application - also depending on the calculated gradient values - and it can be checked whether the values lie within this range. Values outside this range can then be excluded.

A learning process can also be performed in which the positions of the target are varied and multiple values of the slope of the linear function are calculated for different positions of the target. Finally, the calculated values are averaged and the averaged slope value is used for the later detection of the position of the target.

If such a learning process is planned, the calculated gradient is optionally updated. After a slope value has initially been determined in the learning process, the values measured when detecting the position of the target can also be used according to the self-calibration described above to update the slope value.

The invention also relates to a linear magnetic position sensor which comprises at least two sensor elements. The sensor elements are set up to measure the magnetic field vector of the target. According to the invention, the linear magnetic position sensor is set up to carry out the above method. For this purpose, the linear magnetic position sensor can have a computing device set up for this purpose or can be connected to a computing device set up for this purpose. Reference is made to the above description and advantages.

Brief description of the drawings

• 1 zeigt ein Ortdiagramm von zwei Sensorelementen eines erfindungsgemäßen linearen magnetischen Positionssensors und eines zu messenden Ziels.
• 2 zeigt Diagramme der Komponenten des magnetischen Felds (a), des Vektorwinkels des Magnetfeldvektors (b) und der retan-Funktion (c) bezüglich der Position des Ziels, jeweils für vier unterschiedliche Orientierungen des magnetischen Dipols des Ziels.
• 3 zeigt ein Diagramm der retan-Funktion bezüglich der Position für die zwei Sensorelemente des erfindungsgemäßen linearen magnetischen Positionssensors bei der Selbstkalibrierung.
• 4 und 5 zeigen jeweils Diagramme der Komponenten des magnetischen Felds (a), des Vektorwinkels des Magnetfeldvektors (b) und der retan-Funktion (c) und einer mit dem erfindungsgemäßen Verfahren erfassten Position sowie eines Fehlers (d) bezüglich der Position des Ziels für zwei unterschiedliche Anwendungsfälle.

Exemplary embodiments of the invention are shown in the drawings and explained in more detail in the following description.

• 1 shows a location diagram of two sensor elements of a linear magnetic position sensor according to the invention and a target to be measured.
• 2 shows diagrams of the components of the magnetic field (a), the vector angle of the magnetic field vector (b) and the retan function (c) with respect to the position of the target, each for four different orientations of the target magnetic dipole.
• 3 shows a diagram of the retan function with respect to the position for the two sensor elements of the linear magnetic position sensor according to the invention during self-calibration.
• 4 and 5 each show diagrams of the components of the magnetic field (a), the vector angle of the magnetic field vector (b) and the retan function (c) and a position detected using the method according to the invention as well as an error (d) with respect to the position of the target for two different applications .

Embodiments of the invention

In 1 A location diagram is shown in the form of a Cartesian coordinate system with two axes x and z. Two sensor elements E ₁ , E ₂ of a linear magnetic position sensor according to the invention are shown. The origin of the coordinate system was placed in the second sensor element E ₂ , which is arranged at position x ₂ . The first sensor element E ₁ is also arranged on the x-axis, so that the two sensor elements E ₁ and E ₂ lie on a common axis, and are arranged at a distance S from the second sensor element E ₂ at the position x ₁ . The position sensor can have further sensor elements, not shown here, which are also arranged on the x-axis, for example at the same distance S from one another. Likewise, further components of the position sensor, for example a computing device on which the method according to the invention runs, are not shown. The sensor elements E ₁ , E ₂ have a sensitive axis in the direction of the x-axis and a sensitive axis in the direction of the z-axis.

Furthermore, a target T whose position is to be recorded is shown. The target T moves along a path P on a straight line that is parallel to the x-axis and thus to the straight line on which the Sen sor elements E ₁ , E ₂ are arranged, runs and is spaced apart in the direction of the z-axis by the distance z ₀ . The location vector r of the target T is also shown. The location vector r forms an angle α with the x-axis. In this case, the target itself is a magnet, which is approximated as a dipole and has a magnetic dipole moment M. In this example, the magnetic dipole moment M points in the direction of the movement path P of the target T and against the x-axis. Such an orientation is referred to as an axial arrangement and is marked here with the letter A. In practice, the target is typically arranged to use the following orientations of the magnetic dipole moment M. Below is a list of the orientation of the dipole moment M in (x,z) space, the letters A, B, C and D used here for identification and a quantity φ ₊ described in detail later: Axial arrangement: A (-M,0) φ ₊ = 0 b (M,0) φ ₊ = π Radial arrangement: C (0,-M) φ ₊ = π/2 D (0,M) φ ₊ = 3π/2

For those in 1 In the situation shown, in which the target T is in the position represented by the location vector r, the magnetic field vector B measured by the second sensor element E ₂ is as follows: $$\underset{\_}{b}=\frac{{\mathrm{<figure-callout\; id="0"\; label="\mu "\; filenames="DE102022122599B3\_0028.png,DE102022122599B3\_0029.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_0}{4\pi }\left(\frac{3\left(\underset{\_}{M}\underset{\_}{r}\right)\underset{\_}{r}}{{\mathrm{<figure-callout\; id="5"\; label="r"\; filenames="DE102022122599B3\_0032.png"\; state="\{\{state\}\}">r</figure-callout>}}^5}-\frac{\underset{\_}{M}}{r^3}\right)$$

$$\underset{\_}{r}=\underset{\_}{\rho }\cdot \left|\underset{\_}{r}\right|=\underset{\_}{\rho }\cdot r$$

$$\underset{\_}{b}=3\left(\underset{\_}{\mu }\underset{\_}{\rho }\right)\underset{\_}{\rho }-\underset{\_}{\mu }$$

kann der Magnetfeldvektor B in folgender Form geschrieben werden: $$\underset{\_}{B}=\underset{\_}{b}\frac{{\mu }_{0}M}{4\pi r^3}$$

b ist ein Vektor, der in dieselbe Richtung wie der Magnetfeldvektor B zeigt, aber nicht notwendigerweise ein Einheitsvektor.With the following substitutions: $$\underset{\_}{M}=\underset{\_}{\mu }\cdot \left|\underset{\_}{M}\right|=\underset{\_}{\mu }\cdot M$$

$$\underset{\_}{r}=\underset{\_}{\rho }\cdot \left|\underset{\_}{r}\right|=\underset{\_}{\rho }\cdot r$$

$$\underset{\_}{b}=3\left(\underset{\_}{\mu }\underset{\_}{\rho }\right)\underset{\_}{\rho }-\underset{\_}{\mu }$$

The magnetic field vector B can be written in the following form: $$\underset{\_}{b}=\underset{\_}{b}\frac{{\mu }_0\mathrm{<figure-callout\; id="4"\; label="M"\; filenames="DE102022122599B3\_0029.png,DE102022122599B3\_0030.png"\; state="\{\{state\}\}">M</figure-callout>}}{4\mathrm{<figure-callout\; id="3"\; label="\pi \; r"\; filenames="DE102022122599B3\_0032.png"\; state="\{\{state\}\}">\pi </figure-callout>}{r}^{}{}^3}$$

b is a vector pointing in the same direction as the magnetic field vector B, but not necessarily a unit vector.

For the case of the axial arrangement A, the vector b ^A can be described as follows: $${\underset{\_}{b}}^A=3\left(-{\rho }_x\cdot \underset{\_}{\rho }\right)-\left(1.0\right)=3\left({\mathrm{<figure-callout\; id="2"\; label="\rho \; x"\; filenames="DE102022122599B3\_0028.png,DE102022122599B3\_0029.png"\; state="\{\{state\}\}">\rho </figure-callout>}}_x^{},{\rho }_x{\rho }_{\mathrm{e.g}}\right)+\left(1.0\right)$$

erhält man die Vektorkomponenten von b^A als $$\begin{array}{c}{b}_x^A=-\frac{3}{2}\text{cos}\left(2\alpha \right)-\frac{1}{2}\\ b_z^A=-\frac{3}{2}\text{sin}\left(2\alpha \right)\end{array}$$

Under the use of $${\rho }_x=\text{cos}\left(\alpha \right)\text{and}{\rho }_{\mathrm{e.g}}=\text{sin}\left(\alpha \right)$$

one obtains the vector components of b ^A as $$\begin{array}{c}{b}_x^A=-\frac{3}{2}\text{cos}\left(2\alpha \right)-\frac{1}{2}\\ b_{\mathrm{e.g}}^A=-\frac{3}{2}\text{sin}\left(2\alpha \right)\end{array}$$

Since the two vectors B and b point in the same direction, they have the same vector angle α _B. This vector angle α _B is approximately - if the term -1/2 in formula 3 is neglected - twice the position vector angle α. The vector angle α _B of these vectors can be calculated using Formula 2: $${\mathrm{\alpha }}_b=\text{arctan2}\left(b_x^A,b_{\mathrm{e.g}}^A\right)$$

The above calculation can also be carried out for the other cases B, C, D with different orientation.

In 2 are each for the cases A, B, C, D with different orientation of the magnetic dipole moment M in 2 a a diagram of the components of the magnetic field vector in the x direction B _x and in the z direction B _z as well as the absolute value of the magnetic field vector |B| over the position x of the target T, in 2 B a plot of the vector angle α _B versus the position x of the target T and in 2c a diagram of the retan function retan, over the position x of the target T. The second sensor element E ₂ at the origin was used for detection. However, the following explanations can also be applied to the first sensor element E ₁ and to each additional sensor element of the position sensor.

The vector angle α _B was calculated using formula 2 from the components of the magnetic field vector in the x direction B _x and in the z direction B _z .

In diagrams 2a and 2b the horizontal scaling of the magnetic field components is B _x , B _z , |B| and the vector angle α _B depending on the distance z ₀ between the center of the target T and the straight line on which the sensor elements E ₁ , E ₂ are arranged. The vertical scaling of the magnetic field components B _x , B _z , |B| is dependent on both the stated distance z ₀ and the Strength of the magnetic field - i.e. the magnitude of the magnetic dipole moment |M|.

The angle α of the position vector r can be approximately expressed - if one ignores the additive term -1/2 in formula 3 - by the following formula 13: $$\mathrm{\alpha }\approx \frac{1}{2}\text{arctan2}\left(b_x^A,b_{\mathrm{e.g}}^A\right)=\frac{1}{2}\text{arctan2}\left(b_x^A,b_{\mathrm{e.g}}^A\right)$$

The tangent of the location vector angle α multiplied by the distance z ₀ gives the actual position of the target T. Since the value of the distance z ₀ is not known, only the calculation of the tangent of the location vector angle α is carried out, where the location vector angle α is approximately half of the vector angle α _B of the magnetic field vector B. This is achieved by the “retan” function.

The retan function in 2c was calculated using the formula 1 described at the beginning from the components of the magnetic field vector in the x direction B _x and in the z direction B _z and the quantity φ ₊ which depends on the orientation of the magnetic dipole moment M: $$\text{retan}\left(b_x,b_{\mathrm{e.g}},{\phi }_{+}\right)=\text{tan}\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\left(\text{arctan2}\left(b_x,b_{\mathrm{e.g}}\right)+{\phi }_{+}\right)\right)$$

In the diagram of 2c The horizontal scaling also depends on the distance z ₀ between the center of the target T and the straight line on which the sensor elements E ₁ , E ₂ are arranged.

For case A, in which the magnetic dipole moment M points against the x-axis, the graph of the vector angle α _B passes through the origin of the diagram in 2 B . The size φ ₊ is therefore chosen to be 0 so that the retan function is not shifted. For cases B, C and D, in which the magnetic dipole moment M has a different orientation, this leads to the graphs of the vector angle α _B no longer being at the origin of the diagram in 2 B are centered, but are vertically offset. This vertical offset is taken into account in Formula 1 by the quantity φ ₊ . The orientation of the magnetic dipole moment M and thus the size φ ₊ is assumed here to be known for the respective application.

Since the arctan2 function can assume values in the range of (-π,π], the graphs of the vector angle α _B are additionally shown with dotted lines and show discontinuities. These discontinuities can, if necessary, be resolved by adding 2π. Due to the periodic nature The tangent function leads to the same result after division by 2.

It can be seen that the retan function retan in 2c for all cases A, B, C, D is highly linear with respect to the position x, even at a large distance from the near point of the sensor element at the origin. For cases A and B, the nonlinearity is less than 0.005 on the vertical scale and for cases C and D, the nonlinearity is less than 0.007 on the vertical scale. The error for linearity is deterministic and can be reduced by retroactive corrections or by applying an appropriate function that is already specifically precompensated for these nonlinear errors and is in particular different for the axial case and the radial case. However, the non-linearity can also be accepted since other sources of the error also exist, e.g. B. the non-ideal character of the magnetic field, which deviates from a dipole, inaccurate radial or axial alignment, an unknown parasitic magnetic field in the background or an offset at the zero point of one of the magnetic field-sensitive axes of the sensor elements. One can also accept nonlinearity to maintain the simplicity of calculation, especially in the presence of a CORDIC (Coordinate Rotation Digital Computer) core in a microcontroller

The graphs of the retan function retan are identical in cases A and B - i.e. in an axial arrangement. Likewise, the graphs of the retan function retan are identical in cases C and D - i.e. in a radial arrangement. Furthermore, the slope of the retan function in cases A and B with an axial arrangement is always half as large as the slope in cases C and D with a radial arrangement.

$$x=m{R}_2+x_2$$

The two sensor elements E ₁ and E ₂ point due to the in 1 The arrangement described essentially has the same characteristics with regard to the retan function and differs essentially in its position x ₁ or x ₂ . In general, one sensor element E ₁ , E ₂ is sufficient to detect the position x of the target T. In order to determine the position x of the target T, a linear function is formed for the retan functions according to Formula 4 or Formula 4*, where R ₁ and R ₂ are the values of the respective retan functions at the position x of the target T represent, and from this the longitudinal position x of the target T relative to the position x ₁ or x ₂ of the sensor element sensor element E ₁ or E ₂ is calculated. $$x=m{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="DE102022122599B3\_0029.png,DE102022122599B3\_0032.png"\; state="\{\{state\}\}">R</figure-callout>}}_1+x_1$$

$$x=m{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="DE102022122599B3\_0028.png,DE102022122599B3\_0029.png"\; state="\{\{state\}\}">R</figure-callout>}}_2+x_2$$

The slope m of the linear function for the retan function depends, as described above, on the distance z ₀ between the center of the target T and the straight line on which the sensor elements E ₁ , E ₂ are arranged. However, this distance z ₀ is generally not known. The position sensor is therefore calibrated.

The position sensor performs a self-calibration as described below 3 is described by. In 3 a diagram of the retan function retan is shown over the position x of the target T. The target here occupies the arbitrary actual position x _T. The two sensor elements E ₁ and E ₂ are as in 1 already described, arranged at a distance S from one another, the second sensor element E ₂ being arranged at the origin of the coordinate system at the position x ₂ and the first sensor element being arranged at the position x ₁ . There are also the retan functions retan(B _x1 , B _z1 , φ ₊ ) for the first sensor element E ₁ and the retan functions retan(B _x2 , B _z2 , φ ₊ ) for the second sensor element E ₂ , which are as above were calculated as described. Since the two sensor elements E ₁ and E ₂ have essentially the same characteristics with regard to the retan function due to the arrangement, the two retan functions run retan(B _x1 , B _z1 , φ ₊ ), retan(B _x2 , B _z2 , φ ₊ ) parallel to each other and have the same gradient m. At the actual position x _T of the target T, a value R ₁ , R ₂ is obtained for each retan function retan(B _x1 , B _z1 , φ ₊ ), retan(B _x2 , B _z2 , φ ₊ ). According to formula 5, the slope m can be determined from the two values R ₁ , R ₂ for the retan functions and the distance S between the two sensor elements E ₁ , E ₂ , which is then used for the linear functions according to formula 4 and 4* . $$m=\left(x_2-x_1\right)/\left({\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="DE102022122599B3\_0029.png,DE102022122599B3\_0032.png"\; state="\{\{state\}\}">R</figure-callout>}}_1-R_2\right)=S/\left({\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="DE102022122599B3\_0029.png,DE102022122599B3\_0032.png"\; state="\{\{state\}\}">R</figure-callout>}}_1-R_2\right)$$

4 and 5 show two application examples in which the linear magnetic position sensor was arranged on two different pneumatic cylinders with radially oriented cylinder magnets. The position sensor comprises three collinearly arranged sensor elements, each arranged at a distance S of 9.03 mm. In 4a and 5a is a diagram of the components of the magnetic field vector in the x direction B _x and in the z direction B _z as well as the absolute value of the magnetic field vector |B|, which were measured by the three sensor elements, shown over the position x of the target T, in 4b and 5b a diagram of the vector angle α _B is shown over the position x of the target T for the three sensor elements, in 4c and 5c a diagram of the retan functions retan is shown over the position x of the target T for the three sensor elements and in 4d and 5d A diagram of the position x _e recorded by the method and the actual position x as well as an error F is shown. The detected position x _e is seen from one of the sensor elements.

For measuring the components of the magnetic field vector B _x , B _z , |B| and the calculation of the vector angle α _B as well as the calculation of the retan function retan is referred to the description above. For the retan function, the gradient m was taught at a position x _T of the target T at 34 mm. Each sensor element was determined to have a slope value and the slope values were weighted according to the amount of the magnetic field vector measured by the respective sensor element involved. In the example 4 the gradient m is -1.40 and in the example 5 the gradient is m -2.51. To determine the recorded position x _e, the measurements of the individual sensor elements were also weighted. The amount of the magnetic field vector reduced by 1000 LSB, which corresponds to a factor of approximately 10% to 15% of the maximum absolute value of the digitized magnetic field vector, was used for the weighting. The reduction of 1000 LSB ensures a sufficient signal-to-noise ratio or signal-to-background ratio for reliable evaluation and also suppresses abnormal angle values that occur when there is a large distance between the target and the affected sensor element. The weighting was set to 0 if the magnitude of the magnetic field vector reduced by 1000 LSB is negative.

It can be seen that despite errors due to the offset with respect to the zero point of the sensor elements, the non-ideal character of the magnetic field structure, such as. B. a small-scale rotation of the magnet in the example 5 and the like, the comparison between the position x _e detected by the method and the actual position x is linear, at least in a region in which the sensor elements are arranged. The large linear range allows long-range sensors to be manufactured in a small package. Since the detection range extends beyond the housing, even larger detection ranges can be achieved by connecting multiple position sensors together, either physically, through internal data exchange between the sensor elements, or simply by fusing the position sensors' simultaneously measured sensor signals. In addition, the number of sensor elements per unit length can be reduced, whereby the costs for the position sensor can be reduced.

Claims (10)

Method for detecting a position (x) of a target (T) using a linear magnetic Position sensor with at least two sensor elements (E ₁ , E ₂ ), which are set up to measure a magnetic field vector (B) of the target (T), characterized by the following steps: - measuring the magnetic field vector (B) of the target (T) by at least one Sensor element (E ₁ , E ₂ ); - Calculating a value (R1, R2) of a tangent function retan of half the vector angle α _B from the magnetic field vector (B); - Determining a position (x _e ) of the target (T) using a linear function from the tangent function retan of half the vector angle α _B and the position (x ₁ , x ₂ ) of the at least one sensor element (E ₁ , E ₂ ), where the tangent function retan is calculated according to the following formula: $$\text{retan}\left(b_x,b_{\mathrm{e.g}},{\phi }_{+}\right)=\text{tan}\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\left(\text{arctan2}\left(b_x,b_{\mathrm{e.g}}\right)+{\phi }_{+}\right)\right),$$

where B _x denotes the axial component and B _z the radial component of the magnetic field vector and φ ₊ is an optional quantity indicating the orientation of the target magnetic dipole, and the vector angle α _B is calculated according to the following formula: ${\mathrm{\alpha }}_b=\text{arctan2}\left(b_x^A,b_{\mathrm{e.g}}^A\right),$

where the following applies: $$b_x^A=-\frac{3}{2}\text{cos}\left(2\alpha \right)-\frac{1}{2}\text{and}{b}_{\mathrm{e.g}}^A=-\frac{3}{2}\text{sin}\left(2\alpha \right),$$

where α is the position vector angle. Procedure according to Claim 1 , characterized in that when calculating the tangent function retan of half the vector angle α _B , the orientation of the magnetic dipole of the target (T) is taken into account. Procedure according to Claim 1 or 2 , characterized in that a self-calibration of the at least two sensor elements (E ₁ , E ₂ ) is carried out with the following steps: - measuring two magnetic field vectors (B) by two sensor elements (E ₁ , E ₂ ); - Calculating the values (R ₁ , R ₂ ) of the tangent functions retan of half the vector angle α _B at the position of the target (x _T ) from the two magnetic field vectors (B); - Calculating a difference between the values (R ₁ , R ₂ ) of the tangent functions retan of half the vector angle α _B ; - Forming the ratio of the distance (S) between the two sensor elements (E ₁ , E ₂ ) and the difference of the values (R ₁ , R ₂ ) of the tangent functions retan of half the vector angle α _B to calculate the slope (m). linear function. Procedure according to Claim 3 , wherein the linear magnetic position sensor comprises at least three sensor elements (E ₁ , E ₂ ), characterized in that during self-calibration two calculated slopes (m) of the linear function for the at least three sensor elements (E ₁ , E ₂ ) are fused together in pairs . Procedure according to Claim 4 , characterized in that to fuse the calculated slopes (m), a weighted arithmetic mean of the pairwise calculated slopes (m) is calculated. Procedure according to Claim 4 or 5 , characterized in that slope values (m) that were obtained in unreliable measurement situations are suppressed or excluded during fusion. Procedure according to Claim 3 , wherein the linear magnetic position sensor comprises at least three sensor elements (E ₁ , E ₂ ), characterized in that the calculated slope values (m) are compared with one another and conflicting slope values (m) or slope values (m) that are outside one for the respective application within the assumed range can be excluded. Procedure according to Claim 3 , wherein the linear magnetic position sensor comprises at least three sensor elements (E ₁ , E ₂ ), characterized in that during self-calibration a learning process is carried out in which slopes (m) of the linear function are determined for different positions (x) of the target (T). are calculated and the calculated gradient values (m) are averaged. Procedure according to one of the Claims 7 or 8th , characterized in that the calculated slopes (m) are updated after the learning process, during the detection of the position (x) of the target (T). Linear magnetic position sensor, comprising at least two sensor elements (E ₁ , E ₂ ), wherein the sensor elements (E ₁ , E ₂ ) are set up to measure the magnetic field vector (B) of the target T, the linear magnetic position sensor being set up, the method according to one of the Claims 1 until 9 to carry out.

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