A method for compensating line and subdivision errors of incremental optical encoders

Abstract

The present invention discloses a method for compensating the line error and subdivision error of an incremental encoder. The method first collects the encoder angle signal at a 2x frequency and calculates it into an IAS signal. Then, the IAS signal is subjected to S-G filtering to suppress speed fluctuations caused by line position and signal width error components. Then, its amplitude modulation function is calculated and the signal width error is calculated. Finally, the line position error is calculated using the signal width error and the amplitude modulation function. The 4x frequency angle signal is compensated using the signal width error and the line position error. The non-orthogonal error is estimated using the compensated 4x frequency angle signal. The 4x frequency angle signal of the encoder is further compensated using the signal width error, the line position error, and the non-orthogonal error, thereby improving the measurement accuracy of the incremental encoder. The method can improve the performance of equipment such as machine tools and industrial robots equipped with servo systems without increasing costs.

Description

Technical Field

[0001] The present invention belongs to the field of instrumentation technology and signal processing and analysis technology, and in particular relates to a method for compensating for line and subdivision errors of an incremental optical encoder. Background Art

[0002] Incremental optical encoders primarily consist of LEDs, a circular grating disk, and a photosensitive chip. When the measured shaft drives the circular grating disk to rotate, light from the LED passes through the disk, forming light bands. These light bands are converted by the photosensitive chip into electrical signals with three phases, A, B, and Z. Phases A and B are orthogonal encoded signals, differing by half a cycle. Phase A leads phase B during forward rotation, and phase B leads phase A during reverse rotation. Line errors can be divided into line position error and width error, while subdivision errors can be divided into electronic subdivision error and non-orthogonality error. During the manufacturing process of the circular grating disk, position errors caused by deviations from the ideal position of the grating lines due to environmental factors, systematic errors in the grating equipment, and vibration are called line position errors. Deviations from the ideal width of the grating width and electronic subdivision error cause the output electrical signal width to deviate from the ideal width, which is called signal width error. Non-orthogonality errors are caused by misalignment of the A and B phases' light-sensitive components in the photosensitive chip, resulting in misalignment of the A and B phases' signals. The above errors may cause fluctuations in the instantaneous angular speed (IAS) signal measured by the encoder.

[0003] Incremental optical encoders, used as sensors for detecting and providing feedback on angular position, are widely used in key applications such as servo systems, industrial robots, and high-end machine tools. Their accuracy determines the positioning precision of servo systems, but during the manufacturing and installation process, incremental optical encoders inevitably experience scale and interpolation errors. These errors can reduce the accuracy of servo systems, leading to reduced machining accuracy for machine tools and the motion and control accuracy of industrial robots. Directly using precision optical rotary stages to estimate and compensate for incremental optical encoder errors presents challenges such as low efficiency and high cost. Existing compensation methods also suffer from limitations such as low error compensation efficiency and difficulty in field deployment. For example, curve fitting methods cannot effectively adapt to conditions with rapidly fluctuating speeds; encoders with multiple readheads are uncommon in actual industrial applications; and using neural networks to correct encoder errors requires extensive data training and suffers from poor transferability. Furthermore, research has shown that scale and interpolation errors can cause fluctuations in the instantaneous angular velocity signal. Therefore, using the instantaneous angular velocity signal to self-compensate for scale and interpolation errors in incremental optical encoders is of great significance. Summary of the Invention

[0004] In response to the problems of the prior art, the present invention provides a method for compensating the line error and subdivision error of an incremental encoder. The present invention uses a 2-fold IAS signal to estimate the line and subdivision errors of the incremental encoder, and uses a 4-fold IAS signal to estimate the non-orthogonal error. According to the cause of the error, the line error is divided into a line position error and a line width error, and the subdivision error is divided into an electronic subdivision error and a non-orthogonal error. On this basis, a method for compensating the line error and subdivision error of the encoder using the IAS signal is derived; the line error and subdivision error of the incremental optical encoder are compensated using the IAS signal. Compared with existing methods such as curve fitting, neural networks, and filtering, the method of the present invention has the characteristics of high efficiency, real-time performance, no need to disassemble the encoder, and low cost. The error compensation method proposed by the present invention can compensate for the line and subdivision errors of the incremental encoder without disassembling the encoder. After the line and subdivision errors are estimated, the measurement angle can be compensated in real time.

[0005] The compensation method for the incremental encoder line error and subdivision error of the present invention is as follows:

[0006] (1) Acquire the angle signals of the three phases A, B, and Z of the incremental optical encoder at 2x and 4x frequencies to obtain the 2x frequency angle signal of phase A, the 2x frequency angle signal of phase B, and the 4x frequency angle signal; and simultaneously acquire the time intervals when the angle changes;

[0007] The acquisition card in patent ZL202110253437.6 "A wireless transmission rotary encoder acquisition card and its application" is used to collect angle signals and corresponding time intervals;

[0008] (2) The forward difference method is used to convert the A-phase double frequency angle signal and the B-phase double frequency angle signal into the A-phase double frequency instantaneous angular velocity signal and the B-phase double frequency instantaneous angular velocity signal. The SG filter is used to suppress the velocity fluctuation caused by the error components of the scale position and signal width in the A-phase double frequency instantaneous angular velocity signal and the B-phase double frequency instantaneous angular velocity signal.

[0009] The forward difference calculation formula is:

[0010]

[0011] Where, ω (×2) (i) is the 2-fold instantaneous angular velocity signal, θ (×2) is the 2-fold frequency angle signal, △t is the time interval, i is the signal number, i.e. i=1, 2, 3...;

[0012] The SG filter is:

[0013] W (×2) =S·C(×2) +E

[0014] Where W (×2) is the 2-fold instantaneous angular velocity signal ω (×2) The matrix form of; S is the polynomial coefficient; C (×2) is the 2-fold frequency angle signal θ (×2) The matrix form of ; E is the residual; the least squares solution of the polynomial coefficient S is:

[0015]

[0016] ω of the 2nd frequency instantaneous angular velocity signal after being suppressed by the SG filter (×2) The matrix form is W′ (×2) =C (×2) ·S;

[0017] (3) using the A-phase double frequency instantaneous angular velocity signal and the B-phase double frequency instantaneous angular velocity signal after suppressing the velocity fluctuation caused by the line position and signal width error components in step (2), respectively calculating the A-phase double frequency amplitude modulation function and the B-phase double frequency amplitude modulation function, and then using the A-phase double frequency amplitude modulation function and the B-phase double frequency amplitude modulation function to respectively estimate the A-phase signal width error and the B-phase signal width error;

[0018] The 2-fold frequency amplitude demodulation function is expressed as:

[0019]

[0020] Where, SG(ω (×2) (i)) is the 2-fold instantaneous angular velocity signal of phase A or phase B, which suppresses the velocity fluctuation caused by the error components of the scale line position and signal width;

[0021] The signal width error ξ estimation formula of phase A and phase B is:

[0022]

[0023] Where N is the signal length, M is the number of encoder gratings, is a 2-fold frequency amplitude modulation function, i is the signal number, i.e. i = 1, 2, 3...;

[0024] (4) using the double frequency amplitude modulation function and signal width error of phase A and phase B in step (3) to estimate the position error of the line of phase A and phase B respectively;

[0025] The line position error The estimation formula is:

[0026]

[0027] Where, M is the number of encoder gratings;

[0028] (5) compensating the 4-fold frequency angle signal in step (1) by using the signal width error of phase A and phase B in step (3) and the line position error of phase A and phase B in step (4);

[0029] The compensation formula is:

[0030]

[0031] Where, To compensate for the 4-fold frequency angle after the line position error and signal width error, θ (×4) is a 4-fold frequency angle signal, is the position error of the A phase scale line, is the position error of the B phase scale line, is the A-phase signal width error, is the B-phase signal width error;

[0032] (6) using the forward difference method to convert the 4-fold frequency angle signal compensated in step (5) into a 4-fold frequency instantaneous angular velocity signal, and then using the SG filter to suppress the velocity fluctuation caused by the non-orthogonal error on the 4-fold frequency instantaneous angular velocity signal;

[0033] The forward difference calculation formula is:

[0034]

[0035] Where, ω (×q) is the 4-fold instantaneous angular velocity signal, θ (×q) is the 4-fold frequency angle signal, △t is the time interval, i is the signal number, i.e. i = 1, 2, 3...;

[0036] The SG filter is:

[0037] W (×4) =S·C (×4) +E

[0038] Where W (×4) is the 4-fold instantaneous angular velocity signal ω (×4) The matrix form of; S is the polynomial coefficient; C (×4) 4-fold frequency angle signal The matrix form of ; E is the residual, and the least squares solution of the polynomial coefficient S is:

[0039]

[0040] The 4-fold instantaneous angular velocity signal ω after the SG filter suppresses the non-orthogonal error (×4) The matrix form is W′ (×4)=C (×4) ·S;

[0041] (7) calculating a 4-fold frequency amplitude modulation function using the 4-fold frequency instantaneous angular velocity signal after suppressing the velocity fluctuation caused by the non-orthogonal error in step (6), and then estimating the non-orthogonal error using the 4-fold frequency amplitude modulation function;

[0042] The 4-fold frequency amplitude demodulation function is expressed as:

[0043]

[0044] Where, SG(ω (×4) (i)) is the 4-fold frequency instantaneous angular velocity signal that suppresses the velocity fluctuation caused by non-orthogonality error, ω (×4) It is the 4-fold frequency instantaneous angular velocity signal;

[0045] The non-orthogonal error estimation formula is:

[0046]

[0047] Where, is the 4-fold frequency amplitude modulation function, is the non-orthogonal error;

[0048] (8) using the signal width error of phase A and phase B in step (3), the line position error of phase A and phase B in step (4), and the non-orthogonal error in step (7) to compensate the encoder's 4-fold frequency angle signal to improve the measurement accuracy of the incremental encoder;

[0049] The compensation formula is:

[0050]

[0051] Where, This is the 4-fold frequency angle after compensating for subdivision and line errors.

[0052] The beneficial effects of the present invention are as follows: using instantaneous angular velocity, errors of existing incremental encoders can be compensated without disassembling the encoder or adding additional devices. The method of using instantaneous angular velocity signals for line and subdivision error compensation proposed in the present invention has the advantages of no need for disassembly or modification of the encoder structure, high efficiency, high precision, and low cost, compared with encoder error compensation methods such as curve fitting, multi-reader correction, and neural network compensation. The method proposed in the present invention can effectively improve the angle measurement accuracy of the incremental encoder without increasing the cost. As the angle measurement accuracy is improved, the positioning capability and accuracy of the servo system are also improved, making the mechanical system more precise. The encoder line and subdivision error estimation and compensation method proposed in the present invention can improve the positioning accuracy of the existing servo system without increasing the cost, thereby improving the performance of machine tools, industrial robots, and other equipment equipped with servo systems.

[0053] The method of the present invention is suitable for industrial production and market promotion application. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is a schematic diagram of the incremental encoder outputting level signals of three phases A, B, and Z;

[0055] Figure 2 is the incremental encoder error model of the present invention;

[0056] Figure 3 Schematic diagram of the RV transmission platform tested in the embodiment;

[0057] Figure 4 It is the 2-fold instantaneous angular velocity signal;

[0058] Figure 5 To suppress the 2-fold frequency instantaneous angular velocity signal after the velocity fluctuation caused by the error components of the line position and signal width;

[0059] Figure 6 is the 2-fold frequency amplitude modulation function of phases A and B;

[0060] Figure 7 is the position error of the A-phase and B-phase scale lines;

[0061] Figure 8 It is the 4-fold frequency instantaneous angular velocity signal;

[0062] Figure 9 This is the structural diagram of the precision optical rotating platform;

[0063] Figure 10 The error comparison chart before and after compensation. DETAILED DESCRIPTION

[0064] The present invention is further described in detail below through examples, but the protection scope of the present invention is not limited to the contents described above.

[0065] Example 1:

[0066] When the circular grating disk in the incremental optical encoder rotates, the photosensitive chip converts the light signal passing through the grating into level signals of three phases A, B, and Z. The output signal is as follows Figure 1 As shown, phase A and phase B are orthogonal encoding signals containing angle and direction information; Z is the zero-phase signal. The incremental optical encoder error can be divided into line error and subdivision error according to the type of error it produces.

[0067] Grating error: Grating error during the manufacturing process is divided into line position error and line width error. Line position error refers to the deviation between the actual line position and the theoretical position caused by the influence of measurement and control system errors and external environment interference during the marking process. Line width error is caused by the fact that the line width during the grating marking process is not equal to the theoretical line width.

[0068] Subdivision error: Subdivision error includes electronic subdivision error and orthogonal error. In the process of converting optical signals into level signals, the angle signal is subdivided by identifying the light intensity passing through the grating to achieve the purpose of increasing resolution. The deviation in light intensity judgment leads to electronic subdivision error. On the other hand, the position of the photosensitive components of the A and B phases in the photosensitive chip deviates from the theoretical orthogonal position, which will lead to non-orthogonal error when 4x subdivision occurs.

[0069] According to the causes of the above-mentioned line error and subdivision error, the following is established: Figure 2 The error model for an incremental optical encoder is shown below; the line position error is denoted as ε; the signal width error of phases A and B, caused by grating width error and electronic interpolation error, is denoted as ξ; and the non-orthogonality error of phases A and B is denoted as p. During the grating ruling process, the gratings on the grating disk have similar grating widths due to identical processing conditions, so the signal width error ξ can be considered a constant. However, the line position error is affected by measurement error, control system error, and external environmental interference, resulting in a corresponding line position error for each grating. The error model shows that the line position error and signal width error will cause fluctuations in the IAS signal at 2x and 4x interpolation, while the non-orthogonality error will cause fluctuations in the IAS signal at 4x interpolation. Therefore, the line position error and signal width error should be estimated first at 2x interpolation, followed by an estimate of the non-orthogonality error at 4x interpolation, and finally, compensation should be performed on the measured angle signal.

[0070] Based on the above error model, a compensation method for the incremental encoder line error and subdivision error of the present invention is proposed. The method proposed in this paper is described in detail, and the RV transmission platform is used as the object for description. The RV transmission platform is as follows: Figure 3 As shown, it consists of a servo motor, an RV reducer, a magnetic powder brake, an incremental optical encoder (grating number M = 2500 lines), etc. The incremental optical encoder is installed at the end of the servo motor to control the servo motor to run at a speed of about 15r / min. The specific steps of the method are as follows:

[0071] 1. The acquisition card in patent ZL202110253437.6, "A Wireless Transmission Rotary Encoder Acquisition Card and Application," simultaneously acquires the level signals of the A, B, and Z phases of the incremental optical encoder at 2x and 4x frequencies, and converts the level signals into angle signals through orthogonal decoding. The 2x frequency angle signal of phase A, the 2x frequency angle signal of phase B, and the 4x frequency angle signal are obtained, while the time intervals when the angle changes are also acquired.

[0072] 2. Use the following forward difference method to convert the A-phase 2-fold frequency angle signal and the B-phase 2-fold frequency angle signal into the A-phase 2-fold frequency instantaneous angular velocity signal and the B-phase 2-fold frequency instantaneous angular velocity signal. The results are as follows: Figure 4 As shown:

[0073]

[0074] Where, ω (×2) (i) is the 2-fold instantaneous angular velocity signal, θ (×2) is the 2-fold frequency angle signal, △t is the time interval, i is the signal number, i.e. i=1, 2, 3...;

[0075] The SG filter is used to suppress the velocity fluctuation caused by the error components of the scale position and signal width in the A-phase 2-fold frequency instantaneous angular velocity signal and the B-phase 2-fold frequency instantaneous angular velocity signal. The suppressed 2-fold frequency instantaneous angular velocity signal is as follows: Figure 5 As shown;

[0076] The SG filter is:

[0077] W (×2) =S·C (×2) +E

[0078] Where W (×2) is the 2-fold instantaneous angular velocity signal ω (×2) The matrix form of; S is the polynomial coefficient; C (×2) is the 2-fold frequency angle signal θ (×2) The matrix form of ; E is the residual; the least squares solution of the polynomial coefficient S is:

[0079]

[0080] ω of the 2nd frequency instantaneous angular velocity signal after being suppressed by the SG filter (×2) The matrix form is W′(×2) =C (×2) ·S; 3. Calculate the A-phase 2-fold frequency amplitude modulation function and the B-phase 2-fold frequency amplitude modulation function respectively using the A-phase 2-fold frequency instantaneous angular velocity signal and the B-phase 2-fold frequency instantaneous angular velocity signal after suppressing the velocity fluctuation caused by the line position and signal width error components in step 2. The results are as follows: Figure 6 As shown;

[0081] The 2-fold frequency amplitude demodulation function is expressed as:

[0082]

[0083] Where, SG(ω (×2) (i)) is the 2-fold instantaneous angular velocity signal of phase A or phase B, which suppresses the velocity fluctuation caused by the error components of the scale line position and signal width;

[0084] Then, the A phase signal width error is estimated using the A phase 2 frequency amplitude modulation function and the B phase 2 frequency amplitude modulation function. B-phase signal width error

[0085] The signal width error of phase A and phase B The estimation formula is:

[0086]

[0087] Where N is the signal length, M=2500, is a 2-fold frequency amplitude modulation function, i is the signal number, i.e. i = 1, 2, 3...;

[0088] 4. Use the 2-fold frequency amplitude modulation function and signal width error of phase A and phase B in step 3 to estimate the position error of the A and B line respectively. Figure 7 As shown;

[0089] The line position error The estimation formula is:

[0090]

[0091] Where, M = 2500;

[0092] 5. Compensate the 4-fold frequency angle signal in step 1 using the signal width error of phase A and phase B in step 3 and the line position error of phase A and phase B in step 4.

[0093] The compensation formula is:

[0094]

[0095] Where, To compensate for the 4-fold frequency angle after the line position error and signal width error, θ (×4) is a 4-fold frequency angle signal, is the position error of the A phase scale line, is the position error of the B phase scale line, is the A-phase signal width error, is the B-phase signal width error;

[0096] 6. Use the following forward difference method to convert the 4-fold frequency angle signal compensated in step 5 into a 4-fold frequency instantaneous angular velocity signal. The result is shown in Figure 8 :

[0097]

[0098] Where, ω (×q) is the 4-fold instantaneous angular velocity signal, θ (×q) is the 4-fold frequency angle signal, △t is the time interval, i is the signal number, i.e. i = 1, 2, 3...;

[0099] Then, the SG filter is used to suppress the velocity fluctuation caused by the non-orthogonal error on the 4-fold frequency instantaneous angular velocity signal. After the SG filter suppresses the non-orthogonal error, the 4-fold frequency instantaneous angular velocity signal ω (×4) ;

[0100] The SG filter is:

[0101] W (×4) =S·C (×4) +E

[0102] Where W (×4) is the 4-fold instantaneous angular velocity signal ω (×4) The matrix form of; S is the polynomial coefficient; C (×4) 4-fold frequency angle signal The matrix form of ; E is the residual, and the least squares solution of the polynomial coefficient S is:

[0103]

[0104] The 4-fold instantaneous angular velocity signal ω after the SG filter suppresses the non-orthogonal error (×4) The matrix form is W′ (×4) =C (×4) ·S;

[0105] 7. After the velocity fluctuation caused by the non-orthogonal error is suppressed in step 6, the 4-fold frequency instantaneous angular velocity signal is used to calculate the 4-fold frequency amplitude modulation function. The 4-fold frequency amplitude demodulation function is expressed as:

[0106]

[0107] Where, SG(ω (×4) (i)) is the 4-fold frequency instantaneous angular velocity signal that suppresses the velocity fluctuation caused by non-orthogonality error, ω (×4) It is the 4-fold frequency instantaneous angular velocity signal;

[0108] Then use the 4-fold frequency amplitude modulation function to estimate the non-orthogonal error using the following non-orthogonal error estimation formula rad:

[0109]

[0110] Where, is the 4-fold frequency amplitude modulation function, is the non-orthogonal error;

[0111] 8. Use the signal width error of phase A and phase B in step 3, the line position error of phase A and phase B in step 4, and the non-orthogonality error in step 7 to compensate the encoder's 4-fold frequency angle signal to improve the measurement accuracy of the incremental encoder;

[0112] The compensation formula is:

[0113]

[0114] Where, This is the 4-fold frequency angle after compensating for the error.

[0115] Finally, in order to verify the effectiveness of the method of the present invention, a precision optical rotating platform is used to measure the error of the encoder before and after compensation using the method of the present invention. The precision optical rotating platform is composed of a servo motor, a planetary gear reducer, an optical rotating platform, etc. Figure 9 As shown;

[0116] The encoder error is measured using a precision optical rotary platform, and the encoder error before and after compensation is as follows: Figure 10 As shown on the left, the encoder error before and after compensation is evaluated using the root mean square error (RMSE). The root mean square error before error compensation is 1.8925×10 -5 rad, the root mean square error after compensation is 0.7085×10 - 5 rad, the error compensation method of the present invention compensates for nearly 62.56% of the encoder error, and the RMSE before and after compensation is as follows: Figure 10 As shown on the right, the root mean square error formula is as follows:

[0117]

[0118] Where: RMSE is the root mean square error; N is the signal length, Figure 10 It can be seen that the line and subdivision error compensation method proposed in the present invention can effectively compensate for the line and subdivision errors of the incremental encoder.

Claims

1. A method for compensating for line error and subdivision error of an incremental encoder, characterized in that: Here are the steps: (1) Acquire the angle signals of the three phases A, B, and Z of the incremental optical encoder at 2x and 4x frequencies, obtain the 2x frequency angle signal of phase A, the 2x frequency angle signal of phase B, and the 4x frequency angle signal, and simultaneously acquire the time interval when the angle changes; (2) The forward difference method is used to convert the A-phase double frequency angle signal and the B-phase double frequency angle signal into the A-phase double frequency instantaneous angular velocity signal and the B-phase double frequency instantaneous angular velocity signal. The SG filter is used to suppress the velocity fluctuation caused by the error components of the scale position and signal width in the A-phase double frequency instantaneous angular velocity signal and the B-phase double frequency instantaneous angular velocity signal. (3) using the A-phase double frequency instantaneous angular velocity signal and the B-phase double frequency instantaneous angular velocity signal after suppressing the velocity fluctuation caused by the line position and signal width error components in step (2), respectively calculating the A-phase double frequency amplitude modulation function and the B-phase double frequency amplitude modulation function, and then using the A-phase double frequency amplitude modulation function and the B-phase double frequency amplitude modulation function to respectively estimate the A-phase signal width error and the B-phase signal width error; The signal width error of phase A and phase B The estimation formula is: Where N is the signal length, M is the number of encoder gratings, is the 2-fold frequency amplitude modulation function of phase A or phase B, i is the signal number, i.e. i = 1, 2, 3, etc.; (4) using the double frequency amplitude modulation function of phase A and phase B and the signal width error in step (3) to estimate the line position error of phase A and phase B respectively; The line position error The estimation formula is: (5) compensating the 4-fold frequency angle signal in step (1) by using the signal width error of phase A and phase B in step (3) and the line position error of phase A and phase B in step (4); The compensation formula is: Where, To compensate for the 4-fold frequency angle signal after the line position error and signal width error are compensated, θ (×4) is a 4-fold frequency angle signal, is the position error of the A phase scale line, is the position error of the B phase scale line, is the A-phase signal width error, is the B-phase signal width error; (6) using the forward difference method to convert the 4-fold frequency angle signal compensated in step (5) into a 4-fold frequency instantaneous angular velocity signal, and then using the SG filter to suppress the velocity fluctuation caused by the non-orthogonal error on the 4-fold frequency instantaneous angular velocity signal; (7) calculating a 4-fold frequency amplitude modulation function using the 4-fold frequency instantaneous angular velocity signal after suppressing the velocity fluctuation caused by the non-orthogonal error in step (6), and then estimating the non-orthogonal error using the 4-fold frequency amplitude modulation function; The non-orthogonal error estimation formula is: Where, is the 4-fold frequency amplitude modulation function, is the non-orthogonal error; (8) using the signal width error of phase A and phase B in step (3), the line position error of phase A and phase B in step (4), and the non-orthogonal error in step (7) to compensate the encoder's 4-fold frequency angle signal to improve the measurement accuracy of the incremental encoder; The compensation formula is: Where, This is the 4-fold frequency angle after compensating for subdivision and line errors.

2. The method for compensating for line error and subdivision error of an incremental encoder according to claim 1, characterized in that: The forward difference calculation formula in step (2) and step (6) is: Where q is the frequency multiplication number, q = 2 or q = 4; ω (×q) is the q-fold instantaneous angular velocity signal, θ (×q) is the q-fold frequency angle signal, △t is the time interval, and i is the signal number, that is, i=1, 2, 3...

3. The method for compensating for line error and subdivision error of an incremental encoder according to claim 2, characterized in that: The SG filter in step (2) and step (6) is: W (×q) =S·C (×q) +E Where W (×q) is the q-fold instantaneous angular velocity signal ω (×q) The matrix form of; S is the polynomial coefficient; C (×q) is the q-fold frequency angle signal θ (×q) The matrix form of ; E is the residual; the least squares solution of the polynomial coefficient S is: ω of the q-fold instantaneous angular velocity signal after being suppressed by the SG filter (×q) The matrix form is W ( ' ×q) =C (×q) ·S.

4. The method for compensating for line error and subdivision error of an incremental encoder according to claim 3, characterized in that: Amplitude demodulation function in step (3) and step (7) for: In the formula, when q=2, SG(ω (×q) (i)) is the instantaneous angular velocity signal of phase A or phase B with double frequency, which suppresses the velocity fluctuation caused by the error components of the scale position and signal width, ω (×q) is the 2-fold frequency instantaneous angular velocity signal; when q=4, SG(ω (×q) (i)) is the 4-fold frequency instantaneous angular velocity signal that suppresses the velocity fluctuation caused by non-orthogonality error, ω (×q) It is a 4-fold frequency instantaneous angular velocity signal.

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