METHOD AND DEVICE FOR MEASURING AT LEAST ONE PROPERTY OF A COIL, METHOD AND DEVICE FOR MEASURING THE POSITION OF AN ACTUATION MEMBER, AND MOTOR VEHICLE

Abstract

A method for measuring a property of a measuring coil, which is modeled as a parallel circuit including a capacitance with a series circuit including a DC voltage resistance, a frequency-dependent resistance, and an inductance, and a current-voltage converter is connected in series, by performing: applying an AC voltage, having a first frequency and having a DC voltage component differing from zero, to the coil and a voltage at the current-voltage converter is captured at a second frequency which is a multiple of the first frequency, wherein the multiple is an n-tuple, and the impedance and the phase angle at the first frequency are derived from at least n measured values captured in succession; and applying an AC voltage, having a third frequency differing from the first frequency and having a DC voltage component differing from zero, to the coil and the voltage at the current-voltage converter is captured at the second frequency or at a fourth frequency which is a multiple of the fourth frequency, wherein the multiple is an m-tuple, and the impedance and the phase angle at the third frequency are derived from m measured values captured in succession; at least one of the values for the DC voltage resistance, the frequency-dependent resistance, and the inductance being derived from the impedances and the phase angles.

Claims

1-17. (canceled)

18. A method for measuring at least one property of a coil, which includes a measuring coil used during measurements of other variables, wherein the coil is modeled as a parallel circuit including a capacitance with a series circuit including a DC voltage resistance, a frequency-dependent resistance, and an inductance, and a current-voltage converter is connected in series, the method comprising: a) applying an AC voltage, having a first frequency and having a DC voltage component which differs from zero, to the coil and a voltage at the current-voltage converter is captured at a second frequency which is a multiple of the first frequency, wherein the multiple, as an n-tuple where n is a natural number, is at least four, and the impedance and the phase angle at the first frequency are derived from at least n measured values captured in succession in this manner; and b) applying an AC voltage, having a third frequency which differs from the first frequency and having a DC voltage component which differs from zero, to the coil and the voltage at the current-voltage converter is captured at the second frequency or at a fourth frequency which is a multiple of the fourth frequency, wherein the multiple, as an m-tuple with a natural number, is at least four, and the impedance and the phase angle at the third frequency are derived from at least m measured values captured in succession in this manner; wherein at least one of the values for the DC voltage resistance, the frequency-dependent resistance, and the inductance is derived from the two impedances and from the two phase angles.

19. The method of claim 18, wherein the AC voltage in tasks a) and b) respectively includes a sinusoidal voltage, wherein the voltages differ from one another in terms of their frequency.

20. The method of claim 19, wherein in task b), the third frequency is three times the first frequency in task a).

21. The method of claim 18, wherein the same square-wave voltage is respectively generated in tasks a) and b) and is passed through different filters in tasks a) and b).

22. The method of claim 18, wherein the voltage at the current-voltage converter is captured in phase with the applied AC voltage.

23. The method of claim 18, wherein the measuring coil is for measuring a position of an actuation member, the actuation member plunging into the measuring coil in at least one measurable position, and wherein the position of the actuation member is derived from an inductance of the measuring coil, wherein the imaginary part of the impedances (Z.sub.1, Z.sub.2) of the measuring coil is determined at at least two different frequencies (.sub.1, .sub.2) and an ideal inductance (L0) independent of a capacitance (Cp) of the measuring coil is determined therefrom and the position is derived using the ideal inductance (L0).

24. The method of claim 23, wherein Im{Z.sub.1} is the imaginary part of the impedance Z.sub.1 measured at a first frequency .sub.1 and Im{Z.sub.2} is the imaginary part of the impedance Z.sub.2 measured at a second frequency 2 and the ideal inductance (L0) results as: $L.Math..Math.0=\frac{\mathrm{Im}.Math.\left\{Z_1\right\}.Math.\mathrm{Im}.Math.\left\{Z_{2.Math.}\right\}.Math.\left(\frac{{}_1}{{}_2}+\frac{{}_2}{{}_1}\right)}{{}_2.Math.\mathrm{Im}.Math.\left\{Z_2\right\}-{}_1.Math.\mathrm{Im}.Math.\left\{Z_1\right\}}.$

25. The method of claim 23, wherein the ideal inductance is temperature-dependent, the temperature is measured, and the measured value for the temperature is used when determining the position.

26. The method of claim 23, wherein the value for the DC voltage resistance and the value for the frequency-dependent resistance are also used when determining the position.

27. A device for measuring at least one property of a coil, which is a measuring coil, comprising: a current-voltage converter, preferably a measuring resistor which is connected in series with the coil; a generator for inputting an AC voltage which has a DC voltage component; a frequency converter; a sampling circuit for providing the output signal from the current-voltage converter, wherein the sampling circuit carries out sampling in phase with the input AC voltage at a multiple of the frequency of the input AC voltage, wherein the multiple is at least four; and h an evaluation device which is supplied with the measured values sampled by the sampling circuit and, by modeling the coil as a parallel circuit including a capacitance with a series circuit including a DC voltage resistance, a frequency-dependent resistance and an inductance, calculates at least one of the value for the DC voltage resistance, the frequency-dependent resistance and the inductance.

28. The device of claim 27, wherein the frequency converter includes a frequency divider which can be optionally switched on.

29. The device of claim 27, wherein the sampling circuit includes a low-pass filter downstream of the output of the frequency converter and downstream of the output of the current-voltage converter, and the outputs of both low-pass filters are supplied to a multiplexer, the output of which is supplied to an analog/digital converter, the output of which is supplied to a microprocessor as an evaluation device.

30. The device of claim 27, wherein the sampling circuit jointly supplies the output signal from the frequency converter and from the current-voltage converter to a multiplexer, the output signal from which first of all passes through a low-pass filter, the output of which is supplied to a first analog/digital converter, the output of which is in turn supplied to a microprocessor as an evaluation device, wherein the output signal from the multiplexer is secondly supplied to a bandpass filter, the output signal from which is supplied to the first or a second analog/digital converter, the output signal from which is in turn supplied to the microprocessor.

31. A device for measuring a position of an actuation member, comprising: a measuring coil into which at least sections of the actuation member plunge in at least one position to be measured and/or over which at least sections of the actuation member slide in at least one position to be measured; and a measuring device for measuring the impedance of the measuring coil or at least the imaginary part of the impedance of the measuring coil (Im{Z.sub.1}, Im{Z.sub.2}) at two different frequencies (.sub.1, .sub.2) for the purpose of determining an ideal inductance (L0) of the coil, which ideal inductance is independent of the capacitance (Cp) of the measuring coil and from which the position of the actuation member is derivable; and an apparatus for determining the position of the actuation member from the ideal inductance; wherein the measuring device is configured for measuring at least one property of a coil, which includes a measuring coil used during measurements of other variables, wherein the coil is modeled as a parallel circuit including a capacitance with a series circuit including a DC voltage resistance, a frequency-dependent resistance, and an inductance, and a current-voltage converter is connected in series, by performing the following: a) applying an AC voltage, having a first frequency and having a DC voltage component which differs from zero, to the coil and a voltage at the current-voltage converter is captured at a second frequency which is a multiple of the first frequency, wherein the multiple, as an n-tuple where n is a natural number, is at least four, and the impedance and the phase angle at the first frequency are derived from at least n measured values captured in succession in this manner; and b) applying an AC voltage, having a third frequency which differs from the first frequency and having a DC voltage component which differs from zero, to the coil and the voltage at the current-voltage converter is captured at the second frequency or at a fourth frequency which is a multiple of the fourth frequency, wherein the multiple, as an m-tuple with a natural number, is at least four, and the impedance and the phase angle at the third frequency are derived from at least m measured values captured in succession in this manner; wherein at least one of the values for the DC voltage resistance, the frequency-dependent resistance, and the inductance is derived from the two impedances and from the two phase angles.

32. The device of claim 31, wherein Im{Z.sub.1} is the imaginary part of the impedance Z.sub.1 measured at a first frequency .sub.1 and Im{Z.sub.2} is the imaginary part of the impedance Z.sub.2 measured at a second frequency .sub.2 and the ideal inductance (L0) results as: $L_0=\frac{\mathrm{Im}.Math.\left\{Z_1\right\}.Math.\mathrm{Im}.Math.\left\{Z_{2.Math.}\right\}.Math.\left(\frac{{}_1}{{}_2}+\frac{{}_2}{{}_1}\right)}{{}_2.Math.\mathrm{Im}.Math.\left\{Z_2\right\}-{}_1.Math.\mathrm{Im}.Math.\left\{Z_1\right\}}.$

33. A motor vehicle, comprising: an actuation element having an actuation member; a measuring device for measuring a position of the actuation member, including: a measuring coil into which at least sections of the actuation member plunge in at least one position to be measured and/or over which at least sections of the actuation member slide in at least one position to be measured; and a measuring device for measuring the impedance of the measuring coil or at least the imaginary part of the impedance of the measuring coil (Im{Z.sub.1}, Im{Z.sub.2}) at two different frequencies (.sub.1, .sub.2) for the purpose of determining an ideal inductance (L0) of the coil, which ideal inductance is independent of the capacitance (Cp) of the measuring coil and from which the position of the actuation member is derivable; and an apparatus for determining the position of the actuation member from the ideal inductance; wherein the measuring device is configured for measuring at least one property of a coil, which includes a measuring coil used during measurements of other variables, wherein the coil is modeled as a parallel circuit including a capacitance with a series circuit including a DC voltage resistance, a frequency-dependent resistance, and an inductance, and a current-voltage converter is connected in series, by performing the following: a) applying an AC voltage, having a first frequency and having a DC voltage component which differs from zero, to the coil and a voltage at the current-voltage converter is captured at a second frequency which is a multiple of the first frequency, wherein the multiple, as an n-tuple where n is a natural number, is at least four, and the impedance and the phase angle at the first frequency are derived from at least n measured values captured in succession in this manner; and b) applying an AC voltage, having a third frequency which differs from the first frequency and having a DC voltage component which differs from zero, to the coil and the voltage at the current-voltage converter is captured at the second frequency or at a fourth frequency which is a multiple of the fourth frequency, wherein the multiple, as an m-tuple with a natural number, is at least four, and the impedance and the phase angle at the third frequency are derived from at least m measured values captured in succession in this manner; wherein at least one of the values for the DC voltage resistance, the frequency-dependent resistance, and the inductance is derived from the two impedances and from the two phase angles; wherein to measure a position of the actuation member, at least sections of the actuation member of the actuation element plunge into the measuring coil of the device and/or at least sections slide over the measuring coil of the device, and wherein a reaction of a unit of the motor vehicle is prompted based on the position of the actuation member at least under predetermined conditions.

34. The motor vehicle of claim 33, wherein the actuation element includes a brake pedal, a gas pedal, a clutch pedal or a manual actuation element.

35. The method of claim 18, wherein the voltage at the current-voltage converter is captured in phase with the applied AC voltage at a phase of 0, 90, 180 and 270.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0027] FIG. 1 shows the principle of travel measurement in a pedal, on which the present invention is based in some aspects.

[0028] FIG. 2 shows an equivalent circuit diagram according to which a measuring coil provided by the principle according to FIG. 1 is modeled.

[0029] FIG. 3A shows a basic circuit diagram of an inductance connected in series with a resistance.

[0030] FIG. 3B shows a matching phasor diagram with phasors for the current and voltage.

[0031] FIG. 4A shows a modification of the basic circuit from FIG. 3A with a current-voltage converter.

[0032] FIG. 4B shows a matching phasor diagram.

[0033] FIG. 5A shows the principle of sampling measured values with a 90 spacing.

[0034] FIG. 5B shows a matching phasor diagram.

[0035] FIG. 6 shows a circuit diagram illustrating the basic principle of the voltage generation used in one embodiment of the invention.

[0036] FIGS. 7A, 7B, and 7C show the voltages tapped off at a plurality of points shown in FIG. 6.

[0037] FIG. 8 shows a basic circuit diagram of a circuit which is used to carry out the method for determining at least one property of the measuring coil using the principle explained on the basis of FIG. 6.

[0038] FIG. 9 shows a phasor diagram used to explain the invention.

[0039] FIG. 10A shows a second embodiment of a circuit according to the invention having a frequency divider.

[0040] FIG. 10B shows the associated evaluation circuit illustrated in more detail.

[0041] FIG. 11A shows a third embodiment of a circuit according to the invention having a flip-flop.

[0042] FIG. 11B shows the associated evaluation circuit in detail in the case of a minor modification.

[0043] FIG. 12 shows a modified equivalent circuit diagram for a measuring coil provided in accordance with the principle according to FIG. 2, and

[0044] FIG. 13 shows a modification of the principle of travel measurement according to FIG. 1.

DETAILED DESCRIPTION

[0045] FIG. 1 shows an actuation member 2 on a pedal 3 which penetrates a coil 1, as used in a motor vehicle for example, and a device 10 for reading the travel signal from the coil 1.

[0046] As illustrated in FIG. 2, the coil 1 may be modeled as a parallel circuit firstly comprising a capacitance Cp and secondly a series circuit comprising a DC voltage resistance Rdc, a frequency-dependent resistance Rs and an inductance Ls. The variable Ls is dependent on mechanical properties, in particular is dependent on the travel, that is to say is dependent on the position of the actuation member 2 of the pedal 3, and is also dependent on the temperature, for example. Rs is also dependent on the travel. It is also dependent on the mechanism and on the interturn fault. The DC voltage resistance Rdc is dependent on the temperature of the coil 1 and the contact resistance thereon. The capacitance Cp of the turns of the coil 1 depends mainly on the moisture prevailing in the coil.

[0047] The present invention describes a possible way of being able to depart from the conventional principle of keeping the capacitance Cp constant by sealing the coil 1 in a watertight manner.

[0048] As known, a series circuit comprising an inductance Ls and a frequency-dependent resistance Rs, as illustrated in the basic diagram in FIG. 3A, can be represented by a phasor diagram shown in FIG. 3B when an AC voltage U is applied. The resulting voltage has an angle (phase angle ) and an absolute value. The impedance can be calculated from the angle and the absolute value.

[0049] In the less idealized basic diagram, there is additionally a current-voltage converter at which the voltage u_IU can be tapped off, see FIG. 4A and the associated phasor diagram in FIG. 4B. In this case too, the phase angle can be determined, now in the relationship of two voltages u and u_IU.

[0050] The phasor representations shown in FIGS. 3B and 4B are snapshots for an AC voltage; during operation, the phasor rotates at a constant rotational frequency .sub.1 (the frequency of the AC voltage), with the result that the real part of the phasor can be read at a particular phase angle and the imaginary part can be read at another phase angle which is offset by 90. This becomes clear on the basis of FIG. 5A where the real part can be read at an angle of zero (measured in arc lengths, that is to say one full revolution is 2, 6.28 . . . ), and the imaginary part can be read at an angle of 90 (/2). FIG. 5B shows the corresponding phasor diagram.

[0051] The invention is based on the knowledge that the impedance and the phase angle can be derived from corresponding measurements of real and imaginary parts and the variables Rdc, Rs and Ls can be calculated therefrom.

[0052] The embodiment is based on the idea that measured values are intended to be sampled at 0, 90, 180 and 270. In this respect, FIG. 6 shows a basic diagram of the corresponding voltage generator complex.

[0053] A voltage generator 12 generates a square-wave voltage 14 (FIG. 7A) which is passed through a low-pass filter 16, the output 18 of which outputs the generator voltage u_GEN (see curve 20 in FIG. 7A). The voltage 22 (FIG. 7B) shown in FIG. 7B is tapped off at a tap Q0 upstream of the low-pass filter, wherein a frequency divider 24 is followed by an output Q1, where the voltage 26 (FIG. 7C) can be tapped off. It is possible to carry out sampling at an angle of 90 by using the variables Q0 and Q1.

[0054] The complete diagram is shown in FIG. 8. A current-voltage converter 28 which is in the form of a simple measuring resistor R_FP, for example, is connected in series with the coil 1 which is connected to the output 18. The current-voltage converter is followed by a low-pass filter or bandpass filter 30. A microprocessor 32 receives the voltages according to FIGS. 7B and 7C at its inputs Q0 and Q1 and controls the supply of signals to an analog/digital converter 34 (that is to say the sampling) which is in turn also supplied with the original square-wave voltage 14. The microprocessor 32 contains a unit 36 which calculates the values Rs and Ls and possibly also Rdc.

[0055] As stated above, the voltage is intended to be sampled at angular spacings of 90. This is illustrated in FIG. 9 using the samples S1, S2, S3 and S4. It should be noted that, on account of the square-wave voltage, a DC voltage component which differs from zero is impressed on the overall system. The DC voltage component in the generator voltage results as:

[00002]$\begin{array}{cc}.Math..Math.\mathrm{U\_GEN}.Math.\mathrm{\_DC}=\frac{\frac{u_{{\mathrm{GEN}}_{0.Math.}}+U_{{\mathrm{GEN}}_{180.Math.}}}{2}+\frac{u_{{\mathrm{GEN}}_{90.Math.}}+U_{{\mathrm{GEN}}_{270.Math.}}}{2}}{2}& \left(1\right)\end{array}$

and the DC voltage component at the current-voltage converter resistor R_FP accordingly results as:

[00003]$\begin{array}{cc}.Math..Math.\mathrm{U\_FP}.Math.\mathrm{\_DC}=\frac{\frac{u_{{\mathrm{FP}}_{0.Math.}}+U_{{\mathrm{FP}}_{180.Math.}}}{2}+\frac{u_{{\mathrm{FP}}_{90.Math.}}+U_{{\mathrm{FP}}_{270.Math.}}}{2}}{2}& \left(2\right)\end{array}$

The variables u_GEN 0, u_GEN 90, u_GEN 180, u_GEN 270 are samples for the generator voltage which are measured at the angles with the phases 0, 90, 180 and 270. A corresponding situation applies to the values u_FP_0, u_FP_90, u_FP_180, u_FP_270 for the voltage at the current-voltage converter.

[0056] The value Rdc, the DC voltage resistor plunging in the coil 1, can then be derived from the two variables according to:

[00004]$\begin{array}{cc}\mathrm{Rdc}=\frac{.Math..Math.u_{{\mathrm{GEN}}_{D.Math..Math.C}}*R_{\mathrm{FP}}}{{}_{u_{{\mathrm{FP}}_{D.Math..Math.C}}}}-R_{\mathrm{FP}}& \left(3\right)\end{array}$

[0057] With the aid of u.sub.uGEN.sub._.sub.DC and u.sub.FP.sub._.sub.DC, it is now possible to subtract the DC voltage component from the samples.

[0058] An impedance Z results as:

[00005]$\begin{array}{cc}Z=\frac{u_{\mathrm{GEN}}}{u_{\mathrm{FP}}}*R_{\mathrm{FP}}-\left(R_{\mathrm{FP}}+\mathrm{Rdc}\right)& \left(4\right)\end{array}$

and the frequency-dependent resistance Rs accordingly results as:

[00006]$\begin{array}{cc}R=\frac{u_{{\mathrm{GEN}}_{0.Math.}}*u_{{\mathrm{FP}}_{0.Math.}}+u_{{\mathrm{GEN}}_{90.Math.}}+u_{{\mathrm{FP}}_{90.Math.}}}{u_{{\mathrm{FP}}_{0.Math.}}^2+u_{{\mathrm{FP}}_{90.Math.}}^2}*R_{\mathrm{FP}}-\left(R_{\mathrm{FP}}+\mathrm{Rdc}\right)& \left(5\right)\end{array}$

and the inductance Ls as:

[00007]$\begin{array}{cc}\mathrm{Ls}=\frac{u_{{\mathrm{GEN}}_{90.Math.}}*u_{{\mathrm{FP}}_{0.Math.}}+u_{{\mathrm{GEN}}_{0.Math.}}+u_{{\mathrm{FP}}_{90.Math.}}}{u_{{\mathrm{FP}}_{0.Math.}}^2+u_{{\mathrm{FP}}_{90.Math.}}^2}& \left(6\right)\end{array}$

[0059] The variable Ls is therefore nothing other than the imaginary part of the respective impedance, Ls=Im{Z}.

[0060] Two embodiments of the circuit are explained more specifically in detail below.

[0061] FIG. 10A shows that a square-wave voltage generated by the generator 12 at a frequency of 120 kHz in the present example passes through a frequency divider 38, this voltage then passes through a bandpass filter 40 with a DC voltage offset and is supplied to the coil 1. The input signal for the coil (that is to say the output of the bandpass filter 40) passes through a low-pass filter 42, the output signal from the coil passes through a further low-pass filter 44 and the outputs of both low-pass filters are multiplexed with one another in a multiplexer 46, and the result is supplied to an analog/digital converter 48 where an evaluation is then carried out. As illustrated in more detail in FIG. 10B, the angles 0, 90, 180 and 270 are read in a unit 50 downstream of the analog/digital converter and then pass through a filter 52 before the calculation 54 is carried out according to the above formulas and the variables Rdc, Rs and Ls are output.

[0062] In a modification of the embodiment according to FIG. 10A, the square-wave voltage 14 generated by the generator 12 at 120 kHz in the present example passes through a flip-flop 56 according to FIG. 11A, the output of which is supplied to a low-pass filter 58 where a frequency of 30 kHz is output, for example. The output of the low-pass filter 58 and the output of the coil 1 are multiplexed in a multiplexer 60 and this is then supplied to a further low-pass filter 62 and to a bandpass filter 64 in another branch, which are followed by respective analog/digital converters 66 and 68. This evaluation is illustrated in detail in FIG. 11B, wherein the indication HW and SW in FIG. 11B is used to show which units are present in the form of hardware HW, that is to say physical assemblies, and which units are provided by software SW, that is to say in a computing unit. The multiplexer 60 can also be provided by two multiplexing units in order to reduce measuring times. Instead of two analog/digital converters 66 and 68, it is also possible to use an individual analog/digital converter with a further multiplexer connected upstream.

[0063] In a slight modification of FIG. 11A, FIG. 11B illustrates the bandpass filter at a later time; see unit 64 with the low-pass filter 62 in the parallel branch. The unit 70 then determines the corresponding variables at the angles 0, 90, 180 and 270 and the unit 72 calculates the variables Rdc, Rs and Ls.

[0064] The previously described method is used to determine the properties of the coil 1 which are present according to the model illustrated in FIG. 2, that is to say the resistances Rdc, Rs and the inductance Ls. The inductance Ls is still dependent on Cp.

[0065] In order to reliably measure the travel, that is to say to precisely determine the position of the actuation member 2, other variables are now calculated in accordance with the model according to FIG. 12. In this case, there is an inductance L0 which is not dependent on Cp, and the dependence on Cp is found in the other variables.

[0066] The impedance of the coil can be represented according to FIG. 12 as:

[00008]$\begin{array}{cc}\underset{\_}{Z}=\frac{1}{\frac{1}{\mathrm{Rdc}+\mathrm{Rs}+j.Math..Math..Math..Math.\mathrm{Lo}}+j.Math..Math..Math..Math.\mathrm{Cp}}& \left(7\right)\end{array}$

[0067] The idea used when determining the theoretical inductance L0 involves measuring the inductance at different frequencies 1 and 2. In the case of 1, the formula for the inductance is:

[00009]$\begin{array}{cc}{\underset{\_}{Z}}_1=\frac{1}{\frac{1}{\mathrm{Rdc}+\mathrm{Rs}+j.Math..Math.{}_1.Math.\mathrm{Lo}}+j.Math..Math.{}_1.Math.\mathrm{Cp}}& \left(8\right)\end{array}$

and, in the case of 2, it is:

[00010]$\begin{array}{cc}{\underset{\_}{Z}}_2=\frac{1}{\frac{1}{\mathrm{Rdc}+\mathrm{Rs}+j.Math..Math.{}_2.Math.\mathrm{Lo}}+j.Math..Math.{}_2.Math.\mathrm{Cp}}.& \left(9\right)\end{array}$

[0068] If Rdc=Rs=0 is now set in an approximation, the following variables are obtained for the imaginary part of the impedance Z.sub.1 and of the impedance Z.sub.2:

[00011]$\begin{array}{cc}\mathrm{Im}.Math.\left\{{\underset{\_}{Z}}_1\right\}=\frac{1}{\frac{1}{{}_1.Math.\mathrm{Lo}}+j.Math..Math.{}_1.Math.\mathrm{Cp}}& \left(10\right)\\ \mathrm{Im}.Math.\left\{{\underset{\_}{Z}}_2\right\}=\frac{1}{\frac{1}{{}_2.Math.\mathrm{Lo}}+j.Math..Math.{}_2.Math.\mathrm{Cp}}.& \left(11\right)\end{array}$

[0069] This can be solved according to L0 and the following formula is obtained:

[00012]$\begin{array}{cc}L.Math..Math.0=\frac{\mathrm{Im}.Math.\left\{Z_1\right\}.Math.\mathrm{Im}.Math.\left\{Z_{2.Math.}\right\}.Math.\left(\frac{{}_1}{{}_2}+\frac{{}_2}{{}_1}\right)}{{}_2.Math.\mathrm{Im}.Math.\left\{Z_2\right\}-{}_1.Math.\mathrm{Im}.Math.\left\{Z_1\right\}}.& \left(12\right)\end{array}$

[0070] It is clear in the examples above that, if the first measuring frequency 1 is 25 kHz for example, the second measuring frequency 2 relates to the third harmonic, that is to say 75 kHz, and the sampling is carried out at 100 kHz. A third measuring frequency could in theory be five times the first measuring frequency, that is to say 125 kHz. A frequency of 25 kHz is also produced in the case of the latter by sampling at 100 kHz, but the sampled values must then be used in a suitable sequence.

[0071] The position of the actuation member 2 can now be clearly derived using the determined variable L0 which could be dependent only on the temperature; the temperature dependence can also be additionally compensated for, if necessary, with the aid of Rdc. This makes it possible to use the coil 1 without sealing, that is to say without it having to be protected from moisture.

[0072] The above-described measurements of the variables Rdc, Rs and Ls and, following from this, the variable L0 can be carried out in a motor vehicle, for example in a five-minute cycle, a 15-minute cycle or other cycles with a duration of between 1 second and 24 hours, which may be with a duration of between 1 second and 1 hour. If a corresponding pedal 3 is actuated, the respective current value for the capacitance Cp, which is dependent on moisture possibly ingressing into the coil 1, is thus reliably taken into account.

[0073] In a modification of FIG. 1, an actuation member 2 on a pedal 3 can also surround a coil 1, wherein the extent to which the actuation member 2 surrounds the coil 1 is varied by actuating the pedal 3. The actuation member 2 is therefore slid over the coil 1.

[0074] In a further modification in an embodiment which is not shown, it would also be possible to combine the principles according to FIG. 1 and FIG. 13, that is to say an inner section of an actuation member can penetrate the coil and an outer section can surround the coil and can be slid over the latter.

[0075] Instead of being arranged on a pedal 3, the actuation member 2 or 2 can also be arranged on a handle or another mechanically displaceable unit as an actuation element.

[0076] Although the present invention has been described in detail on the basis of the exemplary embodiments, the invention is not restricted to these exemplary embodiments, but rather deviations are possible such that individual features can be omitted or other combinations of features can be implemented as long as the scope of protection of the accompanying claims is not left. The present disclosure concomitantly includes all combinations of the individual features presented.

[0077] In particular, measured values can be sampled at 360/n, where n is a natural number and n>4. The above equations can then be replaced with the corresponding equations matching n.