Rotary table positioning error real-time compensation method based on transfer function

Abstract

The invention relates to the technical field of angle measurement, and discloses a rotary table positioning error real-time compensation method based on a transfer function, which comprises the following steps of: outputting angle measurement signals by using two reading heads which are arranged around a grating disc in a rotary table at a specific angle interval; the method comprises the following steps: performing subtraction on two angle measurement signals, performing harmonic analysis on a result, multiplying a harmonic analysis result by a transfer function constructed based on a reading head mounting angle interval to obtain harmonic information of a rotary table positioning error curve, and obtaining a rotary table positioning error compensation value through a CORDIC algorithm and a series summation method. Real-time compensation of the positioning error of the rotary table is realized by using the compensation value; the turntable positioning error real-time compensation method based on the transfer function solves the problems of tedious operation, low real-time performance and the like caused by the fact that traditional turntable positioning error compensation depends on regular calibration of external reference equipment, and can ensure long-term stability of turntable positioning precision.

Description

Technical Field

[0001] This invention relates to the field of angle measurement technology, and specifically to a method for real-time compensation of turntable positioning error. Background Technology

[0002] Precision rotary stages are commonly used angle generating devices, widely applied in CNC machine tools, angle measurement, aerospace, and other fields. These fields typically have high requirements for rotary stage positioning accuracy, which is usually limited by factors such as mechanical structure, mechanical vibration, grating engraving errors, and grating installation eccentricity. Furthermore, factors such as load variations and mechanical structure performance degradation can cause changes in rotary stage positioning error, necessitating periodic calibration of the rotary stage positioning accuracy—a tedious and time-consuming process.

[0003] Traditional methods for calibrating turntable positioning errors involve using a multifaceted prism or a multi-tooth indexing stage with an external mirror and an autocollimator, or using a laser interferometer. However, these methods are limited by the number of faces of the prism and the angular resolution of the multi-tooth indexing stage, resulting in a limited number of sampling points. Furthermore, the calibration process is cumbersome and not conducive to automation. Existing real-time compensation methods rely on external traditional calibration methods to provide compensation data. For example, the paper "Analysis and application of real-time compensation of positioning precision of the turntable with a harmonic function" (https: / / doi.org / 10.24425 / mms.2022.142269) proposes using a harmonic compensation method for real-time compensation of turntable positioning errors. However, this method relies on the measurement results of the prism and autocollimator, which has drawbacks such as complex operation and inaccurate harmonic extraction.

[0004] The paper "High resolution Self-A rotary table by the interpolation signal calibration" (https: / / doi.org / 10.4028 / www.scientific.net / KEM.625.53) proposes a multi-readhead equal-division averaging method, which can achieve real-time calibration and compensation of turntable positioning errors. However, it uses a large number of readheads and has a limited number of harmonic orders that can be separated. With the increase in the number of readheads, the mechanical installation complexity and the turntable manufacturing cost also gradually increase.

[0005] While the methods mentioned above can achieve real-time compensation to some extent, they have limitations such as being partially offline, costly, or cumbersome to operate. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to overcome the limitations of the prior art and propose a real-time compensation method for turntable positioning error. This method does not use external auxiliary measuring equipment but only uses two reading heads to achieve online calibration and real-time compensation of turntable positioning error, thereby improving the positioning accuracy of the turntable.

[0007] The technical solution adopted in this invention is:

[0008] A real-time compensation method for turntable positioning error based on transfer function includes the following steps:

[0009] Step 1) Install two reading heads inside the turntable at a set angle. One of them is a reference reading head, whose measurement signal serves as both the feedback control signal and the calibration signal for the turntable; the other is a calibration reading head, whose measurement signal serves only as the calibration signal.

[0010] Step 2) The turntable rotates one revolution, and the two reading heads synchronously acquire the angle signal of the turntable. The measurement result of the reference reading head is recorded as follows. The measurement results of calibrating the reading head are recorded as follows: ;

[0011] Step 3) Calculate the measurement results of the calibration reading head. Measurement results from the reference reading head Subtracting, we get and to Perform Fourier transform to obtain ;

[0012] Step 4) Calculate the transfer function based on the included angle between the two reading heads. : ;

[0013] Step 5) and Multiplying them together yields the turntable positioning error harmonic signal. The amplitude information of each harmonic order is obtained through calculation. and phase information ;in The signal length;

[0014] Step 6) Construct the streamline structure and calculate the turntable positioning error compensation value using the CORDIC method and series summation method. ;

[0015] Step 7) Real-time compensation of turntable positioning errors is achieved using the turntable positioning error compensation system: .

[0016] Furthermore, the two reading heads are mounted on an arc centered on the grating disk, and the distances from the reading heads to the center of the grating disk are equal. The angular interval between the two reading heads is denoted as... .

[0017] Furthermore, the turntable positioning error compensation system includes a phase calculation unit, a harmonic calculation unit, a delay compensation unit, and an error compensation unit, respectively.

[0018] The phase calculation unit receives data from the reference reading head and harmonic phase information of the turntable positioning error from the system input, and completes the calculation using a multiplier and a lookup table. The calculation is performed, and then the calculation results of each order are output to the harmonic calculation unit.

[0019] The harmonic calculation unit receives the calculation results from the phase calculation unit and uses the CORDIC hardware pipeline architecture to complete the calculation. The calculation is performed, and then the calculation results of each order are output to the error compensation unit.

[0020] The delay compensation unit delays the received reference reading head angle value through a multi-level buffer. The delay duration is consistent with the time taken for the phase calculation unit and the harmonic calculation unit to complete one calculation.

[0021] The error compensation unit receives the output data from the harmonic calculation unit and the delay compensation unit, as well as the harmonic amplitude information of the turntable positioning error, and finally completes the calculation. Calculation and The calculation is performed, and the calculation result is output to the outside of the compensated encoder quadrature square wave signal according to the level state machine.

[0022] A real-time compensation system for turntable positioning error based on transfer function includes an angle preprocessing subsystem, a turntable positioning error self-calibration subsystem, and a turntable positioning error real-time compensation subsystem.

[0023] The angle preprocessing subsystem preprocesses the orthogonal square wave signals output by the reference reading head and the calibrated reading head, converts them into absolute angular position data related to the zero position of the grating disk reference, and sends the data to the subsequent system for processing.

[0024] The turntable positioning error self-calibration subsystem receives data from the reference reading head and calibration reading head output by the angle preprocessing subsystem, calculates the turntable positioning error data, and transmits the amplitude and phase information of the turntable positioning error harmonics to the turntable positioning error real-time compensation subsystem.

[0025] The turntable positioning error real-time compensation subsystem receives data from the reference reading head and the amplitude and phase information of the turntable positioning error harmonics. It then performs compensation based on the turntable positioning error at the current position. Finally, the compensation result is converted back into an orthogonal square wave as the feedback quantity of the turntable servo control system.

[0026] The technical concept of this invention is as follows:

[0027] This invention utilizes the angle measurement signals output by two reading heads installed at specific angular intervals around the grating disk inside the turntable. The difference between the two angle measurement signals is calculated, and harmonic analysis is performed on the result. The harmonic analysis result is multiplied by a transfer function constructed based on the angular intervals of the reading heads to obtain the harmonic information of the turntable positioning error curve. The turntable positioning error compensation value is then obtained using the CORDIC algorithm and series summation method. This compensation value is used to achieve real-time compensation of the turntable positioning error. The real-time turntable positioning error compensation method based on the transfer function proposed in this invention solves the problems of cumbersome operation and low real-time performance caused by the reliance on periodic calibration of external reference equipment in traditional turntable positioning error compensation, and can ensure the long-term stability of the turntable positioning accuracy.

[0028] The beneficial effects of this invention are: it proposes a method for real-time compensation of turntable positioning error without changing the turntable's working state or installing additional measuring equipment. This method can achieve long-term online detection and real-time compensation of turntable positioning error using only two reading heads, effectively improving and maintaining the long-term accuracy of the turntable; compared with existing methods, it is more suitable for low-cost or compact applications. Attached Figure Description

[0029] Figure 1 This is a schematic diagram showing the mounting position of the reading head around the encoder;

[0030] Figure 2 This is a system block diagram of the real-time compensation method for turntable positioning errors;

[0031] Figure 3 This is a schematic diagram of the turntable positioning error real-time compensation subsystem;

[0032] Figure 4 This is a flowchart of the real-time compensation method for turntable positioning errors;

[0033] Figure 5 These are comparison images of the turntable positioning error before and after calibration. Detailed Implementation

[0034] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0035] like Figure 1 The diagram shown illustrates the mounting position of the reading head around the encoder. Figure 1 It can be seen that, For reference reading head, To calibrate the reading heads, two reading heads are mounted on an arc centered on the grating disk, with each reading head equidistant from the center of the grating disk; the angular interval between them is denoted as . (This embodiment) (Set to 33°), and the installation tolerance of the two reading heads must meet the requirement that the installation tolerance of the angular interval does not exceed ±50″.

[0036] Assume the following relationship exists between the measured value of the reference reading head and the true angular position: ;

[0037] In the formula This represents the true angular position. Let this be the positioning error of the turntable. Then, the measured value from the calibration reading head and the true angular position satisfy the following: ;

[0038] By subtracting the measurements from the two reading heads, we can obtain: ;

[0039] Performing a Fourier transform on both sides of the equation yields: ;

[0040] Constructing a transfer function : ;

[0041] transfer function and By multiplying the results and summing them using a series, the turntable positioning error can be obtained: ;

[0042] like Figure 2 The diagram shown is a system block diagram for constructing a real-time compensation method for turntable positioning errors. The system constructed using this method can be divided into three subsystems: an angle preprocessing subsystem, a turntable positioning error self-calibration subsystem, and a turntable positioning error real-time compensation subsystem.

[0043] The angle preprocessing subsystem preprocesses the orthogonal square wave signals output by the reference reading head and the calibration reading head, converts them into absolute angular position data related to the zero position of the grating disk reference, and sends the data to the subsequent system for processing. The turntable positioning error self-calibration subsystem receives the data output by the reference reading head and the calibration reading head from the angle preprocessing subsystem, calculates the turntable positioning error data using the methods described in equations (1) to (6), and transmits the amplitude and phase information of the turntable positioning error harmonics to the turntable positioning error real-time compensation subsystem. The turntable positioning error real-time compensation subsystem receives the data from the reference reading head and the amplitude and phase information of the turntable positioning error harmonics, calculates the turntable positioning error at the current position according to equation (6), and compensates according to equation (7): ;

[0044] Finally, the compensation result is converted back into an orthogonal square wave, which is used as the feedback quantity of the turntable servo control system.

[0045] like Figure 3 The diagram shown is a structural schematic of the turntable positioning error real-time compensation subsystem. The real-time performance of the turntable positioning error real-time compensation subsystem is crucial to ensuring the operational accuracy of the entire system.

[0046] The system can be divided into four units: a phase calculation unit, a harmonic calculation unit, a delay compensation unit, and an error compensation unit. The phase calculation unit receives data from the reference reading head and harmonic phase information of the turntable positioning error from the system input, and completes the calculation using a multiplier and a lookup table. The calculations are then performed. The results of each order of calculation are output to the harmonic calculation unit. The harmonic calculation unit receives the results from the phase calculation unit and, using the CORDIC hardware pipeline architecture, completes the calculation. The calculations are performed, and then the results of each order are output to the error compensation unit. The delay compensation unit delays the received reference reading head angle value through a multi-stage buffer, with the delay duration being consistent with the calculation time of the phase calculation unit and the harmonic calculation unit for one calculation. The error compensation unit receives the output data from the harmonic calculation unit and the delay compensation unit, as well as the harmonic amplitude information of the turntable positioning error, and finally completes the calculation. The calculation of the encoder and the calculation of equation (7) are performed, and the calculation results are output to the outside of the compensated encoder quadrature square wave signal according to the level state machine.

[0047] like Figure 4 The diagram shows a flowchart of a real-time compensation method for turntable positioning errors. The method described above is used to perform online calibration and real-time compensation for turntable positioning errors.

[0048] a) The system starts working and determines whether the turntable has completed one full rotation; if it has, proceed to step b); otherwise, proceed directly to step d).

[0049] b) Perform self-calibration of the turntable positioning error according to the self-calibration method described above.

[0050] c) Update the harmonic information of the turntable positioning error obtained from calibration.

[0051] d) Determine if there is harmonic data for turntable positioning error; if so, proceed to e); otherwise, proceed directly to f).

[0052] e) Calculate the turntable positioning error corresponding to the current turntable position and compensate according to the formula. Then, use the compensated result as the measured value of the turntable angular position at the current moment.

[0053] f) Convert the current angular position measurement into an orthogonal square wave and send it to the feedback terminal of the turntable servo control system.

[0054] like Figure 5 The image shows a comparison before and after real-time compensation for turntable positioning errors. It can be seen that when this invention is applied to a turntable, the error is controlled within ±150″ before compensation and within ±2″ after compensation. Therefore, applying this invention directly to a turntable for real-time error compensation can effectively and significantly improve the accuracy of the turntable.

[0055] The above embodiments are merely preferred embodiments of the present invention and are not intended to limit the technical solutions of the present invention. Any technical solution that can be implemented based on the above embodiments without creative effort should be considered to fall within the scope of protection of the patent of the present invention.

Claims

1. A real-time compensation method for turntable positioning error based on transfer function, characterized in that, Includes the following steps: Step 1) Install two reading heads inside the turntable at a set angle. One of them is a reference reading head, whose measurement signal serves as both the feedback control signal and the calibration signal for the turntable; the other is a calibration reading head, whose measurement signal serves only as the calibration signal. Step 2) The turntable rotates one revolution, and the two reading heads synchronously acquire the angle signal of the turntable. The measurement result of the reference reading head is recorded as follows. The measurement results of calibrating the reading head are recorded as follows: ; Step 3) Calculate the measurement results of the calibration reading head. Measurement results from the reference reading head Subtracting, we get and to Perform Fourier transform to obtain ; Step 4) Calculate the transfer function based on the included angle between the two reading heads. : ； Step 5) and Multiplying them together yields the turntable positioning error harmonic signal. The amplitude information of each harmonic order is obtained through calculation. and phase information ;in The signal length; Step 6) Construct the streamline structure and calculate the turntable positioning error compensation value using the CORDIC method and series summation method. ; Step 7) Real-time compensation of turntable positioning errors is achieved using the turntable positioning error compensation system: .

2. The real-time compensation method for turntable positioning error based on transfer function according to claim 1, characterized in that, The two reading heads are mounted on an arc centered on the grating disk, and the distances from the reading heads to the center of the grating disk are equal. The angular interval between the two reading heads is denoted as . .

3. The real-time compensation method for turntable positioning error based on transfer function according to claim 1, characterized in that, The turntable positioning error compensation system includes a phase calculation unit, a harmonic calculation unit, a delay compensation unit, and an error compensation unit; The phase calculation unit receives data from the reference reading head and harmonic phase information of the turntable positioning error from the system input, and completes the calculation using a multiplier and a lookup table. The calculation is performed, and then the calculation results of each order are output to the harmonic calculation unit. The harmonic calculation unit receives the calculation results from the phase calculation unit and uses the CORDIC hardware pipeline architecture to complete the calculation. The calculation is performed, and then the calculation results of each order are output to the error compensation unit. The delay compensation unit delays the received reference reading head angle value through a multi-level buffer. The delay duration is consistent with the time taken for the phase calculation unit and the harmonic calculation unit to complete one calculation. The error compensation unit receives the output data from the harmonic calculation unit and the delay compensation unit, as well as the harmonic amplitude information of the turntable positioning error, and finally completes the calculation. Calculation and The calculation is performed, and the calculation result is output to the outside of the compensated encoder quadrature square wave signal according to the level state machine.

4. A real-time compensation system for turntable positioning error based on transfer function, characterized in that, It includes an angle preprocessing subsystem, a turntable positioning error self-calibration subsystem, and a turntable positioning error real-time compensation subsystem; The angle preprocessing subsystem preprocesses the orthogonal square wave signals output by the reference reading head and the calibrated reading head, converts them into absolute angular position data related to the zero position of the grating disk reference, and sends the data to the subsequent system for processing. The turntable positioning error self-calibration subsystem receives data from the reference reading head and calibration reading head output by the angle preprocessing subsystem, calculates the turntable positioning error data, and transmits the amplitude and phase information of the turntable positioning error harmonics to the turntable positioning error real-time compensation subsystem. The turntable positioning error real-time compensation subsystem receives data from the reference reading head and the amplitude and phase information of the turntable positioning error harmonics. It then performs compensation based on the turntable positioning error at the current position. Finally, the compensation result is converted back into an orthogonal square wave as the feedback quantity of the turntable servo control system.

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