DE102022116956A1 - Inductive position sensor, method for compensating measurement errors in an inductive position sensor, computer program product, electrical machine and X-by-wire system for a motor vehicle - Google Patents

Abstract

The invention relates to an inductive position sensor (1), comprising a transmitter coil (6) which can be energized by a control unit (3) and a sensor target (7) which can be moved relative to the sensor carrier (2), a first arranged on and/or in the sensor carrier (2). , a substantially cosine-shaped receiver coil (4) from which a first voltage URX1 can be tapped, a second, substantially sinusoidal receiver coil (5) arranged on and/or in the sensor carrier (2) from which a second voltage URX2 can be tapped, wherein the first, essentially cosinusoidal receiving coil (4) has a curve that corresponds to a cosinusoidal fundamental wave with at least one harmonic and/or the second, essentially sinusoidal receiving coil (5) has a curve that corresponds to a sinusoidal fundamental wave with at least one harmonic .

Description

The present invention relates to an inductive position sensor, comprising a transmitter coil that can be energized by a control unit and a sensor target that can be displaced relative to the sensor carrier, a first, essentially cosine-shaped receiver coil arranged on and/or in the sensor carrier, on which a first voltage U _RX1 can be tapped is, a second, essentially sinusoidal receiver coil arranged on and/or in the sensor carrier, on which a second voltage U _RX2 can be tapped. The invention further relates to a method for compensating for measurement errors in an inductive position sensor, a computer program product, an electrical machine and an X-by-wire system for a motor vehicle.

Electric motors are increasingly being used to drive motor vehicles in order to create alternatives to combustion engines that require fossil fuels. Significant efforts have already been made to improve the suitability of electric drives for everyday use and to offer users the usual driving comfort.

In addition to purely electrically operated drive trains, hybrid drive trains are also known. Such drive trains of a hybrid vehicle usually include a combination of an internal combustion engine and an electric motor, and - for example in metropolitan areas - enable purely electric operation with sufficient range and availability, especially for cross-country journeys. There is also the possibility of being driven simultaneously by the internal combustion engine and the electric motor in certain operating situations.

Many of these drive trains use sensors that record the angle and rotation information, for example of an electric machine. In a simplified principle, these sensors consist of a sensor rotor and a sensor stator. The sensor itself is usually firmly connected to the housing of the electrical machine. The sensor rotor is usually a rotationally symmetrical component that rotates with the rotor of the electrical machine.

Permanent magnet synchronous machines are used in many of the electromobility applications mentioned above. Such a permanently excited synchronous machine includes a stator to be energized and a permanently excited rotor. The rotor usually includes a shaft, balancing plates, rotor laminated cores and magnets. The magnets are generally fixed in the rotor laminated cores.

To control such electronically commutated electrical machines, electrical control variables are applied to the stator windings of the machine in order to drive them, depending on the angular position of the rotor. The rotor position is usually detected using a rotor position sensor and fed to a control unit to generate the control signals required for commutation of the electrical machine. Rotor position sensors either provide an analog electrical quantity that depends on the position of the rotor, e.g. B. a voltage, signal pulses or a digitized information about the absolute rotor position. Such rotor position sensors are basically known from the prior art, in which a signal transmitter (magnetic target) mounted in a rotationally fixed manner on the rotor is read out by means of a magnetic field sensor mounted in a rotationally fixed manner on the stator.

For example, this shows DE 10 2009 001 353 A1 an electric machine, comprising a rotor with a rotor hub, a stator arranged in a stator housing, a cover which is connected to the stator housing and extends to the inner diameter of the rotor hub and over which the rotor is mounted by means of a rotor bearing. The electric machine has a rotor position sensor for detecting the rotational position of the rotor relative to the magnetic field of the stator. The rotor position sensor is arranged on the cover near the rotor bearing in such a way that the rotor hub or a component connected in a rotationally fixed manner to the rotor hub serves as the encoder track of the rotor position sensor.

In addition to the rotor position sensors that work with a magnetic target, inductive rotor position sensors are also known, which have the advantage of being able to do without a permanent magnet. This advantage counteracts the challenge of being able to generate sufficiently accurate sensor signals using an inductive sensor arrangement.

The sensors usually have an oscillator circuit, which induces an alternating voltage in at least two receiver coils through a transmitter coil.

In addition to the use of such inductive sensors in electric drive machines, they are also often used in mechatronic, steerable axles for determining the steering position, the steering angle, and the steering angle, which is explained in more detail below.

In particular, a growing need for individual mobility, an increasing number of cars and increasing car dimensions require measures to improve the parking situation in urban areas. In addition to aspects such as urban densification and increasing vehicle numbers, constantly increasing vehicle dimensions lead to a shortage of parking spaces and complicated parking procedures. One way to overcome this challenge is to implement new vehicle and transport concepts that aim to replace conventional cars. Alternative vehicle structures and new steering technologies are able to meet specific parking and important customer requirements simultaneously.

For this reason, such cars are increasingly being equipped with rear-axle steering, which significantly improves the maneuverability of these vehicles and, in particular, also supports automatic parking of the car. Electrically and/or hydraulically actuated actuators are usually used to actuate the rear axle steering. For obvious safety-relevant reasons, it is important to detect the exact position of the actuator or the rear axle steering safely and as accurately as possible.

From the DE 10 2018 130 228 A1 an actuator for a rear axle steering of a motor vehicle is known, comprising a push rod which is longitudinally displaceable within a housing and has an anti-rotation device. A sensor unit is integrated into the housing of the rear axle steering actuator.

To measure the steering angle in such rear axle steering systems, inductive linear positioning sensors (LPS) are used, among other things. These are based on the inductive principle, i.e. external transmitter coils induce a measurement signal into internal receiving coils, with part of the emitted field being shielded by the eddy currents in a movable, electrically conductive target, for example an aluminum plate, so that the resulting induced voltage provides information about the position of the target. Such an inductive linear displacement sensor usually consists of a transmitter coil and two reception coils, with the reception coils each having a sine shape or cosine shape. The measurement signals are sine or cosine shaped. The relationship between the target position and the measurement signal is linear according to an arc tangent function.

From the US 2002/0043972 A1 An inductively operating position sensor for detecting a linearly moving metallic target is already known. The position sensor comprises a circuit board with a plurality of receiver coils arranged on a circuit board and an exciter or transmitter coil arranged circumferentially around the receiver coils, the transmitter coil being supplied with an alternating voltage signal via a control device, so that in the event of a change in position of the metallic target, at a short distance parallel to the coil arrangement arranged on the circuit board, a differential voltage dependent on the position of the target is generated in the respective receiver coils. These differential voltage signals are demodulated in the control device, evaluated and a corresponding position signal of the target is determined.

The US 2016/0349084 A1 describes an evaluation method for evaluating voltage signals generated by an inductive position sensor on the receiver coils for determining a path signal of a metallic target moved via the position sensor.

Such linear and rotary inductive position sensors fundamentally have different error curves. Fourth-order errors are typical, i.e. with four times the frequency of the measurement period. This quadruple error results from irregular flow through the sensor coils.

It is therefore the object of the invention to provide an inductive position sensor that avoids or at least reduces the disadvantages known from the prior art and in particular achieves high measurement accuracy. It is also the object of the invention to provide an optimized method for compensating for measurement errors in an inductive position sensor. It is also the object of the invention to realize an improved computer program product for compensating for measurement errors in an inductive position sensor. Another object of the invention is to provide an improved electrical machine. Finally, it is also an object of the invention to realize an improved X-by-wire system for a motor vehicle.

This object is achieved by an inductive position sensor, comprising a transmitter coil that can be energized by a control unit and a sensor target that can be moved relative to the sensor carrier, a first, essentially cosine-shaped receiver coil arranged on and/or in the sensor carrier, on which a first voltage U _RX1 can be tapped , a second, essentially sinusoidal receiver coil arranged on and/or in the sensor carrier, on which a second voltage U _RX2 can be tapped, the first, essentially cosinusoidal receiver coil having a profile which corresponds to a cosinusoidal fundamental wave with at least one harmonic and or
the second, essentially sinusoidal receiving coil has a course that corresponds to a sinusoidal fundamental oscillation with at least one harmonic.

This has the advantage that typical “multiple errors”, for example a fourth-order angular error, can be largely eliminated in the coil design. Such an error can be compensated for in the coil design, in particular by geometrically modulating the otherwise pure sinusoidal shape of the receiving coils with higher harmonics. The receiving coils deviate from their pure sine or cosine shape. This deviation is usually comparatively small and can hardly or only very difficultly be seen on the coils with the naked eye.

In the following description of an exemplary embodiment based on the figures, a fully rotary, inductive position sensor with triple modulation is specifically described. For non-symmetrical sensors such as segment or linear position sensors, the error can also be influenced and the measurement accuracy of the inductive position sensor can be improved using other harmonics. In principle, it is possible to vary any harmonic separately for each receiver coil, which is very useful due to the inevitable non-symmetry in segment and analog linear position sensors.

The receiving coils are preferably designed as a circuit printed on a substrate. Most preferably, the transmitter coil is also designed as a circuit printed on a substrate. These are also known as PCBs - printed circuit boards.

The position sensor can preferably be designed as a linear path sensor - in particular as a linear path sensor for a rear axle steering of a motor vehicle, for a steer-by-wire front wheel steering of a motor vehicle, for a clutch actuator of a motor vehicle or for an electronic clutch pedal of a motor vehicle.

Alternatively, the position sensor can also be designed as a rotation sensor or angular segment sensor and detect an angular position.

It is also preferred that the essentially cosine-shaped first receiver coil and the essentially sinusoidal second receiver coil have a substantially identical amplitude.

The transmitter coil as well as the receiver coils can be connected to a control unit. A control unit in particular has a wired or wireless signal input for receiving electrical signals, in particular, such as sensor signals. Furthermore, a control unit also preferably has a wired or wireless signal output for transmitting, in particular, electrical signals, for example to electrical actuators or electrical consumers of the motor vehicle.

Control operations and/or regulation operations can be carried out within the control unit. It is particularly preferred that the control unit comprises hardware that is designed to execute software. The control unit preferably comprises at least one electronic processor for executing program sequences defined in software.

The control unit can also have one or more electronic memories in which the data contained in the signals transmitted to the control unit can be stored and read out again. Furthermore, the control unit can have one or more electronic memories in which data can be stored in a changeable and/or unchangeable manner.

A control unit can comprise a plurality of control devices, which are in particular arranged spatially separated from one another. Control units are also called Electronic Control Unit (ECU) or Electronic control modules (ECM) refer to and preferably have electronic microcontrollers for carrying out arithmetic operations for processing data, particularly preferably using software. The control devices can preferably be networked with one another, so that wired and/or wireless data exchange between control devices is possible. In particular, it is also possible to network the control devices with one another via bus systems, such as CAN bus or LIN bus.

$$\begin{array}{l}{y}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)+{\text{b}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{x}_{\text{cos}}=[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(np\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{cos}}=[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(np\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

• mit φ = [0;2π] für in einem Vollkreis ausgebildete Empfangsspulen
• mit φ = [0;2π q/p] für bogenförmig ausgebildete Empfangsspulen mit q= Anzahl der tatsächlich ausgebildeten elektrischen Perioden und p = Anzahl der Polpaare
• mit a₁ = Grundschwingung der sinusförmigen Empfangsspule
• mit b₁ = Grundschwingung der cosinusförmigen Empfangsspule
• mit a_n = Sinusförmige Harmonische n-ter Ordnung der Empfangsspule
• mit b_n = Cosinusförmige Harmonische n-ter Ordnung der Empfangsspule

According to an advantageous embodiment of the invention, it can be provided that the inductive position sensor is designed as a rotation sensor. According to a further preferred further development of the invention, it can also be provided in this context that the first, essentially cosine-shaped receiving coil and the second, essentially sinusoidal receiving coil have a circular ring-like course around a common circular path with a radius r _m , whereby the Course of the first, essentially cosine-shaped receiving coil and/or the second, essentially sinusoidal receiving coil of a function defined as $$\begin{array}{l}{x}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{x}_{\text{cos}}=[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(np\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{cos}}=[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(np\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

• with φ = [0;2π] for receiving coils designed in a full circle
• with φ = [0;2π q/p] for arcuate receiving coils with q = number of actually formed electrical periods and p = number of pole pairs
• with a ₁ = fundamental oscillation of the sinusoidal receiving coil
• with b ₁ = fundamental oscillation of the cosine-shaped receiving coil
• with a _n = nth order sinusoidal harmonic of the receiving coil
• with b _n = cosine-shaped harmonic of the nth order of the receiving coil

It has also proven to be advantageous that the harmonic used in the receiving coils corresponds to an odd harmonic greater than one. An odd harmonic with an atomic number from the set: 3,5,7 is most preferably selected.

$$y_{\text{sin}}=\left[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)\right]\ast \text{sin}\left(\phi \right)$$

$$x_{\text{cos}}=\left[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)\right]\ast \text{cos}\left(\phi \right)$$

$$y_{\text{cos}}=\left[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)\right]\ast \text{sin}\left(\phi \right)$$

• mit φ = [0;2π] für in einem Vollkreis ausgebildete Empfangsspulen
• mit φ = [0;2π q/p] für bogenförmig ausgebildete Empfangsspulen mit q= Anzahl der tatsächlich ausgebildeten elektrischen Perioden und p = Anzahl der Polpaare
• mit a₁ = Grundschwingung der sinusförmigen Empfangsspule
• mit b₁ = Grundschwingung der cosinusförmigen Empfangsspule
• mit a_n = Sinusförmige Harmonische n-ter Ordnung der Empfangsspule
• mit b_n = Cosinusförmige Harmonische n-ter Ordnung der Empfangsspule

Furthermore, according to a likewise advantageous embodiment of the invention, it can be provided that the first, essentially cosine-shaped receiving coil and the second, essentially sinusoidal receiving coil have a circular ring-like course around a common circular path with a radius r _m , the course the first, essentially cosine-shaped receiving coil and / or the second, essentially sinusoidal receiving coil of a function defined as $$x_{\text{sin}}=\left[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)\right]\ast \text{cos}\left(\phi \right)$$

$$y_{\text{sin}}=\left[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)\right]\ast \text{sin}\left(\phi \right)$$

$$x_{\text{cos}}=\left[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)\right]\ast \text{cos}\left(\phi \right)$$

$$y_{\text{cos}}=\left[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)\right]\ast \text{sin}\left(\phi \right)$$

• with φ = [0;2π] for receiving coils designed in a full circle
• with φ = [0;2π q/p] for arcuate receiving coils with q = number of actually formed electrical periods and p = number of pole pairs
• with a ₁ = fundamental oscillation of the sinusoidal receiving coil
• with b ₁ = fundamental oscillation of the cosine-shaped receiving coil
• with a _n = nth order sinusoidal harmonic of the receiving coil
• with b _n = cosine-shaped harmonic of the nth order of the receiving coil

The advantageous effect of this configuration is that the highest proportions of the error in the signal are compensated for, thereby enabling the greatest possible error compensation. In this way, in particular, a reduction in the simulation effort when designing the receiver coils can be achieved.

• • Bereitstellung eines Models eines Sensortargets;
• • Bereitstellen eines Models wenigstens einer Sendespule;
• • Bereitstellung eines Models einer ersten, im Wesentlichen cosinusförmig ausgebildeten Empfangsspule, die einen Verlauf aufweist, der einer cosinusförmigen Grundschwingung mit wenigstens einer Oberschwingung entspricht und/oder einer zweiten, im Wesentlichen sinusförmig ausgebildeten Empfangsspule, die einen Verlauf aufweist, der einer sinusförmigen Grundschwingung mit wenigstens einer Oberschwingung entspricht.
• • Manipulation der ersten im Wesentlichen cosinusförmig ausgebildeten Empfangsspule, die einen Verlauf aufweist, der einer cosinusförmigen Grundschwingung mit wenigstens einer Oberschwingung entspricht und/oder der zweiten, im Wesentlichen sinusförmig ausgebildeten Empfangsspule, die einen Verlauf aufweist, der einer sinusförmigen Grundschwingung mit wenigstens einer Oberschwingung entspricht, in der Art, dass eine Kompensation von Messfehlern bei dem induktiven Positionssensor bewirkt ist.

The object of the invention is further achieved by a method for compensating for measurement errors in an inductive position sensor, wherein a first, essentially cosine-shaped receiver coil is formed on and/or in the sensor carrier and on which a first voltage U _RX1 can be tapped, as well as a A second, essentially sinusoidal receiver coil, on which a second voltage U _RX2 can be tapped, is arranged on and/or in the sensor carrier, comprising the following steps:

• • Providing a model of a sensor target;
• • Providing a model of at least one transmission coil;
• • Providing a model of a first, essentially cosine-shaped receiving coil, which has a curve that corresponds to a cosine-shaped fundamental oscillation with at least one harmonic and/or a second, essentially sinusoidal-shaped receiving coil, which has a curve that corresponds to a sinusoidal fundamental oscillation with at least corresponds to a harmonic.
• • Manipulation of the first essentially cosinusoidal receiving coil, which has a curve that corresponds to a cosinusoidal fundamental oscillation with at least one harmonic and/or the second, essentially sinusoidal receiving coil, which has a curve that corresponds to a sinusoidal fundamental oscillation with at least one harmonic , in such a way that measurement errors are compensated for in the inductive position sensor.

In this way, the effect can be achieved in particular that significantly improved measurement accuracy can be achieved.

$$\begin{array}{l}{y}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)+{\text{b}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{x}_{\text{cos}}=[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(np\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{cos}}=[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(np\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

• mit φ = [0;2π] für in einem vollkreis ausgebildete Empfangsspulen
• mit φ = [0;2π q/p] für bogenförmig ausgebildete Empfangsspulen mit q= Anzahl der tatsächlich ausgebildeten elektrischen Perioden und p = Anzahl der Polpaare
• mit a₁ = Grundschwingung der sinusförmigen Empfangsspule
• mit b₁ = Grundschwingung der cosinusförmigen Empfangsspule
• mit a_n = Sinusförmige Harmonische n-ter Ordnung der Empfangsspule
• mit b_n = Cosinusförmige Harmonische n-ter Ordnung der Empfangsspule

Furthermore, the invention can also be further developed in this context in such a way that the first, essentially cosine-shaped receiving coil and the second, essentially sinusoidal receiving coil have a circular ring-like course around a common circular path with a radius r _m , the course of the first , essentially cosine-shaped receiving coil and / or the second, essentially sinusoidal receiving coil of a function defined as $$\begin{array}{l}{x}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{x}_{\text{cos}}=[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(np\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{cos}}=[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(np\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

• with φ = [0;2π] for receiving coils designed in a full circle
• with φ = [0;2π q/p] for arcuate receiving coils with q = number of actually formed electrical periods and p = number of pole pairs
• with a ₁ = fundamental oscillation of the sinusoidal receiving coil
• with b ₁ = fundamental oscillation of the cosine-shaped receiving coil
• with a _n = nth order sinusoidal harmonic of the receiving coil
• with b _n = cosine-shaped harmonic of the nth order of the receiving coil

In a likewise preferred embodiment variant of the invention, it can also be provided that the parameter a ₃ is manipulated to compensate for measurement errors in the inductive position sensor, which leads to a particularly large and therefore effective error reduction.

The object of the invention is further achieved by a computer program product which is stored on a machine-readable carrier, or computer data signal, embodied by an electromagnetic wave, with program code which is suitable for carrying out the method according to claims 5-7.

The object of the invention is also achieved by means of an electric machine, in particular for a drive train of a motor vehicle, comprising an inductive position sensor according to one of the preceding claims 1-4.

Finally, the object of the invention can also be achieved by an X-by-wire system for a motor vehicle, comprising an inductive position sensor according to one of the preceding claims 1-4.

The invention will be explained in more detail below using figures without restricting the general idea of the invention.

• 1 einen induktiven Positionssensor als Linearsensor in einer schematischen perspektivischen Darstellung,
• 2 einen induktiven Positionssensor als Rotationssensor in einer schematischen Darstellung,
• 3 Verlauf von sinus- und cosinus-förmigen Empfangsspulen eines induktiven Rotationssensors in einer Koordinatensystemdarstellung.

It shows:

• 1 an inductive position sensor as a linear sensor in a schematic perspective representation,
• 2 an inductive position sensor as a rotation sensor in a schematic representation,
• 3 Course of sine- and cosine-shaped receiving coils of an inductive rotation sensor in a coordinate system representation.

The 1-2 each show an inductive position sensor 1, comprising a transmitter coil 6 that can be energized by a control unit 3 and a sensor target 7 that can be moved relative to the sensor carrier 2. The position sensors 1 have a first, essentially cosine-shaped receiver coil 4 arranged on and/or in the sensor carrier 2 from which a first voltage U _RX1 can be tapped, as well as a second, essentially sinusoidal receiver coil 5 arranged on and/or in the sensor carrier 2, from which a second voltage U _RX2 can be tapped.

Here, the first, essentially cosine-shaped receiving coil 4 has a course that corresponds to a cosine-shaped oscillation of a higher order greater than one or, in other words, which corresponds to a cosinus-shaped fundamental oscillation with at least one harmonic. The second, essentially sinusoidal receiving coil 5 also has a curve that corresponds to a sinusoidal oscillation of a higher order greater than one or a sinusoidal fundamental oscillation with at least one harmonic.

The compensation of measurement errors in such an inductive position sensor 1 is based on the in 2 rotation sensor shown explained in more detail.

$$\begin{array}{l}{y}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)+{\text{b}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{x}_{\text{cos}}=[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(np\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{cos}}=[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(np\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

• mit φ = [0;2π] für in einem vollkreis ausgebildete Empfangsspulen
• mit φ = [0;2π q/p] für bogenförmig ausgebildete Empfangsspulen mit q= Anzahl der tatsächlich ausgebildeten elektrischen Perioden und p = Anzahl der Polpaare
• mit a₁ = Grundschwingung der sinusförmigen Empfangsspule
• mit b₁ = Grundschwingung der cosinusförmigen Empfangsspule
• mit a_n = Sinusförmige Harmonische n-ter Ordnung der Empfangsspule
• mit b_n = Cosinusförmige Harmonische n-ter Ordnung der Empfangsspule

In the mathematical description of sine or cosine-shaped receiving coils 4.5 in rotary position sensors 1, as shown in the 2 are known, the geometry of the receiving coils 4.5 basically follows the mathematical relationship: $$\begin{array}{l}{x}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{x}_{\text{cos}}=[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(np\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{cos}}=[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(np\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

• with φ = [0;2π] for receiving coils designed in a full circle
• with φ = [0;2π q/p] for arcuate receiving coils with q = number of actually formed electrical periods and p = number of pole pairs
• with a ₁ = fundamental oscillation of the sinusoidal receiving coil
• with b ₁ = fundamental oscillation of the cosine-shaped receiving coil
• with a _n = nth order sinusoidal harmonic of the receiving coil
• with b _n = cosine-shaped harmonic of the nth order of the receiving coil

In principle, a p-periodic sine is curved around a circular path of radius r _m . This is in the 3 sketched. A receiving coil 4.5 is completed by copying and rotating by electrical π. By further copying and twisting by electrical π/2, the second receiving coil 4.5 is created for a fully rotary sensor. In the example of the 3 is r _m = 2 and p = 4. The amplitude a is 1.

The transmitter coil 6 is in the example in the 2 Rotary position sensor 1 shown is mounted radially outside of the receiving coils 4.5. In principle, it would of course also be possible to arrange the transmitting coil 6 radially within the receiving coils 4.5. The flow through the receiving coils 4.5 is not homogeneous in the radially outside or inside direction. This creates a third-order error in the corresponding useful signals, which propagates into a fourth-order error after the angle calculation in the arc tangent.

In order to reduce or completely avoid this error, the above-mentioned mathematical description of the sine or cosine-shaped path of the receiving coils 4.5 is modified, so that the above-mentioned errors can be compensated for by an adapted path of the receiving coils 4.5 can.

$$\begin{array}{l}{y}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)+{\text{b}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{x}_{\text{cos}}=[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(np\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{cos}}=[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(np\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

• mit φ = [0;2π] für in einem vollkreis ausgebildete Empfangsspulen
• mit φ = [0;2π q/p] für bogenförmig ausgebildete Empfangsspulen mit q= Anzahl der tatsächlich ausgebildeten elektrischen Perioden und p = Anzahl der Polpaare
• mit a₁ = Grundschwingung der sinusförmigen Empfangsspule
• mit b₁ = Grundschwingung der cosinusförmigen Empfangsspule
• mit a_n = Sinusförmige Harmonische n-ter Ordnung der Empfangsspule
• mit b_n = Cosinusförmige Harmonische n-ter Ordnung der Empfangsspule

This essentially happens because the first, essentially cosine-shaped receiving coil 4 and the second, essentially sinusoidal receiving coil 5 have a circular ring-like course around a common circular path with a radius r _m , the course of the first, essentially cosinus-shaped Receiving coil 4 and/or the second, essentially sinusoidal receiving coil 5 follows a function that is defined as $$\begin{array}{l}{x}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{x}_{\text{cos}}=[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(np\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{cos}}=[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(np\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

• with φ = [0;2π] for receiving coils designed in a full circle
• with φ = [0;2π q/p] for arcuate receiving coils with q = number of actually formed electrical periods and p = number of pole pairs
• with a ₁ = fundamental oscillation of the sinusoidal receiving coil
• with b ₁ = fundamental oscillation of the cosine-shaped receiving coil
• with a _n = nth order sinusoidal harmonic of the receiving coil
• with b _n = cosine-shaped harmonic of the nth order of the receiving coil

Harmonics are therefore already introduced into the geometry or the course of the receiving coils 4.5. The goal is now to use optimization, particularly computer-aided, to determine the parameters a ₁ ... a _n for which the expected measurement error reaches a minimum.

Previous studies have shown that for inductive rotation sensors such as those in the 2 are shown, a variation of a ₃ can already be sufficient to achieve sufficiently good error compensation. Additional harmonics may be necessary for linear or angular segment sensors.

$$y_{\text{sin}}=\left[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)\right]\ast \text{sin}\left(\phi \right)$$

$$x_{\text{cos}}=\left[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)\right]\ast \text{cos}\left(\phi \right)$$

$$y_{\text{cos}}=\left[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)\right]\ast \text{sin}\left(\phi \right)$$

• mit φ = [0;2π] für in einem vollkreis ausgebildete Empfangsspulen
• mit φ = [0;2π q/p] für bogenförmig ausgebildete Empfangsspulen mit q= Anzahl der tatsächlich ausgebildeten elektrischen Perioden und p = Anzahl der Polpaare
• mit a₁ = Grundschwingung der sinusförmigen Empfangsspule
• mit b₁ = Grundschwingung der cosinusförmigen Empfangsspule
• mit a_n = Sinusförmige Harmonische n-ter Ordnung der Empfangsspule
• mit b_n = Cosinusförmige Harmonische n-ter Ordnung der Empfangsspule

Therefore, the course of the receiving coils 4, 5 can also follow a simplified mathematical description, in which the first, essentially cosine-shaped receiving coil 4 and the second, essentially sinusoidal receiving coil 5 have a circular ring-like course around a common circular path with a radius r _m have, wherein the course of the first, essentially cosine-shaped receiving coil 4 and / or the second, essentially sinusoidal receiving coil 5 is defined as a function $$x_{\text{sin}}=\left[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)\right]\ast \text{cos}\left(\phi \right)$$

$$y_{\text{sin}}=\left[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)\right]\ast \text{sin}\left(\phi \right)$$

$$x_{\text{cos}}=\left[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)\right]\ast \text{cos}\left(\phi \right)$$

$$y_{\text{cos}}=\left[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956A1\_0037.png,DE102022116956A1\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)\right]\ast \text{sin}\left(\phi \right)$$

• with φ = [0;2π] for receiving coils designed in a full circle
• with φ = [0;2π q/p] for arcuate receiving coils with q = number of actually formed electrical periods and p = number of pole pairs
• with a ₁ = fundamental oscillation of the sinusoidal receiving coil
• with b ₁ = fundamental oscillation of the cosine-shaped receiving coil
• with a _n = nth order sinusoidal harmonic of the receiving coil
• with b _n = cosine-shaped harmonic of the nth order of the receiving coil

The invention is not limited to the embodiments shown in the figures. The foregoing description is therefore not to be viewed as limiting but rather as illustrative. The following patent claims are to be understood as meaning that a stated feature is present in at least one embodiment of the invention. This does not exclude the presence of other features. If the patent claims and the above description define 'first' and 'second' features, this designation serves to distinguish two similar features without establishing a ranking.

Reference symbol list

1

Position sensor

2

Sensor carrier

3

Control unit

4

Receiver coil

5

Receiver coil

6

Transmitter coil

7

Sensor target

QUOTES INCLUDED IN THE DESCRIPTION

This list of documents listed by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• DE 102009001353 A1 [0007]
• DE 102018130228 A1 [0013]
• US 20020043972 A1 [0015]
• US 20160349084 A1 [0016]

Claims (10)

Inductive position sensor (1), comprising a transmitter coil (6) which can be energized by a control unit (3) and a sensor target (7) which can be displaced relative to the sensor carrier (2), a first, essentially cosine-shaped one which is arranged on and/or in the sensor carrier (2). designed receiver coil (4), from which a first voltage U _RX1 can be tapped, a second, essentially sinusoidal receiver coil (5) arranged on and/or in the sensor carrier (2), from which a second voltage U _RX2 can be tapped, thereby characterized in that the first, essentially cosinusoidal receiving coil (4) has a profile which corresponds to a cosinusoidal fundamental oscillation with at least one harmonic and/or the second, essentially sinusoidal receiving coil (5) has a profile which corresponds to a sinusoidal fundamental oscillation corresponds to at least one harmonic. Position sensor (1). Claim 1 , characterized in that the inductive position sensor (1) is designed as a rotation sensor. Position sensor (1). Claim 2 , characterized in that the first, essentially cosine-shaped receiving coil (4) and the second, essentially sinusoidal receiving coil (5) have a circular ring-like course around a common circular path with a radius r _m , the course of the first, essentially cosine-shaped receiving coil (4) and / or the second, essentially sinusoidal receiving coil (5) of a function defined as $$\begin{array}{l}{x}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)+{\text{b}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)+{\text{b}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{x}_{\text{cos}}=[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\cdot \phi \right)+a_2\\ \text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\cdots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{cos}}=[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\cdot \phi \right)+a_2\\ \text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\cdots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

with <p = [0;2π] for receiving coils designed in a full circle with φ = [0;2π q/p] for arcuate receiving coils with q = number of actually formed electrical periods and p = number of pole pairs with a ₁ = fundamental oscillation the sinusoidal receiving coil with b ₁ = fundamental oscillation of the cosinusoidal receiving coil with a _n = nth order sinusoidal harmonic of the receiving coil with b _n = nth order cosinusoidal harmonic of the receiving coil Position sensor (1). Claim 2 or 3 , characterized in that the first, essentially cosine-shaped receiving coil (4) and the second, essentially sinusoidal receiving coil (5) have a circular ring-like course around a common circular path with a radius r _m , the course of the first, essentially cosine-shaped receiving coil (4) and/or the second, essentially sinusoidal receiving coil (5) are/will be defined by the following functions: $$x_{\text{sin}}=\left[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)\right]\ast \text{cos}\left(\phi \right)$$

$$y_{\text{sin}}=\left[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)\right]\ast \text{sin}\left(\phi \right)$$

$$x_{\text{cos}}=\left[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)\right]\ast \text{cos}\left(\phi \right)$$

$$y_{\text{cos}}=\left[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{sin}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)\right]\ast \text{sin}\left(\phi \right)$$

with φ = [0;2π] for receiving coils designed in a full circle with φ = [0;2π q/p] for arcuate receiving coils with q = number of actually formed electrical periods and p = number of pole pairs with a ₁ = fundamental oscillation of sinusoidal receiving coil with b ₁ = fundamental oscillation of the cosinusoidal receiving coil with a _n = nth order sinusoidal harmonic of the receiving coil with b _n = nth order cosinusoidal harmonic of the receiving coil Method for compensating for measurement errors in an inductive position sensor (1), wherein a first, essentially cosine-shaped receiver coil (4) is formed on and/or in the sensor carrier (2), at which a first voltage U _RX1 can be tapped, and a A second, essentially sinusoidal receiver coil (5), on which a second voltage U _RX2 can be tapped, is arranged on and/or in the sensor carrier (2), comprising the following steps: • Providing a model of a sensor target (7); • Providing a model of at least one transmission coil (6); • Providing a model of a first, essentially cosinusoidal receiving coil (4), which has a curve that corresponds to a cosinusoidal fundamental oscillation with at least one harmonic and/or a second, essentially sinusoidal receiving coil (5), which has a curve, which corresponds to a sinusoidal fundamental wave with at least one harmonic. • Manipulation of the first essentially cosinusoidal receiving coil (4), which has a curve that corresponds to a cosinusoidal fundamental oscillation with at least one harmonic and/or the second, essentially sinusoidal receiving coil (5), which has a curve that corresponds to a sinusoidal Fundamental oscillation corresponds to at least one harmonic, in such a way that compensation for measurement errors in the inductive position sensor (1) is effected. Method for compensating measurement errors in an inductive position sensor (1). Claim 5 , characterized in that the first, essentially cosine-shaped receiving coil (4) and the second, essentially sinusoidal receiving coil (5) have a circular ring-like course around a common circular path with a radius r _m , the course of the first, essentially cosine-shaped receiving coil (4) and/or the second, essentially sinusoidal receiving coil (5) are/will be defined by the following functions: $$\begin{array}{l}{x}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_{\text{n}}\text{sin}\left(\text{n}p\cdot \phi \right)+{\text{b}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+\cdots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_{\text{n}}\text{sin}\left(\text{n}p\cdot \phi \right)+{\text{b}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+\cdots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{x}_{\text{cos}}=[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\cdot \phi \right)+a_2\\ \text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\cdots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{cos}}=[r_m+{\text{b}}_1\text{cos}\left(p\ast \phi \right)+{\text{b}}_2\text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\cdot \phi \right)+a_2\\ \text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\cdots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

with φ = [0;2π] for receiving coils designed in a full circle with φ = [0;2π q/p] for arcuate receiving coils with q = number of actually formed electrical periods and p = number of pole pairs with a ₁ = fundamental oscillation of sinusoidal receiving coil with b ₁ = fundamental oscillation of the cosinusoidal receiving coil with a _n = sinusoidal harmonics of the nth order of the receiving coil with b _n = cosinusoidal harmonics of the receiving coil Method for compensating for measurement errors in an inductive position sensor (1), characterized in that the parameter a ₃ is manipulated to compensate for measurement errors in the inductive position sensor (1). Computer program product stored on a machine-readable medium, or computer data signal embodied by an electromagnetic wave, with program code suitable for carrying out the method according to Claim 5 - 7 . Electric machine, in particular for a drive train of a motor vehicle, comprising an inductive position sensor (1) according to one of the above Claims 1 - 4 . X-by-wire system for a motor vehicle, comprising an inductive position sensor (1) according to one of the above Claims 1 - 4 .

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