TW201809604A - Electromagnetic-induction type position detector capable of detecting interpolation errors according to gap changes in order to correct a detection position - Google Patents

Abstract

The present invention provides an electromagnetic-induction type position detector which can detect interpolation errors according to gap changes in order to correct a detection position. The electromagnetic-induction type position detector of the present invention includes: a sampling circuit 19 which samples peak values of induction signals induced by a scale coil 105 and outputs a sampling signal; a control circuit 20 which calculates a synchronous wave-detection signal according to the sampling signal, obtains a detection position according to the synchronous detection signal, calculates an excitation amplitude according to the detection position and outputs the excitation amplitude to excitation circuits 106, 107; gap detection excitation circuits 11, 12 which applies gap detection excitation signals to slider coils 103, 104; a detection circuit 13 which calculates an average voltage of the sampling signals, subtracts the average voltage from each of voltages of the sampling signals, calculates the sum of absolute values, and eliminates changes caused by the aforementioned detection position from the sum of the absolute values; and a correction circuit 14 which calculates a correction amount corresponding to the sum of the absolute values from which the changes caused by the detection position has been eliminated, and corrects the detection position by adding the correction amount to the detection position.

Description

Electromagnetically induced position detector

The invention relates to an electromagnetically induced position detector.

Inductosyn scales, which are electromagnetically induced position detectors, are used to detect the position of various machines such as machine tools, automobiles, and robots. Induction synchronizer scales include linear scales and rotary scales. A linear scale is installed on a mobile body such as a machine tool platform and detects the linear movement position of the mobile body, and a rotary scale is installed on a mobile body (rotary body) such as the machine's rotary platform and detects the rotational position of the mobile body (Rotation angle). Linear scales and rotary scales detect positions using electromagnetic induction generated by coils arranged so as to face each other in parallel. This detection principle will be described based on the principle diagram of FIG. 10. Fig. 10 (a) is a perspective view showing a state in which a slider and a scale of a linear scale are arranged so as to face each other in parallel, and Fig. 10 (b) is a schematic diagram showing the slider and the scale side by side. 10 (c) is a graph showing the degree of electromagnetic coupling between the slider and the scale. Furthermore, the detection principle of the rotary scale is the same as the linear scale. The stator and rotor of the rotary scale correspond to the slider and scale of the linear scale, respectively. As shown in FIGS. 10A and 10B, the detection unit 100 of the linear scale includes a slider 101 as a primary-side member and a scale 102 as a secondary-side member. The slider 101 is a movable portion, and includes a first slider coil 103 as a first primary coil and a second slider coil 104 as a second primary coil. The scale 102 is a fixed portion and includes a scale coil 105 as a secondary-side coil. The coils 103, 104, and 105 are formed by bending in a rectangular wave shape. The slider 101 is mounted on a moving body such as a platform of a machine tool, and moves linearly with the moving body. The scale 102 is fixed to a fixed portion such as a base of the machine tool. As shown in FIG. 10 (a), the slider 101 (the first slider coil 103 and the second slider coil 104) and the scale 102 (the scale coil 105) are maintained with a specific gap between them ( In the state of g) in the figure, they are arranged so as to face each other in parallel. If the positional relationship between the first slider coil 103 and the second slider coil 104 is described, as shown in FIG. 10 (a) (b), the slider 101 exists in the first slider coil 103. When the pattern coincides with the pattern of the scale coil 105, the pattern of the second slider coil 104 is shifted from the pattern of the scale coil 105 (in the direction in which the scale coil 105 extends) by 1/4 pitch. Further, as shown in FIG. 10 (c), the electromagnetic coupling degree of the first slider coil 103 (and the scale coil 105) becomes cosX, and the electromagnetic coupling degree of the second slider coil 104 (and the scale coil 105) becomes sinX (X: relative position of slider 101 and scale 102 (moving position of moving body)). FIG. 11 is a block diagram illustrating a conventional electromagnetically induced position detector. As shown in FIG. 11, the conventional electromagnetic induction type position detector includes a sin excitation circuit 106, a cos excitation circuit 107, an amplifier circuit 108, a filter circuit 109, a sampling circuit 110, and a control circuit in addition to the detection unit 100. 111. If the excitation signal "I * sin (θ) * sin (ωt)" is applied to the first slider coil 103 by the sin excitation circuit 106, the excitation signal "-" is applied to the second slider coil 104 by the cos excitation circuit 107. I * cos (θ) * sin (ωt) ”, then the signal (evoked signal V) induced by the scale 102 becomes: V = k * (I * sin (θ) * cosX-I * cos (θ) * sinX) * sin (ωt) = k * I * sin (θ-X) * sin (ωt) (* means multiplication). Among them, set I: the magnitude of the current of the position detection excitation signal, ω: the frequency of the position detection excitation signal, t: time, θ: detection position. Also, k represents a coefficient that depends on the signal transmission strength of the gap. The wider the gap, the smaller k becomes, and the smaller the induced signal V becomes. In the amplifying circuit 108, the transmission signal is amplified at a fixed rate, and in the filtering circuit 109, a noise component higher than the frequency of the position detection excitation signal is usually cut off by a low-pass filter. The sampling circuit 110 samples the peak of the induced signal V and outputs it to the control circuit 111. The control circuit 111 controls θ so that V = 0 based on the voltage value (sampling voltage) of the sampling signal sampled in the sampling circuit 110. As a result, sin (θ-X) = 0, that is, θ = X, and the relative position X of the scale 102 and the slider 101 can be detected regardless of the coefficient k. FIG. 12 is a graph illustrating the detection of the induced signal V. FIG. The detection of the induced signal V is performed by sampling the peak value of the induced signal V as a sin wave in the sampling circuit 110 and performing synchronous detection in the control circuit 111. If the sampling voltage at a certain point is set to V (i) and the next sampling voltage is set to V (i + 1), then the synchronous detection signal Vp of the induced signal V becomes "Vp = [V (i) + ( ‑V (i + 1))] / 2 ". Here, the so-called synchronous detection is data obtained by inverting the sampling signal at a determined period, and the synchronous detection signal Vp becomes a negative value according to the phase of the induced signal V. [Prior Art Literature] [Patent Literature] [Patent Literature 1] Japanese Patent Laid-Open No. 2014-153294 [Patent Literature 2] Japanese Patent Laid-Open No. 2013-174521

[Problems to be Solved by the Invention] In the scale of the above-mentioned induction synchronizer method, in general, the error that is prominently expressed as an error is a coil pitch period error, and this is called an interpolation error. Interpolation errors occur due to signal interference, pattern width, or pattern pitch, and errors in components that are synchronized with the pitch of the scale coil 105 (for example, 1-pitch component of the scale coil 105, or 1/2 pitch composition, etc.). In the above, the position detection can be performed independently of the coefficient k depending on the signal transmission intensity of the gap. The reason is that it is designed to control the induced signal V including the coefficient k so that it becomes 0 (θ = X). However, regarding the interpolation error, the magnitude of the error varies depending on the gap variation. That is, the signal generating the interpolation error is not a signal designed in advance like the induced signal V, and therefore, the influence caused by the change in the coefficient k cannot be ignored. For example, in the graph of FIG. 13 explaining the relationship between the gap and the interpolation error, the error components δa and δb mainly change depending on the gap. In the prior art, although corrections for interpolation errors have been proposed, it is not possible to cope with such changes in interpolation errors due to gap variations. For example, in the above-mentioned Patent Document 1, correction data is obtained at a fixed speed and a fixed sampling interval, and interpolation errors corresponding to the period inherent to the scale coil are extracted for correction. However, the gap cannot be detected and the change due to the gap cannot be dealt with. Interpolation error. In addition, for example, in the above-mentioned Patent Document 2, the circulating and detecting signals are disconnection detection signals of different frequencies, and abnormality is detected by comparing the induced voltage with the disconnection level, but the induced voltage V depends on the detection position. θ fluctuates, so it cannot cope with gap detection. Further, in the aforementioned Patent Document 2, although the frequency of the abnormality detection signal is set to "ω * (n + 0.5)", it is higher than the frequency of the position detection excitation signal and is affected by the influence of the low-pass filter. The intensity of the induced voltage changes, so it cannot cope with gap detection. Therefore, an object of the present invention is to provide an electromagnetically induced position detector that can accurately detect interpolation errors according to gap fluctuations, thereby accurately correcting the detection position. [Technical means to solve the problem] The electromagnetically induced position detector of the first invention to solve the above-mentioned problems is characterized by having a primary-side member including a primary-side coil, a secondary-side member including a secondary-side coil, and An excitation circuit that applies an excitation signal to a side coil, and the primary side member or the secondary side member is mounted on a moving body and moves together with the moving body. The primary side coil and the secondary side coil system have a gap and become The electromagnetically induced position detectors are arranged in parallel to each other, and the electromagnetic induction position detector includes: a sampling circuit that samples the induced signal induced by the secondary coil and outputs a sampling signal; a control circuit that is based on the sampling signal Calculate a synchronous detection signal, obtain a detection position based on the synchronous detection signal, calculate an excitation amplitude based on the detection position, and output the excitation amplitude to the excitation circuit; a gap detection excitation circuit that applies a gap detection excitation signal to the primary coil; The gap detection circuit obtains the average voltage of the sampling signals, and The average voltage is subtracted from the voltage of the sample signal, and the sum of its absolute value is calculated, and then the change caused by the above-mentioned detection position is excluded from the sum of the absolute value; and the gap correction circuit, which calculates and excludes the above-mentioned detection. The correction amount corresponding to the sum of the absolute values after the change caused by the position is added to the detection position to correct the detection position. The electromagnetically induced position detector of the second invention that solves the above-mentioned problems is characterized by having a primary-side member including a first primary-side coil and a second primary-side coil, a secondary-side member including a secondary-side coil, and The first primary coil applies a position detection excitation signal I * sin (θ) * sin (ωt) to the first excitation circuit, and the second primary coil applies a position detection excitation signal-I * cos (θ) * sin (ωt) A second excitation circuit, in which the primary side member or the secondary side member is mounted on a moving body and moves together with the moving body, the first primary side coil and the second primary side coil system are staggered by 1 / 4 pitches are arranged side by side, the first primary coil and the second primary coil and the secondary coil are arranged so as to face each other in parallel with a gap; and the electromagnetically induced position detector is provided with : A sampling circuit that outputs a sampling signal obtained by sampling a plurality of times of the peak value of the induced signal induced by the secondary-side coil; a control circuit that performs synchronous detection and addition on the sampling signal The synchronous detection signal Vp is calculated uniformly, and the detection position θ is obtained by controlling such that the synchronous detection signal Vp becomes 0, and the excitation amplitude sin (θ) and the excitation amplitude cos (θ) are calculated based on the detection position θ. And output to the first excitation circuit and the second excitation circuit; the first excitation circuit for gap detection applies a gap detection excitation signal I '* sin (ω't) to the first primary coil; the gap detection A second excitation circuit is used to apply a gap detection excitation signal I '* cos (ω't) to the second primary side coil; a gap detection circuit calculates the voltages of the plurality of sampling signals obtained in the sampling circuit. The average value Vave is obtained by subtracting the average value Vave from the voltage of each sampling signal, calculating the absolute value sum Vabs, and calculating the normalized Vθ of the change in the absolute value sum Vabs caused by the detection position θ, and Based on the Vθ, calculate the Vgap after excluding the change caused by the detection position θ from the sum of the absolute values Vabs; and a gap correction circuit whose memory is used as a reference for the amplitude of each error component of the interpolation error The interpolation error and Vgap0 as the gap detection excitation signal at this time, and based on the Vgap, the Vgap0, and the reference interpolation error, a correction component amplitude of each of the error components corresponding to the gap is calculated, and based on the correction The component amplitude calculates the correction amount, and adds the correction amount to the detection position θ to obtain the corrected detection position θh; where: I represents the magnitude of the current of the position detection excitation signal; ω represents the position detection excitation signal. Frequency; I 'represents the current of the excitation signal for gap detection; ω' represents the frequency of the excitation signal for gap detection; t represents time. The third aspect of the invention, an electromagnetically induced position detector, is characterized by having a primary member including a first primary coil and a second primary coil, a secondary member including a secondary coil, and The first primary coil applies a position detection excitation signal I * sin (θ) * sin (ωt) to the first excitation circuit, and the second primary coil applies a position detection excitation signal-I * cos (θ) * sin (ωt) A second excitation circuit, in which the primary side member or the secondary side member is mounted on a moving body and moves together with the moving body, the first primary side coil and the second primary side coil system are staggered by 1 / 4 pitches are arranged side by side, the first primary coil and the second primary coil and the secondary coil are arranged so as to face each other in parallel with a gap; and the electromagnetically induced position detector is provided with : A sampling circuit that outputs a sampling signal obtained by sampling a plurality of times of the peak value of the induced signal induced by the secondary-side coil; a control circuit that performs synchronous detection and addition on the sampling signal The synchronous detection signal Vp is calculated uniformly, and the detection position θ is obtained by controlling such that the synchronous detection signal Vp becomes 0, and the excitation amplitude sin (θ) and the excitation amplitude cos (θ) are calculated based on the detection position θ. And output to the first excitation circuit and the second excitation circuit; the first excitation circuit for gap detection applies a gap detection excitation signal I '* sin (ω't) to the first primary coil; the gap detection A second excitation circuit is used to apply a gap detection excitation signal I '* cos (ω't) to the second primary side coil; a gap detection circuit calculates the voltages of the plurality of sampling signals obtained in the sampling circuit. The average value Vave is obtained by subtracting the average value Vave from the voltage of each of the sampling signals, calculating the absolute value sum Vabs, and based on the standardization of the change in the absolute value sum Vabs caused by the detection position θ, which is prepared in advance The table of Vθ is used to calculate the Vgap after excluding the change caused by the detection position θ from the sum of the absolute values Vabs; and the gap correction circuit whose memory is used as the basis of the amplitude of each error component of the interpolation error The interpolation error and Vgap0 as the gap detection excitation signal at this time, and based on the Vgap, the Vgap0, and the reference interpolation error, a correction component amplitude of each of the error components corresponding to the gap is calculated, and based on the The correction component amplitude is used to calculate a correction amount, and the correction position is added to the above-mentioned detection position θ to obtain a corrected detection position θh; where: I is the magnitude of the current of the position detection excitation signal; ω is the position detection excitation The frequency of the signal; I 'represents the current of the excitation signal for gap detection; ω' represents the frequency of the excitation signal for gap detection; t represents time. The fourth aspect of the invention, an electromagnetically induced position detector, is characterized by having a primary member including a first primary coil and a second primary coil, a secondary member including a secondary coil, and The first primary coil applies a position detection excitation signal I * sin (θ) * sin (ωt) to the first excitation circuit, and the second primary coil applies a position detection excitation signal-I * cos (θ) * sin (ωt) A second excitation circuit, in which the primary side member or the secondary side member is mounted on a moving body and moves together with the moving body, the first primary side coil and the second primary side coil system are staggered by 1 / 4 pitches are arranged side by side, the first primary coil and the second primary coil and the secondary coil are arranged so as to face each other in parallel with a gap; and the electromagnetically induced position detector is provided with : A sampling circuit that outputs a sampling signal obtained by sampling a plurality of times of the peak value of the induced signal induced by the secondary-side coil; a control circuit that performs synchronous detection and addition on the sampling signal The synchronous detection signal Vp is calculated uniformly, and the detection position θ is obtained by controlling such that the synchronous detection signal Vp becomes 0, and the excitation amplitude sin (θ) and the excitation amplitude cos (θ) are calculated based on the detection position θ. And output to the first excitation circuit and the second excitation circuit; the first excitation circuit for gap detection applies a gap detection excitation signal I '* sin (ω't) to the first primary coil; the gap detection A second excitation circuit is used to apply a gap detection excitation signal I '* cos (ω't) to the second primary side coil; a gap detection circuit calculates the voltages of the plurality of sampling signals obtained in the sampling circuit. The average value Vave is subtracted from the voltage of each sampling signal, the average value Vave is calculated, and the absolute value sum Vabs is calculated, and the value of the detection position θ at a specific position is obtained from the absolute value sum Vabs, and the value is Vgap; and a gap correction circuit that stores the reference interpolation error as the amplitude of each error component of the interpolation error and Vgap0 as the excitation signal for gap detection at this time, and is based on the Vgap, the Vgap0, And the reference interpolation error, calculate the correction component amplitude of each of the error components corresponding to the gap, calculate a correction amount based on the correction component amplitude, and add the correction amount to the detection position θ to obtain a corrected detection position. θh; where: I represents the current of the position detection excitation signal; ω represents the frequency of the position detection excitation signal; I 'represents the current of the gap detection excitation signal; ω' represents the gap detection excitation signal Frequency; t is time. The fifth aspect of the invention, an electromagnetically induced position detector, is characterized by having a primary member including a first primary coil and a second primary coil, a secondary member including a secondary coil, and The first primary coil applies a position detection excitation signal I * sin (θ) * sin (ωt) to the first excitation circuit, and the second primary coil applies a position detection excitation signal-I * cos (θ) * sin (ωt) A second excitation circuit, in which the primary side member or the secondary side member is mounted on a moving body and moves together with the moving body, the first primary side coil and the second primary side coil system are staggered by 1 / 4 pitches are arranged side by side, the first primary coil and the second primary coil and the secondary coil are arranged so as to face each other in parallel with a gap; and the electromagnetically induced position detector is provided with : A sampling circuit that outputs a sampling signal obtained by sampling a plurality of times of the peak value of the induced signal induced by the secondary-side coil; a control circuit that performs synchronous detection and addition on the sampling signal The synchronous detection signal Vp is calculated uniformly, and the detection position θ is obtained by controlling such that the synchronous detection signal Vp becomes 0, and the excitation amplitude sin (θ) and the excitation amplitude cos (θ) are calculated based on the detection position θ. And output to the first excitation circuit and the second excitation circuit; the first excitation circuit for gap detection applies a gap detection excitation signal I '* sin (ω't) to the first primary coil; the gap detection A second excitation circuit is used to apply a gap detection excitation signal I '* cos (ω't) to the second primary side coil; a gap detection circuit calculates the voltages of the plurality of sampling signals obtained in the sampling circuit. The average value Vave, subtract the average value Vave from the voltage of each sampling signal, calculate the absolute value sum Vabs, and set the absolute value sum Vabs to Vgap; and the gap correction circuit, whose memory is The reference interpolation error of the amplitude of each error component of the interpolation error and Vgap0, which is the excitation signal for gap detection at this time, are calculated based on the Vgap, the Vgap0, and the reference interpolation error. According to the amplitude of the correction component of each of the above error components, a correction amount is calculated based on the amplitude of the correction component, and the correction position is added to the detection position θ to obtain a corrected detection position θh; where: I represents position detection Use the magnitude of the current of the excitation signal; ω represents the frequency of the excitation signal for position detection; I 'represents the magnitude of the current of the excitation signal for gap detection; ω' represents the frequency of the excitation signal for gap detection, ω '= ω / m, and Is a natural number above m = 4; t represents time. The electromagnetically induced position detector of the sixth invention that solves the above-mentioned problems is characterized in that in the electromagnetically induced position detector of the second invention, m is a natural number, and ω ′ is set to ω ′ = In the case of ω / m, the above-mentioned gap detection circuit is based on [Number 1] Calculate the above-mentioned Vθ; and calculate the above-mentioned Vgap according to Vgap = Vabs / Vθ; where abs represents an absolute value, respectively; PIT represents a pitch of the secondary-side coil. The electromagnetically induced position detector of the seventh invention for solving the above-mentioned problems is characterized in that: In the electromagnetically induced position detector of any one of the above-mentioned second to sixth inventions, if the variation of each of the above error components according to the gap is changed And one or more components that are changed are collectively set to δx, and one or more components that are not changed are collectively set to δy. The above gap correction circuit is based on Δx = δx0 * Vgap0 / Vgap and Δy = δy0. Get the correction component amplitudes Δx and Δy; and calculate the correction amounts Hx and Hy according to Hx = Δx * sin (2π * θ / PITx) and Hy = Δy * sin (2π * θ / PITy); respectively, where For: PITx represents the periodic pitch of the δx among the above-mentioned error components; PITy represents the periodic pitch of the δy among the above-mentioned error components. [Effects of the Invention] According to the electromagnetically induced position detector of the present invention, it is possible to accurately detect the interpolation error according to the gap variation, thereby accurately correcting the detection position.

The electromagnetically induced position detector of the present invention includes, in addition to the conventional electromagnetically induced position detection circuit, a sin excitation circuit for gap detection, a cos excitation circuit for gap detection, a gap detection circuit, and a gap correction circuit. Correction of accurate interpolation errors corresponding to gap variations. Hereinafter, the electromagnetically induced position detector of the present invention will be described using examples and drawings. [Embodiment 1] Fig. 1 is a block diagram illustrating an electromagnetically induced position detector of this embodiment. The electromagnetically induced position detector of this embodiment includes, in addition to the conventional electromagnetically induced position detector shown in FIG. 11, a sin excitation circuit 11 for gap detection, a cos excitation circuit 12 for gap detection, a gap detection circuit 13, And the gap correction circuit 14. The gap detection sin excitation circuit 11 applies "I '* sin (ω't)" to the first slider coil 103 as the gap detection excitation signal, and the gap detection cos excitation circuit 12 applies "the second slider coil 104" I '* cos (ω't) "is used as the gap detection excitation signal (where I': the magnitude of the current of the gap detection excitation signal, and ω ': the frequency of the gap detection excitation signal). The signal (induced signal) induced by the scale coil 105 by the applied gap detection excitation signal is as shown in the following formula (1). k * I '* sin (ω't) * cosX + k * I' * cos (ω't) * sinX = k * I '* sin (ω't + X)… (1) Also includes position The induced signal V of the detection excitation signal has the following expression (2). V = k * I * sin (θ-X) * sin (ωt) + k * I '* sin (ω't + X)… (2) In addition, the frequency ω ′ of the excitation signal for gap detection is eliminated by the filter circuit. The influence of 109 is lower than the frequency ω of the excitation signal for position detection. In particular, it is set to ω ′ = ω / m (m is an integer of 2 or more). With this, position detection can be performed without adding a circuit such as a filter circuit (this aspect will be described later). In the sampling circuit 19, the peak value of the induced signal V is sampled and output as a sampling signal to the control circuit 20 (for position detection) and the gap detection circuit 13 (for gap detection). That is, the self-sampling circuit 19 outputs the same sampling signal to the control circuit 20 and the gap detection circuit 13. This makes it possible to obtain data using the same sampling circuit as before without additional sampling circuits. As the sampling signal, a one-cycle portion of the excitation signal for gap detection is used. For example, if m = 2, the period of the gap detection excitation signal becomes twice the period of the position detection excitation signal, and at least four sampling signals are obtained and used as the gap detection excitation signal and the position detection excitation signal. In the gap detection circuit 13, a sampling signal obtained in the sampling circuit 19 is input, and k * I 'including gap information is extracted from the signal. The details will be described in the following processing flow, but as a basic operation, the absolute value of the sampling voltage is obtained, and the Vabs obtained by accumulating the 1-cycle part of the gap detection excitation signal is calculated and converted into consideration of the gap due to the gap. The changed data is output by Vgap. FIG. 2 is a graph showing an acquired image of a sampling signal. The induced signal V includes a signal (position-induced signal) “k * I * sin (θ-X) * sin (ωt)” which is induced by the scale 102 by the excitation signal for position detection (see FIG. 2). As shown by the dashed line, the position detection evoked signal is controlled to be approximately 0, so it is the same as the signal indicated by the solid line by the scale detection evoked signal (clearance detection evoked signal) (m = 2) The situation) is small enough to be ignored. Therefore, Vabs can be considered to be obtained by accumulating a period of one period by sampling the gap detection induced signal "k * I '* sin (ω't + X)" and acquiring the absolute value of the sampling voltage. Furthermore, if the position X changes, the phase of the gap detection induced signal "k * I '* sin (ω't + X)" changes, and therefore, the phase of the sampling also changes. Therefore, for example, when m = 2, as shown in FIG. 5, Vabs also changes according to the detection position. Therefore, a signal Vgap is obtained after excluding the influence of the change. The gap correction circuit 14 calculates a correction amount corresponding to the gap based on Vgap, adds the correction amount to the detection position θ, and outputs the correction position as a corrected detection position θh. However, as in the error component δc of FIG. 13, there are also components that do not change from the gap in the interpolation error. Therefore, the gap correction circuit 14 corrects the error component peculiar to the scale, and corrects the component corresponding to the gap for the component whose accuracy changes in accordance with the gap fluctuation. FIG. 3 is a block diagram showing a processing flow performed by the electromagnetically induced position detector of this embodiment. Hereinafter, based on Fig. 3, a case where m = 2 is taken as a main example, the processing performed by the electromagnetically induced position detector of this embodiment will be specifically described (in addition, the following steps S11 to 14 are the same processing as before) ). << Step S1 (Sampling) >> In the sampling circuit 19, as shown in the graph of FIG. 2, four sampling voltages are obtained. The obtained sampling voltages are V (i), V (i + 1), V (i + 2), and V (i + 3). << Step S2 (Sampling Average Calculation) >> In the gap detection circuit 13, the average value Vave (average voltage) of the sampling voltages obtained in the sampling circuit 19 is calculated using the following formula (3). Vave = (V (i) + V (i + 1) + V (i + 2) + V (i + 3)) / 4 (3) "Step S3 (Sampling Absolute Value Calculation)" in the gap detection circuit 13 In the following formula (4), the sampling average value Vave is subtracted from each sampling voltage, and the absolute value sum Vabs is calculated. In addition, abs in the following formula represents an absolute value. Vabs = abs (V (i) -Vave) + abs (V (i + 1) -Vave) + abs (V (i + 2) -Vave) + abs (V (i + 3) -Vave)… (4 ) In this way, by subtracting the sampling average value Vave from each sampling signal, it can be set as data in which the influence of the offset contained in the sampling signal is excluded, and accurate amplitude information Vabs of the excitation signal for gap detection can be obtained. However, as described above, the Vabs signal changes according to the detection position θ. Figure 4 shows the change in the intensity of the Vabs signal caused by the detection position θ when the amplitude of the sampling signal is set to 1 when the sample is set to 1 (4 samples) and m = 3 (6 samples). Graph. As long as the graph is observed, it can be seen that the intensity of the Vabs signal changes according to the detection position θ. "Step S4 (Vabs fluctuation calculation)" In parallel with the processing up to step S3 above, in the gap detection circuit 13, calculate the Vθ after normalizing the change in Vabs according to the detection position θ (the calculation of the detection position θ will be (Described in steps S11 and S12 below). In the case of m = 2, it becomes like the following formula (5). [Number 2] Among them, it is set to PIT: scale pitch (pitch of the scale coil 105). In the case of m = 3, it becomes like the following formula (6). [Number 3] That is, as long as m is a natural number, the following formula (7) holds. [Number 4] << Step S5 (Gap Calculation) >> Based on Vabs calculated in the above step S3 and Vθ calculated in the above step S4, the gap detection circuit 13 calculates after excluding the change caused by the detection position θ from the Vabs signal Vgap. Specifically, the following formula (8) is used. Vgap = Vabs / Vθ (8) Figure 5 is a graph showing the calculation result of Vgap when m = 2. As shown in FIG. 5, Vgap does not depend on the detection position θ and has a fixed value. "Step S6 (reference interpolation error, reference gap memory)" In parallel with the gap calculation up to step S5, the gap correction circuit 14 stores the (actual) interpolation error measured in another inspection device in advance. The amplitudes (reference interpolation errors) δa0, δb0, δc0, ... of the respective error components δa, δb, and δc and the excitation signals for gap detection (reference gap detection excitation signal Vgap0) at this time. "Step S7 (Gap Correction Amplitude Calculation)" Based on the Vgap calculated in the above step S5 and the δa0, δb0, δc0, ..., and Vgap0 memorized in the above step S6, the gap correction circuit 14 calculates a value corresponding to the gap Correct component amplitudes (amplitudes of error signals that take into account the effects of gaps) Δa, Δb, Δc. For example, in the gap detection excitation signal Vgap, the reference gap detection excitation signal Vgap0, and the reference interpolation errors δa0, δb0, and δc0, δa and δb are components that change in accuracy according to the gap variation, and δc is set to The component whose accuracy does not change due to the gap fluctuation, the correction component amplitudes Δa, Δb, and Δc of each interpolation error are as shown in the following formula (9). Δa = δa0 * Vgap0 / Vgap Δb = δb0 * Vgap0 / Vgap Δc = δc0… (9) "Step S8 (Gap correction amount calculation)" In the gap correction circuit 14, as shown in the following formula (10), it corresponds to the gap. The correction component amplitude is used to calculate correction amounts Ha, Hb, and Hc. In addition, in the following formula (10), only the error is a sin component as an example. Ha = Δa * sin (2π * θ / PITa) Hb = Δb * sin (2π * θ / PITb) Hc = Δc * sin (2π * θ / PITc)… (10) where PITa, PITb, and PITc are set to The periodic pitch of each error component of the interpolation error. For example, if PITa = 2 mm, it means the error component of the 2 mm period. << Step S9 (correction position calculation) >> In the gap correction circuit 14, the detection position θ calculated in the following step S12 is added to the correction amounts Ha, Hb, and Hc calculated in the above step S8, and the added correction amount is output. The subsequent detection position θh. Specifically, the following formula is used. θh = θ + Ha + Hb + Hc The following steps S11 to S14 are processing for position detection by the control circuit 20. << Step S11 (Sampling Synchronous Detection) >> As the position detection, the control circuit 20 performs synchronous detection on the sampling signals V (i), V (i + 1), V (i + 2), and V (i + 3). , And add and average them to calculate the synchronous detection signal Vp. When m = 2, the following formula is used. Vp = [V (i) -V (i + 1) + V (i + 2) -V (i + 3)] / 4 where i = 0, 2, 4, ... (even) (i is an even number The reason is that it is set to a negative value in the odd-numbered sampling.) In this way, the synchronous detection and addition of the four sampling signals in one cycle of the gap detection excitation signal are performed for averaging. The influence is eliminated, and only the excitation signal component for position detection can be extracted. The gap detection excitation signal is different in frequency and position detection excitation signal, so it can be eliminated by setting a new filter circuit. However, by the method described above, the position detection can be performed without adding a filter circuit. «Step S12 (detection position calculation)» The control circuit 20 changes the detection position θ so that the Vp signal becomes zero. As explained in the prior art, the detection position θ is equal to the relative position X of the scale and the slider, and θ is output as the detection position. << Step S13 (Sin excitation amplitude calculation) >> The control circuit 20 calculates the excitation amplitude I * sin (θ) (sin excitation amplitude calculation) based on θ, and outputs it to the sin excitation circuit 106 in FIG. 1. << Step S14 (cos excitation amplitude calculation) >> In the control circuit 20, the excitation amplitude I * cos (θ) (cos excitation amplitude calculation) is calculated based on θ, and is output to the cos excitation circuit 107 of FIG. 1. In this way, the electromagnetically induced position detector of this embodiment can accurately detect the interpolation error according to the gap variation, thereby accurately correcting the detection position. [Embodiment 2] The gap detection circuit 13 in FIG. 1 of the electromagnetically induced position detector of this embodiment is provided with a data table (Vθ table) of Vθ after normalizing the changes in Vabs according to the detection position θ. FIG. 6 is a block diagram showing a processing flow of the electromagnetically induced position detector of this embodiment. In this embodiment, step S4 (calculation of Vabs variation) in the first embodiment is changed as described below. The other configuration and processing are the same as those of the first embodiment, and therefore description thereof will be omitted. << Step S4a (Vabs change memory) >> The gap detection circuit 13 outputs a Vθ based on a detection position θ based on a Vθ table prepared in advance. In this way, in the electromagnetically induced position detector of this embodiment, not only the same data as the sampling signal for position detection can be used, but also gap detection can be performed without depending on the detection position θ. The calculation process of Vθ described in step S4 of the first embodiment. [Embodiment 3] The electromagnetically induced position detector of this embodiment is obtained by changing a part of the configuration and operation of the gap detection circuit 13 in Fig. 1. FIG. 7 is a block diagram showing a processing flow of the electromagnetically induced position detector of this embodiment. In this embodiment, step S4 (Vabs change calculation) in Embodiment 1 is omitted, and step S5 (gap calculation block) is changed as described below. The other configuration and processing are the same as those of the first embodiment, and therefore description thereof will be omitted. << Step S5a (gap selection) >> The gap detection circuit 13 obtains a Vabs signal when the detection position θ is a specific position (pitch), and sets it as Vgap. For example, if m = 2, as long as the Vabs data when the detection position θ is at 0, 0.25, 0.5, and 0.75 pitch positions is obtained, the data becomes the same intensity data, so that the gap variation can be accurately obtained (see Figure 4) . Here, although a position having a minimum value (minimum value) is selected, any position may be used as long as the specific position is a position having the same strength. This makes it possible to use the same data (sampling voltages V (i), V (i + 1), V (i + 2), and V (i + 3)) as the sampling data for position detection. Data, so that the circuit configuration becomes simple. [Embodiment 4] The electromagnetically induced position detector of this embodiment changes a part of the configuration and operation of the gap detection sin excitation circuit 11, the gap detection cos excitation circuit 12, and the gap detection circuit 13 in FIG. Successor. FIG. 8 is a block diagram showing a processing flow of the electromagnetically induced position detector of this embodiment. In this embodiment, step S4 (Vabs variation calculation) in Embodiment 1 is omitted. Furthermore, in the gap detection sin excitation circuit 11 and the gap detection cos excitation circuit 12, by increasing m in the frequency ω '= ω / m of the gap detection excitation signal, step S5 (gap calculation block) ) Make changes as described below. The other configuration and processing are the same as those of the first embodiment, and therefore description thereof will be omitted. "Step S5b (Vabs = Vgap)" By increasing m, the variation of the value of Vabs due to the detection position θ is reduced, and Vabs data is used as Vgap data. For example, in FIG. 4, if m = 2 (4 samples) and m = 3 (6 samples) are compared, the variation range of the signal strength of Vabs is smaller when m = 3. When m is further increased, the range of variation is further reduced. In this embodiment, the value of m is increased to the required variation range of the signal strength, and the Vabs signal is used as the Vgap signal. For example, in order to set the built-in error to 1 or less, it is necessary to set the variation of the value of Vabs to 14% or less. The variation of the value of Vabs is 40% when m = 2, 15% when m = 3, and 8% when m = 4. In this case, as long as m = 4, interpolation can be performed. The error is suppressed to 1 or less. This makes it possible to use the same data (sampling voltages V (i), V (i + 1), V (i + 2), and V (i + 3)) as the sampling data for position detection. Data, so that the circuit configuration becomes simple. The electromagnetically induced position detector of the present invention has been described using the embodiments above. Regarding the electromagnetically induced position detector of the present invention, the error component δa will be included in the interpolation error change caused by the gap variation in FIG. The results of the gap correction calculation with δb are shown in FIG. 9. It can be seen that the measured error component agrees well with the calculated correction component. [Industrial Applicability] The present invention is suitable as an electromagnetically induced position detector.

11‧‧‧Sin excitation circuit for gap detection (first excitation circuit for gap detection)
12‧‧‧Cos excitation circuit for gap detection (second excitation circuit for gap detection)
13‧‧‧Gap detection circuit
14‧‧‧Gap Correction Circuit
19‧‧‧Sampling circuit
20‧‧‧Control circuit
100‧‧‧Testing Department
101‧‧‧ slider (primary side member)
102‧‧‧ scale (secondary side member)
103‧‧‧The first slider coil (the first primary coil)
104‧‧‧Second slider coil (secondary coil)
105‧‧‧scale coil (secondary coil)
106‧‧‧sin excitation circuit (first excitation circuit)
107‧‧‧cos excitation circuit (second excitation circuit)
108‧‧‧amplified circuit
109‧‧‧Filter circuit
110‧‧‧Sampling circuit
111‧‧‧Control circuit
g‧‧‧ clearance
P‧‧‧ pitch
Steps S1 ~ S9‧‧‧‧
S11 ~ S14‧‧‧step
S4a‧‧‧step
S5a‧‧‧step
S5b‧‧‧Step θ‧‧‧ Detection position

FIG. 1 is a block diagram illustrating an electromagnetically induced position detector according to Embodiment 1 of the present invention. FIG. 2 is a graph showing an acquired image of a sampling signal. FIG. 3 is a block diagram showing a processing flow performed by the electromagnetically induced position detector according to the first embodiment of the present invention. Figure 4 shows the changes in the Vabs signal caused by the detection position θ when the amplitude of the sampling signal is set to 1 (4 samples) and m = 3 (6 samples). Graph. FIG. 5 is a graph showing the calculation result of Vgap when m = 2. FIG. 6 is a block diagram showing a processing flow of the electromagnetically induced position detector according to the second embodiment of the present invention. FIG. 7 is a block diagram showing a processing flow of the electromagnetically induced position detector according to the third embodiment of the present invention. Fig. 8 is a block diagram showing a processing flow of an electromagnetically induced position detector according to a fourth embodiment of the present invention. FIG. 9 is a graph showing a result obtained by performing a gap correction calculation on the error components δa and δb. FIG. 10 is a schematic diagram illustrating a detection principle of a conventional electromagnetically induced position detector. (a) is a perspective view showing a state in which a slider of a linear scale and a scale are arranged so as to face each other in parallel, (b) is a schematic diagram showing a slider and a scale side by side, and (c) is a representation Graph of electromagnetic coupling between slider and scale. FIG. 11 is a block diagram illustrating a conventional electromagnetically induced position detector. FIG. 12 is a graph illustrating the detection of the induced signal V. FIG. FIG. 13 is a graph illustrating a relationship between a gap and an interpolation error.

11‧‧‧Sin excitation circuit for gap detection (first excitation circuit for gap detection)

12‧‧‧Cos excitation circuit for gap detection (second excitation circuit for gap detection)

13‧‧‧Gap detection circuit

14‧‧‧Gap Correction Circuit

19‧‧‧Sampling circuit

20‧‧‧Control circuit

100‧‧‧Testing Department

101‧‧‧ slider (primary side member)

102‧‧‧ scale (secondary side member)

103‧‧‧The first slider coil (the first primary coil)

104‧‧‧Second slider coil (secondary coil)

105‧‧‧scale coil (secondary coil)

106‧‧‧sin excitation circuit (first excitation circuit)

107‧‧‧cos excitation circuit (second excitation circuit)

108‧‧‧amplified circuit

109‧‧‧Filter circuit

Claims (7)

An electromagnetically induced position detector, comprising: a primary side member including a primary coil; a secondary side member including a secondary coil; and an excitation circuit for applying an excitation signal to the primary coil. The member or the secondary-side member is mounted on a moving body and moves together with the moving body, and the primary-side coil and the secondary-side coil are arranged to face each other in parallel with a gap; and the electromagnetically induced position detection The device includes: a sampling circuit that samples the induced signal induced by the secondary coil and outputs a sampling signal; a control circuit that calculates a synchronous detection signal based on the sampling signal and obtains a detection position based on the synchronous detection signal; The excitation amplitude is calculated based on the detection position and output to the above-mentioned excitation circuit. The gap detection excitation circuit applies a gap detection excitation signal to the primary coil. The gap detection circuit obtains an average voltage of the sampling signals. Subtract this average voltage from the voltage of the sampled signal and calculate its absolute Sum of the values, further excluding the change caused by the detection position from the sum of the absolute values; and a gap correction circuit that calculates a correction corresponding to the sum of the absolute values excluding the change caused by the detection position The detection position is corrected by adding the correction amount to the detection position. An electromagnetically induced position detector, comprising: a primary member including a first primary coil and a second primary coil; a secondary member including a secondary coil; and applying a position to the first primary coil. The first excitation circuit for the detection excitation signal I * sin (θ) * sin (ωt) and the second detection coil for the position detection excitation signal-I * cos (θ) * sin (ωt) the second An excitation circuit, and the primary side member or the secondary side member is mounted on a moving body and moves together with the moving body, and the first primary side coil and the second primary side coil are arranged side by side with a shift of 1/4 pitch The first primary coil, the second primary coil, and the secondary coil are arranged so as to face each other in parallel with a gap; and the electromagnetically induced position detector includes: a sampling circuit whose output is A sampling signal obtained by performing multiple sampling on the peak value of the induced signal induced by the secondary coil; the control circuit calculates the synchronous detection signal Vp by performing synchronous detection on the sampling signal and adding and averaging the same. The detection position θ is obtained by controlling such that the synchronous detection signal Vp becomes 0, and the excitation amplitude sin (θ) and the excitation amplitude cos (θ) are calculated based on the detection position θ, and output to the first Excitation circuit and the second excitation circuit; a first excitation circuit for gap detection, which applies a gap detection excitation signal I '* sin (ω't) to the first primary side coil; a second excitation circuit for gap detection, which A gap detection excitation signal I '* cos (ω't) is applied to the second primary coil. The gap detection circuit calculates an average value Vave of the voltages of the plurality of sampling signals obtained in the sampling circuit. The average value Vave is subtracted from the voltage of the sampling signal, the absolute value sum Vabs is calculated, and the Vθ after normalizing the change of the absolute value sum Vabs caused by the detection position θ is calculated, and based on the Vθ, The calculation of Vgap after excluding the change caused by the above-mentioned detection position θ in the sum of absolute values Vabs; and the gap correction circuit which memorizes the reference interpolation error as the amplitude of each error component of the interpolation error, and as the current time Based on the Vgap0, the Vgap0, and the reference interpolation error, calculate a correction component amplitude of each error component corresponding to the gap, and calculate a correction amount based on the correction component amplitude. The detection position θ is added to the correction amount to obtain the corrected detection position θh; where: I represents the magnitude of the current of the position detection excitation signal; ω represents the frequency of the position detection excitation signal; I ′ represents the gap detection Use the magnitude of the excitation signal's current; ω 'represents the frequency of the gap detection excitation signal; t represents time. An electromagnetically induced position detector, comprising: a primary member including a first primary coil and a second primary coil; a secondary member including a secondary coil; and applying a position to the first primary coil. The first excitation circuit for the detection excitation signal I * sin (θ) * sin (ωt) and the second detection coil for the position detection excitation signal-I * cos (θ) * sin (ωt) the second An excitation circuit, and the primary side member or the secondary side member is mounted on a moving body and moves together with the moving body, and the first primary side coil and the second primary side coil are arranged side by side with a shift of 1/4 pitch The first primary coil, the second primary coil, and the secondary coil are arranged so as to face each other in parallel with a gap; and the electromagnetically induced position detector includes: a sampling circuit whose output is A sampling signal obtained by performing multiple sampling on the peak value of the induced signal induced by the secondary coil; the control circuit calculates the synchronous detection signal Vp by performing synchronous detection on the sampling signal and adding and averaging the same. The detection position θ is obtained by controlling such that the synchronous detection signal Vp becomes 0, and the excitation amplitude sin (θ) and the excitation amplitude cos (θ) are calculated based on the detection position θ, and output to the first Excitation circuit and the second excitation circuit; a first excitation circuit for gap detection, which applies a gap detection excitation signal I '* sin (ω't) to the first primary side coil; a second excitation circuit for gap detection, which A gap detection excitation signal I '* cos (ω't) is applied to the second primary coil. The gap detection circuit calculates an average value Vave of the voltages of the plurality of sampling signals obtained in the sampling circuit. The average value Vave is subtracted from the voltage of the sampling signal, and the absolute value sum Vabs is calculated. Based on the table of Vθ that is provided beforehand and normalizes the change of the absolute value sum Vabs caused by the detection position θ, The calculation of Vgap after excluding the change caused by the above-mentioned detection position θ in the sum of absolute values Vabs; and the gap correction circuit which memorizes the reference interpolation error as the amplitude of each error component of the interpolation error, and at this time Vgap0 of the gap detection excitation signal, and based on the Vgap, the Vgap0, and the reference interpolation error, calculate a correction component amplitude of each of the error components corresponding to the gap, and calculate a correction amount based on the correction component amplitude. The detection position θ is added to the correction amount to obtain the corrected detection position θh; where: I represents the magnitude of the current of the position detection excitation signal; ω represents the frequency of the position detection excitation signal; I ′ represents the gap detection Use the magnitude of the excitation signal's current; ω 'represents the frequency of the gap detection excitation signal; t represents time. An electromagnetically induced position detector, comprising: a primary member including a first primary coil and a second primary coil; a secondary member including a secondary coil; and applying a position to the first primary coil. The first excitation circuit for the detection excitation signal I * sin (θ) * sin (ωt) and the second detection coil for the position detection excitation signal-I * cos (θ) * sin (ωt) the second An excitation circuit, and the primary side member or the secondary side member is mounted on a moving body and moves together with the moving body, and the first primary side coil and the second primary side coil are arranged side by side with a shift of 1/4 pitch The first primary coil, the second primary coil, and the secondary coil are arranged so as to face each other in parallel with a gap; and the electromagnetically induced position detector includes: a sampling circuit whose output is A sampling signal obtained by performing multiple sampling on the peak value of the induced signal induced by the secondary coil; the control circuit calculates the synchronous detection signal Vp by performing synchronous detection on the sampling signal and adding and averaging the same. The detection position θ is obtained by controlling such that the synchronous detection signal Vp becomes 0, and the excitation amplitude sin (θ) and the excitation amplitude cos (θ) are calculated based on the detection position θ, and output to the first Excitation circuit and the second excitation circuit; a first excitation circuit for gap detection, which applies a gap detection excitation signal I '* sin (ω't) to the first primary side coil; a second excitation circuit for gap detection, which A gap detection excitation signal I '* cos (ω't) is applied to the second primary coil. The gap detection circuit calculates an average value Vave of the voltages of the plurality of sampling signals obtained in the sampling circuit. Subtract the average value Vave from the voltage of the sampling signal, calculate the sum Vabs of its absolute value, and obtain the value of the above-mentioned detection position θ at a specific position from the sum of absolute values Vabs, and set this value to Vgap; and the gap correction The circuit memorizes the reference interpolation error as the amplitude of each error component of the interpolation error, and Vgap0 as the excitation signal for gap detection at this time, and based on the above Vgap, the Vgap0, and the reference interpolation error, Calculate the correction component amplitude of each of the error components corresponding to the gap, calculate a correction amount based on the correction component amplitude, and add the correction amount to the detection position θ to obtain a corrected detection position θh; where: I represents the current of the position detection excitation signal; ω represents the frequency of the position detection excitation signal; I 'represents the magnitude of the current of the gap detection excitation signal; ω' represents the frequency of the gap detection excitation signal; t represents time. An electromagnetically induced position detector, comprising: a primary member including a first primary coil and a second primary coil; a secondary member including a secondary coil; and applying a position to the first primary coil. The first excitation circuit for the detection excitation signal I * sin (θ) * sin (ωt) and the second detection coil for the position detection excitation signal-I * cos (θ) * sin (ωt) the second An excitation circuit, and the primary side member or the secondary side member is mounted on a moving body and moves together with the moving body, and the first primary side coil and the second primary side coil are arranged side by side with a shift of 1/4 pitch The first primary coil, the second primary coil, and the secondary coil are arranged so as to face each other in parallel with a gap; and the electromagnetically induced position detector includes: a sampling circuit whose output is A sampling signal obtained by performing multiple sampling on the peak value of the induced signal induced by the secondary coil; the control circuit calculates the synchronous detection signal Vp by performing synchronous detection on the sampling signal and adding and averaging the same. The detection position θ is obtained by controlling such that the synchronous detection signal Vp becomes 0, and the excitation amplitude sin (θ) and the excitation amplitude cos (θ) are calculated based on the detection position θ, and output to the first Excitation circuit and the second excitation circuit; a first excitation circuit for gap detection, which applies a gap detection excitation signal I '* sin (ω't) to the first primary side coil; a second excitation circuit for gap detection, which A gap detection excitation signal I '* cos (ω't) is applied to the second primary coil. The gap detection circuit calculates an average value Vave of the voltages of the plurality of sampling signals obtained in the sampling circuit. The average value Vave is subtracted from the voltage of the sampling signal, and the absolute value sum Vabs is calculated, and the value of the absolute value sum Vabs is set to Vgap; and the gap correction circuit stores its memory as the error component of each interpolation error The reference interpolation error of the amplitude and Vgap0, which is the gap detection excitation signal at this time, and based on the Vgap, the Vgap0, and the reference interpolation error, a correction of each of the error components corresponding to the gap is calculated. Component amplitude, and calculate a correction amount based on the correction component amplitude, and add the correction amount to the detection position θ to obtain the corrected detection position θh; where: I represents the magnitude of the current of the position detection excitation signal; ω indicates the frequency of the excitation signal for position detection; I 'indicates the magnitude of the current of the excitation signal for gap detection; ω' indicates the frequency of the excitation signal for gap detection, ω '= ω / m, and m = a natural number greater than 4; t represents time. For example, the electromagnetically induced position detector of claim 2, wherein when m is a natural number and ω ′ is ω ′ = ω / m, the gap detection circuit is based on [Number 1] Calculate the above-mentioned Vθ; and calculate the above-mentioned Vgap according to Vgap = Vabs / Vθ; where: respectively, abs represents an absolute value; PIT represents a pitch of the secondary-side coil. The electromagnetically induced position detector according to any one of claims 2 to 6, wherein if one or more components that change according to the variation of the gap among the above error components are collectively set to δx, If one or more components are collectively set to δy, the gap correction circuit obtains the correction component amplitudes Δx and Δy respectively according to Δx = δx0 * Vgap0 / Vgap and Δy = δy0; 2π * θ / PITx), and Hy = Δy * sin (2π * θ / PITy), respectively, to obtain the above-mentioned correction amounts Hx and Hy; respectively, where: PITx represents each period section of the above-mentioned δx among the above-mentioned error components PITy represents the periodic pitch of the above-mentioned δy among the above-mentioned error components.