CN117553838A - Dynamic angle measurement error calibration method and system for encoder - Google Patents

Abstract

This application discloses an encoder dynamic angle measurement error calibration method and system, which are used in the field of instrument measurement and application technology. The method includes: obtaining a priori information of the encoder dynamic angle measurement error; obtaining the encoder dynamic angle measurement error posteriori information; establish an error calibration model based on the a priori information and the posterior information; use the least square method to identify the undetermined parameters of the error calibration model to complete the calibration; solve the problem of the encoder's angle measurement error being too large during the rotation process problem and improve measurement accuracy.

Description

An encoder dynamic angle measurement error calibration method and system

Technical field

The invention relates to the technical field of instrument measurement and application, and in particular to an encoder dynamic angle measurement error calibration method and system.

Background technique

As a high-precision measuring instrument that integrates optics, mechanics and electronics, the encoder has been widely used in industrial and aerospace fields such as CNC machine tools, intelligent robots, measuring instruments, photoelectric theodolite, aerial cameras and space manipulators, involving Civilian and military products are mostly used as key measurement devices for system closed-loop control. Therefore, the accuracy of encoder measurement will directly affect the system control performance and thus the overall product performance. According to the composition and working principle of the encoder, there are inevitably various error factors that affect its measurement accuracy. In particular, in the moving state, due to the subdivision measurement delay of the encoder electronics and the dynamic error of the amplitude-frequency response, the angle measurement error increases much compared with the static state, and the measurement accuracy decreases significantly, making it difficult to meet the high-precision measurement requirements of the system or product. .

Therefore, in order to overcome these shortcomings, this application proposes an encoder dynamic angle measurement error calibration method and system.

Contents of the invention

The purpose of this application is to provide an encoder dynamic angle measurement error calibration method and system, aiming to solve the problem of reduced measurement accuracy of the encoder in a moving state.

In order to achieve the above purpose, this application provides the following technical solutions:

This application provides an encoder dynamic angle measurement error calibration method, including:

Obtain the prior information of the encoder dynamic angle measurement error;

Obtain the posterior information of the encoder dynamic angle measurement error;

Establish an error calibration model based on the prior information and the posterior information;

The least squares method is used to identify the undetermined parameters of the error calibration model and complete the calibration.

Further, the step of obtaining a priori information of the encoder's dynamic angle measurement error specifically includes the following steps:

Calculate the subdivision hysteresis error, dynamic response error and shaft system shaking error caused by angle measurement when the encoder is moving;

The calculation formula of the subdivision hysteresis error θ _{err_chizhi} is:

θ _{err_chizhi} =ω(t ₁ +t ₂ )

Among them, ω is the encoder speed, t ₁ is the A/D conversion time, and t ₂ is the remaining signal processing time;

The calculation formula of the dynamic response error θ _{err_dongtai} is:

Among them, A is the amplitude of the two precise code signals with a phase difference of 90°; ΔA is the difference between the amplitudes of the two signals; Δx and Δy are the changes in the DC components of the two precise code signals; α _ij and λ _ij are the rotational speed influence coefficients and Amplitude attenuation coefficient, where (i,j=1,2); θ is the encoder subdivision angle, its period is 2π/n, n is the fine code subdivision number; ω is the encoder speed;

The calculation formula of the shafting shake error θ _{err_zhxiebo} is:

Among them, A ₁ and A ₃ are the fundamental wave and third harmonic amplitude respectively; θ is the encoder subdivision angle, its period is 2π/n, and n is the fine code subdivision number.

Further, the step of obtaining the posterior information of the encoder dynamic angle measurement error specifically includes the following steps:

Suppose the dynamic angle measurement error value of the encoder at different rotational speeds ω _i and different angular positions θ _j is d _ij ; perform a two-dimensional Fourier transform on d _ij to obtain the original data spectrum, and extract the peak node of the posterior information spectrum, The calculation formula is:

Among them, k and q are the abscissas of the frequency spectrum in the rotational speed dimension and the rotation angle dimension respectively.

Further, the step of establishing an error calibration model based on the a priori information and the a posteriori information specifically includes the following steps:

Establish an error calibration model for the two-dimensional Fourier series:

Among them, a _pq , b _pq and c are the undetermined coefficients of the model;

Since the value range of ω and θ in the above formula is [-π, π], the following transformation is performed:

Among them, ω ₁ , ω ₂ and θ ₁ , θ ₂ satisfy ω∈[ω ₁ ,ω ₂ ] and θ∈[θ ₁ ,θ ₂ ] respectively; then the final calibration model becomes:

in are the equivalent rotational speed and rotation angle respectively.

Further, the step of using the least squares method to identify the undetermined parameters of the error calibration model and completing the calibration specifically includes the following steps:

Substituting (w _i , θ _j , d _ij ) into the error calibration model, the following observation equations are established:

The system of observation equations can be abbreviated as:

AX＝d

The least squares method is used to solve the observation equations, and the undetermined parameters of the error calibration model are identified as:

X＝(A ^T A) ^-1 A ^T d

Among them, A is the coefficient matrix of the observation equation system, X is the model parameter vector to be found, and d is the observation vector.

Further, the a priori information is the precise code subdivision number n of the encoder, thereby determining the harmonic component of the dynamic angle measurement error; the a posteriori information is the spectrum peak node obtained by analyzing the data spectrum.

Further, the error calibration model is established by a Fourier series composed of a cluster of two-dimensional trigonometric functions.

This application provides an encoder dynamic angle measurement error calibration system, including:

Acquisition module: obtains the prior information of the encoder's dynamic angle measurement error; obtains the posterior information of the encoder's dynamic angle measurement error;

Establishing module: establishing an error calibration model based on the a priori information and the a posteriori information;

Calibration module: Use the least squares method to identify the undetermined parameters of the error calibration model and complete the calibration.

The present application provides a device, which includes a processor and a memory coupled to the processor, wherein the memory stores program instructions for implementing an encoder dynamic angle measurement error calibration method; the processing The device is used to execute the program instructions stored in the memory to implement an encoder dynamic angle measurement error calibration.

The present application provides a storage medium that stores program instructions executable by a processor. The program instructions are used to execute an encoder dynamic angle measurement error calibration method.

This application provides an encoder dynamic angle measurement error calibration method and system, which has the following beneficial effects:

This application is based on the composition and classification of the encoder's dynamic angle measurement error, obtains a priori information based on the encoder's hardware composition, and then combines the posterior spectrum analysis of the encoder's measured dynamic angle measurement error data to establish a two-dimensional trigonometric function based on The function's Fourier series error calibration model is then used to identify the undetermined parameters in the error calibration model based on the measured dynamic angle measurement error data, using the least squares method to complete the calibration of the encoder's dynamic angle measurement error. The method proposed in this application can effectively reduce the angle measurement error during the rotation of the encoder, improve the measurement accuracy, and provide theoretical and method support for the accurate measurement of the encoder.

Description of the drawings

Figure 1 is a schematic flow chart of an encoder dynamic angle measurement error calibration method according to Embodiment 1 of the present application;

Figure 2 is a flow chart of an encoder dynamic angle measurement error calibration method according to Embodiment 1 of the present application;

Figure 3 is a schematic diagram of the original data of the dynamic angle measurement error in Example 1;

Figure 4 is a schematic diagram of the posterior spectrum analysis results of dynamic angle measurement error data in Embodiment 1 of the present application;

Figure 5 is a schematic diagram of the dynamic angle measurement error calibration and fitting results of Example 1 of the present application;

Figure 6 is a schematic diagram of dynamic angle measurement residuals in Embodiment 1 of the present application;

Figure 7 is a schematic structural diagram of an encoder dynamic angle measurement error calibration system according to Embodiment 2 of the present application;

Figure 8 is a schematic diagram of the equipment structure of Embodiment 3 of the present application;

Figure 9 is a schematic structural diagram of a storage medium in Embodiment 4 of the present application.

Detailed ways

It should be understood that the specific embodiments described here are only used to explain the present application and are not used to limit the present application.

The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of this application.

Example 1

Please refer to Figure 1 and Figure 2, which are respectively a schematic flow chart and a flow block diagram of an encoder dynamic angle measurement error calibration method according to Embodiment 1 of the present application; the steps include:

S1: Obtain the prior information of the encoder dynamic angle measurement error.

In this embodiment, after analyzing the composition and working principle of the encoder, it is known that due to processing and assembly deviations in some electronic components, electrical or electromagnetic inertia hysteresis, and optical-mechanical structural parts, the details generated by angle measurement when the encoder is moving are calculated separately. It is divided into hysteresis error, dynamic response error and shafting shaking error;

The calculation formula of the subdivision hysteresis error θ _{err_chizhi} is:

θ _{err_chizhi} =ω(t ₁ +t ₂ )

Among them, ω is the encoder speed, t ₁ is the A/D conversion time, and t ₂ is the remaining signal processing time;

The calculation formula of the dynamic response error θ _{err_dongtai} is:

Among them, A is the amplitude of the two precise code signals with a phase difference of 90°; ΔA is the difference between the amplitudes of the two signals; Δx and Δy are the changes in the DC components of the two precise code signals; α _ij and λ _ij are the rotational speed influence coefficients and Amplitude attenuation coefficient, where (i,j=1,2); θ is the encoder subdivision angle, its period is 2π/n, n is the fine code subdivision number; ω is the encoder speed;

The calculation formula of the shafting shake error θ _{err_zhxiebo} is:

Among them, A ₁ and A ₃ are the fundamental wave and third harmonic amplitude respectively; θ is the encoder subdivision angle, its period is 2π/n, and n is the fine code subdivision number.

It can be understood that the dynamic angle measurement error specifically includes: DC component proportional to the rotational speed; long period error related to the rotational speed and angle position, nth harmonic error, 2nth harmonic error, 3nth harmonic error, and 4nth harmonic error. error and 8nth harmonic error, where n is the fine code subdivision number, and for the encoder in this embodiment, n=256.

S2: Obtain the posterior information of the encoder dynamic angle measurement error.

In this embodiment, please refer to Figure 3, which is a schematic diagram of the original data of the dynamic angle measurement error in Embodiment 1; assume that the dynamic angle measurement error value of the encoder at different rotation speeds ω _i and different angular positions θ _j is d _ij .

Please refer to Figure 4, which is a schematic diagram of the posterior spectrum analysis results of the dynamic angle measurement error data in Embodiment 1 of the present application; perform a two-dimensional Fourier transform on d _ij to obtain the original data spectrum, and extract the peak node of the posterior information spectrum, which The calculation formula is:

Among them, k and q are the abscissas of the frequency spectrum in the rotational speed dimension and the rotation angle dimension respectively.

S3: Establish an error calibration model based on the prior information and the posterior information.

In this embodiment, a priori harmonic information and posterior spectrum peak node information are combined to establish a two-dimensional Fourier series error calibration model:

The frequency component consists of a priori harmonic frequency points and a posteriori peak frequency points, a _pq , b _pq , c are the undetermined coefficients of the model;

Since the value range of ω and θ in the above formula is [-π, π], the following transformation is performed:

Among them, ω ₁ , ω ₂ and θ ₁ , θ ₂ satisfy ω∈[ω ₁ ,ω ₂ ] and θ∈[θ ₁ ,θ ₂ ] respectively; then the final calibration model becomes:

in are the equivalent rotational speed and rotation angle respectively.

S4: Use the least squares method to identify the undetermined parameters of the error calibration model and complete the calibration.

In this embodiment, (w _i , θ _j , d _ij ) are substituted into the error calibration model to establish the following observation equations:

The system of observation equations can be abbreviated as:

AX＝d

The least squares method is used to solve the observation equations, and the undetermined parameters of the error calibration model are identified as:

X＝(A ^T A) ^-1 A ^T d

Among them, A is the coefficient matrix of the observation equation system, X is the model parameter vector to be found, and d is the observation vector.

Please refer to FIG. 5 , which is a schematic diagram of the dynamic angle measurement error calibration and fitting results in Example 1 of the present application. By substituting the undetermined parameters and measured dynamic error data into the error calibration model, the encoder dynamic angle measurement error calibration fitting results can be obtained.

Please refer to FIG. 6 , which is a schematic diagram of dynamic angle measurement residuals in Embodiment 1 of the present application. By making the difference between the measured dynamic error data of the encoder and the calibration fitting results, the dynamic angle measurement residual of the encoder can be obtained. Comparing Figure 6 with Figure 3, it can be seen that the dynamic angle measurement error of the encoder is effectively calibrated, and the dynamic angle measurement accuracy is significantly improved.

To sum up, Embodiment 1 of the present application is based on the composition and classification of the encoder's dynamic angle measurement error, obtains a priori information based on the hardware composition of the encoder, and then combines it with the posterior spectrum analysis of the encoder's measured dynamic angle measurement error data, Establish a Fourier series error calibration model with two-dimensional trigonometric functions as the basis function, and then use the least square method to identify the undetermined parameters in the error calibration model based on the measured dynamic angle measurement error data, and then complete the calculation of the encoder's dynamic angle measurement error. Calibration. The method proposed in this application can effectively reduce the angle measurement error during the rotation of the encoder, improve the measurement accuracy, and provide theoretical and method support for the accurate measurement of the encoder.

Example 2

Please refer to Figure 7, which is a schematic structural diagram of an encoder dynamic angle measurement error calibration system according to Embodiment 2 of the present application; the specific content includes:

Acquisition module: obtains the prior information of the encoder's dynamic angle measurement error; obtains the posterior information of the encoder's dynamic angle measurement error;

Establishing module: establishing an error calibration model based on the a priori information and the a posteriori information;

Calibration module: Use the least squares method to identify the undetermined parameters of the error calibration model and complete the calibration.

Example 3

Please refer to Figure 8, which is a schematic diagram of the equipment structure of Embodiment 3 of the present application. The device 50 includes a processor 51 and a memory 52 coupled to the processor 51 .

The memory 52 stores program instructions for implementing the above-mentioned dynamic angle measurement error calibration method of an encoder.

The processor 51 is used to execute program instructions stored in the memory 52 to implement an encoder dynamic angle measurement error calibration.

The processor 51 may also be called a CPU (Central Processing Unit).

The processor 51 may be an integrated circuit chip with signal processing capabilities. The processor 51 may also be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), an off-the-shelf programmable gate array (FPGA) or other programmable logic device, a discrete gate or transistor logic device, or a discrete hardware component. . A general-purpose processor may be a microprocessor or the processor may be any conventional processor, etc.

Example 4

Please refer to FIG. 9 , which is a schematic structural diagram of a storage medium according to Embodiment 4 of the present application. The storage medium of the embodiment of the present application stores a program file 61 that can implement all the above methods. The program file 61 can be stored in the above storage medium in the form of a software product and includes a number of instructions to make a computer device (can It is a personal computer, server, or network device, etc.) or processor that executes all or part of the steps of the various embodiments of the present invention. The aforementioned storage media include: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), magnetic disk or optical disk and other media that can store program code. , or computers, servers, mobile phones, tablets and other devices.

It should be noted that, in this document, the terms "include", "comprises" or any other variation thereof are intended to cover a non-exclusive inclusion, such that a process, device, article or method that includes a series of elements not only includes those elements, It also includes other elements not expressly listed or inherent in the process, apparatus, article or method. Without further limitation, an element defined by the statement "comprises a..." does not exclude the presence of additional identical elements in a process, apparatus, article or method that includes that element.

The above are only preferred embodiments of the present application, and do not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made by using the contents of the description and drawings of the present application, or directly or indirectly used in other related The technical fields are all equally included in the scope of patent protection of this application.

Although the embodiments of the present application have been shown and described, those of ordinary skill in the art will understand that various changes, modifications, and substitutions can be made to these embodiments without departing from the principles and spirit of the present application. and variations, the scope of the application is defined by the appended claims and their equivalents.

Of course, the present invention can also have various other implementations. Based on this implementation, other implementations obtained by those of ordinary skill in the art without any creative work fall within the scope of protection of the present invention.

Claims (10)

1. The dynamic angle measurement error calibration method for the encoder is characterized by comprising the following steps of:

acquiring the prior information of the dynamic angle measurement error of the encoder;

acquiring posterior information of dynamic angle measurement errors of an encoder;

establishing an error calibration model according to the prior information and the posterior information;

and identifying undetermined parameters of the error calibration model by adopting a least square method, and completing calibration.

2. The method for calibrating dynamic angle measurement error of an encoder according to claim 1, wherein the step of obtaining the priori information of the dynamic angle measurement error of the encoder comprises the steps of:

respectively calculating subdivision hysteresis errors, dynamic response errors and shafting shaking errors generated by angle measurement when the encoder moves;

the subdivision hysteresis error theta _{err_chizhi} The calculation formula of (2) is as follows:

θ _{err_chizhi} ＝ω(t ₁ +t ₂ )

wherein ω is encoder speed, t ₁ For A/D conversion time, t ₂ Processing time for the remaining signal;

the dynamic response error theta _{err_dongtai} The calculation formula of (2) is as follows:

wherein A is the amplitude of two paths of fine code signals with 90 DEG phase difference; Δa is the difference between the amplitudes of the two signals, and Δx and Δy are the fluctuation amounts of the direct current components of the two paths of fine code signals; alpha _ij And lambda (lambda) _ij A rotation speed influence coefficient and an amplitude attenuation coefficient, respectively, wherein (i, j=1, 2); θ is the encoder subdivision angle, the period is 2pi/n, n is the fine code subdivision number; omega is the encoder rotation speed;

the shafting shaking error theta _{err_zhxiebo} The calculation formula of (2) is as follows:

wherein A is ₁ 、A ₃ The amplitudes of fundamental waves and third harmonic waves are respectively; θ is the encoder subdivision angle, its period is 2pi/n, n is the fine code subdivision number.

3. The method for calibrating dynamic angular error of an encoder according to claim 1, wherein the step of obtaining the posterior information of the dynamic angular error of the encoder comprises the steps of:

the encoder is arranged at different rotation speeds omega _i Different angular positions theta _j The dynamic angle error value is d _ij The method comprises the steps of carrying out a first treatment on the surface of the Will d _ij Performing two-dimensional Fourier transform to obtain an original data spectrum, and extracting a posterior information spectrum peak node, wherein the calculation formula is as follows:

wherein k and q are rotational speed dimension and rotational angle dimension frequency spectrum abscissa.

4. The method for calibrating dynamic angular error of an encoder according to claim 1, wherein in the step of establishing an error calibration model according to the prior information and the posterior information, the method specifically comprises the following steps:

establishing an error calibration model of a two-dimensional Fourier series:

wherein a is _pq 、b _pq C is a model undetermined coefficient;

since the values of ω and θ in the above formula are [ -pi, pi ], the following conversion is performed:

wherein omega ₁ 、ω ₂ And theta ₁ 、θ ₂ Respectively meet omega E [ omega ] ₁ ，ω ₂ ]，θ∈[θ ₁ ，θ ₂ ]The method comprises the steps of carrying out a first treatment on the surface of the The final standard model becomes:

wherein the method comprises the steps ofThe equivalent rotation speed and the rotation angle are respectively adopted.

5. The method for calibrating dynamic angle measurement error of encoder according to claim 1, wherein in the step of identifying undetermined parameters of said error calibration model by using least square method, calibration is completed, specifically comprising the steps of:

will (w) _i ，θ _j ，d _ij ) Substituting the set of observation equations into the error calibration model, and establishing the following observation equation sets:

the set of observation equations can be abbreviated as:

AX＝d

solving an observation equation set by adopting a least square method, and identifying undetermined parameters of the error calibration model as follows:

X＝(A ^T A) ^-1 A ^T d

wherein A is an observation equation set coefficient matrix, X is a model parameter vector to be solved, and d is an observation vector.

6. The method for calibrating dynamic angle measurement error of an encoder according to claim 1, wherein the prior information is a fine code fraction n of the encoder, so as to determine a harmonic component of the dynamic angle measurement error; the posterior information is a spectrum peak value node obtained by analyzing the data spectrum.

7. The method for calibrating dynamic angular errors of an encoder according to claim 1, wherein the error calibration model is built up by a fourier series of two-dimensional trigonometric functions.

8. A system for an encoder dynamic angular error calibration method according to claim 1, comprising:

the acquisition module is used for: acquiring the prior information of the dynamic angle measurement error of the encoder; acquiring posterior information of dynamic angle measurement errors of an encoder;

and (3) a building module: establishing an error calibration model according to the prior information and the posterior information;

and (3) a calibration module: and identifying undetermined parameters of the error calibration model by adopting a least square method, and completing calibration.

9. An apparatus comprising a processor, a memory coupled to the processor, wherein the memory stores program instructions for implementing an encoder dynamic angular error calibration method of any of claims 1-7; the processor is used for executing the program instructions stored in the memory to realize dynamic angle measurement error calibration of the encoder.

10. A storage medium storing program instructions executable by a processor for performing a method of calibrating dynamic angular error of an encoder according to any of claims 1-7.