Linear conversion of sine-cosine displacement sensing signal and displacement analysis method

Abstract

The application discloses a linear conversion and displacement analysis method of a sine-cosine displacement sensing signal, which comprises the following steps: S1) constructing a linear conversion function based on Fourier series approximation to convert a nonlinear sine-cosine displacement sensing signal into a linear sensing signal; S2) constructing a displacement direction distinguishing signal to realize slope adaptive discrimination and conversion of the linear sensing signal; S3) performing amplitude cutting and subdivision on the linear sensing signal to obtain a quadrature subdivision pulse signal; S4) performing forward and reverse counting on the quadrature subdivision pulse signal to obtain a total number of subdivision pulses; and S5) multiplying the total number of subdivision pulses by a pulse equivalent to obtain an analytical displacement. The linear conversion and displacement analysis circuit of the sine-cosine displacement sensing signal is developed by using an A / D+FPGA hardware architecture, and the theoretical error of displacement analysis is as low as ±0.054% of a sine-cosine displacement sensing signal period, which can be used for photoelectric encoders and magneto-electric encoders to realize deep submicron precision displacement measurement.

Description

Technical Field

[0001] This invention belongs to the field of precision displacement sensing technology, and in particular relates to a linear conversion and displacement analysis method for sine and cosine displacement sensing signals. Background Technology

[0002] Sine and cosine displacement sensing signals are the most common signal output form for photoelectric encoders and magnetoelectric encoders. Subdivision of sine and cosine displacement sensing signals by hundreds or even tens of thousands of times is an effective way for encoders to achieve high-precision, high-resolution displacement analysis. From the perspective of the basic principles of electronic subdivision, it is mainly divided into phase subdivision and amplitude subdivision of sine and cosine displacement sensing signals.

[0003] Arctangent subdivision is the most widely used phase subdivision method, which divides the phase angle of sine and cosine displacement sensing signals by calculating the arctangent value. Common methods for implementing arctangent calculation include the lookup table method and the CORDIC (Coordinate Rotation Digital Calculation) algorithm. The former is generally used for subdivisions below 400 times, while the latter is generally used for subdivisions above 1024 times. For ideal sine and cosine displacement sensing signals, the arctangent subdivision algorithm has extremely high subdivision accuracy and is unaffected by signal amplitude fluctuations. However, due to the complexity of the arctangent calculation, its delay is relatively large.

[0004] Amplitude subdivision involves segmenting the amplitude of a sine or cosine displacement sensing signal or its transformed signal. Changes in voltage amplitude trigger the generation of subdivision pulses. Due to the nonlinearity of the sine and cosine displacement sensing signal waveform, the sensitivity of the sensing signal amplitude to the measured displacement is not constant across the entire range, exhibiting significant amplitude subdivision uncertainty near troughs and peaks. Amplitude linearization subdivision transforms the sine and cosine displacement sensing signal into an approximately linear signal, generating subdivision pulses by segmenting the amplitude of this linear signal. This method has the advantages of low logic resource consumption and short delay, but the accuracy of amplitude subdivision is limited by the linear conversion accuracy of the sine and cosine displacement sensing signal. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, this invention provides a linear conversion and displacement analysis method for sine and cosine displacement sensing signals, which converts nonlinear sine and cosine displacement sensing signals into high-precision linear sensing signals, achieving constant sensitivity of the signal waveform relative displacement within the range; the linear sensing signal is further subdivided by amplitude cutting to obtain orthogonal subdivided pulse sensing signals, achieving high-precision analysis with displacement analysis error as low as ±0.35% of the sensing signal period.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A linear transformation and displacement analysis method for sine and cosine displacement sensing signals specifically includes the following steps:

[0008] S1: Obtain nonlinear sine and cosine displacement sensing signals V through photoelectric encoders or magneto-electric encoders. S (θ) and V C (θ), based on Fourier series approximation, a linear transformation function is constructed to transform the acquired nonlinear sine and cosine displacement sensing signal V. S (θ) and V C (θ) is converted into a linear sensing signal V2(θ):

[0009]

[0010] c n The Fourier coefficients are expressed as follows:

[0011] c1 = k1a1 + k2

[0012] c n =k1a n n≥3

[0013] To ensure good linearity of the linear sensing signal V2(θ), the optimal values ​​of k1 and k2 should satisfy:

[0014] k1a1+k2=b1

[0015] k1a n →b n n≥3

[0016] Therefore, we can conclude that:

[0017]

[0018] V2(θ) deviates from V tri The maximum nonlinear waveform deviation of (θ) is expressed as:

[0019] |E2(θ)| max =Max{|V2(θ)-V tri (θ)|}

[0020] S2: Construct the displacement direction discrimination signal Direc(θ) to achieve adaptive slope discrimination of V2(θ), and transform V2(θ) into V 2R (θ): When Direc(θ)=0, V 2R (θ)=V2(θ); when Direc(θ)=1, V 2R (θ) = -V²(θ). During positive displacement, V 2R The slope of (θ) is positive.

[0021] The logic level of the displacement direction discrimination signal Direc(θ) is generated as follows: when V S (θ) and V CWhen the magnitudes of (θ) have the same sign, Direc(θ) = 0; when V S (θ) and V C Direc(θ) = 1 when the sign of the amplitude of (θ) is different.

[0022] S3: For the linearly transformed signal V 2R (θ) Perform N times amplitude cutting and subdivision, with a division interval ΔU=2U / N, to obtain two orthogonal square wave signals A and B.

[0023] S4: Distinguish the levels of orthogonal square wave signals A and B, and generate forward and reverse counting pulse signals. The number of forward counting pulses is M1, and the number of reverse counting pulses is M2.

[0024] S5: Based on the number of forward and reverse counting pulses, obtain the analytical displacement: x C = (M1-M2)×δ.

[0025] δ is the pulse equivalent, which is calculated by the formula δ=P / (4N), where P is the displacement represented by one cycle of sine and cosine displacement sensing signals.

[0026] Preferably, the preferred value of k1 is k1 = 0.7090, at which point k2 = 0.2953, |E2(θ)| max The minimum value is obtained, and the theoretical nonlinear waveform error is 0.43%. The expression for V2(θ) is:

[0027]

[0028] Preferably, the orthogonal square wave signals A and B are generated as follows: during positive displacement, whenever V... 2R When the amplitude of (θ) increases by ΔU, A and B each generate a square wave, with B shifted by 90° relative to A; during the reverse displacement, whenever V 2R When the amplitude of (θ) decreases by ΔU, A and B each generate a square wave, and the phase shift of B relative to A is -90°.

[0029] Preferably, the conditions for generating the positive counting pulse are: the level changes of the orthogonal square wave signals A and B are "AB=01→AB=00" or "AB=11→AB=01" or "AB=00→AB=10" or "AB=10→AB=11"; the conditions for generating the reverse counting pulse are: the level changes of the orthogonal square wave signals A and B are "AB=01→AB=11" or "AB=11→AB=10" or "AB=10→AB=00" or "AB=01→AB=11".

[0030] A digital signal processing module, wherein the digital signal processing module uses an FPGA as a high-speed digital signal processor to realize linear conversion of sine and cosine displacement sensing signals and displacement analysis methods.

[0031] A linear conversion and displacement analysis circuit for sine and cosine displacement sensing signals is disclosed. The circuit is developed using an "A / D+FPGA" hardware architecture and includes a power supply module, an analog signal conditioning module, an analog-to-digital conversion module, and a digital signal processing module.

[0032] Preferably, the power supply module is powered by an external DC power supply of 12-24V, and then obtains a power supply voltage of 5V, 3.3V, 2.5V, and 1.2V through a power conversion chip; the analog signal conditioning module performs amplitude conditioning, common-mode level conditioning, and low-pass filtering on the sine and cosine displacement sensing signals; the analog-to-digital conversion module uses a 12-bit or 14-bit A / D chip.

[0033] Compared with the prior art, the beneficial effects of the present invention are:

[0034] 1) The present invention is based on the linear conversion method of grating sensing signals by Fourier series approximation, which can convert grating sine and cosine nonlinear sensing signals into linear sensing signals with high precision, so that the sensitivity of the sensing signal amplitude with the measured displacement remains constant throughout the entire range.

[0035] 2) The linear sensing signal is subdivided by amplitude cutting to obtain orthogonal subdivided pulse sensing signal, achieving high-precision analysis with displacement analysis error as low as ±0.35% of the sensing signal period. Attached Figure Description

[0036] Figure 1 To transform the signal V1(θ) and the ideal linear signal V tri Comparison of Fourier coefficients of (θ).

[0037] Figure 2 This is a flowchart of the linear transformation and displacement analysis of sine and cosine displacement sensing signals.

[0038] Figure 3 For V2(θ) to deviate from V tri (θ) The curve showing the relationship between the maximum value and k1.

[0039] Figure 4 When the displacement is positive, V S (θ), V C (θ), Direc(θ), V2(θ), V 2R Waveform of (θ).

[0040] Figure 5 When the displacement is positive, for the linear transformation signal V 2R(θ) A schematic diagram of the orthogonal square wave signals A and B generated by amplitude cutting subdivision.

[0041] Figure 6 This is the theoretical error curve for the linear conversion of sine and cosine displacement sensing signals and the displacement analysis method.

[0042] Figure 7 This describes the composition of a linear conversion circuit for sine and cosine displacement sensing signals and a displacement analysis circuit.

[0043] Figure 8 The waveforms of the subdivided orthogonal square wave signals A and B are shown when the input is a 20μm grating sine and cosine displacement sensing signal, and the displacement is positive.

[0044] Figure 9 The waveforms of the subdivided orthogonal square wave signals A and B are obtained when the 20μm grating sine and cosine displacement sensing signal is used as input and the displacement is reversed.

[0045] Figure 10 The experimental error of the linear conversion and displacement analysis circuit is calculated using a 20μm grating sine and cosine displacement sensing signal as input. Detailed Implementation

[0046] The following provides a detailed description of embodiments of the present invention. These embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments:

[0047] A linear transformation and displacement analysis method for sine and cosine displacement sensing signals is proposed, based on the transformation signal V1(θ) and its corresponding ideal linear signal V tri Fourier series expansion of (θ) and coefficient comparison:

[0048]

[0049]

[0050] In the formula, a n and b n These are the Fourier coefficients, where n is an integer. V1(θ) and V tri (θ) are all symmetric about the central axis (θ=0), therefore, when n is even, a n and b n All equal to 0. n b n a n / b n The values ​​are shown in Table 1, indicating that V1(θ) and V tri (θ) has comparable harmonic coefficients. Therefore, by introducing proportionality coefficients k1 and k2, V1(θ) can be made comparable to V. triFourier series approximation of (θ): 1) When n≥3, a n >b n Therefore, V1(θ) can be multiplied by a proportionality coefficient k1 (k1 < 1) such that k1a n ≈b n ;2) When n=1, a n <b n Therefore, V1(θ) can be compensated with the first-order Fourier series k2cos(2θ-π)=k2C(θ), such that k1a1+k2≈b1. C(θ) can be obtained through real-time calculation of the sine and cosine displacement sensing signals:

[0051]

[0052] Table 1 V1(θ) and V tri Fourier expansion coefficients of (θ) and their ratios

[0053]

[0054] Example 1

[0055] refer to Figure 2-5 A linear transformation and displacement analysis method for sine and cosine displacement sensing signals, based on the idea of ​​Fourier series approximation, specifically includes the following steps:

[0056] S1: Obtain nonlinear sine and cosine displacement sensing signals V through photoelectric encoders or magneto-electric encoders. S (θ) and V C (θ), based on Fourier series approximation, a linear transformation function is constructed to transform the acquired nonlinear sine and cosine displacement sensing signal V. S (θ) and V C (θ) is converted into a linear sensing signal V2(θ):

[0057]

[0058] c n The Fourier coefficients are expressed as follows:

[0059] c1=k1a1+k2 (5)

[0060] c n =k1a n n≥3 (6)

[0061] To ensure good linearity of the linear sensing signal V2(θ), the optimal values ​​of k1 and k2 should satisfy:

[0062] k1a1+k2=b1 (7)

[0063] k1a n →bn ,n≥3 (8)

[0064] Therefore, we can conclude that:

[0065]

[0066] V2(θ) deviates from V tri The maximum nonlinear waveform deviation of (θ) is expressed as:

[0067] |E2(θ)| max =Max{|V2(θ)-V tri (θ)|} (10)

[0068] Figure 3 Let the coefficients k1 and |E2(θ)| be the coefficients. max The relationship between them.

[0069] Preferably, the preferred value of k1 is k1 = 0.7090, at which point k2 = 0.2953, |E2(θ)| max The minimum value is obtained, and the theoretical nonlinear waveform error is 0.43%. The expression for V2(θ) is:

[0070]

[0071] S2: Construct the displacement direction discrimination signal Direc(θ) to achieve adaptive slope discrimination of V2(θ), and transform V2(θ) into V 2R (θ): When Direc(θ)=0, V 2R (θ)=V2(θ); when Direc(θ)=1, V 2R (θ) = -V²(θ). During positive displacement, V 2R The slope of (θ) is positive, such as Figure 4 As shown.

[0072] The logic level of the displacement direction discrimination signal Direc(θ) is generated as follows: when V S (θ) and V C When the magnitudes of (θ) have the same sign, Direc(θ) = 0; when V S (θ) and V C Direc(θ) = 1 when the sign of the amplitude of (θ) is different.

[0073] S3: For the linearly transformed signal V 2R (θ) Perform N times amplitude cutting and subdivision, with a division interval ΔU=2U / N, to obtain two orthogonal square wave signals A and B.

[0074] like Figure 5 As shown, the orthogonal square wave signals A and B are generated as follows: during positive displacement, whenever V...2R When the amplitude of (θ) increases by ΔU, A and B each generate a square wave, with B shifted by 90° relative to A; during the reverse displacement, whenever V 2R When the amplitude of (θ) decreases by ΔU, A and B each generate a square wave, and the phase shift of B relative to A is -90°.

[0075] S4: Distinguish the levels of orthogonal square wave signals A and B, and generate forward and reverse counting pulse signals. The number of forward counting pulses is M1, and the number of reverse counting pulses is M2.

[0076] The conditions for generating the positive counting pulse are: the level changes of the orthogonal square wave signals A and B are "AB=01→AB=00" or "AB=11→AB=01" or "AB=00→AB=10" or "AB=10→AB=11"; the conditions for generating the reverse counting pulse are: the level changes of the orthogonal square wave signals A and B are "AB=01→AB=11" or "AB=11→AB=10" or "AB=10→AB=00" or "AB=01→AB=11".

[0077] S5: Based on the number of forward and reverse counting pulses, obtain the analytical displacement: x C = (M1-M2)×δ.

[0078] δ is the pulse equivalent, which is calculated by the formula δ=P / (4N), where P is the displacement represented by one cycle of sine and cosine displacement sensing signals.

[0079] refer to Figure 6 A linear conversion and displacement analysis method for sine and cosine displacement sensing signals, wherein the theoretical phase angle analytical error of the displacement analysis method is θ. C –θ=±0.0034rad, when the period of the sine and cosine displacement sensing signal is P=20μm, the theoretical error of the displacement analysis method is x. C –x=(θ C –θ)P / (2π)=±0.0108μm. That is, the theoretical error of the displacement analysis method is ±0.054% of the period of the sine and cosine displacement sensing signal.

[0080] Example 2

[0081] A digital signal processing module, wherein the digital signal processing module uses an FPGA as a high-speed digital signal processor to realize linear conversion of sine and cosine displacement sensing signals and displacement analysis methods.

[0082] Example 3

[0083] A linear conversion and displacement analysis circuit for sine and cosine displacement sensing signals is disclosed. The circuit is developed using an "A / D+FPGA" hardware architecture and includes a power supply module, an analog signal conditioning module, an analog-to-digital conversion module, and a digital signal processing module.

[0084] The power supply module is powered by an external DC power supply of 12-24V, and then obtains a power supply voltage of 5V, 3.3V, 2.5V, and 1.2V through a power conversion chip; the analog signal conditioning module performs amplitude conditioning, common-mode level conditioning, and low-pass filtering on the sine and cosine displacement sensing signals; the analog-to-digital conversion module uses a 12-bit or 14-bit A / D chip.

[0085] refer to Figure 7 The hardware architecture of A / D+FPGA is adopted to develop the linear conversion and displacement analysis digital circuit of the sine and cosine displacement sensing signals. It mainly includes the power supply section, analog signal conditioning section, analog-to-digital conversion section, and digital signal processing section.

[0086] The power module is powered by an external DC power supply of 12-24V. First, a 7V intermediate voltage is obtained using the MPQ2315 DC-DC switching power converter chip. Then, the analog circuit section is powered by the LM1085-5 linear power converter chip, with a typical ripple of 0.015% under no-load and 0.1% under load. The digital circuit section is powered by the MP2359 switching power converter chip. The PLL section inside the FPGA is powered by the AMS-1117-2.5 linear power converter chip, and the FPGA core is powered by the MP2359 switching power converter chip.

[0087] The analog signal conditioning module performs amplitude conditioning, common-mode level conditioning, and low-pass filtering on the sine and cosine displacement sensing signals. The cutoff frequency (-3dB) of the differential low-pass filter is approximately 5MHz. A fully differential amplifier THS4531A with configurable output common-mode voltage is used for differential amplification to achieve signal amplitude and common-mode level conditioning. The reference voltage output from the A / D conversion chip is used as the common-mode voltage and directly supplied to the THS4531A to reduce offset and drift errors.

[0088] The analog-to-digital converter (ADC) module uses the AD9220, a 12-bit multi-stage differential pipelined AD chip. The AD9220 is single-supply operated, with an integral nonlinearity of 0.5 LSB, a differential nonlinearity of 0.3 LSB, and a reference noise of 0.09 LSB. It integrates an on-chip reference voltage source and a high-performance sample-and-hold circuit, achieving a data conversion rate of 10 MSPS. A 2V reference voltage is used to directly provide the common-mode bias voltage for the THS4531A amplifier, minimizing offset errors.

[0089] The digital signal processing module uses an FPGA as a high-speed digital signal processor to achieve linear conversion and displacement analysis of sine and cosine displacement sensing signals. The FPGA selected is Altera's Cyclone IV series EP4CE30F23C8N. The communication interface mainly includes a JTAG interface for FPGA development and debugging, an RS232 serial port for displacement data output, and an incremental data output interface. To ensure the reliability of long-distance transmission, a differential line driver MC3487 is used for differential transmission of incremental quadrature pulse AB signals.

[0090] refer to Figure 8-10 Using a 20μm grating sine and cosine displacement sensing signal as the input signal, after linear conversion of the sine and cosine displacement sensing signal and processing by the displacement analysis digital circuit, the waveforms of orthogonal square wave signals A and B are obtained. By discriminating the levels of the orthogonal square wave signals A and B and generating pulse signals, the measured displacement x can be obtained. C Using the measured value x of the laser interferometer as a reference, the experimental error of the linear conversion of the sine and cosine displacement sensing signals and the displacement analytical digital circuit is x. C -x, with a maximum error of ±0.07μm.

[0091] The above description is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention. All components not explicitly stated in this embodiment can be implemented using existing technology.

Claims

1. A method for linear conversion and displacement analysis of a sine-cosine displacement sensing signal, characterized in that, Specifically, the following steps are included: S1: Obtain a nonlinear sine displacement sensing signal V1(θ) through an optical encoder or a magneto-electric encoder S (θ) and V C (θ), based on Fourier series approximation, construct a linear conversion function, and convert the obtained nonlinear sine displacement sensing signal V S (θ) and V C (θ) into a linear sensing signal V2(θ); S2: Construct the displacement direction discrimination signal Direc(θ) to achieve adaptive slope discrimination of V2(θ), and transform V2(θ) into... V 2R (θ): When Direc(θ) = 0, V 2R (θ) = V2(θ); when Direc(θ) = 1, V 2R (θ) = -V2(θ); During positive displacement, V 2R The slope of (θ) is positive; S3: linearly transformed signal V 2R (θ) is performed N Amplitude doubling cut subdivision, cut interval Δ U = 2 U / N , obtaining two orthogonal square wave signals A and B; S4: discriminate the level of the orthogonal square wave signals A and B, generate forward and reverse counting pulse signals, the number of forward counting pulses is M 1, and the number of reverse counting pulses is M 2; S5: According to the number of forward counting pulses and reverse counting pulses, the analytical displacement is obtained: x C = ( M 1 - M 2) × δ; δ is the pulse equivalent, which is calculated as δ = 1 / (4 f) P , N , P is the displacement represented by 1 positive sine displacement sensor signal period; S1 is specifically: ；c n is the Fourier coefficient, and the expression is: ; ; in order to make the linear sensing signal V2(θ) have better linearity, k 1 and k 2 values should satisfy: ; ; thus: ; V2(0) deviates from V tri the maximum non-linear waveform deviation of V2(0), expressed as: ； k 1 = 0.7090, and k 1 = 0.7090, and k 2 = 0.2953, |V2(θ)| E 2(θ)| max achieves a minimum value, and the theoretical nonlinear waveform error is 0.43%; the expression of V2(θ) is: ； The logic level of the displacement direction signal Direc(θ) in S2 is generated as follows: when V S (θ) and V C (θ) have the same amplitude sign, Direc(θ) = 0; when V S (θ) and V C (θ) have different amplitude signs, Direc(θ) = 1. The generation of the orthogonal square wave signals A and B in S3 is as follows: when the amplitude of (θ) increases by Δ V 2R , A and B generate a square wave respectively, and the phase shift of B relative to A is 90°; when the amplitude of (θ) decreases by Δ U , A and B generate a square wave respectively, and the phase shift of B relative to A is -90°. V 2R U ​​ The conditions for generating the positive counting pulse in S4 are: the level changes of the orthogonal square wave signals A and B are "AB = 01 → AB = 00" or "AB = 11 → AB = 01" or "AB = 00 → AB = 10" or "AB = 10 → AB = 11"; the conditions for generating the negative counting pulse are: the level changes of the orthogonal square wave signals A and B are "AB = 01 → AB = 11" or "AB = 11 → AB = 10" or "AB = 10 → AB = 00" or "AB = 01 → AB = 11".

2. A digital signal processing module, said digital signal processing module having an FPGA as a high speed digital signal processor, characterized by, The digital signal processing module implements the linear conversion and displacement analysis method of the sine and cosine displacement sensing signals as described in claim 1.

3. A linear conversion and displacement resolving circuit for sine-cosine displacement sensing signals, characterized by The circuit is developed using an "A / D+FPGA" hardware architecture, including a power supply module, an analog signal conditioning module, an analog-to-digital conversion module, and the digital signal processing module as described in claim 2.

4. The linear conversion and displacement resolving circuit of sine and cosine displacement sensing signals as claimed in claim 3, wherein, The power supply module is powered by an external DC power supply of 12~24V, and then obtains a power supply voltage of 5V, 3.3V, 2.5V and 1.2V through a power conversion chip; the analog signal conditioning module performs amplitude conditioning, common mode level conditioning and low-pass filtering on the sine and cosine displacement sensing signals; the analog-to-digital conversion module uses a 12-bit or 14-bit A / D chip.

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