Correction value calculation method, correction value calculation program, correction value calculation device, and encoder

Abstract

2相正弦波状信号の内挿誤差のうち高次高調波について、簡易な方法で効率よく高精度に算出することができる補正値演算方法を提供する。【解決手段】補正値演算方法は、エンコーダが出力する2相正弦波状信号(X、Y)におけるk次の高調波成分を補正するための補正値を演算する。当該補正値演算方法は、2相正弦波状信号によって描かれるリサージュ波形におけるN個の位相角θiと各位相角θiに対応するリサージュ半径Riについて、各位相角θiに対応するリサージュ半径Riの2乗である二乗半径Ri2を算出する極座標演算ステップと、k次の高調波成分を含んだ2相正弦波状信号の二乗半径R2を表す近似式モデルにおける係数を求め、求めた係数から補正値を求める補正値演算ステップと、を備える。補正値演算ステップでは、近似式モデルの係数を最小二乗法により求め、得られた補正値を累積加算して補正値を求める。

Description

[Technical Field]

[0001] The present invention relates to a correction value calculation method for correcting a two-phase sinusoidal wave signal, a correction value calculation program, a correction value calculation device, and an encoder. [Background technology]

[0002] Conventional methods have been known for correcting errors such as offset errors, amplitude ratio errors, and phase difference errors in the two-phase sinusoidal signals output by encoders. For more accurate interpolation correction, in addition to correcting these errors, it is important to correct for the reduction of higher-order harmonics in the two-phase sinusoidal wave.

[0003] For example, Patent Document 1 discloses a method for correcting the second harmonic, which is a higher-order harmonic. When a two-phase sine wave contains the second harmonic, a correction value can be obtained by performing a Fourier analysis, utilizing the characteristic that the Lissajous radius changes with a period of λ / 3.

[0004] Here, electromagnetic induction encoders detect displacement by driving AC signals, so sampling takes longer compared to photoelectric encoders. Also, low-power encoders may have a reduced sampling rate. With such low-sampling-rate encoders, sampling may not be possible near the desired point (for example, the zero-crossing point or the point where y=x and y=-x intersect), which may result in insufficient error reduction.

[0005] Furthermore, when obtaining correction values ​​for higher-order harmonic correction using Fourier analysis as shown in Patent Document 1, there is a problem that Fourier analysis is difficult if the sampling data has an uneven pitch. Also, there is a problem that the detection error may become large if the number of samples is small. [Prior art documents] [Patent Documents]

[0006] [Patent Document 1] Japanese Patent Publication No. 2008-232649 [Overview of the project] [Problems that the invention aims to solve]

[0007] In light of these circumstances, in one aspect, the present invention aims to provide a correction value calculation method, a correction value calculation program, and a correction value calculation device that can calculate higher harmonics among the interpolation errors of a two-phase sinusoidal wave signal efficiently and with high accuracy using a simple method, as well as an encoder equipped with the correction value calculation device. [Means for solving the problem]

[0008] To solve the above problems, a correction value calculation method according to one aspect of the present invention calculates a correction value for correcting the k-th harmonic component in a two-phase sinusoidal signal (X, Y) output by an encoder. This correction value calculation method calculates the N phase angles θ in the Lissajous waveform drawn by the two-phase sinusoidal signal. i and each phase angle θ i Lissajous radius R corresponding to the Lissajous radius i Regarding each phase angle θ, i Lissajous radius R corresponding to the Lissajous radius i The square radius R is the square of the square of the radius. i 2 A polar coordinate calculation step to calculate the radius R of squares of a two-phase sinusoidal signal containing the k-th harmonic component. 2 The system includes a step of calculating a correction value by determining the coefficients in an approximate formula model that represents the formula, and then calculating a correction value from the determined coefficients. In the correction value calculation step, the coefficients of the approximate formula model are determined by the least squares method, and the resulting correction values ​​are accumulated and added together as correction residuals to obtain the correction value. [Brief explanation of the drawing]

[0009] [Figure 1] This is a block diagram showing the basic configuration of the correction value calculation device 1 according to the first embodiment, together with the encoder detection unit 11 and the wide-range phase angle calculation unit 50 in the encoder 10. [Figure 2]This is a flowchart showing the procedure for calculating the correction value in the first embodiment. [Figure 3] This is a block diagram of the correction value calculation device 1a according to the second embodiment. [Figure 4] This flowchart shows the procedure for calculating the correction value in the second embodiment. [Figure 5] This graph shows the uncorrected two-phase sinusoidal signal in the third embodiment. [Figure 6] This is a flowchart showing the procedure for calculating the correction value in the third embodiment. [Figure 7] This graph shows a two-phase sinusoidal signal with corrected offset, amplitude ratio, and phase difference in the third embodiment. [Figure 8] This graph shows a two-phase sinusoidal signal in the third embodiment, with the second and fifth harmonics further corrected. [Modes for carrying out the invention]

[0010] [First Embodiment] The first embodiment will be described below with reference to Figures 1 and 2.

[0011] The correction value calculation device 1 calculates a correction value for correcting the two-phase sinusoidal signal in the encoder. Figure 1 is a block diagram showing the basic configuration of the correction value calculation device 1 according to the first embodiment, together with the encoder detection unit 11 and the wide-range phase angle calculation unit 50 in the encoder 10.

[0012] As shown in Figure 1, the correction value calculation device 1 is implemented built into the encoder 10 together with the encoder detection unit 11 and the wide-range phase angle calculation unit 50. In this embodiment, the encoder 10 includes an encoder detection unit 11 that outputs a two-phase sinusoidal wave signal corresponding to the displacement along the measurement direction, a correction value calculation device 1, and a wide-range phase angle calculation unit 50 that calculates the wide-range phase angle φ (corresponding to, for example, the rotational displacement of a rotary encoder) which is the final output of the encoder 10 from the phase angle θ calculated by the correction value calculation device 1. The correction value calculation device 1 includes a correction unit 20, an error detection unit 40, and a polar coordinate transformation unit 30. The correction value calculation device 1 performs a correction value calculation process that calculates a correction value based on the two-phase sinusoidal wave signal output by the encoder detection unit 11, and a correction process that applies a pre-calculated correction value to the two-phase sinusoidal wave signal output by the encoder detection unit 11. In this implementation form built into the encoder 10, if the correction value calculation device 1 can calculate the correction value quickly enough, it can dynamically update the correction value while detecting the displacement.

[0013] Another implementation form of the correction value calculation device 1 is to implement it separately from the encoder 10. For example, the correction value calculation device 1 may be implemented by a computer separate from the encoder detection unit 11. When the encoder detection unit 11 is installed at the displacement measurement location, the correction value calculation device 1 may acquire the data of the two-phase sinusoidal wave signal acquired by the installed encoder detection unit 11 via a communication means or storage medium, and calculate a correction value based on the acquired data. The calculated correction value may then be provided to the encoder detection unit 11 via a communication means or storage medium.

[0014] The encoder detection unit 11 may be of, for example, a photoelectric type, a magnetic type, an electromagnetic induction type, etc., regardless of its detection principle. Using the two-phase sinusoidal wave signal output by the encoder detection unit 11 (for example, with X on the horizontal axis and Y on the vertical axis), a Lissajous waveform can be drawn. Ideally, such a Lissajous waveform should have a constant Lissajous radius R regardless of the phase angle θ. However, the two-phase sinusoidal wave signal output from the encoder detection unit 11 usually contains errors such as amplitude error, phase difference error, and offset, so the Lissajous radius R does not remain constant regardless of the phase angle θ.

[0015] The analog two-phase sinusoidal wave signal output by the encoder detection unit 11 is sampled and digitized at a predetermined frequency by an ADC (not shown). In this specification, the collection of data of this digitized two-phase sinusoidal wave signal is simply referred to as "two-phase sinusoidal wave signals X, Y". Also, for the digitized two-phase sinusoidal wave signals X, Y, in order to explicitly show the individually sampled data as needed, they are represented using a common subscript as "two-phase sinusoidal wave signal X i , Y i ". In this specification, when calculating the correction value, it is described as using N pairs of digital data of the two-phase sinusoidal wave signals X, Y. That is, in the data of the two-phase sinusoidal wave signals X i , Y i used for calculating the correction value, i is an integer in the range of 1 to N. Other parameters calculated from the "two-phase sinusoidal wave signals X i , Y i " are also expressed using subscripts as needed, such as the squared radius R i 2 , the phase angle θ i .

[0016] The two-phase sinusoidal wave signals X, Y are input to the correction unit 20. The correction unit 20 holds the correction value to be applied to the two-phase sinusoidal wave signal. This correction value is calculated by the error detection unit 40. The correction unit 20 corrects the two-phase sinusoidal wave signals X, Y using the correction value and outputs output signals X', Y'. The output signals X', Y' of the correction unit 20 are input to the polar coordinate conversion unit 30.

[0017] The correction method in the correction unit 20 will be explained below, using N (R 2 This section explains the "least squares sine wave approximation," which accurately determines the amplitude of the k-th harmonic contained in a two-phase sinusoidal signal using the least squares method, given by (k±1)θ). First, consider the radius of square R of a two-phase sinusoidal wave containing the k-th harmonic. 2 We derive the relationship between and the Lissajous angle θ.

[0018] An ideal two-phase sine wave x1, y1 and a higher-order harmonic x k , y k The two-phase sinusoidal waves X and Y, which include the , can be expressed by equations (1) and (2). Furthermore, if the radius R of an ideal two-phase sinusoidal wave is 1, then x1 and y1 can be expressed by equations (3) and (4), respectively.

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[0019] Here, the amplitude of the k-th harmonic is a. k The phase difference with the first (fundamental) wave is p k Let the phase difference between X and Y be -π / 2 radian (-90°) or +π / 2 radian (+90°). That is, the harmonic amplitudes and the phase differences between the first and higher harmonics are assumed to be equal for X and Y. Furthermore, if the phase difference between the first-order X and Y is +π / 2 radian (+90°), the phase difference in the higher harmonics is -π / 2 radian (-90°), and if the phase difference between the first-order X and Y is -π / 2 radian (-90°), the phase difference in the higher harmonics is +π / 2 radian (+90°). By introducing these assumptions, the four parameters of the higher harmonics can be reduced to two.

[0020] Under the above premise, if the two-phase sinusoidal signals X and Y contain only one harmonic of order k, then X is given by equations (5) and (6), and Y is given by equations (7) and (8).

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[0021] From now on, the square radius R 2 When we find the value, we get equation (9).

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[0022] In other words, the radius of square R of a two-phase sine wave containing the k-th harmonic. 2 It can be expressed as the sum of the cosine and sine of (k+1)θ or (k-1)θ. The amplitude of the cosine is 2a k coskp k Therefore, the amplitude of the sine is -2a k linep k That is the case.

[0023] For example, when the order of the higher harmonic is k=2 and the polarity is -90°, in equation (9) above, by setting k=2 and selecting the positive sign in the upper row, the radius of square R is obtained with cos3θ and sin3θ. 2 This expression can be used to represent the result, and correction calculations can be performed using this formula.

[0024] A ka and A kb If we define x as in equation (10), then x k (Equation (6)) and y k Equation (7) can be expressed as the sum of a cosine (coskθ) term, a sine (sinkθ) term, and a constant term, as shown in equations (11) and (12). When performing numerical calculations, the notation in equations (11) and (12) is easier to use than the notation in terms of amplitude and phase, as shown in the second line of equation (6). Therefore, we will use this notation method of summing cosines and sines from now on.

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[0025] Next, A ka and A kb (Equation (10)) is the square radius R of a two-phase sine wave containing the kth harmonic. 2By substituting into (Equation (9)), the radius of square R for a two-phase sine wave containing the kth harmonic is obtained. 2 The relationship between the Lissajous angle θ and the Lissajous angle is derived as shown in equation (13).

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[0026] Next, in equation (13), k ± 1st order cosine wave amplitude + 2A ka and sine wave amplitude -2A kb N pieces (R 2 The value is calculated using the least squares method from (k±1)θ). The specific calculation method is as follows.

[0027] First, the data of the two-phase sine wave at N points is X i ,Y i Let i be an integer from 1 to N, and R i 2 and θ i We will find R i 2 is X i and Y i Since it is the sum of the squares of θ, it can be easily calculated as shown in equation (14). Also, (k±1)θ i This can be calculated using equation (15).

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[0028] On the other hand, equation (16) is given by the radius of square R of a two-phase sinusoidal signal containing the k-th harmonic component. 2 R is an approximate model that represents this. i 2 and (k±1)θ i We construct a system of three linear equations with respect to matrix A. (k±1) The inverse matrix A (k±1) -1 and B (k±1) By multiplying each matrix, we obtain C as shown in equation (17). (k±1) A, which is a coefficient in the above approximation model, is used as an element of the matrix. c(k±1) , A s(k±1) , R o(k±1) We can find the three variables.

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[0029] Also, A c(k±1) , A s(k±1) By substituting this into equation (18), the correction value A ka and A kb It is possible to find this.

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[0030] Thus, the amplitude A of cos(k±1)θ in model equation (16) can be obtained by the least squares method. c(k±1) and the amplitude A of sin(k±1)θ s(k±1) By calculating this, the cosine wave amplitude A ka and sinusoidal amplitude A kb The following is obtained. Furthermore, the data X of the two-phase sine wave is obtained by equations (19) and (20). i , Y i The k-th harmonic component x ki , y ki These harmonic components are obtained, and the data X of the two-phase sine wave is obtained. i , Y i By subtracting these values ​​from each other, we can obtain ideal sinusoidal signals x1 and y1 from which the k-th harmonic component has been removed.

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[0031] The k-th harmonic component x obtained in this way ki , y ki θ included i It is preferable to obtain this from x1, y1 that do not contain higher harmonics, but as an alternative, use the data of a two-phase sinusoidal wave X that does contain higher harmonics. i ,Y i The method for obtaining it from was explained. Therefore, in this method, x ki , y kiThere is an error included. By using the cumulative algorithm, this error can be reduced. Next, the cumulative algorithm for k-th harmonic correction will be described.

[0032] The correction value A of the k-th harmonic obtained from the above-mentioned least squares method sine wave approximation ka and A kb Regarding, as shown in Equation (21), A ka is replaced with the correction residual ΔA ka to, and A kb is replaced with the correction residual ΔA kb to, and the corrected values A ka and A kb obtained by cumulative addition are calculated respectively as shown in Equation (22). Here, in Equation (22), the correction residuals ΔA ka and the correction residual ΔA kb are multiplied by the feedback gain G f (where 0 < G f ≤ 1) and used to update each correction value. When updating the correction value, if the feedback gain G f is set to G f < 1, it is possible to prevent the influence of the correction residual from being overly reflected in the correction value and make it easier for the correction residual to converge to a value with a small error.

Equation

[0033] Then, using Equations (19) and (20), the k-th harmonics x ka and A kb are obtained from the correction values A ki , y ki .

[0034] Furthermore, as shown in Equation (23), taking m as the number of times of cumulative calculation, the k-th harmonics x i (m) and Y i (m) which are the signals of the m-th feedback loop of cumulative addition are subtracted from the k-th harmonics x ki and y <00001​​​​​ka and A kb This method can reduce the approximation error. Using this correction method, a correction value can be obtained for the case where there is no offset error, amplitude ratio error, or phase difference error, and only the k-th harmonic error is present, thereby correcting the k-th harmonic error.

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[0035] Next, the correction value calculation process, which calculates the correction value using the correction value calculation device 1, will be described. Figure 2 is a flowchart showing the procedure for the correction value calculation process in the first embodiment. The correction value calculation process is performed by the correction unit 20, the polar coordinate transformation unit 30, and the error detection unit 40. In the correction value calculation process, the correction value A of the kth harmonic is calculated from the two-phase sinusoidal signals X and Y. ka and A kb We seek.

[0036] When the correction value calculation process starts, the correction unit 20 first uses the output data of the encoder detection unit 11 used for correction, which is a pair of N points of digital data of the two-phase sinusoidal wave signals X and Y (X i , Y i ; where i is 1 to N) is obtained (step S01). This data may be obtained in real time from the encoder detection unit 11, or the data may be obtained in advance from the encoder detection unit 11 and recorded, and then obtained via communication means or storage medium. Subsequently, the polar coordinate transformation unit 30 obtains the phase angle θ for each of the N data pairs of the two-phase sinusoidal signal. i and the corresponding square radius R i 2 Calculate (Step S02; polar coordinate calculation step).

[0037] Next, the error detection unit 40 analyzes each phase angle θ calculated in step S01. i and the square radius R i 2 Based on this, the amplitude A is obtained by the least squares sine wave approximation. c(k±1) ,A s(k±1) We calculate the corrected residual ΔAka and ΔA kb Calculate (Step S03; least squares sine wave approximation step).

[0038] Then, the corrected residual ΔA was calculated. ka and ΔA kb The values ​​are cumulatively added using equation (20), and the correction value A for the k-th harmonic is obtained. ka ,A kb Update (Step S04; Harmonic Correction Value Calculation Step).

[0039] Next, the correction unit 20 processes the correction value A calculated by the error detection unit 40. ka and A kb Based on this, the two-phase sinusoidal signal is corrected, and the data X of the corrected two-phase sinusoidal signal is obtained. i , Y i Output (Step S05; Correction step).

[0040] If the calculation of the correction value is to be repeated (Step S06; Yes), the process returns to Step S02. Steps S02 to S05 are repeated as many times as necessary, and when repetition is no longer needed (Step S06; No), the correction value calculation process ends. The correction value at the end of the correction value calculation process becomes the final correction value. The number of times the calculation and updating of the correction value is repeated may be a predetermined number of times. Alternatively, it may be repeated until the correction residual becomes sufficiently small (for example, until it falls below a predetermined threshold).

[0041] According to the correction value calculation device 1 and correction value calculation process of the first embodiment described above, arbitrary k-th harmonic correction is possible, and correction can be performed even if the data has an uneven pitch without using a master encoder. For this reason, high-precision correction can be performed even with a small number of data points without requiring a high-precision feed mechanism or control. Furthermore, even if it is desired to increase the number of data points and improve accuracy, the radius of square R 2The calculation for this is the sum of the squares of two-phase sine waves, so it can be easily calculated. Therefore, the higher-order harmonics of the interpolation error of a two-phase sinusoidal signal can be calculated efficiently and accurately using a simple method, reducing computational resources and speeding up the calculation.

[0042] [Second Embodiment] Next, a second embodiment of the present invention will be described. This second embodiment performs the correction value calculation process at high speed with less computational effort than the first embodiment. Figure 3 is a block diagram of the correction value calculation device 1a according to the second embodiment. As shown in Figure 3, the configuration of the correction value calculation device 1a is substantially the same as that of the first embodiment, but it differs from the first embodiment in that the error detection unit 40a also uses two-phase sinusoidal waves X' and Y' to calculate the correction value. However, since the other configurations are the same, the following will mainly describe the calculations in the correction value calculation process of the second embodiment.

[0043] In the first embodiment described above, the correction value A ka and A kb To obtain this, trigonometric calculations are required. In contrast, in the second embodiment, the calculation can be simplified by replacing the trigonometric functions with polynomials of two-phase sinusoidal signals X and Y. Below, the calculation method will be explained using the case where the harmonic to be removed is the second harmonic (k=2, polarity -90°) as an example. First, the two-phase sinusoidal signal X containing the second harmonic component is expressed by equation (24), and the second harmonic component x2 is expressed by equation (25). Also, the two-phase sinusoidal signal Y containing the second harmonic component is expressed by equation (26), and the second harmonic component y2 is expressed by equation (27).

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[0044] Next, the data X of N pairs of two-phase sine waves i=1,2,...,N i ,Y i Normalized to one neighborhood (in other words, ΣR i 2 Data X' of a two-phase sine wave (where / N ≈ 1) i ,Y' iWe will find the following. The normalization method is arbitrary, but for example, an amplitude normalization coefficient K such that R=1 when the relative position of the encoder scale and the reading head is the design reference position. x The amplitude normalization coefficient K is determined in advance, and then calculated using equations (28) and (29). x Data X i ,Y i Apply to data X' i ,Y' i It is advisable to normalize it by obtaining the square radius R, or by other methods. i 2 If the average can be considered to be 1, the two-phase sine wave data X can be processed without normalization. i ,Y i X' i ,Y' i It may be used as such.

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[0045] Then, the normalized two-phase sine wave data X' i ,Y' i For R, equations (30) and (31) respectively apply. i 2 and θ i We seek.

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[0046] Then, the least squares sine wave approximation using equation (32) as the model equation is applied to the data (R i 2 ,3θ i ), to apply this to i=1,2,...,N, solve the system of equations shown in the matrix operation of equation (33) to obtain matrix C3, A c3 ,A s3 We obtain the following. At this time, as shown in equations (34) and (35), we apply the triple angle formula for trigonometric functions and further cosθ i , sinθ i X' i , Y' i By approximating it to X', the trigonometric functions contained in each element of the matrix are expressed as X'i and Y' i It can be replaced with a polynomial. This simplifies the calculation. Note that, as shown in equations (34) and (35), cos3θ i An approximation of this is CS3 i , sin3θ i An approximation of this is SN3 i This will be abbreviated as follows:

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[0047] Subsequently, in substantially the same manner as when k=2 in equations (19) to (23) in the first embodiment, X after m cumulative calculations of second harmonic correction is obtained by equations (36) to (42). i '(m+1) and Y i '(m+1) can be obtained. That is, the corrected residual ΔA can be obtained by equation (36). 2a and ΔA 2b The corrected residual ΔA is calculated using equation (37). 2a and ΔA 2b Correction value A using 2a and A 2b Update.

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[0048] And, correction value A 2a and A 2b Using equations (38) and (39), the second harmonic x 2i , y 2i We will find x. 2i , y 2i In the calculation, as shown in equations (40) and (41), the double-angle formula for trigonometric functions is used to obtain cos2θ i and sin2θ i The term X i 'and Y i By approximating by replacing it with a polynomial of ', the calculation can be simplified. Note that, as shown in equations (40) and (41), cos2θ i An approximation of this is CS2i , sin2θ i An approximation of this is SN2 i This will be abbreviated as follows:

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[0049] Furthermore, as shown in equation (42), the mth signal of the cumulative sum feedback loop is X i (m) and Y i (m) to the second harmonic x 2i and y 2i Subtracting this, the (m+1)th signal X i (m+1) and Y i The signal at (m+1) is obtained. By repeating this the desired number of times, the correction value A is obtained. 2a and A 2b This can reduce the approximation error.

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[0050] Next, the correction value calculation process, which calculates the correction value using the correction value calculation device 1a, will be described. Figure 4 is a flowchart showing the procedure for the correction value calculation process in the second embodiment. The correction value calculation process is performed by the correction unit 20, the polar coordinate transformation unit 30, and the error detection unit 40a.

[0051] When the correction value calculation process starts, the correction unit 20 first uses the output data of the encoder detection unit 11 used for correction, which is a pair of N points of digital data of the two-phase sinusoidal wave signals X and Y (X i , Y i ; where i is 1 to N) is obtained (step S11). This data may be obtained in real time from the encoder detection unit 11, or the data may be obtained in advance from the encoder detection unit 11 and recorded, and then obtained via communication means or storage medium. Next, the correction unit 20 calculates ΣR i 2 X satisfies the relationship / N ≈ 1 i and Y i to X'i and Y' i Convert to (step S12). This results in R 2 The amplitude of the two-phase sinusoidal signal is adjusted to satisfy the condition = 1. After the conversion by the correction unit 20, the polar coordinate conversion unit 30 performs X' i and Y' i For each of the N data pairs of the two-phase sinusoidal signal, the phase angle θ i and the corresponding square radius R i 2 Calculate (Step S13).

[0052] Next, the error detection unit 40a detects the two-phase sinusoidal signal X' i , Y' i and the square radius R i 2 Based on this, the cosine wave amplitude A is obtained by the least squares sine wave approximation using equations (33) to (35). c3 and sinusoidal amplitude A s3 The corrected residual ΔA is calculated using equations (36) and (37). 2a and ΔA 2b Calculate (Step S14).

[0053] Then, the corrected residual ΔA was calculated. 2a and ΔA 2b The cumulative sum is calculated, and the correction value A 2a and A 2b Update (Step S15).

[0054] Next, the correction unit 20 adjusts the correction value A of the second harmonic calculated by the error detection unit 40a. 2a and A 2b Based on x 2i and y 2i We find x from the two-phase sinusoidal signal. 2i and y 2i Subtracting this results in a two-phase sinusoidal signal X' i , Y' i Correct the value (step S16).

[0055] If the calculation of the correction value is to be repeated (Step S17; Yes), the process returns to Step S13. Steps S13 to S16 are repeated as many times as necessary, and when repetition is no longer needed (Step S17; No), the correction value calculation process ends. The correction value at the end of the correction value calculation process becomes the final correction value. The number of times the calculation and updating of the correction value is repeated may be a predetermined number of times. Alternatively, it may be repeated until the correction residual becomes sufficiently small (for example, until it falls below a predetermined threshold).

[0056] Furthermore, in the second embodiment described above, the trigonometric function that appears in the calculation of the correction value for the second harmonic is X i and Y i The calculation was simplified by replacing it with a polynomial, and the calculation can be similarly simplified when correcting harmonics other than the second order. That is, when the order of the harmonic to be corrected is k, the trigonometric function (i.e., cos(k+1)θ) appearing in equations (17), (19), and (20) in the first embodiment can be used. i , sin(k+1)θ i coskθ i sinkθ i ) can be expressed using the known formulas for k-th and k+1-th angle trigonometric functions as cosθ i and sinθ i Expressed as, and further cosθ i and sinθ i X i and Y i By approximating with X, i 'and Y i The operation can be simplified by replacing it with a polynomial of '. Unless there are other constraints such as computational resources or computation time, there is no upper limit due to the degree of k. Also, y k x k In the case of opposite polarity (when the phase shift is in the opposite direction), R 2 The variation is of order (k-1). In this case, it can be corrected for any integer k≧4 in the same way as in the case of positive polarity.

[0057] In other words, equation (17) can be simplified as shown in equations (43) to (45).

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[0058] Furthermore, equations (19) and (20) can be simplified as shown in equations (46) to (49).

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[0059] Table 1 shows the polynomials in X' and Y' that can substitute coskθ and sinkθ (k=1~6), along with their simplified notations. [Table 1]

[0060] Thus, according to this embodiment, correction values ​​can be obtained by simplified calculations that do not involve trigonometric functions. Since simplified calculations that do not involve trigonometric functions reduce calculation time and computing resources, they can be implemented in low-cost, small, and low-power embedded devices. Furthermore, similar to the first embodiment, the higher harmonics of the interpolation error of a two-phase sinusoidal signal can be calculated efficiently and with high accuracy using a simple method.

[0061] [Third Embodiment] Next, a third embodiment of the present invention will be described with reference to Figures 5 to 8.

[0062] In the first and second embodiments described above, for the sake of clarity, the case of correcting only higher harmonics in a two-phase sinusoidal signal that does not include errors in offset, amplitude ratio, and phase difference was described. In this embodiment, a correction method for a two-phase sinusoidal signal that includes errors in offset, amplitude ratio, and phase difference in addition to higher harmonics will be described. In this embodiment, the effect of the correction will be explained using actual measurement data obtained from an electromagnetic induction encoder. Furthermore, since the configuration of the correction value calculation device 1a is the same as in the second embodiment, the calculation in the correction value calculation process of the third embodiment will be described below.

[0063] Figure 5 is a graph showing the errors contained in the uncorrected two-phase sinusoidal signal in the third embodiment. Figure 5(A) displays the horizontal axis as position, and Figure 5(B) displays the waveform from Figure 5(A) after a Fourier transform, with the horizontal axis as frequency (spatial frequency). As shown in Figure 5(B), the two-phase sinusoidal signal used in the third embodiment includes offset errors (indicated as DC in the figure) and amplitude ratio and phase difference errors (indicated as AM / PM in the figure). Furthermore, the two-phase sinusoidal signal contains more second (k+1=3) and fifth (k+1=6) harmonics compared to other orders. Thus, encoders may contain harmonic components of specific orders as errors depending on their detection method and operating environment. In this embodiment, correction is performed to remove the second and fifth harmonics, which are present in large quantities as other orders. In addition to harmonic correction, offset errors, amplitude ratio errors, and phase difference errors are also corrected.

[0064] Figure 6 is a flowchart showing the procedure for calculating the correction value in the third embodiment. The correction value calculation process is performed by the correction unit 20, the polar coordinate transformation unit 30, and the error detection unit 40a.

[0065] When the correction value calculation process starts, the correction unit 20 first uses the output data of the encoder detection unit 11 used for correction, which is a pair of N points of digital data of the two-phase sinusoidal wave signals X and Y (X i , Y i; where i is 1 to N) is obtained (step S21). This data may be obtained in real time from the encoder detection unit 11, or the data may be obtained in advance from the encoder detection unit 11 and recorded, and then obtained via communication means or storage medium. Next, the correction unit 20 obtains the radius squared R i 2 The mean of is 1 (that is, ΣR i 2 The amplitude normalization coefficient K is calculated using equations (28) and (29) such that / N ≈ 1. x Calculate and apply X i and Y i to X' i and Y' i Convert to (step S22). This results in R 2 The amplitude of the two-phase sinusoidal signal is roughly adjusted to satisfy the condition = 1. Subsequently, the polar coordinate transformation unit 30 performs X' i and Y' i For each of the N data pairs of the two-phase sinusoidal signal, the phase angle θ i and the corresponding square radius R i 2 Calculate (Step S23).

[0066] Next, R 2 To satisfy the condition = 1 with higher precision, the amplitude normalization coefficient K x Error (corrected residual) ΔK x Calculate the existing amplitude normalization coefficient K x The cumulative amount is added (step S24).

[0067] Next, correction values ​​for the offset, amplitude ratio, and phase difference errors are determined by any method (step S25). For example, the error detection unit 40a may determine the correction residual for each of the offset, amplitude ratio, and phase difference errors by the method described in Japanese Patent Application No. 2023-109451, which was not published at the time of filing this application, and update the correction values ​​based on said correction residual.

[0068] Next, the error detection unit 40a calculates the correction value for the second harmonic using the least squares sinusoidal approximation method R 2The cosine wave amplitude A in the model equation expressed using trigonometric functions of 3θ c3 and sinusoidal amplitude A s3 We calculate the corrected residual ΔA 2a and ΔA 2b We calculate the corrected residual ΔA. 2a and ΔA 2b The cumulative summation is used to obtain the second harmonic correction value A. 2a and A 2b We find this (step S26).

[0069] Next, the error detection unit 40a calculates the correction value for the 5th harmonic using the least squares sinusoidal approximation method R 2 The cosine wave amplitude A in the model equation expressed using trigonometric functions of 6θ c6 and sinusoidal amplitude A s6 We calculate the corrected residual ΔA 5a and ΔA 5b We calculate the corrected residual ΔA. 5a and ΔA 5b The cumulative summation is used to obtain the correction value for the 5th harmonic, A. 5a and A 5b We find this (step S27).

[0070] Next, the correction unit 20 applies the correction values ​​obtained in each step to the two-phase sinusoidal signal and performs the correction (step S28). That is, the correction unit 20 corrects the error ΔK of the amplitude normalization coefficient obtained in step S23. x Based on this, the amplitude normalization coefficient K x The correction unit 20 corrects the offset, amplitude ratio, and phase difference based on the correction values ​​of the offset, amplitude ratio, and phase difference obtained in step S24. The correction unit 20 also corrects the second harmonic correction value A calculated in step S25. 2a and A 2b Based on this, the second harmonic x 2i and y 2i The second harmonic correction is performed by calculating this value and subtracting it from the two-phase sinusoidal signal. In addition, the fifth harmonic correction value A calculated in the two-phase sinusoidal signal step S26 is also calculated. 5a and A 5b Based on this, the 5th harmonic x 5i and y 5iThe fifth harmonic correction is performed by calculating and subtracting this from the two-phase sinusoidal signal. Then, the correction unit 20 calculates the data X' of the two-phase sinusoidal signal that reflects these corrections. i , Y' i Outputs.

[0071] If the calculation and updating of the correction value is to be repeated (step S29; Yes), the process returns to step S22. Steps S23 to S28 are repeated as many times as necessary, and when repetition is no longer needed (step S29; No), the correction value calculation process ends. The correction value at the end of the correction value calculation process becomes the final correction value. The number of times the calculation and updating of the correction value is repeated may be a predetermined number of times. Alternatively, it may be repeated until the correction residual becomes sufficiently small (for example, until it falls below a predetermined threshold).

[0072] Next, the effect of the correction method of this embodiment will be shown. As shown in Figure 5(B), the frequency components of the error contained in the two-phase sinusoidal wave signal before correction included errors in the offset (DC in the figure), amplitude ratio, and phase difference (AP / PM in the figure), as well as second and fifth harmonics. In contrast, when the correction values ​​for the offset, amplitude ratio, and phase difference calculated in step S23 are applied to the two-phase sinusoidal wave signal, the remaining error becomes the waveform shown in Figure 7(A) and the frequency spectrum shown in Figure 7(B), and the error components of the offset, amplitude ratio, and phase difference are sufficiently reduced to the point where they are buried in the noise floor.

[0073] Furthermore, when the correction values ​​for the second harmonic calculated in step S24 and the correction values ​​for the fifth harmonic calculated in step S25 are applied to the two-phase sinusoidal signal, the frequency components of the remaining error are the waveform shown in Figure 8(A) and the frequency spectrum shown in Figure 8(B), and the components of the second and fifth harmonics are sufficiently reduced to the point where they are buried in the noise floor.

[0074] As can be seen from Figures 5, 7, and 8, the method of this embodiment allows for a significant reduction in each error by performing correction of second and fifth harmonics in addition to offset correction, amplitude ratio error correction, and phase difference error correction. Therefore, it can be seen that the correction method of the present invention functions effectively in actual encoders.

[0075] In the third embodiment, in calculating the correction values ​​for the second and fifth harmonics, a method was used to simplify the calculation by approximating the trigonometric functions described in the second embodiment with polynomials in X' and Y'. From the error reduction effect described above, it can be seen that even with the simplified calculation method described in the second embodiment, correction with sufficient accuracy can be achieved.

[0076] [Variations of the Embodiment] Although this embodiment has been described above, the present invention is not limited to this example. For example, in the first to third embodiments described above, an electromagnetic induction encoder was used as an example, but the present invention is not limited to an electromagnetic induction encoder and may be applied to interpolation correction of encoders of other detection methods (optical, magnetic, etc.) having a two-phase sinusoidal wave. Furthermore, the encoder to which the present invention is applied may be a rotary encoder or a linear encoder. For example, in the case of a linear encoder, if there is a factor that fluctuates periodically in the guide mechanism, applying the correction value calculation process of this embodiment makes it possible to calculate the correction value after reducing the periodic fluctuation.

[0077] Furthermore, in each of the above embodiments, the wide-area phase angle calculation unit 50 sets φ to the rotational number n of the Lissajous signal. i Although the example given was the case where φ is determined from the phase angle θ, φ may be determined by other methods. For example, in an absolute encoder, φ may be obtained by absolute detection.

[0078] In the third embodiment described above, equipitch data was used to verify the correction effect, but when calculating using the least squares sinusoidal approximation method, it can also be performed with unequal pitch data, and the same approximation accuracy as that of equipitch data can be obtained. In the case of unequal pitch data, a position reference is not required, so autonomous self-calibration is possible. Furthermore, corrections were performed in the order of offset error, amplitude ratio error, phase difference error, second harmonic error, and fifth harmonic error, but the items and their order are not limited to those described above and are arbitrary.

[0079] Furthermore, in the first to third embodiments described above, no correction was performed for harmonics of other orders, such as the third, fourth, and sixth harmonics. However, it is also possible to select and correct harmonics of any order (orders that tend to be frequently present in two-phase sinusoidal signals depending on the encoder's characteristics and operating environment).

[0080] In the third embodiment described above, the amplitude normalization process to 1 using the amplitude normalization coefficient Kx was divided into two stages. However, depending on the correction item, the correction error target, or the amplitude of the signal before normalization, both or either of the two stages of amplitude normalization may be omitted.

[0081] Furthermore, any modifications made by those skilled in the art to the aforementioned embodiments, including additions, deletions, or design changes to components, or combinations of features from each embodiment, are also included within the scope of the present invention, as long as they retain the essence of the present invention.

[0082] The following additional information is disclosed regarding the embodiments described above.

[0083] (Note 1) A method for calculating a correction value to correct the k-th harmonic component in a two-phase sinusoidal signal (X, Y) output by an encoder, N phase angles θ in the Lissajous waveform drawn by the aforementioned two-phase sinusoidal signal i and each phase angle θ i Lissajous radius R corresponding to the Lissajous radius i Regarding each phase angle θ, i The corresponding Lissajous radius R i The square radius R is the square of the square of the radius.i 2 A polar coordinate calculation step to calculate, Each phase angle θ calculated by the aforementioned polar coordinate calculation step i and the phase angle θ i The square radius R corresponding to i 2 Based on this, the radius of square R of a two-phase sinusoidal signal containing the k-th harmonic component. 2 The process includes a step of calculating a correction value by determining the coefficients in an approximate formula model representing the formula, and then calculating the correction value from the determined coefficients, The correction value calculation step involves determining the coefficients of the approximation model by the least squares method, and then accumulating and adding the resulting correction values ​​as correction residuals to obtain the correction value. A method for calculating a correction value characterized by the following features.

[0084] (Note 2) In the correction value calculation step, Each phase angle θ calculated by the aforementioned polar coordinate calculation step i and the phase angle θ i The square radius R corresponding to i 2 Based on this, when the k-th harmonic component contained in a two-phase sinusoidal signal (X, Y) is expressed by equations (11) and (12), the cosine wave amplitude A ka Corrected residual ΔA ka and sinusoidal amplitude A kba Corrected residual ΔA kb The cosine wave amplitude A is calculated based on each corrected residual. ka and sinusoidal amplitude A kba Calculate,

number

number

number

[0085] (Note 3) The correction value calculation step is: Coefficient A in equation (16) c(k±1) and A s(k±1) According to equation (17), C (k±1) To obtain as elements of a matrix

number

[0086] (Note 4) The correction value calculation step is: Coefficient A in equation (16) c(k±1) and A s(k±1) From equation (43) to equation (45), C (k±1) To obtain as elements of a matrix

number

[0087] (Note 5) The correction step further comprises correcting the two-phase sinusoidal wave signal based on the correction value, In the correction step, the k-th harmonic x ki and y ki We can find this using equations (46) to (49).

number

[0088] (Note 6) The correction step includes correcting the two-phase sinusoidal wave signal based on the correction value, The correction value calculation method according to any one of the appendices 1 to 5, characterized in that the correction value calculation step is applied again to the two-phase sinusoidal signal corrected by the correction step to update the correction value.

[0089] (Note 7) Each correction value is updated using formula (22).

number

[0090] (Note 8) A program that causes a computer to execute the correction value calculation method described in Note 1.

[0091] (Note 9) A correction value calculation device that calculates a correction value for correcting the two-phase sinusoidal wave signal (X, Y) output by an encoder, N phase angles θ in the Lissajous waveform drawn by the aforementioned two-phase sinusoidal signal i and each phase angle θ i Lissajous radius R corresponding to the Lissajous radius i Regarding each phase angle θ, i The corresponding Lissajous radius R i The square radius R is the square of the square of the radius. i 2 A polar coordinate transformation unit that calculates, Each phase angle θ calculated by the polar coordinate transformation unit i and the phase angle θ i The square radius R corresponding to i 2Based on this, the radius of square R of a two-phase sinusoidal signal containing the k-th harmonic component. 2 An error detection unit that determines the coefficients in the approximate formula model representing the model and calculates the correction value from the obtained coefficients, Equipped with, The error detection unit is characterized by determining the coefficients of the approximation formula model by the least squares method, and calculating the correction value by accumulating and adding the resulting correction values ​​as correction residuals.

[0092] (Note 10) The error detection unit is, Each phase angle θ calculated by the polar coordinate transformation unit i and the phase angle θ i The square radius R corresponding to i 2 Based on this, when the k-th harmonic component contained in a two-phase sinusoidal signal (X, Y) is expressed by equations (11) and (12), the cosine wave amplitude A ka Corrected residual ΔA ka and sinusoidal amplitude A kba Corrected residual ΔA kb The cosine wave amplitude A is calculated based on each corrected residual. ka and sinusoidal amplitude A kba Calculate,

number

number

Number

[0093] (Appended note 11) The error detection unit the coefficient A in formula (16) c(k±1) and A s(k±1) are obtained as elements of the C (k±1) matrix by formula (17)

Number

[0094] (Appended note 12) The error detection unit the coefficient A in formula (16) c(k±1) and A s(k±1) are obtained as elements of the C (k±1) matrix from formula (43) to formula (45)

Number

[0095] (Appended note 13) Further comprising a correction unit for correcting the two-phase sinusoidal signal based on the correction value, the correction unit obtains the k-th harmonic x ki and y ki by formula (46) and formula (47),

Number

[0096] (Note 14) The system includes a correction unit that corrects the two-phase sinusoidal wave signal based on the correction value, The polar coordinate transformation unit calculates the square radius R, which is the square of the Lissajous radius R corresponding to each phase angle θ, for the two-phase sinusoidal wave signal corrected by the correction unit. 2 Calculate, The error detection unit uses each phase angle θ calculated by the polar coordinate transformation unit and the square radius R corresponding to the phase angle θ. 2 A correction value calculation device according to any one of the appendices 9 to 13, characterized by calculating a new correction value based on the above and updating the correction value.

[0097] (Note 15) The error detection unit updates each correction value according to equation (22).

number

[0098] (Note 16) A correction value calculation device as described in any one of Notes 9 to 15, An encoder detection unit that outputs a two-phase sinusoidal wave signal corresponding to the displacement along the measurement direction, Equipped with, The correction value calculation device is A correction value calculation process that calculates a correction value based on the two-phase sinusoidal wave signal output by the encoder detection unit, An encoder characterized by performing a correction process that applies a calculated correction value to the two-phase sinusoidal wave signal output by the encoder detection unit. [Explanation of symbols]

[0099] 1, 1a Correction Value Calculation Device 10 encoders 11 Encoder section 20 Correction section 30 Polar Coordinate Transformation Section 40, 40a Error detection unit 50 Wide-area phase angle calculation unit

Claims

1. A correction value calculation method for calculating a correction value to correct the k-th harmonic component in a two-phase sinusoidal signal (X, Y) output by an encoder, The N phase angles θ in the Lissajous waveform drawn by the two-phase sinusoidal signal described above. ｉ and each phase angle θ ｉ Lissajous radius R corresponding to ｉ Regarding each phase angle θ, ｉ The Lissajous radius R corresponding to the Lissajous radius R ｉ The square radius R is the square of ｉ ２ A polar coordinate calculation step to calculate, Each phase angle θ calculated by the polar coordinate calculation step ｉ and the phase angle θ ｉ Based on the corresponding squared radius R ｉ ２ And based on the squared radius R of the two-phase sinusoidal signal including the k-th harmonic component, a correction value calculation step of obtaining the coefficients in the approximate formula model representing the squared radius R and obtaining the correction value from the obtained coefficients, and ２ including, The correction value calculation step involves determining the coefficients of the approximation model by the least squares method, and then accumulating and adding the resulting correction values ​​as correction residuals to obtain the correction value. A method for calculating a correction value characterized by the following features.

2. In the correction value calculation step, Each phase angle θ calculated by the aforementioned polar coordinate calculation step ｉ and the phase angle θ ｉ The square radius R corresponding to ｉ ２ Based on this, when the k-th harmonic component contained in a two-phase sinusoidal signal (X, Y) is expressed by equations (11) and (12), the cosine wave amplitude A ｋａ Corrected residual ΔA ｋａ and sinusoidal amplitude A ｋｂａ Corrected residual ΔA ｋｂ The cosine wave amplitude A is calculated based on each corrected residual. ｋａ and sinusoidal amplitude A ｋｂａ Calculate, [Math 1] Equation (16) is given by the square radius R ２ As an approximate model, the coefficient A in equation (16) is ｃ（ｋ±１） and A ｓ（ｋ±１） Each phase angle (k±1)θ ｉ and each phase angle (k±1)θ ｉ The square radius R corresponding to ｉ ２ Using the least squares method, [Math 2] The obtained coefficient A ｃ（ｋ±１） and A ｓ（ｋ±１） Therefore, according to equation (21), the cosine wave amplitude A ｋａ Corrected residual ΔA ｋａ and sinusoidal amplitude A ｋｂａ Corrected residual ΔA ｋｂ To seek [Math 3] The correction value calculation method according to feature 1.

3. The correction value calculation step is: Coefficient A in equation (16) ｃ（ｋ±１） and A ｓ（ｋ±１） According to equation (17), C （ｋ±１） To obtain as elements of a matrix [Math 4] The correction value calculation method according to feature 2.

4. The correction value calculation step is: Coefficient A in equation (16) ｃ（ｋ±１） and A ｓ（ｋ±１） From equation (43) to equation (45), C （ｋ±１） To obtain as elements of a matrix [Math 5] However, in equations (44) and (45), [x] is the Gaussian symbol representing the largest integer not exceeding x. The correction value calculation method according to feature 2.

5. The system further includes a correction step of correcting the two-phase sinusoidal wave signal based on the correction value, In the correction step, the k-th harmonic x ｋｉ and y ｋｉ This can be found using equations (46) to (49). [Math 6] However, in equations (48) and (49), [x] is the Gaussian symbol representing the largest integer not exceeding x, and the obtained x ｋｉ and y ｋｉ The correction value calculation method according to claim 4, characterized in that the correction is performed by subtracting from the corresponding data of the two-phase sinusoidal wave signal.

6. The system includes a correction step for correcting the two-phase sinusoidal signal based on the correction value, The correction value calculation method according to any one of claims 1 to 5, characterized in that the correction value calculation step is applied again to the two-phase sinusoidal signal corrected by the correction step to update the correction value.

7. Each correction value is updated using equation (22). [Number 7] The correction value calculation method according to feature 6.

8. A program that causes a computer to execute the correction value calculation method described in claim 1.

9. A correction value calculation device that calculates correction values ​​for correcting a two-phase sinusoidal wave signal (X, Y) output by an encoder, The N phase angles θ in the Lissajous waveform drawn by the two-phase sinusoidal signal described above. ｉ and each phase angle θ ｉ Lissajous radius R corresponding to ｉ Regarding each phase angle θ, ｉ The Lissajous radius R corresponding to the Lissajous radius R ｉ The square radius R is the square of ｉ ２ A polar coordinate transformation unit that calculates, Each phase angle θ calculated by the polar coordinate transformation unit ｉ and the phase angle θ ｉ The square radius R corresponding to ｉ ２ Based on this, the radius of square R of a two-phase sinusoidal signal containing the k-th harmonic component. ２ An error detection unit that determines the coefficients in the approximate formula model representing the model and calculates the correction value from the obtained coefficients, Equipped with, The error detection unit is characterized by determining the coefficients of the approximation formula model by the least squares method, and calculating the correction value by accumulating and adding the resulting correction values ​​as correction residuals.

10. The error detection unit, Each phase angle θ calculated by the polar coordinate transformation unit ｉ and the phase angle θ ｉ The square radius R corresponding to ｉ ２ Based on this, when the k-th harmonic component contained in a two-phase sinusoidal signal (X, Y) is expressed by equations (11) and (12), the cosine wave amplitude A ｋａ Corrected residual ΔA ｋａ and sinusoidal amplitude A ｋｂａ Corrected residual ΔA ｋｂ The cosine wave amplitude A is calculated based on each corrected residual. ｋａ and sinusoidal amplitude A ｋｂａ Calculate, [Number 8] Equation (16) is given by the square radius R ２ As an approximate model, the coefficient A in equation (14) ｃ（ｋ±１） and A ｓ（ｋ±１） Each phase angle (k±1)θ ｉ and each phase angle (k±1)θ ｉ The square radius R corresponding to ｉ ２ Using the least squares method, [Number 9] The obtained coefficient A ｃ（ｋ±１） and A ｓ（ｋ±１） Therefore, according to equation (21), the cosine wave amplitude A ｋａ Corrected residual ΔA ｋａ and sinusoidal amplitude A ｋｂａ Corrected residual ΔA ｋｂ To seek [Number 10] The correction value calculation device according to feature 9.

11. The error detection unit, Coefficient A in equation (16) ｃ（ｋ±１） and A ｓ（ｋ±１） According to equation (17), C （ｋ±１） To obtain as elements of a matrix [Math 11] The correction value calculation device according to claim 10.

12. The error detection unit, Coefficient A in equation (16) ｃ（ｋ±１） and A ｓ（ｋ±１） From equation (43) to equation (45), C （ｋ±１） To obtain as elements of a matrix [Math 12] However, in equations (44) and (45), [x] is the Gaussian symbol representing the largest integer not exceeding x. The correction value calculation device according to claim 10.

13. The system further includes a correction unit that corrects the two-phase sinusoidal wave signal based on the correction value, The correction unit processes the k-th harmonic x ｋｉ and y ｋｉ We obtain this using equations (46) and (47). [Number 13] However, in equations (48) and (49), [x] is the Gaussian symbol representing the largest integer not exceeding x, The obtained x ｋｉ and y ｋｉ The correction value calculation device according to claim 12, wherein correction is performed by subtracting from the corresponding data of the two-phase sine wave signal.

14. The system includes a correction unit that corrects the two-phase sinusoidal wave signal based on the correction value, The polar coordinate transformation unit calculates the square radius R, which is the square of the Lissajous radius R corresponding to each phase angle θ, for the two-phase sinusoidal wave signal corrected by the correction unit. ２ Calculate, The error detection unit uses each phase angle θ calculated by the polar coordinate transformation unit and the square radius R corresponding to that phase angle θ. ２ A correction value calculation device according to any one of claims 9 to 13, characterized in that it calculates a new correction value based on and updates the correction value.

15. The error detection unit updates each correction value according to equation (22). [Number 14] The correction value calculation device is characterized in that it is described in 14.

16. A correction value calculation device according to any one of claims 9 to 13, An encoder detection unit that outputs a two-phase sinusoidal wave signal corresponding to the displacement along the measurement direction, Equipped with, The correction value calculation device is A correction value calculation process that calculates a correction value based on the two-phase sinusoidal wave signal output by the encoder detection unit, An encoder characterized by performing a correction process that applies a calculated correction value to the two-phase sinusoidal wave signal output by the encoder detection unit.

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