DE102022116956B4 - 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

Inductive position sensor (1), comprising a transmitter coil (6) that can be powered by a control unit (3) and a sensor target (7) that can be displaced relative to the sensor carrier (2), a first, essentially cosinusoidal receiving coil (4) arranged on and/or in the sensor carrier (2), from which a first voltage URX1 can be tapped, a second, essentially sinusoidal receiving 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 profile that corresponds to a cosinusoidal fundamental oscillation with at least one harmonic and/or the second, essentially sinusoidal receiving coil (5) has a profile that corresponds to a sinusoidal fundamental oscillation with at least one harmonic,wherein the inductive position sensor (1) is designed as a rotation sensor and wherein the first, essentially cosinusoidal receiving coil (4) and the second, substantially sinusoidal receiving coil (5) has a circular ring-like course around a common circular path with a radius rm, wherein the course of the first, substantially cosinusoidal receiving coil (4) and/or the second, substantially sinusoidal receiving coil (5) follows a function which is defined alsxsin=[rm+a1 sin (p∗φ)+a2 sin (2p∗φ)+a3 sin (3p∗φ)+⋯+an sin (np∗φ)+b2cos(2p∗φ)+b3cos(3p∗φ)+…+bncos(np∗φ)]∗cos(φ)ysin=[rm+a1 sin (p∗φ)+a2 sin (2p∗φ)+a3 sin (3p∗φ)+⋯+an sin (np∗φ)+b2cos(2p∗φ)+b3cos(3p∗φ)+…+bncos(np∗φ)]∗sin (φ)xcos=[rm+b1cos(p∗φ)+b2cos(2p∗φ)+b3cos(3p∗φ)+⋯+bn sin (np∗φ)+a2sin (2p∗φ)+a3sin(3p∗φ)+…+an sin (np∗φ)]∗cos(φ)ycos=[rm+b1cos(p∗φ)+b2cos(2p∗φ)+b3cos(3p∗φ)+⋯+bn sin (np∗φ)+a2sin (2p∗φ)+a3sin(3p∗φ)+…+an sin (np∗φ)]∗sin(φ)with φ = [0;2π] for receiving coils (4, 5) formed in a full circle, with φ = [0;2π q/p] for arc-shaped receiving coils (4, 5), with q= number of actually formed electrical periods and p = number of pole pairs, with a1= fundamental oscillation of the sinusoidal receiving coil (5), with b1= fundamental oscillation of the cosinusoidal receiving coil (4), with an= sinusoidal harmonic of the nth order of the receiving coil (4, 5), with bn= cosinusoidal harmonic of the nth order of the receiving coil (4, 5).

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 moved relative to the sensor carrier, a first, essentially cosinusoidal receiver coil arranged on and/or in the sensor carrier, from which a first voltage U _RX1 can be tapped, a second, essentially sinusoidal receiver coil arranged on and/or in the sensor carrier, from which a second voltage U _RX2 can be tapped. The invention further relates to a method for compensating 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 power motor vehicles in order to create alternatives to combustion engines that require fossil fuels. Considerable efforts have already been made to improve the suitability of electric drives for everyday use and to offer users the same driving comfort they are used to.

In addition to purely electrically operated drive trains, hybrid drive trains are also known. Such drive trains in a hybrid vehicle usually comprise a combination of an internal combustion engine and an electric motor and enable - for example in urban areas - purely electric operation while at the same time providing sufficient range and availability, especially for cross-country journeys. In addition, in certain operating situations it is possible to drive the vehicle simultaneously using the internal combustion engine and the electric motor.

Sensors are used in many of these drive trains to record angle and rotation information, for example from an electrical 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.

Permanently excited synchronous machines are used in many of the electromobility applications mentioned above. Such a permanent-excited synchronous machine comprises a stator to be energized and a permanently excited rotor. The rotor usually comprises a shaft, balancing plates, rotor laminations and magnets. The magnets are generally fixed in the rotor laminations.

To control such electronically commutated electrical machines, electrical control variables are applied to the stator windings of the machine depending on the angular position of the rotor in order to drive them. 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 variable that depends on the position of the rotor, e.g. a voltage, signal pulses or a digitized indication of the absolute rotor position. Such rotor position sensors are basically known from the state of the art, in which a signal generator (magnetic target) mounted on the rotor in a rotationally fixed manner is read out by means of a magnetic field sensor mounted on the stator in a rotationally fixed manner.

For example, the EN 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 to the rotor hub in a rotationally fixed manner serves as the encoder track of the rotor position sensor.

In addition to rotor position sensors that work with a magnetic target, inductive rotor position sensors are also known, which have the advantage of not requiring 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 application of such inductive sensors in electric drive machines, they are also frequently used in mechatronic, steerable axles to determine the steering position, the steering angle, 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 processes. One way to overcome this challenge is to implement new vehicle and transport concepts that aim to replace conventional cars. Alternative vehicle bodies 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 operated actuators are usually used to actuate the rear-axle steering, whereby for obvious safety-related reasons it is important to detect the exact position of the actuator or the rear-axle steering safely and as precisely as possible.

From the EN 10 2018 130 228 B3 An actuator for a rear axle steering of a motor vehicle is known, comprising a push rod that can be displaced longitudinally within a housing and has an anti-twist device. A sensor unit is integrated into the housing of the rear axle steering actuator.

Inductive linear position sensors (LPS - linear positioning sensor) are used to measure the steering angle in such rear axle steering systems. These are based on the inductive principle, i.e. external transmitter coils induce a measurement signal in internal receiver coils, whereby part of the emitted field is 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 position sensor usually consists of a transmitter coil and two receiver coils, whereby the receiver coils each have a sinusoidal or cosinusoidal shape. The measurement signals are sinusoidal or cosinusoidal. The relationship between the target position and the measurement signal is linear according to an arctangent function.

From the US 2002 / 0 043 972 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 excitation or transmitter coil arranged circumferentially around the receiver coils, wherein the transmitter coil is supplied with an alternating voltage signal via a control device, so that in the event of a change in position of the metallic target, a differential voltage dependent on the position of the target is generated in the respective receiver coils at a short distance parallel to the coil arrangement arranged on the circuit board. These differential voltage signals are demodulated and evaluated in the control device and a corresponding position signal of the target is determined.

The US 2016 / 0 349 084 A1 describes an evaluation method for evaluating voltage signals generated by an inductive position sensor at the receiver coils for determining a displacement signal of a metallic target moved over the position sensor.

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

The EN 11 2019 004 235 T5 describes an inductive sensor arrangement with a transmitter coil and a two-part receiver coil. A target is formed from a first planar surface and a second planar surface at a first end of a shaft. When the target is moved about the shaft axis, the first and second planar surfaces modify an inductive coupling between the transmitter coil and the two-part receiver coil.

The EN 10 2020 133 028 A1 describes an electric powertrain with a sensor control interface, an inverter control electrically connected to the battery pack, and an electrical machine connected to the inverter control and having a rotor with an angular position.

The EN 10 2020 131 042 A1 describes a position sensor with a sensor carrier on which a transmitter coil and a first and a second receiver coil are arranged. An electrically conductive sensor target is arranged so as to be movable relative to the sensor carrier over a predetermined measuring distance at a defined, constant distance from the sensor carrier.

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 measurement errors in an inductive position sensor. It is also the object of the invention to realize an improved computer program product for compensating measurement errors in an inductive position sensor. A further 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 displaced relative to the sensor carrier, a first, essentially cosinusoidal receiver coil arranged on and/or in the sensor carrier, from which a first voltage U _RX1 can be tapped, a second, essentially sinusoidal receiver coil arranged on and/or in the sensor carrier, from which a second voltage U _RX2 can be tapped, wherein the first, essentially cosinusoidal receiver coil has a profile that corresponds to a cosinusoidal fundamental oscillation with at least one harmonic and/or
the second, substantially sinusoidal receiving coil has a course which corresponds to a sinusoidal fundamental oscillation with at least one harmonic.

This has the advantage that typical "multiple errors", such as a fourth-order angle 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 thus deviate from their pure sinusoidal or cosinusoidal 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 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 using other harmonics and the measurement accuracy of the inductive position sensor can be improved. It is basically 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.

Preferably, the receiving coils are designed as a circuit printed on a substrate. Most preferably, the transmitting coil is also designed as a circuit printed on a substrate. These are also referred to as PCBs - printed circuit boards.

Not included in the invention is an embodiment of the position sensor as a linear travel sensor - in particular as a linear travel 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.

According to the invention, the position sensor is designed as a rotation sensor or angle segment sensor and detects an angular position.

It is also preferred that the substantially cosinusoidal first receiver coil and the substantially sinusoidal second receiver coil have a substantially identical amplitude.

The transmitting coil as well as the receiving coils can be connected to a control unit. A control unit has in particular a wired or wireless signal input for receiving of in particular electrical signals, 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. The control unit can also 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 arranged spatially separated from one another in particular. Control devices are also referred to as Electronic Control Unit (ECU) or Electronic Control Module (ECM) and preferably have electronic microcontrollers for carrying out computing operations for processing data, particularly preferably using software. The control devices can preferably be networked with one another, so that a 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.

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

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

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

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 EmpfangsspuleAccording to the invention, the inductive position sensor is designed as a rotation sensor. It is provided that the first, essentially cosinusoidal 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 , wherein the course of the first, essentially cosinusoidal receiving coil and/or the second, essentially sinusoidal receiving coil follows a function which is defined as $$\begin{array}{l}{x}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\cdots +a_n\text{sin}\left(np\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_2\\ \text{cos}\left(2p\ast \phi \right)+b_{3}cOs\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\cdots +a_n\text{sin}\left(np\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_2\\ \text{cos}\left(2p\ast \phi \right)+b_{3}cOs\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{x}_{\text{cos}}=[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\cdots +a_{\text{n}}\text{sin}\left(np\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{cos}}=[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\cdots +a_{\text{n}}\text{sin}\left(np\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

with φ = [0;2π] for receiving coils formed in a full circle
with φ = [0;2π q/p] for arc-shaped 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 cosinusoidal receiving coil
with a _n = sinusoidal harmonic of nth order of the receiving coil
with b _n = cosinusoidal harmonic of nth order of the receiving coil

It has also proven advantageous that the harmonic used in the receiving coils corresponds to an odd harmonic greater than one. Most preferably, an odd harmonic with an ordinal number from the set: 3,5,7 is 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 EmpfangsspuleNot included in the invention is an embodiment in which the first, essentially cosinusoidal 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 , wherein the Course of the first, substantially cosinusoidal receiving coil and/or the second, substantially sinusoidal receiving coil follows a function which is defined as $$x_{\text{sin}}=\left[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)\right]\ast \text{cos}\left(\phi \right)$$

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

$$x_{\text{cos}}=\left[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)\right]\ast \text{cos}\left(\phi \right)$$

$$y_{\text{cos}}=\left[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)\right]\ast \text{sin}\left(\phi \right)$$

with φ = [0;2π] for receiving coils formed in a full circle
with φ = [0;2π q/p] for arc-shaped 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 cosinusoidal receiving coil
with a _n = sinusoidal harmonic of nth order of the receiving coil
with b _n = cosinusoidal harmonic of nth order of the receiving coil

The advantageous effect of this design is based on the fact that the highest proportions of the signal error are compensated, thus enabling the greatest possible error compensation. This also makes it possible to reduce the amount of simulation required when designing the receiver coils.

• • 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 measurement errors in an inductive position sensor, wherein a first, essentially cosinusoidal receiver coil formed on and/or in the sensor carrier, from which a first voltage U _RX1 can be tapped, and a second, essentially sinusoidal receiver coil arranged on and/or in the sensor carrier, from which a second voltage U _RX2 can be tapped, are arranged, comprising the following steps:

• • Providing a model of a sensor target;
• • Providing a model of at least one transmitting coil;
• • Providing a model of a first, substantially cosinusoidal receiving coil having a profile corresponding to a cosinusoidal fundamental oscillation with at least one harmonic and/or a second, substantially sinusoidal receiving coil having a profile corresponding to a sinusoidal fundamental oscillation with at least one harmonic;
• • Manipulation of the first essentially cosinusoidal receiving coil, which has a course that corresponds to a cosinusoidal fundamental oscillation with at least one harmonic, and/or the second essentially sinusoidal receiving coil, which has a course that corresponds to a sinusoidal fundamental oscillation with at least one harmonic, in such a way that compensation of measurement errors in the inductive position sensor is effected.

This has the particular effect of achieving significantly improved measurement accuracy.

$$\begin{array}{l}{y}_{\text{sin}}=[r_m+a_1\text{ sin}\left(p\ast \phi \right)+a_2\text{ sin}\left(2p\ast \phi \right)+a_3\text{ sin}\left(3p\ast \phi \right)+\cdots +a_n\text{ sin }\left(np\ast \phi \right)+b_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

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

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

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 EmpfangsspuleAccording to the invention, the method is further developed in this context in such a way that the first, essentially cosinusoidal 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 , wherein the course of the first, essentially cosinusoidal receiving coil and/or the second, essentially sinusoidal receiving coil follows a function which is defined as $$\begin{array}{l}{x}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\cdots +a_n\text{sin}\left(np\ast \phi \right)+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png"\; state="\{\{state\}\}">b</figure-callout>}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\cdots +a_n\text{sin}\left(np\ast \phi \right)+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png"\; state="\{\{state\}\}">b</figure-callout>}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{x}_{\text{cos}}=[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\cdots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{cos}}=[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\cdots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)+a_2\text{sin}\\ \left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\dots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

with φ = [0;2π] for receiving coils formed in a full circle
with φ = [0;2π q/p] for arc-shaped 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 cosinusoidal receiving coil
with a _n = sinusoidal harmonic of nth order of the receiving coil
with b _n = cosinusoidal harmonic of 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 thus effective error reduction.

The object of the invention is further achieved by a computer program product stored on a machine-readable carrier or computer data signal embodied by an electromagnetic wave, with program code suitable for carrying out the method according to claim 2 or 3.

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 claim 1.

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 claim 1.

The invention will be explained in more detail below with reference to figures without limiting the general inventive concept.

• 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 view,
• 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 powered by a control unit 3 and a sensor target 7 that can be displaced relative to the sensor carrier 2. The position sensors 1 have a first, essentially cosinusoidal receiver coil 4 arranged on and/or in the sensor carrier 2, from which a first voltage U _RX1 can be tapped, and 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.

The first, essentially cosinusoidal receiving coil 4 has a profile that corresponds to a cosinusoidal oscillation of a higher order greater than one or, in other words, to a cosinusoidal fundamental oscillation with at least one harmonic. The second, essentially sinusoidal receiving coil 5 also has a profile 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 carried out using the 2 The rotation sensor shown is explained in more detail.

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

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

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

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 EmpfangsspuleIn the mathematical description of sinusoidal or cosinusoidal receiving coils 4,5 in rotary position sensors 1, as they are known from the 2 are known, the geometry of the receiving coils 4,5 basically follows the mathematical relationship: $$\begin{array}{l}{x}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\cdots +a_n\text{sin}\left(np\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_{\text{2}}\\ \text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_{\text{3}}\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left({\text{n}}_p\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\cdots +a_n\text{sin}\left(np\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_{\text{2}}\\ \text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_{\text{3}}\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left({\text{n}}_p\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{x}_{\text{cos}}=[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)+a_{\text{2}}\text{sin}\\ \left(2p\ast \phi \right)+a_{\text{3}}\text{sin}\left(3p\ast \phi \right)+\cdots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{cos}}=[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)+a_{\text{2}}\text{sin}\\ \left(2p\ast \phi \right)+a_{\text{3}}\text{sin}\left(3p\ast \phi \right)+\cdots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

with φ = [0;2π] for receiving coils formed in a full circle
with φ = [0;2π q/p] for arc-shaped 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 cosinusoidal receiving coil
with a _n = sinusoidal harmonic of nth order of the receiving coil
with b _n = cosinusoidal harmonic of 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. By copying and rotating by electrical π, a receiving coil 4.5 is completed. By another copy and rotating by electrical π/2, the second receiving coil 4.5 is created for a fully rotating 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 of the 2 shown rotary position sensor 1 is mounted radially outside the receiving coils 4,5. In principle, it would of course also be possible to arrange the transmitting coil 6 radially inside the receiving coils 4,5. The magnetic flux through the receiving coils 4,5 is not homogeneous in the radially outside or inside direction. This results in a third-order error in the corresponding useful signals, which propagates to 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 sinusoidal or cosinusoidal trajectory of the receiving coils 4,5 is modified so that the errors mentioned can be compensated for by an adapted trajectory of the receiving coils 4,5.

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

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

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

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 EmpfangsspuleThis is essentially achieved by the fact that the first, essentially cosinusoidal 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 , wherein the course of the first, essentially cosinusoidal receiving coil 4 and/or the second, essentially sinusoidal receiving coil 5 follows a function which is defined as $$\begin{array}{l}{x}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\cdots +a_n\text{sin}\left(np\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_{\text{2}}\\ \text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_{\text{3}}\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\cdots +a_n\text{sin}\left(np\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_{\text{2}}\\ \text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_{\text{3}}\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{x}_{\text{cos}}=[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)+a_{\text{2}}\text{sin}\\ \left(2p\ast \phi \right)+a_{\text{3}}\text{sin}\left(3p\ast \phi \right)+\cdots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

$$\begin{array}{l}{y}_{\text{cos}}=[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)+a_{\text{2}}\text{sin}\\ \left(2p\ast \phi \right)+a_{\text{3}}\text{sin}\left(3p\ast \phi \right)+\cdots +a_n\text{sin}\left(np\ast \phi \right)]\ast \text{sin}\left(\phi \right)\end{array}$$

with φ = [0;2π] for receiving coils formed in a full circle
with φ = [0;2π q/p] for arc-shaped 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 cosinusoidal receiving coil
with a _n = sinusoidal harmonic of nth order of the receiving coil
with b _n = cosinusoidal harmonic of nth order of the receiving coil

Harmonics are therefore already introduced into the geometry or the course of the receiving coils 4,5. The aim is now to determine, with the help of an optimization, in particular computer-aided optimization, the parameters a ₁ ... a _n at which the expected measurement error reaches a minimum.

Previous studies have shown that for inductive rotation sensors, as used in the 2 shown, a variation of a ₃ can already be sufficient to achieve a sufficiently good error compensation. For linear or angle segment sensors, additional harmonics may be necessary.

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

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

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

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 EmpfangsspuleTherefore, the course of the receiving coils 4, 5 can also follow a simplified mathematical description, in which the first, essentially cosinusoidal 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 , wherein the course of the first, essentially cosinusoidal receiving coil 4 and/or the second, essentially sinusoidal receiving coil 5 follows a function which is defined as $$x_{\text{sin}}=\left[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)\right]\ast \text{cos}\left(\phi \right)$$

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

$$x_{\text{cos}}=\left[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)\right]\ast \text{cos}\left(\phi \right)$$

$$y_{\text{cos}}=\left[r_m+{\text{<figure-callout id="1" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_1\text{cos}\left(p\ast \phi \right)+{\text{<figure-callout id="2" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_2\text{cos}\left(2p\ast \phi \right)+{\text{<figure-callout id="3" label="b" filenames="DE102022116956B4\_0037.png,DE102022116956B4\_0038.png" state="{{state}}">b</figure-callout>}}_3\text{cos}\left(3p\ast \phi \right)\right]\ast \text{sin}\left(\phi \right)$$

with φ = [0;2π] for receiving coils formed in a full circle
with φ = [0;2π q/p] for arc-shaped 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 cosinusoidal receiving coil
with a _n = sinusoidal harmonic of nth order of the receiving coil
with b _n = cosinusoidal harmonic of nth order of the receiving coil

The invention is not limited to the embodiments shown in the figures. The above description is therefore not to be regarded as restrictive, but as explanatory. The following patent claims are to be understood in such a way that a named feature is present in at least one embodiment of the invention. This does not exclude the presence of further features. If the patent claims and the above description define 'first' and 'second' features, this designation serves to distinguish between two similar features without establishing a ranking.

List of reference symbols

1

Position sensor

2

Sensor carrier

3

Control unit

4

Receiving coil

5

Receiving coil

6

Transmitter coil

7

Sensor target

Claims (6)

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

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

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

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

with φ = [0;2π] for receiving coils (4, 5) formed in a full circle with φ = [0;2π q/p] for arc-shaped receiving coils (4, 5) with q = number of actually formed electrical periods and p = number of pole pairs with a ₁ = fundamental oscillation of the sinusoidal receiving coil (5) with b ₁ = fundamental oscillation of the cosinusoidal receiving coil (4) with a _n = sinusoidal harmonic of the nth order of the receiving coil (4, 5) with b _n = cosinusoidal harmonic of the nth order of the receiving coil (4, 5). Method for compensating measurement errors in an inductive position sensor (1), wherein a first, substantially cosinusoidal receiving coil (4) formed on and/or in the sensor carrier (2), from which a first voltage U _RX1 can be tapped, and a second, substantially sinusoidal receiving coil (5) arranged on and/or in the sensor carrier (2), from which a second voltage U _RX2 can be tapped, are arranged, comprising the following steps: providing a model of a sensor target (7); providing a model of at least one transmitting coil (6); providing a model of a first, substantially cosinusoidal receiving coil (4), which has a profile corresponding to a cosinusoidal fundamental oscillation with at least one harmonic and/or a second, substantially sinusoidal receiving coil (5) which has a profile corresponding to a sinusoidal fundamental oscillation with at least one harmonic; Manipulation of the first, essentially cosinusoidal receiving coil (4), which has a course that corresponds to a cosinusoidal fundamental oscillation with at least one harmonic, and/or the second, essentially sinusoidal receiving coil (5), which has a course that corresponds to a sinusoidal fundamental oscillation with at least one harmonic, in such a way that a compensation of measurement errors in the inductive position sensor (1) is effected, wherein the first, essentially cosinusoidal 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 , wherein the course of the first, essentially cosinusoidal receiving coil (4) and/or the second, essentially sinusoidal receiving coil (5) is defined by the following functions: $$\begin{array}{l}{x}_{\text{sin}}=[r_m+a_1\text{sin}\left(p\ast \phi \right)+a_2\text{sin}\left(2p\ast \phi \right)+a_3\text{sin}\left(3p\ast \phi \right)+\cdots +a_n\text{sin}\left(np\ast \phi \right)+{\text{b}}_2\\ \text{cos}\left(2p\ast \phi \right)+{\text{b}}_3\text{cos}\left(3p\ast \phi \right)+\dots +{\text{b}}_{\text{n}}\text{cos}\left(\text{n}p\ast \phi \right)]\ast \text{cos}\left(\phi \right)\end{array}$$

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

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

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

with φ = [0;2π] for receiving coils (4, 5) formed in a full circle with φ = [0;2π q/p] for arc-shaped receiving coils (4, 5) with q = number of actually formed electrical periods and p = number of pole pairs with a ₁ = fundamental oscillation of the sinusoidal receiving coil (5) with b ₁ = fundamental oscillation of the cosinusoidal receiving coil (4) with a _n = sinusoidal harmonic of the nth order of the receiving coil (4, 5) with b _n = cosinusoidal harmonic of the nth order of the receiving coil (4, 5). Method for compensating measurement errors in an inductive position sensor (1) according to Claim 2 , 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, with program code which implements the method according to Claim 2 or 3 is carried out. Electric machine, in particular for a drive train of a motor vehicle, comprising an inductive position sensor (1) according to Claim 1 . X-by-wire system for a motor vehicle, comprising an inductive position sensor (1) according to Claim 1 .

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