TWI616661B - Method of calculating the number of periods of quasi-sinusoidal wave - Google Patents

Abstract

A method for calculating the number of sine-like cycles includes a first conversion step, a second conversion step, a division step, a judgment step, and a counting step. During the first conversion step and the second conversion step, the sine wave-like wave is converted into the triangular wave. In this division step, a division coefficient is selected, and the triangle wave is divided into complex division coordinates. In the determination step, the equal division coordinates are sequentially substituted into an analysis program, thereby determining the number of correct signals to be sent. At the end of the counting step, the number of cycles of the sine wave can be converted based on the division factor and the number of correct signals.

Description

Method for calculating the number of periods of sine waves

The invention relates to a method for calculating the characteristics of a sine wave-like wave, in particular to a method for calculating the number of periods of a sine wave-like wave.

Encoders are widely used in industry, and are mainly used for displacement measurement, such as CNC or servo motor control. Referring to FIG. 1, an encoder 1 includes a light-emitting unit 11, a moving grating 12, a fixed grating 13, and a measuring unit 14 in sequence from left to right; wherein, the moving grating 12 and the fixed grating 13 Have the same periodic stripes.

The light-emitting unit 11 is used to emit two periodic signals, such as a square wave or a sine wave. After these signals are sent out, they will pass through the moving grating 12 and the fixed grating 13 in sequence, and finally be received by the measuring unit 14.

Since the traveling grating 12 and the fixed grating 13 have the same periodic fringes, when the transparent portion of the traveling grating 12 and the transparent portion of the fixed grating 13 overlap each other, the luminous flux is the most at this time, so when these When the signal passes, there will be a maximum peak; and when the transparent and opaque places overlap each other, the luminous flux is the smallest, so when these signals pass, you will get a minimum valley (deep) ). Therefore, when the wandering grating 12 moves up and down, the signals respectively become a sine wave with a certain number of cycles, and are received by the measuring unit 14. Since the period of the sinusoidal wave is proportional to the moving distance of the wandering grating 12, the distance moved by the wandering grating 12 can be accurately converted as long as the number of periods of the sinusoidal wave is calculated. As a simple example, if the fringe period of the wandering grating 12 is 20um, and the aforementioned sine wave calculation has 12.34 cycles, the moving distance of the wandering grating 12 can be obtained as: 20um * 12.34 = 246.8um.

However, because it is limited by various factors such as optical diffraction, the accuracy of the grating process, and the noise of the electronic component itself, as shown in FIG. 2, generally speaking, the measurement unit 14 will not receive the perfect Sine wave, but received a sine-like wave with unstable amplitude. However, if such a sine wave is used for periodic calculation, there is no way to be very accurate, resulting in an inevitable error when calculating the moving distance. Therefore, as the measurement accuracy required by the semiconductor and electronics industry is getting higher and higher, how to calculate the period of the sine-like wave more accurately in order to improve the measurement accuracy has become an important issue.

Therefore, the purpose of the present invention is to provide a method for calculating the number of periods of a sine-like wave that can accurately calculate the period of the sine-like wave.

Therefore, a method for calculating the number of cycles of a sine-like wave of the present invention includes a first conversion step, a second conversion step, a division step, a judgment step, and a counting step. This type of sine wave is a function composed of two mutually perpendicular vibration axes and phase axes.

In the first conversion step, the sine-like wave is input to a comparator, thereby converting the sine-like wave into a corresponding square wave.

In the second conversion step, the square wave is input to an integrator, thereby converting the square wave into a corresponding triangular wave, and the triangular wave has an amplitude on the vibration axis.

In the segmentation step, the triangle wave is input to an analysis processing module, and a segmentation coefficient is selected, thereby cutting the triangle wave into a plurality of segmentation coordinates.

In this judgment step, an analysis program consisting of the division coefficient and the amplitude of the triangle wave is defined, and then the equal division coordinates are sequentially substituted into the analysis program. If the current division coordinates do not satisfy the analysis program, then Substitute the next division coordinate to the analysis program, if the substituted division coordinate satisfies the analysis program, transmit a correct signal, and then substitute the next division coordinate to the analysis program, when all the division coordinates have been substituted, end the judgment step.

In the counting step, the number of correct signals obtained is divided by twice the division factor to obtain the number of cycles of the sine wave.

The effect of the present invention is that: through the first conversion step and the second conversion step, the sine wave is converted into the triangle wave; and then through the division step and the judgment step, the triangle wave is divided into the division coordinates, And select the value of the division coefficient, and then substitute the equal division coordinates into the analysis program in order to determine whether it is necessary to send a correct signal; finally, through the counting step, the number of cycles of the sine wave can be calculated, and When the selected segmentation coefficient is larger, the calculated accuracy is also higher.

Before the present invention is described in detail, it should be noted that in the following description, similar elements are denoted by the same number.

Referring to FIG. 3, a first embodiment of the method for calculating the number of sine-like cycles of the present invention includes a first conversion step 2, a second conversion step 3, a division step 4, a judgment step 5, and a counting step 6, and a displacement calculation step 7. This type of sine wave is a function composed of two mutually perpendicular phase axes and vibration axes, and for convenience of description, the t axis and the y axis will be used to represent the phase axis and the vibration axis, respectively. In addition, it should be particularly explained that each paragraph in the embodiment must refer to FIG. 3. In order to make the description clearer and more concise, subsequent paragraphs will not be specially reminded.

Referring to FIG. 4, during the first conversion step 2, the sine wave-like wave is input to a comparator, thereby converting the sine wave-like wave into a corresponding square wave. In the second conversion step 3, the square wave is input to an integrator, thereby converting the square wave into a corresponding triangular wave. The triangular wave has an amplitude A at the vibration axis, and in the first embodiment, the value of the amplitude A is 2.

Referring to FIG. 5, in the segmentation step 4, the triangle wave is input to an analysis processing module, thereby cutting the triangle wave into a plurality of segmentation coordinates. In the first embodiment, the triangle wave will be divided into (t = 0, y = 0), (t = 1, y = 1), ..., and (t = 12, y = 0), etc. Split coordinates, and define (t = 0, y = 0) as the initial split coordinates.

Next, the implementation of the judgment step 5 will be described using FIGS. 6-7, and the partial flow of the judgment step 5 will be exemplified with FIGS. 8-9.

Referring to FIG. 6, in the judgment step 5, a division coefficient S is selected, and then the equal division coordinates are sequentially substituted into an analysis program 51. If the current segmentation coordinate (t, y) does not satisfy the analysis program 51, the next segmentation coordinate (t, y) is substituted into the analysis program 51. If the subdivided coordinates (t, y) satisfied satisfy the analysis program 51, a correct signal is transmitted, and then the next subordinate coordinates (t, y) are substituted into the analysis program 51. After all the division coordinates are substituted, the judgment step 5 can be ended.

Referring to Figure 7, the above described first configuration of the four parameter analysis program 51: a shaft vibration displacement amount [rho], [Psi] a variable oscillation axis, determining a first number ψ ^+, and determining a second number ψ ^-; wherein, ρ≡ the amplitude A / the division coefficient S, ψ ⁺ ≡ ψ + ρ, ψ ^- ≡ ψ-ρ. In particular, the initial value of the vibration axis variable ψ is equal to the oscillation axis component of the initial division coordinate. For example, in the first embodiment, the initial division coordinate is (t = 0, y = 0), Therefore, the initial value of the vibration axis variable ψ = 0; in addition, in the first embodiment, the vibration axis displacement ρ = A / S = 2/2 = 1.

Next, the flow of the analysis program 51 will be described. When one of the division coordinates (t, y) is substituted into the analysis program 51, the vibration axis component is divided into the following three situations according to the size of the substitution: (1) ψ ⁺ >y> ψ ^-, i.e., the number of the first determination> substituting vibrate axis component> the second number is determined: In this case it is determined that the parser 51 is not satisfied, and directly ends the analysis program 51. (2) y ≧ ψ ⁺ , that is, the substituted vibration axis component ≧ the first judgment number: a first direction signal is output at this time, and it is determined that the analysis program 51 is satisfied, and then the value of the vibration axis variable ψ is updated In order to substitute the value of the vibration axis component, the analysis program 51 is finally ended. (3) y ≦ ψ ^-, i.e. substituting the vibration axis component of the second number ≦ determination: when the output signal in a second direction, and it is determined to meet the analysis program 51, followed by the variable axis vibration value [Psi], update In order to substitute the value of the vibration axis component, the analysis program 51 is finally ended.

In order to explain more clearly, the following example demonstrates part of the flow of this judgment step 5. From the foregoing description that we know the initial value of [Psi] = 0, ρ = 1, then this time ^{ψ + = 1, ψ - =} -1. Therefore, as shown, when the first division coordinate (t = 0, y = 0 ) after substituting the analysis program 51, when ^{ψ 8 +> y = 0>} ψ -, so that analysis program 51 determines not satisfied, The analysis program 51 is directly ended, and the next division coordinate (t = 1, y = 1) is substituted into the analysis program 51.

Then, as shown in FIG. 9, after the next division coordinate (t = 1, y = 1) is substituted, since y = 1 ≧ ψ ⁺ at this time, it is judged that the analysis program 51 is satisfied, and the first direction signal will be output, and [Psi] as the variable to update the oscillating shaft, that is, ψ = y = 1, and at this time ^{ψ + = 1 + 1 = 2} , ψ - = 1-1 = 0. After the update, the analysis program 51 is ended first, then a correct signal is sent out, and then the next division coordinate (t = 2, y = 2) is substituted into the analysis program 51. By analogy, the final judgment step 5 can be completed, and 12 correct signals are obtained. It is worth mentioning that the first direction signal and the second direction signal are used to determine the propagation direction of the sine wave, for example, as shown in FIG. 1, when applied to displacement measurement, just confirm the measurement unit 14 Whether the first direction signal or the second direction signal is received, it can be deduced whether the traveling grating 12 moves upward or downward.

In the counting step 6, the number of correct signals obtained is divided by twice the division factor S to obtain the number of cycles of the sine wave. For example, in the first embodiment, the number of cycles of this type of sine wave = (the number of correct signals) / (2 * the division factor S) = 12 / (2 * 2) = 3.

Therefore, regardless of the application field, when calculating the number of cycles of a sine-like wave, the first conversion step 2 to the counting step 6 can be used to calculate the number of cycles, and when the selected division factor S is larger , The accuracy of the calculation will be higher. If it is to be used in the displacement measurement of the encoder, the displacement calculation step 7 can be used. Referring to FIG. 1, assuming that the period length of the moving grating 12 and the fixed grating 13 is 20 μm, the displacement calculation step 7 is to multiply the number of periods of the sine wave-like (3) by the grating period of the moving grating 12 Length (20um), by which the displacement of the wandering grating 12 can be obtained, that is, 3 * 20um = 60um.

In order to explain the judgment step 5 and the analysis program 51 more completely, a second embodiment is used as an example below. Referring to FIGS. 10 to 11, and assisted by FIGS. 5 to 6, suppose that the sine-like wave of the second embodiment outputs the triangular wave as shown in FIG. 10 after the first conversion step 2 and the second conversion step 3, and The parameters of the second embodiment are similar to those of the first embodiment, that is, the amplitude A = 2, the division coefficient S = 2, and the vibration axis displacement ρ = 1. In addition, due to the triangular wave of the second embodiment, the segmentation coordinates of the front segment are the same as those of the first embodiment, so they will not be repeated here. The segmentation coordinates of the rear segment (t = 10, y = 2) ~ (t = 14, y = 0) The process of this judgment step will be described. Therefore, when the division coordinates (t = 10, y = 2) ~ (t = 14, y = 0) are substituted, they can be divided into the following three stages: (1) When the division coordinates (t = 10, y = 2) are substituted After the analysis program 51, referring to the demonstration of the first embodiment, it can be concluded that the analysis program will be satisfied at this time, so the vibration axis variable ψ will be updated first, that is, ψ = y = 2, and then a The first direction signal and a correct signal are then substituted into the next segmentation coordinate (t = 11, y = 1.5) to the analysis program 51. (2) dividing a current coordinate (t = 11, y = 1.5 ) after substituting, since at this time ^{ψ + = 2 + 1 = 1} , ψ - = 2-1 = 1, i.e. ψ ^+> y = 1.5> ψ ^-Therefore , it is determined that the analysis program 51 is not satisfied. At this time, the value of the vibration axis variable ψ is not updated, and when the analysis program 51 is ended, the correct signal is not output. (3) When the next division coordinate (t = 12, y = 1) is substituted, since y = 1 ≦ ψ ^- at this time, the vibration axis variable ψ, that is, ψ = y = 1, will be updated and the output A first direction signal and a correct signal. By analogy, the next segmentation coordinate (t = 13, y = 0.5) will also not satisfy the analysis procedure until the next segmentation coordinate (t = 14, y = 0). So in the end, as in the first embodiment, 12 correct signals will be obtained.

As mentioned in the prior art, the measurement unit 14 in FIG. 1 receives various sine-like waves due to many factors. For example, when the wandering grating 12 suddenly changes its speed while moving, a triangular wave as shown in FIG. 10 is generated, so the second embodiment shows that even if various kinds of sine waves are generated due to various factors, the present invention can still be utilized The method accurately calculates the period of the sine-like wave, and derives the moving distance of the wandering grating 12.

In summary, the method for calculating the number of periods of the sine-like wave of the present invention converts the sine-like wave into the triangular wave through the first conversion step 2 and the second conversion step 3; In the judgment step 5, the triangle wave is divided into the division coordinates, and the value of the division coefficient S is selected, and then the equal division coordinates are sequentially substituted into the analysis program 51 to judge whether it is necessary to send a correct signal; and finally by In the counting step 6, the number of cycles of the sine wave can be calculated, and the larger the selected division factor S, the higher the accuracy of the calculation, so it can indeed achieve the purpose of the invention.

However, the above are only examples of the present invention, and should not be used to limit the scope of implementation of the present invention, any simple equivalent changes and modifications made in accordance with the scope of the patent application of the present invention and the contents of the patent specification are still Within the scope of the invention patent.

1‧‧‧ Encoder
11‧‧‧Lighting unit
12‧‧‧travel grating
13‧‧‧Fixed grating
14‧‧‧Measurement unit
2‧‧‧ First conversion step
3‧‧‧The second conversion step
4‧‧‧Segmentation step
5‧‧‧Judgment steps
51‧‧‧Analysis procedure
6‧‧‧Counting steps
7‧‧‧Displacement calculation steps
A‧‧‧Amplitude
t‧‧‧Phase axis
y‧‧‧Vibration axis ρ‧‧‧Vibration axis displacement ψ‧‧‧Vibration axis variable ψ <sup> + </ sup> ‧‧‧First judgment number ψ <sup>-</ sup> Dichotomous number

Other features and functions of the present invention will be clearly presented in the embodiment with reference to the drawings, in which: FIG. 1 is a schematic diagram of an encoder; FIG. 2 is a two-dimensional coordinate diagram illustrating a quantity of the encoder The measurement unit receives a sine-like wave; FIG. 3 is a flowchart illustrating a first embodiment of the method for calculating the number of periods of the sine-like wave of the present invention; FIG. 4 is a two-dimensional coordinate graph group, illustrating A first conversion step and a second conversion step of the first embodiment convert a sine-like wave into a triangular wave; FIG. 5 is a two-dimensional coordinate diagram illustrating that the triangular wave is cut into a plurality of division coordinates; FIG. 6 is A flowchart illustrating the flow of a judgment step of the first embodiment; FIG. 7 is a flowchart illustrating the flow of an analysis program in the judgment step; FIGS. 8 and 9 are respectively a two-dimensional coordinate diagram to illustrate Part of the process of this judgment step; FIG. 10 is a two-dimensional coordinate diagram illustrating a second embodiment of the method for calculating the number of periods of a sine-like wave of the present invention; and FIG. 11 is a two-dimensional coordinate FIG., The step of determining a portion of the process described in the second embodiment.

2‧‧‧ First conversion step

3‧‧‧The second conversion step

4‧‧‧Segmentation step

5‧‧‧Judgment steps

51‧‧‧Analysis procedure

6‧‧‧Counting steps

7‧‧‧Displacement calculation steps

Claims (5)

A method for calculating the number of periods of a sine-like wave, which is a function composed of two mutually perpendicular phase axes and vibration axes. The method of the present invention sequentially includes: a first conversion step to convert the sine-like waves Input to a comparator to convert the sine wave to a corresponding square wave; a second conversion step to input the square wave to an integrator to convert the square wave to a corresponding square wave Triangle wave, and the triangle wave has an amplitude on the vibration axis; a division step, input the triangle wave to an analysis processing module, thereby cutting the triangle wave into a plurality of division coordinates; a judgment step, select a division coefficient, and Define an analysis program composed of the segmentation coefficient and the amplitude of the triangle wave, and then substitute the equal segmentation coordinates into the analysis program in sequence. If the current segmentation coordinates do not satisfy the analysis program, then substitute the next segmentation coordinate to In the analysis program, if the segmentation coordinates entered satisfy the analysis procedure, a correct signal is transmitted, and then the next segmentation coordinates are substituted to The analysis procedure ends the judgment step after all the division coordinates have been substituted; and a counting step, which divides the number of correct signals obtained by twice the division coefficient to obtain the Number of cycles. The method for calculating the number of sine wave-like cycles as described in claim 1, wherein, in the judgment step, the first division coordinate substituted into the analysis program is defined as the initial division coordinate; the analysis program is defined by the following parameters A vibration axis displacement is equal to the amplitude of the triangle wave divided by the division factor, a vibration axis variable. When the division coordinates have not been substituted into the analysis program, the vibration axis variable is equal to the vibration axis component of the initial division coordinate, a The first judgment number is equal to the vibration axis variable plus the vibration axis displacement, and a second judgment number is equal to the vibration axis variable minus the vibration axis displacement; therefore, when any one of the division coordinates is substituted into the analysis program, if it is substituted into When the vibration axis component is less than the first judgment number and greater than the second judgment number, it is determined that the analysis procedure is not satisfied, and the analysis procedure is ended, otherwise it is determined that the analysis procedure is satisfied, and the vibration axis variable is determined The value of is updated to the value of the vibration axis component that is substituted, and the analysis process is ended after the update. The method for calculating the number of sine-like cycles as described in claim 2, wherein, in the analysis procedure, if the substituted division coordinates are determined not to satisfy the analysis procedure, and the phase axis component of the substituted division coordinates is not less than the The first judgment number outputs a first direction signal. The method for calculating the number of sine-like cycles as described in claim 3, wherein, in the analysis procedure, if the substituted division coordinates are determined not to satisfy the analysis procedure, and the phase axis component of the substituted division coordinates is not greater than the The second judgment number outputs a second direction signal. The method for calculating the number of periods of a sine wave-like wave as described in any one of claims 1 to 4 further includes a displacement calculation step after the counting step, which is a step of multiplying the number of periods of the sine wave-like wave by One raster period length.