JP6750857B2 - Coordinate data rotation calculation device and coordinate data rotation calculation method - Google Patents

Description

The present invention relates to a coordinate data rotation calculation device and a coordinate data rotation calculation method.

An optical rotary encoder is used to detect the angle, position, movement amount, and the like of a rotating body such as a motor. This type of rotary encoder irradiates uniform light from a light emitting element such as a light emitting diode from one side of a rotation signal plate in which a physical pattern is carved. Then, an electric signal pattern is formed by receiving and detecting transmitted light after passing through the signal pattern or reflected light from the signal plate by a light receiving element such as a photodiode or a phototransistor. Then, an encoder output signal is generated based on the electric signal pattern.

The encoder is known to have an incremental method and an absolute method as functional divisions. In the incremental encoder, a technique for realizing highly accurate position detection by interpolation processing (electric division) is known. This is based on the precondition that the amplitude and offset values of the encoder signal are uniform, and two-phase analog sine wave and cosine wave signals whose phases are different from each other by 90° are output. Therefore, the interpolation process may be performed after correcting the output signal from the encoder so as to approach the precondition.

As a specific interpolation processing method, a method based on arctangent calculation as disclosed in Patent Document 1 is known. As another method of the arctangent calculation, Non-Patent Document 1 discloses a coordinate data rotation calculation processing device called a CORDIC (COordinate Rotation Digital Computer). The CORDIC can treat an input signal as two-dimensional coordinate data, and the coordinate rotation of this two-dimensional coordinate data can realize the arctangent operation only by repeating simple operations such as bit shift and addition/subtraction. Non-Patent Document 1 shows a basic form of CORDIC. However, the actual encoder output signal contains harmonic components and is not an ideal sine wave signal. Therefore, even if the amplitude, offset, and phase between the two-phase analog signals output by the encoder are adjusted and corrected, the corrected signal does not become a sine wave/cosine wave signal, resulting in interpolation processing. A detection error occurs when performing.

Therefore, in Patent Document 2, in order to correct such a detection error, a value obtained by differentiating the detected displacement amount (detected angle) of the encoder, that is, a correction value that makes the displacement speed constant, is generated, and the correction value is generated. There is disclosed a method of correcting the detection position by having a for each detection position. Further, Patent Document 3 discloses a method of correcting the detection position by successively calculating the detection error amount by approximating the detection error amount to a sine wave because the transition of the detection error is periodic. ..

JP, 6-58769, A JP, 2009-303358, A JP 2006-170837 A

J. E. Volder. "The CORDIC trigonometric computing technique", IRE Transaction Electronic Computers, EC-8: 330-334, 1959.

However, for example, in Patent Document 2, since a correction value is required for the resolution of the detection position, there is a problem that the memory area for storing the correction value becomes enormous as the resolution of the detection position increases. Moreover, in Patent Document 3, a calculation time for calculating the correction value is required. In addition, even if the detection error can be approximated to an ideal sine wave, the position information (reference position) used to calculate the detection error becomes the detection position including the error. In addition, there is a problem that the calculation accuracy of the detection error is low in principle.

An object of the present invention is to perform a coordinate data rotation calculation capable of calculating a deviation angle of a vector of a fundamental wave from two-dimensional coordinate data including a fundamental wave and a harmonic without requiring a correction value calculation and a memory for the correction value calculation. An apparatus and a coordinate data rotation calculation method are provided.

A coordinate data rotation calculation device according to the present invention is a coordinate data rotation calculation device which receives two-dimensional coordinate data including a fundamental wave and a harmonic wave and calculates a deviation angle of a vector of a fundamental wave of the two-dimensional coordinate data. A fundamental wave selector that selects fundamental wave coordinate data from the two-dimensional coordinate data at the first time, and fundamental wave rotating coordinate data from the second time and thereafter, and a second time from the two-dimensional coordinate data at the first time. The harmonic selector for selecting the harmonic coordinate data of, and the harmonic selector for selecting the harmonic rotating coordinate data in the second and subsequent times, the coordinate data selected by the fundamental wave selector, and the coordinate data selected by the harmonic selector. A rotation direction determination unit that determines the rotation direction based on the rotation direction, and the rotation direction determined by the rotation direction determination unit, the coordinate data selected by the fundamental wave selector is rotated, and the rotated coordinate data is converted into the fundamental wave. The fundamental wave rotation calculation unit that outputs to the fundamental wave selector as rotational coordinate data, and the coordinate data selected by the harmonic selector in the rotation direction determined by the rotation direction determination unit, and the rotated coordinates A harmonic rotation calculation unit that outputs data to the harmonic selector as the harmonic rotation coordinate data, and a rotation angle rotated by the fundamental wave rotation calculation unit based on the rotation direction determined by the rotation direction determination unit. And a rotation angle accumulative addition unit for converging to the argument of the vector of the fundamental wave of the two-dimensional coordinate data.

According to the present invention, it is possible to calculate the deflection angle of the vector of the fundamental wave from the two-dimensional coordinate data including the fundamental wave and the harmonic wave without requiring the correction value calculation or the memory for the correction value calculation.

It is a figure showing the output signal of two phases which an optical encoder outputs. It is a figure explaining the concept of the vector mode operation of CORDIC. It is explanatory drawing which rotates a reference vector and implement|achieves a vector mode function. It is a figure which shows the structural example of CORDIC of 1st Embodiment. It is a figure which shows the structural example of CORDIC of 2nd Embodiment. It is a figure which shows the structural example of CORDIC of 3rd Embodiment.

(First embodiment)
FIG. 1 is a diagram showing two-phase A-phase signals and two-phase signals output by an optical encoder attached to a motor according to the first embodiment of the present invention. The A-phase signal and the B-phase signal are a cosine wave and a sine wave whose phases differ from each other by 90°. For example, the motor can measure the rotational position of the motor in cycle units of the sine wave by counting the sine wave signal as a pulse. Further, the motor can know the position of which phase at what cycle by detecting the phases of the sine wave and the cosine wave. Since the detection accuracy of the motor rotation position is determined by the accuracy of phase detection, it is necessary to accurately detect the phase. However, since the harmonics are superposed on the actual output signal of the encoder, it is not an ideal sine wave and cosine wave. However, the output signal waveform can be regarded as a substantially symmetrical waveform due to the mechanism of generating the output signal. When the output signal waveform is symmetrical, the superimposed harmonics are limited to odd harmonics. Moreover, when the order becomes higher, the power of the output signal sharply decreases. Therefore, what is first desired is phase detection that considers the third harmonic, and then phase detection that considers the fifth harmonic. These will be described below.

FIG. 2 is a diagram for explaining the operation of the vector mode of CORDIC. CORDIC is a coordinate data rotation calculation device. In the vector mode, the CORDIC calculates the argument of the input two-dimensional vector data (X, Y) by using the CORDIC rotation calculation. CORDIC sequentially rotates the two-dimensional vector data (X, Y) toward the x-axis in a predetermined rotation angle sequence θi=tan ⁻¹ (2 ⁻ⁱ ), and finally the vector after rotation is x. Approximately coincides with the axis, and the cumulative rotation angle θn is taken as a declination angle. Here, i=0, 1, 2,... The cumulative rotation angle θn is calculated by a value obtained by cumulatively adding the rotation angle sequence θi in consideration of the rotation direction determined for each rotation, that is, θn=Σsign(Yi)·θi. Here, sign(Yi) represents the positive/negative sign of the y-axis component of the two-dimensional vector data when rotating θi by ±1, where +1 rotates to the right and −1 rotates to the left.

FIG. 3 is an explanatory diagram for realizing the vector mode function by rotating the reference vector. Unlike the vector mode described above, the CORDIC is a rotation when the reference vector (1,0) on the x-axis is rotated toward the two-dimensional vector data (X,Y) by the CORDIC rotation calculation to match the directions. In principle, it is possible to obtain the declination as an angle. That is, the coordinates after the reference vector (1, 0) is rotated by the left θ becomes (cos θ, sin θ), and the discriminant for determining the next rotation direction is as in the following equation (1).
Y/X≧sin θ/cos θ (1)

The next rotation direction is left if the discriminant (1) is true, and right if it is false. However, in general, such a formula cannot be used in the calculation of the declination angle by CORDIC, and is never seen. This is because the discriminant (1) requires division, and even if the denominator of the discriminant (1) is transposed, the multiplication remains, and a simple operation characteristic of CORDIC, that is, a bit shift operation and an addition/subtraction operation. Because it cannot be replaced with.

However, in the embodiment of the present invention, the discriminant (1) is extremely important. The feature of the CORDIC of the present embodiment is that the discriminant (1) is expanded to a signal in which harmonics are superposed, and the signal is transformed into a discriminant for vector mode. Before expanding the discriminant (1) to a signal on which harmonics are superimposed, if the discriminant (1) is transformed into a discriminant for the vector mode, the following formula (2) is obtained.
−Xsin θ+Y cos θ≧0 (2)

As shown in FIG. 2, the judgment formula (2) determines whether the y-axis component is 0 or more when the vector (X, Y) is rotated rightward by θ, that is, whether the rotated vector exceeds the x-axis. It can be interpreted as an expression that determines whether or not. This discriminant (2) is the discriminant itself in the vector mode of CORDIC.

By the way, in the discriminant (1), the reference vector (1, 0) is rotated, whereas in the discriminant (2), the input two-dimensional vector (X, Y) is rotated. Is reversed. Thus, it can be seen that the discriminant (2) for the vector mode is obtained from the discriminant (1) for rotating the reference vector.

Here, the discriminant (1) is extended to a signal on which the third harmonic is superimposed. When α and β are known for the amplitude values of the fundamental wave and the third harmonic, respectively, the discriminant when the third harmonic is superimposed on the fundamental wave is as shown in the following equation (3).
Y/X≧(αsinθ+βsin3θ)/(αcosθ−βcos3θ) (3)

The numerator on both sides of the discriminant (3) corresponds to the sine wave phase component of the signal on which the third harmonic is superimposed, and both denominators correspond to the cosine wave phase component of the signal on which the third harmonic is superimposed. Then, when both sides of the formula (3) are equal, θ is the declination θn to be obtained. The minus sign before β in the denominator on the right side is because the 90-degree phase difference of the cosine wave in the fundamental wave becomes the 270-degree phase difference in the third harmonic, that is, the -90-degree phase difference. From this, the apparent rotation direction of the third-order harmonic wave is opposite to that of the fundamental wave.

The determination of the rotation direction by the discriminant (3) is as follows. If the discriminant (3) is true, the rotation is still insufficient, so that each of the fundamental wave reference vector (α, 0) and the third harmonic reference vector (β, 0) is further rotated in the initial direction. If the discriminant (3) is false, the fundamental wave reference vector (α, 0) and the third-order harmonic reference vector (β, 0) are rotated in the opposite directions because the rotation is excessive. When the fundamental wave reference vector (α, 0) is rotated by the rotation angle sequence θi, the third harmonic reference vector (β, 0) is rotated by 3 times 3θi. This is a virtual process based on the discriminant (3), and actually, the following process is performed.

If the discriminant (1) is transformed into the discriminant (2) for the vector mode and the discriminant (3) is transformed into the discriminant for the vector mode, the following formula (4) is obtained.
Y (α cos θ-β cos 3 θ) ≧ X (α sin θ + β sin 3 θ)
αYcosθ−βYcos3θ≧αXsinθ+βXsin3θ
(-ΑXsinθ+αYcosθ)-(βXsin3θ+βYcos3θ)≧0 (4)

The expression in the first parenthesis on the left side of the left side of the discriminant (4) corresponds to the right θ rotation of the fundamental wave component of the input two-dimensional vector data, and the expression in the second parenthesis is the left of the third harmonic component. Corresponds to 3θ rotation. Since the fundamental wave component and the third-order harmonic component are mixed in each element of the input two-dimensional vector (X, Y), the third-order harmonic component, the third-order harmonic component, and the third-order harmonic component in the first parenthesis on the left side of the discriminant (4). The fundamental wave components are mixed in the two brackets. Each of these mixed components is an unnecessary component, but when the final stage of rotation, that is, the destination after the rotation of the input two-dimensional vector matches the x axis, it is canceled out and becomes zero, so it can be ignored. Although it can be confirmed by calculation that the mixed components cancel each other out, the calculation is omitted. This is because it can be said that the discriminant (4) obtained by transforming another discriminant guarantees that the unnecessary components are canceled.

By the way, the control of the rotation direction by the discriminant (4) is as follows. If the discriminant (4) is true, the CORDIC does not have sufficient rotation, and therefore the fundamental wave coordinates (αX, αY) and the third-order harmonic coordinates (βX, βY) are further rotated in the initial direction. When the discriminant (4) is false, the CORDIC rotates the fundamental wave coordinate (αX, αY) and the third harmonic coordinate (βX, βY) in opposite directions. The above description has explained the principle of CORDIC based on the discriminant (4).

FIG. 4A is a block diagram showing a configuration example of the CORDIC according to this embodiment, and realizes the principle of the CORDIC. The CORDIC is a coordinate data rotation calculation device, and includes a coordinate conversion generation unit 301, a rotation direction determination unit 302, a fundamental wave CORDIC rotation calculation unit 303, a third harmonic CORDIC rotation calculation unit 304, and a rotation angle accumulation calculation unit 305. And selectors 311 and 312. The coordinate transformation generation unit 301 inputs the input two-dimensional coordinate data (X, Y), the fundamental wave amplitude α, and the third harmonic amplitude β, and triples the fundamental wave coordinate data (αX, αY) to which the fundamental rotation is applied. Third-order harmonic coordinate data (βX, βY) to which rotation is applied is generated. The fundamental wave CORDIC rotation calculation unit 303 is a fundamental wave rotation calculation unit and fundamentally rotates the fundamental wave coordinate data. The third harmonic CORDIC rotation calculator 304 is a third harmonic rotation calculator, and rotates the third harmonic coordinate data three times. The rotation direction determination unit 302 refers to the input data of the two CORDIC rotation calculation units 303 and 304, and determines the rotation direction of the input data based on the determination formula (4). The rotation angle cumulative calculation unit 305 is a rotation angle cumulative addition unit, and cumulatively adds the rotation angles in the fundamental wave CORDIC rotation calculation unit 303.

Next, a method for calculating the coordinate data rotation of CORDIC will be described. The coordinate conversion generation unit 301 multiplies the input two-dimensional coordinate data (X, Y) by the fundamental wave amplitude value α measured in advance, and outputs fundamental wave initial coordinate data (αX, αY) to the selector 311. .. Further, the coordinate conversion generation unit 301 multiplies the input two-dimensional coordinate data (X, Y) by the previously measured third harmonic amplitude value β, and the third harmonic initial coordinate data (βX, βY). Is output to the selector 312. The selector 311 is a fundamental wave selector, and at the first time (i=0), selects fundamental wave initial coordinate data (αX, αY) and outputs it to the fundamental wave CORDIC rotation calculation unit 303. The selector 312 is a third harmonic selector, and at the first time (i=0), selects the third harmonic initial coordinate data (βX, βY) and outputs it to the CORDIC rotation calculation unit 304 for the third harmonic. To do. Further, the selector 311 selects the fundamental wave rotation calculation data output from the fundamental wave CORDIC rotation computation unit 303 and outputs it to the fundamental wave CORDIC rotation computation unit 303 after the second time (i=1 and later). The selector 312 selects the third-order harmonic rotation coordinate data output from the third-order harmonic CORDIC rotation calculation unit 304 in the second and subsequent times (i=1 and thereafter) to select the third-order harmonic CORDIC rotation calculation unit 304. Output to.

The rotation direction determination unit 302 is a rotation direction determination unit, and determines the rotation directions of the CORDIC rotation calculation units 303 and 304 by using the determination formula (4) based on the coordinate data selected by the selectors 311 and 312. .. The fundamental wave CORDIC rotation calculation unit 303 rotates the coordinate data output by the selector 311 in the rotation direction determined by the rotation direction determination unit 302 in the rotation angle sequence θi to select the fundamental wave rotation coordinate data. Output to 311. Specifically, the fundamental wave CORDIC rotation calculation unit 303 rotates a rotation angle of tan ⁻¹ (2 ⁻ⁱ ) in the i-th cycle (i is an integer of 0 or more). The third harmonic CORDIC rotation calculation unit 304 rotates the coordinate data output by the selector 312 in the rotation direction determined by the rotation direction determination unit 302 by 3θi, which is three times the rotation angle sequence θi. The third harmonic rotation coordinate data is output to the selector 312. Specifically, the third harmonic CORDIC rotation calculation unit 304 performs rotation of a rotation angle of 3×tan ⁻¹ (2 ⁻ⁱ ) in the i-th cycle. That is, the third-order harmonic CORDIC rotation calculation unit 304 rotates the rotation angle of the fundamental wave CORDIC rotation calculation unit 303 by the order of multiples (three times) of the harmonic.

When the CORDIC rotation calculation units 303 and 304 repeat the rotation calculation, the rotation coordinate data output by the CORDIC rotation calculation units 303 and 304 eventually match the x-axis. The residual difference between the rotational coordinate data and the x-axis depends on the number of times of rotation calculation and the number of calculation bits. The larger the number of repetitions of calculation and the number of calculation bits, the smaller the difference. The rotation angle cumulative calculation unit 305 cumulatively adds the rotation angles rotated by the CORDIC rotation calculation unit 303 based on the rotation direction determined by the rotation direction determination unit 302, thereby calculating the vector of the fundamental wave of the two-dimensional coordinate data. To a deviation angle θn of. As described above, the CORDIC inputs the two-dimensional coordinate data including the fundamental wave and the third harmonic, and calculates the argument θn of the vector of the fundamental wave of the two-dimensional coordinate data.

Next, the determination of the rotation direction of the rotation direction determination unit 302 will be described. Immediately before the CORDIC rotation calculation units 303 and 304 perform the first CORDIC rotation calculation of the rotation angle sequence θi, the rotation direction determination unit 302 inputs the two y-axis component data αY and βY generated by the coordinate conversion generation unit 301, The difference αY−βY is calculated. Then, the rotation direction determination unit 302 determines the first rotation direction depending on whether the difference αY−βY is 0 or more. The CORDIC rotation calculation units 303 and 304 respectively rotate θi (i=0) and 3θi (i=0) with respect to the rotation direction determined by the rotation direction determination unit 302, and output rotation coordinate data. The selectors 311 and 312 select the rotation coordinate data generated by the CORDIC rotation calculation units 303 and 304, respectively, and output them to the CORDIC rotation calculation units 303 and 304. Next, the CORDIC rotation calculation units 303 and 304 perform the second rotation. The rotation direction determination unit 302 determines the rotation direction for the second time depending on whether the difference between the y-axis components calculated by the following equation (5) is 0 or more.

The two rotation operations on the left side of Expression (5) are performed by the CORDIC rotation operation units 303 and 304, respectively. The difference of the y-axis components of the two rotation calculation results shown on the right side is the same as the left side of the discriminant (4). This has clarified that the configuration of the CORDIC shown in FIG. 4A corresponds to the discriminant (4).

The rotation direction determination unit 302 replaces the rotation direction of the third and subsequent rotation calculations with the rotation angle obtained by accumulating θi in Expression (5), and similarly, based on the determination expression (4), the rotation direction To decide.

Next, a discriminant when the amplitudes of the sine wave and the cosine wave of the fundamental wave and the third harmonic are different will be described. If the amplitudes of the sine wave and the cosine wave of the fundamental wave are α and α′, and the amplitudes of the sine wave and the cosine wave of the third harmonic are β and β′, the discriminants (3) and (4) are It becomes like 6) and (7).
Y/X≧(αsinθ+βsin3θ)/(α′cosθ−β′cos3θ) (6)
(-ΑXsinθ+α'Ycos3)-(βXsin3θ+β'Ycos3θ)≧0 (7)

The coordinate transformation generation unit 301 inputs two-dimensional (α, α′) and (β, β′) instead of one-dimensional α and β, and inputs two-dimensional coordinates (αX, α′Y) and Output (βX, β'Y). The subsequent processing is the same as above. Therefore, it is understood that the coordinate conversion generation unit 301 can be easily applied to the case where the amplitudes of the sine wave and the cosine wave of the fundamental wave and the third harmonic are different by simply changing the coordinate conversion generation unit 301 as described above.

FIG. 4B is a diagram showing another configuration example of the CORDIC according to the present embodiment, in which a scaling correction unit 321 is added to FIG. 4A. Since the CORDIC rotation calculation units 303 and 304 perform coordinate rotation only by simple bit shift and addition/subtraction, the absolute value of the vector after rotation slightly changes. Since the fundamental wave and the third harmonic have different rotation angles, the change rates of the absolute values of both vectors are different, and it becomes impossible to simply add the coordinate data after rotation of both. Therefore, it is necessary to correct both or either of the absolute values to equalize the rate of change of the absolute values.

In the CORDIC of FIG. 4A, when the fundamental wave is rotated by θi and then multiplied by (1+2 ⁻²ⁱ ), the rate of change in the absolute value of the fundamental wave and the absolute value of the third harmonic can be made uniform. This operation can be performed only by bit shift and addition. This is one method and other methods are possible. A calculation for correcting the absolute value of such a vector is called scaling correction. In FIG. 4B, the scaling correction unit 321 calculates the absolute value of each vector of the fundamental wave rotation coordinate data output by the CORDIC rotation calculation unit 303 and the third harmonic rotation coordinate data output by the CORDIC rotation calculation unit 304. Scaling correction is performed to equalize the rate of change. The scaling correction unit 321 is a fundamental wave scaling correction unit and performs scaling correction by bit shift and addition. In the i-th cycle, the scaling correction unit 321 multiplies the rotation coordinate data output by the CORDIC rotation calculation unit 303 by (1+2 ⁻²ⁱ ) and ^outputs the multiplication result to the selector 311 as the fundamental wave rotation coordinate data. After i=1, the selector 311 selects the output data of the scaling corrector 321 and outputs it to the CORDIC rotation calculator 303.

By the way, in the case of the CORDIC that rotates only the fundamental wave on which the harmonics are not superimposed, it is not necessary to perform the scaling correction of the scaling correction unit 321 for each rotation calculation, and the scaling correction is performed only once before or after the full rotation calculation. Should be done. Therefore, it is often performed together with other calculation performed before or after the CORDIC calculation. In this case, the scaling correction unit 321 is not explicitly shown, as shown in FIG. Therefore, CORDIC expressing the basic concept of the present invention is represented in FIG. 4A in which the scaling correction unit 321 is omitted. On the other hand, CORDIC suitable for actual processing is represented in FIG. 4B including the scaling correction unit 321.

(Second embodiment)
In the first embodiment, the harmonic to be superimposed is only the third harmonic, but in the actual device, the fifth and higher harmonics are also superimposed. However, the higher the harmonic power, the more rapidly the harmonic power is attenuated. On the contrary, when highly accurate measurement is required, it is necessary to process higher harmonics without neglecting them, depending on the accuracy. Therefore, in the second embodiment of the present invention, a case will be described in which up to the fifth harmonic is processed as a higher harmonic.

First, the above discriminant equation (3) is expanded to an equation including the fifth harmonic. When the amplitude of the fifth harmonic is γ, the discriminant is as in the following equation (8).
Y/X≧(αsinθ+βsin3θ+γsin5θ)/(αcosθ−βcos3θ+γcos5θ) (8)

The 90-degree phase difference in the fundamental wave becomes 450-degree phase difference at the fifth harmonic, which is the same as the 90-degree phase difference, so the sign before γ in the denominator on the right side is +. The rotation direction of the fifth harmonic wave is the same as that of the fundamental wave.

Next, when the discriminant (8) is transformed into the discriminant for the vector mode, the following formula (9) is obtained.
Y (α cos θ-β cos 3 θ + γ cos 5 θ) ≧ X (α sin θ + β sin 3 θ + γ sin 5 θ)
αYcosθ−βYcos3θ+γYcos5θ≧αXsinθ+βXsin3θ+γXsin5θ
(−αXsinθ+αYcosθ)−(βXsin3θ+βYcos3θ)+(−γXsin5θ+γYcos5θ)≧0 (9)

The expression in the third parenthesis on the left side of the discriminant (9) is a new term that rotates the fifth harmonic component by 5θ to the right. It is an unnecessary component in each of the first to third brackets, but when the destination of rotation of the input two-dimensional vector matches the x axis, it is canceled and becomes zero.

FIG. 5A is a diagram showing a configuration example of a CORDIC according to the second embodiment of the present invention. In FIG. 5A, a selector 413 and a fifth harmonic CORDIC rotation calculation unit 405 are added to FIG. 4A, and instead of the coordinate conversion generation unit 301 and the rotation direction determination unit 302, coordinate conversion generation is performed. The unit 401 and the rotation direction discriminating unit 402 are provided. The fifth-order harmonic CORDIC rotation calculation unit 405 is a fifth-order harmonic rotation calculation unit. The CORDIC of this embodiment performs processing based on the discriminant (9). Hereinafter, the difference between the present embodiment and the first embodiment will be described. The coordinate conversion generation unit 401 inputs the input two-dimensional coordinate data (X, Y), the fundamental wave amplitude α, the third-order harmonic amplitude β, and the fifth-order harmonic amplitude γ, and inputs the fundamental wave initial coordinate data (αX, αY). And third-order harmonic initial coordinate data (βX, βY) and fifth-order harmonic initial coordinate data (γX, γY) are output. Specifically, the coordinate conversion generation unit 401 multiplies the two-dimensional coordinate data (X, Y) by the fundamental wave amplitude α and outputs the fundamental wave initial coordinate data (αX, αY) to the selector 311. Further, the coordinate conversion generation unit 401 multiplies the two-dimensional coordinate data (X, Y) by the third harmonic amplitude β and outputs the third harmonic initial coordinate data (βX, βY) to the selector 312. Further, the coordinate conversion generation unit 401 multiplies the two-dimensional coordinate data (X, Y) by the fifth-order harmonic amplitude γ and outputs the fifth-order harmonic initial coordinate data (γX, γY) to the selector 413. The selector 413 is a fifth-order harmonic selector, and at the first time (i=0), selects the fifth-order harmonic initial coordinate data (γX, γY) output by the coordinate conversion generation unit 401 to select the CORDIC rotation calculation unit. Output to 405. In addition, the selector 413 selects the fifth-order harmonic rotation data output by the CORDIC rotation calculation unit 405 and outputs it to the CORDIC rotation calculation unit 405 after the second time (i=1 and after). The rotation direction determination unit 402 is a rotation direction determination unit, and determines the rotation direction using the determination formula (9) based on the coordinate data selected by the selectors 311, 312 and 413. The CORDIC rotation calculation unit 405 rotates the coordinate data selected by the selector 413 in the rotation direction determined by the rotation direction determination unit 402 by 5 times the rotation angle sequence θi by 5θi, and the fifth harmonic. The rotation coordinate data is output to the selector 413. That is, the CORDIC rotation calculation unit 405 rotates the rotation angle of 5×tan ⁻¹ (2 ⁻ⁱ ) in the i-th cycle. In order to improve the accuracy in response to higher harmonics, a CORDIC rotation calculation unit for the 7th harmonic and the 9th harmonic may be added.

FIG. 5B is a diagram showing another configuration example of the CORDIC according to the present embodiment, in which scaling correction units 421 and 422 are added to FIG. 5A. Similar to FIG. 4B, the scaling correction units 421 and 422 determine one of the CORDIC rotation calculation units 303, 304, and 405 in order to equalize the change rates of the input/output absolute values, and other Scaling correction is applied to the two outputs. As an example, the scaling correction unit 421 is a fundamental wave scaling correction unit. The scaling correction unit 421 performs scaling correction on the output data of the fundamental wave CORDIC rotation calculation unit 303, and the scaling correction unit 422 performs scaling correction on the output data of the third harmonic CORDIC rotation calculation unit 304. To do.

Specifically, in the i-th cycle, the scaling correction unit 421 multiplies the output data of the fundamental wave CORDIC rotation calculation unit 303 by (1+2 ⁻²ⁱ )×(1+2 ^{−2 i} ), and ^calculates the multiplication result. It is output to the selector 311 as fundamental wave rotation coordinate data. The scaling correction unit 422 is a third-order harmonic scaling correction unit, and in the i-th cycle, the output data of the third-order harmonic CORDIC rotation calculation unit 304 is multiplied by (1+2 ⁻²ⁱ ) and the multiplication result is obtained. Is output to the selector 312 as the third harmonic rotation coordinate data. The scaling correction unit 422 performs the operation including the bit shift and the addition once, and the scaling correction unit 421 performs the operation including the bit shift and the addition twice. After i=1, the selector 311 selects the output data of the scaling correction unit 421 and outputs it to the CORDIC rotation calculation unit 303. After i=1, the selector 312 selects the output data of the scaling correction unit 422 and outputs it to the CORDIC rotation calculation unit 304.

(Third Embodiment)
In the first and second embodiments, the case where there is no initial phase difference between the superimposed harmonic and the fundamental wave and the initial phases of the harmonic and the fundamental wave are the same phase has been described. In the actual waveform, a phase difference from the fundamental wave occurs for each harmonic due to the structural factor of the motor. When the initial phase of the third harmonic wave with respect to the fundamental wave is φ, the discriminant equation (3) is expressed by the following equations (10) and (11).
Y/X≧(αsin θ+β sin(3θ+φ))/(αcos θ−β cos(3θ+φ)) (10)
(-ΑXsinθ+αYcosθ)-(βXsin(3θ+φ)+βYcos(3θ+φ))≧0 (11)

This phase φ can be collected by analyzing the observed waveform, and will not change unless the motor structure changes, so basically it can be collected once. The collected phase φ needs to be realized as an initial phase shift process in the CORDIC calculation process. Therefore, as shown in FIG. 6A, a third harmonic for rotating the initial coordinates (βX, βY) input to the selector 312 in the preceding stage of the third harmonic CORDIC rotation calculation unit 304 by the phase φ. A coordinate rotation unit 601 is provided. The third harmonic coordinate rotation unit 601 rotates the input coordinates (βX, βY) and outputs (βXcosφ-βYsinφ, βXsinφ+βYcosφ). The signal processed as the third-order harmonic wave is rotated by the phase rotation φ in the coordinate rotation unit 601, and is then rotated by 3θ in the CORDIC rotation calculation unit 304 for the third-order harmonic wave. Receive a rotation. Therefore, the discrimination corresponding to the above discriminant (11) is performed.

Further, when the fifth harmonic is superimposed and the initial phase with respect to the fundamental wave is ψ, the discriminant equation (9) becomes the following equation (12).
(-ΑXsinθ+αYcosθ)-(βXsin(3θ+φ)+βYcos(3θ+φ))+(-γXsin(5θ+ψ)+γYcos(5θ+ψ))≧0...(12)

The configuration that can be discriminated is the same as the configuration of FIG. 5B, except that the third harmonic coordinate rotation unit 601 that rotates the initial coordinates of the third harmonic and the fifth harmonic that rotates the initial coordinates of the fifth harmonic. The configuration shown in FIG. 6B is provided in which the wave coordinate rotation unit 701 is provided in the preceding stage of the corresponding selector. The third-order harmonic coordinate rotation unit 601 operates in the same manner as 601 in FIG. 6A, and the fifth-order harmonic coordinate rotation unit 701 rotates the input coordinates (γX, γY) to obtain (γXcosψ+γYsinψ, −). γXsin ψ+γYcos ψ) is output. Similar to the third-order harmonic, the signal processed as the fifth-order harmonic undergoes rotation of the phase ψ by the coordinate rotation unit 701, and then rotates by 5θ by the CORDIC rotation calculation unit for the fifth-order harmonic 405. Therefore, it receives a total of 5θ+ψ rotation. Therefore, the discrimination corresponding to the above discriminant (12) becomes possible.

According to the first, second, and third embodiments, the phase of the rotation angle of the fundamental wave at that moment can be detected with high accuracy from the instantaneous value of the sine wave/cosine wave on which the harmonic is superimposed. The correction value calculation and correction value memory for harmonic distortion correction are not required. Further, in the first and second embodiments, since the correction value calculation is not necessary, the phase can be detected with low delay, the rotational position of the motor can be detected at high speed, and the position control of the motor and the like becomes easy.

It should be noted that each of the above-described embodiments is merely an example of an embodiment for carrying out the present invention, and the technical scope of the present invention should not be limitedly interpreted by these. That is, the present invention can be implemented in various forms without departing from its technical idea or its main features.

301, 401 Coordinate conversion generation unit, 302, 402 Rotation direction determination unit, 303 Fundamental wave CORDIC rotation calculation unit, 304 Third harmonic CORDIC rotation calculation unit, 405 Fifth harmonic CORDIC rotation calculation unit, 305 Rotation angle Cumulative calculation unit, 311, 312, 413 selector, 321, 421, 422 scaling correction unit, 601, 701 harmonic coordinate rotation unit

Claims (14)

A coordinate data rotation calculation device for inputting two-dimensional coordinate data including a fundamental wave and a harmonic and calculating a deviation angle of a vector of a fundamental wave of the two-dimensional coordinate data,
A fundamental wave selector that selects fundamental wave coordinate data from the two-dimensional coordinate data at the first time, and fundamental wave rotating coordinate data at the second time and thereafter;
A harmonic selector that selects harmonic coordinate data from the two-dimensional coordinate data at the first time, and harmonic rotational coordinate data at the second time and thereafter;
A rotation direction determining unit that determines a rotation direction based on the coordinate data selected by the fundamental wave selector and the coordinate data selected by the harmonic selector,
A fundamental wave that rotates the coordinate data selected by the fundamental wave selector in the rotation direction determined by the rotation direction determination unit and outputs the rotated coordinate data to the fundamental wave selector as the fundamental wave rotation coordinate data. A rotation calculation unit,
A harmonic that rotates the coordinate data selected by the harmonic selector in the rotation direction determined by the rotation direction determination unit, and outputs the rotated coordinate data as the harmonic rotation coordinate data to the harmonic selector. A rotation calculation unit,
Based on the rotation direction determined by the rotation direction determination unit, the rotation angle rotated by the fundamental wave rotation calculation unit is cumulatively added to converge the deflection angle of the vector of the fundamental wave of the two-dimensional coordinate data. A coordinate data rotation calculation device comprising: a rotation angle cumulative addition unit. Further, scaling correction for performing scaling correction for equalizing the change rates of the absolute values of the vectors of the fundamental rotation coordinate data input to the fundamental selector and the harmonic rotation coordinate data input to the harmonic selector. The coordinate data rotation calculation device according to claim 1, further comprising a section. Furthermore, the two-dimensional coordinate data, the fundamental wave amplitude, and the harmonic amplitude are input, the two-dimensional coordinate data is multiplied by the fundamental wave amplitude, and the coordinate data of the fundamental wave is output to the fundamental wave selector. 3. The coordinate data rotation calculation device according to claim 1, further comprising a coordinate conversion generation unit that multiplies the coordinate data by the harmonic amplitude and outputs the coordinate data of the harmonic to the harmonic selector. The fundamental wave rotation calculation unit rotates a rotation angle of tan ⁻¹ (2 ⁻ⁱ ) in the i-th cycle (i is an integer of 0 or more),
The said harmonic rotation calculation part performs rotation of the rotation angle of the said order of the said harmonic with respect to the rotation angle of the said fundamental wave rotation calculation part, The any one of Claims 1-3 characterized by the above-mentioned. Coordinate data rotation computing device. The harmonic selector is a third harmonic selector that selects the third harmonic coordinate data of the two-dimensional coordinate data at the first time and the third harmonic rotation coordinate data at the second time and thereafter. Have,
The rotation direction determination unit determines a rotation direction based on the coordinate data selected by the fundamental wave selector and the coordinate data selected by the third harmonic selector,
The harmonic rotation calculation unit rotates the coordinate data selected by the third harmonic selector in the rotation direction determined by the rotation direction determination unit, and rotates the rotated coordinate data by the third harmonic rotation. The coordinate data rotation calculation device according to claim 1, further comprising a third harmonic rotation calculation unit that outputs the coordinate data to the third harmonic selector. The fundamental wave rotation calculation unit rotates a rotation angle of tan ⁻¹ (2 ⁻ⁱ ) in the i-th cycle (i is an integer of 0 or more),
The coordinate data rotation calculation device according to claim 5, wherein the third harmonic rotation calculation unit rotates a rotation angle of 3×tan ⁻¹ (2 ⁻ⁱ ) in the i-th cycle. Further, in the i-th cycle, the coordinate data rotated by the fundamental wave rotation calculation unit is multiplied by (1+2 ⁻²ⁱ ) to output the coordinate data to the fundamental wave selector as the fundamental wave rotation coordinate data. The coordinate data rotation calculation device according to claim 6, further comprising a scaling correction unit. Further, the two-dimensional coordinate data, the fundamental wave amplitude, and the third harmonic amplitude are input, the two-dimensional coordinate data is multiplied by the fundamental wave amplitude, and the fundamental wave coordinate data is output to the fundamental wave selector. 8. A coordinate conversion generation unit that multiplies two-dimensional coordinate data by the third harmonic amplitude and outputs the coordinate data of the third harmonic to the third harmonic selector. The coordinate data rotation calculation device according to any one of items. The harmonic selector is
A third-order harmonic selector that selects the third-order harmonic coordinate data from the two-dimensional coordinate data at the first time, and third-order harmonic rotating coordinate data at the second time and thereafter.
The first time has a fifth-order harmonic selector that selects the fifth-order harmonic coordinate data from the two-dimensional coordinate data, and the second time and thereafter selects the fifth-order harmonic rotation coordinate data.
The rotation direction determination unit determines a rotation direction based on the coordinate data selected by the fundamental wave selector, the coordinate data selected by the third harmonic selector, and the coordinate data selected by the fifth harmonic selector. Then
The harmonic rotation calculation unit,
The coordinate data selected by the third-order harmonic selector is rotated in the rotation direction determined by the rotation-direction determining unit, and the rotated coordinate data is used as the third-order harmonic rotation coordinate data. A third-order harmonic rotation calculation unit that outputs to the selector,
The coordinate data selected by the fifth-order harmonic selector is rotated in the rotation direction determined by the rotation-direction determining unit, and the rotated coordinate data is used as the fifth-order harmonic rotation coordinate data. The coordinate data rotation calculation device according to claim 1, further comprising: a fifth-order harmonic rotation calculation unit that outputs to the selector. The fundamental wave rotation calculation unit rotates a rotation angle of tan ⁻¹ (2 ⁻ⁱ ) in the i-th cycle (i is an integer of 0 or more),
In the i-th cycle, the third-harmonic rotation calculation unit rotates a rotation angle of 3×tan ⁻¹ (2 ⁻ⁱ ),
10. The coordinate data rotation calculation device according to claim 9, wherein the fifth harmonic rotation calculation unit performs rotation of a rotation angle of 5×tan ⁻¹ (2 ⁻ⁱ ) in the i-th cycle. Further, in the i-th cycle, the coordinate data rotated by the fundamental wave rotation calculation unit is multiplied by (1+2 ⁻²ⁱ )×(1+2 ^{−2 i} ), and the coordinate data is used as the fundamental wave rotation coordinate data. A fundamental wave scaling correction unit that outputs to the selector,
In the i-th cycle, the coordinate data rotated by the third harmonic rotation calculating unit is multiplied by (1+2 ⁻²ⁱ ) to obtain the coordinate data as the third harmonic rotation coordinate data in the third harmonic selector. 11. The coordinate data rotation calculation device according to claim 10, further comprising a third harmonic scaling correction unit that outputs. Further, two-dimensional coordinate data, fundamental wave amplitude, third harmonic amplitude, and fifth harmonic amplitude are input, the two-dimensional coordinate data is multiplied by the fundamental wave amplitude, and the coordinate data of the fundamental wave is converted into the fundamental wave. Output to a selector, the two-dimensional coordinate data is multiplied by the third harmonic amplitude, the coordinate data of the third harmonic is output to the third harmonic selector, and the two-dimensional coordinate data is converted to the fifth harmonic. The coordinate data according to any one of claims 9 to 11, further comprising a coordinate conversion generation unit that multiplies a wave amplitude and outputs the coordinate data of the fifth harmonic to the fifth harmonic selector. Rotation calculation device. The coordinate data rotation calculation device according to any one of claims 1 to 12, wherein the harmonic rotation coordinate data includes an initial phase difference between the harmonic and the fundamental wave. A coordinate data rotation calculation method for inputting two-dimensional coordinate data including a fundamental wave and a harmonic, and calculating a deviation angle of a vector of a fundamental wave of the two-dimensional coordinate data,
A fundamental wave selector step of selecting fundamental wave coordinate data of the two-dimensional coordinate data in the first time by the fundamental wave selector and selecting fundamental wave rotating coordinate data in the second and subsequent times;
A harmonic selector step of selecting harmonic coordinate data of the two-dimensional coordinate data at the first time by the harmonic selector and selecting harmonic rotating coordinate data at the second time and thereafter.
A rotation direction determination unit, a rotation direction determination step of determining a rotation direction based on the coordinate data selected in the fundamental wave selector step and the coordinate data selected in the harmonic selector step,
The fundamental wave rotation calculation unit rotates the coordinate data selected in the fundamental wave selector step in the rotation direction determined in the rotation direction determination step, and outputs the rotated coordinate data as the fundamental wave rotation coordinate data. Fundamental wave rotation calculation step to
The harmonic rotation calculation unit rotates the coordinate data selected in the harmonic selector step in the rotation direction determined in the rotation direction determination step, and outputs the rotated coordinate data as the harmonic rotation coordinate data. Harmonic rotation calculation step to
The rotation angle cumulative addition unit cumulatively adds the rotation angles rotated in the fundamental wave rotation calculation step based on the rotation direction determined in the rotation direction determination step to obtain the fundamental wave of the two-dimensional coordinate data. And a rotation angle cumulative addition step of converging to a deviation angle of the vector.

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