CN114488944A - Interpolation-based servo displacement error compensation method - Google Patents
Interpolation-based servo displacement error compensation method Download PDFInfo
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- CN114488944A CN114488944A CN202011156405.6A CN202011156405A CN114488944A CN 114488944 A CN114488944 A CN 114488944A CN 202011156405 A CN202011156405 A CN 202011156405A CN 114488944 A CN114488944 A CN 114488944A
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/404—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/34—Director, elements to supervisory
- G05B2219/34117—Machine workpiece along, parallel to largest dimension
Abstract
The invention discloses a servo displacement error compensation method based on interpolation, which comprises the following steps: acquiring reference data by using a tooling plate and an instrument, and corresponding the servo actual position and the theoretical position of a reference point one by one; secondly, function mapping between the servo coordinates and theoretical coordinates is achieved by using an interpolation function and reference data, and coordinate conversion vectors are calculated; and step three, substituting the theoretical coordinate of the target point into an interpolation coordinate calculation formula to obtain a servo coordinate corresponding to the theoretical position point, and giving the servo coordinate to a control system to realize automatic position running. By adopting an interpolation method to carry out error compensation technology, high positioning precision can be realized on the premise of not damaging the reference number.
Description
Technical Field
The invention relates to a multi-axis servo system control technology, in particular to a servo displacement error compensation method based on interpolation.
Background
In the field of industrial automation, servo systems are now being used in large quantities for automatic positioning, and relatively accurate positioning of any position within the range of the servo system hardware structure is achieved, such as automatic spot welding machines, automatic pin inserting machines, machine tools with higher precision requirements, coordinate measuring machines and the like.
In all servo systems, the servo systems can be divided into two types according to control modes, one type is a single-axis servo system, and position control in a single vector direction is realized; the other is a multi-axis servo system, which realizes position and attitude control in two dimensions or higher. However, whether the multi-dimensional servo control system (especially an open-loop system) is accurate in walking needs to be tested and proved by an external tool or equipment, and especially the position accuracy of the servo system with more than two dimensions is proved to be difficult, wherein the relative position relationship between a plurality of servo shafts and the walking accuracy of the servo system are involved.
For error compensation, a multi-axis precision system is generally provided with a grating, a servo system and the grating are subjected to closed-loop control, and the displacement error of an independent servo mechanism is controlled within a certain range through the closed-loop control. However, in practice, the determination of the spatial position is not only accurate in the position along the servo length direction, but also influenced by the geometric relationship among a plurality of servo system vectors, such as whether hardware processing among several axes realizes an orthogonal relationship, and the like. Therefore, compensation methods in the aspect of the servo control principle are researched more at present, but an error compensation algorithm caused by the installation relation of a multi-axis servo system is rare.
For example: many open-loop servo systems do not compensate errors, but only adjust a plurality of fixed positions in advance to work; when a new position is required, a position is debugged according to the actual effect, and so on. The phenomenon is common in the automation industry at present, intelligent walking control of a servo system is not realized, and maintenance and modification of products are difficult.
Error compensation of two-dimensional and above servo system hardware is rare, for example, a plane sliding table in two directions is formed by the combined action of two servo shafting to move at any position in a plane, but the error compensation is rarely performed on the position relation between the two servo shafting and the respective moving precision of the two servo systems. At present, a fitting method for error compensation of a two-dimensional servo system based on coordinate transformation exists, which is better than that without compensation, but the method has the biggest problem that the requirement on basic data is too strict, once one or two data have larger error ratio, the compensated result can wholly deviate, the original datum point data is damaged, and the accurate displacement of the original datum point cannot be realized.
In summary, the main problems of the prior art are as follows:
1. the position relation error of the moving direction vector of the servo axis is determined by the manufacturing accuracy of the structure and the rigidity of a servo system, and if the compensation is not carried out in the later period, the accumulated manufacturing error of hardware can seriously influence the servo displacement accuracy;
2. the existing error compensation method based on coordinate transformation is a fitting method essentially, original reference data is damaged, although the reference data is utilized to construct an algorithm, the reference data is lost during final position shifting, the compensation precision is insufficient, and subjective understanding is not facilitated.
Disclosure of Invention
In order to solve the above problems in the prior art, the present invention provides a servo step error compensation method based on interpolation, which implements error compensation of a two-dimensional open-loop servo system by a nonlinear interpolation algorithm.
A servo displacement error compensation method based on interpolation comprises the following steps: acquiring reference data by using a tooling plate and an instrument, and corresponding the servo actual position and the theoretical position of a reference point one by one; secondly, function mapping between the servo coordinates and theoretical coordinates is achieved by using an interpolation function and reference data, and coordinate conversion vectors are calculated; and step three, substituting the theoretical coordinate of the target point into an interpolation coordinate calculation formula to obtain a servo coordinate corresponding to the theoretical position point, and giving the servo coordinate to a control system to realize automatic positioning.
Further, the first step comprises: the servo coordinate positions of the four reference points are measured A, B, C, D by using a dial indicator and a reference plate.
Further, the second step comprises: and calculating an interpolation conversion vector by using the servo coordinates of A, B, C, D four reference points and the theoretical position on the tooling plate.
Further, the third step comprises: and determining the theoretical position coordinates needing interpolation calculation, and then calculating coordinate values in the servo system through the converted vectors.
Further, the interpolation function is:
wherein(x 'y') is a theoretical coordinate, (x y) is a coordinate of a servo axis, aiIs the undetermined coefficient.
Further, the calculation method of the coordinates of the A, B, C, D four reference points is as follows:
further, the calculation method of the interpolation point comprises the following steps:
further, the translation vector is:
further, an interpolation precision verification point E is included, and the verification point E is set at the center of the reference point A, B, C, D.
In the technical scheme, the servo walking error compensation method and system based on interpolation can realize high positioning precision on the premise of not damaging reference numbers and based on a nonlinear interpolation algorithm.
Drawings
FIG. 1 is a schematic diagram of a multi-axis servo system;
FIG. 2 is a flow chart of the method of the present invention;
FIG. 3 is a schematic representation of A, B, C, D locations of four fiducial points and verification points;
FIG. 4 is a schematic diagram of the location of a plurality of fiducials.
Detailed Description
The servo displacement error compensation method based on interpolation according to the present invention will be further described with reference to the accompanying drawings and embodiments.
Referring to fig. 1, for two-dimensional and above servo systems, most errors are systematic errors under the condition that the servo system is rigid enough, so that the establishment of a mathematical model can completely realize error compensation through an algorithm. In view of this, the present invention mainly establishes an algorithm for compensating the error nonlinear interpolation of the servo system and a corresponding system.
The method of the invention firstly establishes an algorithm model of an interpolation function. The algorithm of the invention can not only use first-order linear interpolation, but also use second-order or high-order nonlinear interpolation to realize the establishment of transformation matrix, and realize the rationalization of algorithm error. Secondly, according to different interpolation functions in the algorithm, the reference point acquisition tool is designed according to the type of the interpolation function, and rationalization of errors and reference point acquisition cost is achieved.
Establishing a mathematical model:
for a multi-axis servo system, in addition to the self-precision of a single-axis servo, the relative position relationship between servo axes is a factor influencing the displacement precision of the system.
For single axis accuracy, which basically has a direct influence on the accuracy of the walking position, the model can be established as f (l); where l is the position of the servo axis step relative to itself.
For the relative position relationship between the axes of the multi-axis system, a one-to-one mapping relationship between a servo coordinate system and a theoretical coordinate system is determined, and the mapping relationship of the two-axis system is as follows:
based on the above analysis, an interpolation function needs to be designed to satisfy the above mapping relationship. Different types of interpolation functions can be designed according to the concept of error rationalization, such as first-order linear interpolation, second-order or higher-order nonlinear interpolation functions. The process of building a mathematical model with only a second order cross term interpolation function is listed below as follows:
where (x 'y') is the theoretical coordinate, (x y) is the coordinate of the servo axis, aiIs the undetermined coefficient.
The interpolation function analysis can obtain that an equation with 8 undetermined coefficients exists, and 8 coordinate values of 4 points are needed for determination. Then with A, B, C, D four coordinate points, the following equation can be obtained
The coordinates of the points to be interpolated are then calculated as follows:
the same is done for higher order interpolation functions, only the order of the change matrix is different.
Obtaining a reference value:
the primary purpose of the baseline value is to obtain a translation vector, as follows:
referring to fig. 2, the interpolation-based servo step error compensation method of the present invention is mainly implemented by the following steps:
s1: and acquiring reference data by using the tooling plate and the instrument, and corresponding the servo actual position and the theoretical position of the reference point one by one.
In a preferred embodiment of the present invention, reference points of the present invention are A, B, C, D four holes, and in this step, servo coordinate positions of A, B, C, D four holes are measured using a dial gauge in combination with a reference plate. For a reference value consisting of four holes (dots), the most common in engineering applications is a rectangular arrangement, as shown in fig. 3, where the reference point (which may also be referred to as a reference hole) is A, B, C, D four locations.
In a preferred embodiment of the present invention, the reference point is formed in a circular hole shape in the tool plate. It should be understood by those skilled in the art that the geometric feature of the reference hole (reference point) on the tooling plate may be designed into a rectangular shape, a circular shape or other shapes, which can be fully designed according to the actual situation of the engineering, and the invention is within the protection scope of the present invention.
S2: and (3) utilizing the interpolation function and the reference data to realize function mapping between the servo coordinates and the theoretical coordinates, and calculating coordinate conversion vectors, namely utilizing the servo coordinates of A, B, C, D four holes and the theoretical positions on the tooling plate to calculate the interpolation conversion vectors.
S3: and substituting the theoretical coordinate of the target point into an interpolation coordinate calculation formula to obtain a servo coordinate corresponding to the theoretical position point, and giving the servo coordinate to a control system to realize automatic position running. In other words, the theoretical position coordinates that need to be interpolated are determined, and then the coordinate values in the servo system are calculated by converting the vector.
As a preferred embodiment of the invention, the method of the invention is provided with a verification point E besides A, B, C, D four reference points, wherein the point E is an interpolation precision verification point, that is, the mathematical model is established by four vertexes on a rectangular edge, and then the verification work of the interpolation error is carried out by using the middle point E. It should be understood by those skilled in the art that the arrangement of the verification points E and their positions are only one of many embodiments of the present invention, and in other embodiments, the positions and the number of the verification points E may be changed according to specific schemes, and all of them are within the protection scope of the present invention.
For a system with a small servo range or a high servo system rigidity, interpolation of any position in the four-point range can be realized by using the reference data of four points, as shown in fig. 3. However, when the servo displacement range is large, the reference value is small, which increases the interpolation error, and in order to improve the interpolation accuracy, one large servo displacement range may be divided into a plurality of small rectangular ranges, as shown in fig. 4.
Referring to fig. 4, for the case of multiple reference points (reference values), the present invention first calculates the transformation vector for each local range, as shown by the range of the dashed line in fig. 4, and can ensure that the values at each reference point can be kept continuous, as shown by the remaining part in fig. 4, and finally, the interpolation compensation in the whole range is realized, and the error value is controlled in the target range.
According to the method, the servo displacement error is calculated by the interpolation method of the specific order, and the method is also suitable for servo system error compensation algorithms constructed by different interpolation functions and interpolation functions of different orders.
In addition, the step of acquiring the reference point according to the present invention is not limited to the method of acquiring the reference point, and in other words, the method of the present invention is applicable to the reference point data acquired by any of the tooling plate and other measurement methods.
On the other hand, the algorithm of the present invention is not limited to specific implementation means, and can be implemented on various software, and programs written by different software based on the algorithm are all suitable for the method of the present invention.
In summary, the method of the present invention mainly has the following advantages:
1. for an error compensation algorithm, an interpolation method is more suitable for error compensation than a fitting method, and reference data cannot be damaged; the fitting algorithm does not necessarily pass through the reference point, so that the value calculated by the algorithm at the reference point has an error.
2. The servo walking precision can be improved by using a high-order nonlinear interpolation function and different reference point numbers and arrangement, and the error is controlled within an acceptable range; the existing algorithm based on coordinate change is linear fitting, and if a servo system is not linear, the linear fitting has larger error.
3. By optimizing the number of the interpolation functions and the reference points, the positioning precision can be controlled to be less than or equal to +/-0.02 mm, and the repeated positioning precision is controlled to be less than or equal to 0.01 mm.
It should be understood by those skilled in the art that the above embodiments are only for illustrating the present invention and are not to be used as a limitation of the present invention, and that changes and modifications to the above described embodiments are within the scope of the claims of the present invention as long as they are within the spirit and scope of the present invention.
Claims (9)
1. A servo displacement error compensation method based on interpolation is characterized by comprising the following steps:
acquiring reference data by using a tooling plate and an instrument, and corresponding the servo actual position and the theoretical position of a reference point one by one;
secondly, function mapping between the servo coordinates and theoretical coordinates is achieved by using an interpolation function and reference data, and coordinate conversion vectors are calculated;
and step three, substituting the theoretical coordinate of the target point into an interpolation coordinate calculation formula to obtain a servo coordinate corresponding to the theoretical position point, and giving the servo coordinate to a control system to realize automatic position running.
2. The interpolation-based servo step error compensation method of claim 1, wherein the first step comprises: the servo coordinate positions of the four reference points are measured A, B, C, D by using a dial indicator and a reference plate.
3. The interpolation-based servo step error compensation method of claim 2, wherein the second step comprises: and calculating an interpolation conversion vector by using the servo coordinates of the A, B, C, D four reference points and the theoretical position on the tooling plate.
4. The interpolation-based servo step error compensation method of claim 3, wherein the third step comprises: and determining the theoretical position coordinates needing interpolation calculation, and then calculating coordinate values in the servo system through the converted vectors.
5. The interpolation-based servo step error compensation method of claim 4, wherein the interpolation function is:
where (x 'y') is the theoretical coordinate, (x y) is the coordinate of the servo axis, aiIs the undetermined coefficient.
6. The interpolation-based servo walking error compensation method of claim 5, wherein the coordinates of the A, B, C, D reference points are calculated by:
7. the interpolation-based servo step error compensation method of claim 6, wherein the interpolation point is calculated by:
8. the interpolation-based servo step error compensation method of claim 7, wherein the translation vector is:
9. the interpolation-based servo step error compensation method of claim 2, further comprising an interpolation accuracy verification point E, wherein the verification point E is disposed at a center position of the reference point A, B, C, D.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114932455A (en) * | 2022-06-29 | 2022-08-23 | 中国航发动力股份有限公司 | Method for automatically eliminating zero point deviation of multi-sister tooling |
| CN115666125A (en) * | 2022-12-27 | 2023-01-31 | 合肥安迅精密技术有限公司 | Method for detecting and compensating positioning error of XY platform of chip mounter based on machine vision |
| CN117161550A (en) * | 2023-11-02 | 2023-12-05 | 珠海市申科谱工业科技有限公司 | 2D platform compensation method and device and laser processing equipment |
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2020
- 2020-10-26 CN CN202011156405.6A patent/CN114488944A/en active Pending
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114932455A (en) * | 2022-06-29 | 2022-08-23 | 中国航发动力股份有限公司 | Method for automatically eliminating zero point deviation of multi-sister tooling |
| CN114932455B (en) * | 2022-06-29 | 2023-09-12 | 中国航发动力股份有限公司 | Method for automatically eliminating zero-point deviation of multiple sister tools |
| CN115666125A (en) * | 2022-12-27 | 2023-01-31 | 合肥安迅精密技术有限公司 | Method for detecting and compensating positioning error of XY platform of chip mounter based on machine vision |
| CN115666125B (en) * | 2022-12-27 | 2023-08-18 | 合肥安迅精密技术有限公司 | Machine vision-based method for detecting and compensating positioning error of XY platform of chip mounter |
| CN117161550A (en) * | 2023-11-02 | 2023-12-05 | 珠海市申科谱工业科技有限公司 | 2D platform compensation method and device and laser processing equipment |
| CN117161550B (en) * | 2023-11-02 | 2024-01-26 | 珠海市申科谱工业科技有限公司 | 2D platform compensation method and device and laser processing equipment |
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