CN107843227A - A kind of method that encoder accuracy is improved based on collimation technique - Google Patents
A kind of method that encoder accuracy is improved based on collimation technique Download PDFInfo
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- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
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Abstract
The present invention is a kind of method that encoder accuracy is improved based on collimation technique, belongs to electromechanical integration, technical field of sensor measurement；On the premise of hardware is not increased, do not reduce encoder resolution, the precision of encoder is improved by polynomial calibration algorithm for the low encoder of high resolution, precision for this method；Polynomial calibration algorithm and calibration parameter are stored in the programmable digital processor of decoder internal, and when encoder works, polynomial calibration algorithm calls calibration parameter to calibrate encoder angular, and encoder accuracy is improved into more than 10 times.The present invention is not increasing hardware cost, does not sacrifice the precision that encoder is improved on the basis of encoder resolution.Handled suitable for the low encoder data of various high resolutions, precision.
Description
Technical field
The invention belongs to parallactic angle degree sensor fields of measurement, particularly a kind of side that encoder accuracy is improved based on collimation technique
Method.
Background technology
Encoder is a kind of angle measurement unit, is widely used in control system.Application field has cannon, radar, led
Bullet, satellite, wind-powered electricity generation, lathe etc..The precision and resolution ratio of raising encoder are the emphasis and difficult point of current encoder development.
Common encoder data processing method has data scaling method, angle sorting method, weights filter method etc..Wherein data
Although demarcation can improve the precision of encoder, continuous digital angle output can not be obtained.It can only namely be compiled sacrificing
On the premise of code device resolution ratio, precision is improved.Angle sorting method is on the contrary, this method can obtain higher resolution ratio, but hardly possible
To improve the precision of encoder, the raising of resolution ratio can only be realized by the subdivision to analog quantity, adds analog measurement
Hardware cost.Although weights filter method can improve precision and the resolution of encoder simultaneously using the method for over-sampling in theory
Rate, but this method only has an effect to the white noise in error, and white noise accounts for smaller in encoder noise in practical application, because
This effect is unsatisfactory.
The content of the invention
The technical problems to be solved by the invention are in view of the shortcomings of the prior art, to propose a kind of new based on collimation technique
The method for improving encoder accuracy, it on the premise of hardware cost is not improved, can improve the precision of encoder, portable
By force, it is applied widely.
The technical problems to be solved by the invention are realized by following technical scheme.The present invention is that one kind is based on
The method that collimation technique improves encoder accuracy, is characterized in, this method is not increasing for the low encoder of high resolution, precision
Stiffened part, on the premise of not reducing encoder resolution, the precision of encoder is improved by polynomial calibration algorithm；Multinomial school
Quasi- algorithm and calibration parameter are stored in the programmable digital processor of decoder internal, when encoder works, multinomial school
Quasi- algorithm calls calibration parameter to calibrate encoder angular, and encoder accuracy is improved.Described programmable digital processing
Device is selected from single-chip microcomputer, DSP, FPGA or PLD.
A kind of method that encoder accuracy is improved based on collimation technique of the present invention, described polynomial calibration algorithm
It is preferred that carrying out data calibration using single order fitting of a polynomial algorithm, calibration parameter is the single order fitting of a polynomial parameter of segmented,
When encoder works, programmable processor calls a rank multinomial school fitting algorithm to be calculated according to single order fitting of a polynomial parameter and obtained
Obtain high-precision encoder angular.
A kind of method that encoder accuracy is improved based on collimation technique of the present invention, its further preferred technical side
Case is：The input of this method is the original angle of encoder, is exported as final precise angle after processing；This method is by using height
Precision turntable, encoder original angle is obtained to the mapping function f (x) of High-precision angle, and the function is saved in encoder
In；When encoder works, the mapping function is called to obtain mapping angle to improve encoder accuracy；According to encoder historical point view
Value, and the motor pattern of encoder are predicted to obtain encoder prediction angle；Original angle, mapping angle and pre- measuring angle are entered
Row fusion calculation, the precision for improving the resolution ratio of angle and further improving encoder obtain final accurate angle.
A kind of method that encoder accuracy is improved based on collimation technique of the present invention, its further preferred technical side
Case is：
Pre- measuring angle determines according to encoder velocity and acceleration, it is assumed that velocity and acceleration is permanent in the encoder short time
Fixed, then short time inner encoder motion model is as follows：
Wherein t is time quantum, and a is amount of acceleration, and v is speed amount, and β is angle constant, and α is encoder current angle value；
Using one-step prediction, i.e., calculate the state of+1 point of kth in known k-th point of state；This pattern (1) does following simplification：
Wherein αpFor pre- measuring angle；αaFor final accurate angle, k moment encoder angulars are substituted with it here；T is number
According to the sampling period.
A kind of method that encoder accuracy is improved based on collimation technique of the present invention, its further preferred technical side
Case is：The method for obtaining mapping function f (x) comprises the following steps that：
(1) turntable zero-bit is alignd with the original zero-bit of encoder first；
(2) turntable is incrementally rotated fixed angle every time, record encoder original angle, be rotated by 360 ° rear stop recording,
This angle is encoder and turntable zero-bit；
(3) in each data segment, the f (x) of each data segment is obtained using polynomial fitting method, it is whole so as to obtain
F (x) in the range of 360 °；
(4) record of turntable angle is completed in decoder internal programmable digital chip, and is solidified in the form of program
Mapping function f (x).
A kind of method that encoder accuracy is improved based on collimation technique of the present invention, its further preferred technical side
Case is：The specific method of wherein fitting of a polynomial algorithm is as follows：
Assuming that mapping function meets the expression of n-order polynomial：
Wherein ajFor undetermined coefficient, calculated and obtained by equation below：
Wherein xiTo be fitted the continuous n encoder initial data of section, f (x)iIt is encoder mapping function value, used here as
Turntable data are approximate, i=1,2...n.
A kind of method that encoder accuracy is improved based on collimation technique of the present invention, its further preferred technical side
Case is：The method for obtaining mapping function f (x), is comprised the following steps that：
(1) first turntable zero-bit is alignd with the original zero-bit of encoder；
(2) turntable is incrementally rotated fixed angle every time, record encoder original angle, be rotated by 360 ° rear stop recording,
This angle is encoder and turntable zero-bit；
(3) turntable angle and corresponding encoder original angle are recorded, the encoder corresponding to turntable angle subtracts is original
Angle obtains the error array of encoder, obtains error curve e (x) using sine curve fitting, wherein x is encoder rudimentary horn
Degree, unit are degree；
(4) mapping function f (x)=x+e (x) is obtained.
A kind of method that encoder accuracy is improved based on collimation technique of the present invention, its further preferred technical side
Case is：Method during error curve e (x) is obtained, summary is repeatedly measured for batch production encoder of fixed production line, technique for fixing
Go out consistent error curve e (x).
A kind of method that encoder accuracy is improved based on collimation technique of the present invention, its further preferred technical side
Case is：When encoder works, predict to obtain encoder prediction according to the motor pattern of encoder historical point view value, and encoder
Angle [alpha]p；Mapping function f (x) is called to obtain mapping angle αf；And encoder original angle alphao；Obtain the final standard of encoder
True angle [alpha]aCalculation formula：
αa=kp·αp+kf·αf+ko·αo (6)
Wherein kp, kf, koFor blending weight coefficient, respectively pre- measuring angle weight coefficient, mapping angle weight coefficient and rudimentary horn
Spend weight coefficient kp+kf+ko=1.
The computational methods of data fusion weight coefficient are specific as follows in fusion calculation：
(1) the weight coefficient k in final precise angle shared by pre- measuring anglepGained speed is calculated by encoder historical point view
Determined with acceleration；Formula is as follows：
Wherein akFor kth point encoder acceleration, vkFor kth point encoder speed；
(2) weight coefficient k shared by mapping angle in final precise anglefBy acquisition mapping function f (x) errors r.m.s. with
All error r.m.s. accountings determine；Formula is as follows：
Wherein εfError is obtained for mapping function, is determined by rotary table error, installation axial system error, curve fit error；εoFor
Encoder original angle error, determined by the initial precision of encoder；
(3) weight coefficient k shared by encoder original angle in final precise angleoBy encoder original angle error Fang Jun
Root determines with all error r.m.s. accountings；Formula is as follows：
Encoder resolution refers to that the axle of encoder revolves the exported positional number that turns around；Encoder accuracy refers to encoder
The degree of accuracy of the output data to measurement real angle.Resolution ratio and precision are two different important indicators of encoder.For one
Platform represents the encoder of angle using 16bit data, and its ultimate resolution is 216, minimum resolving accuracy is：
And encoder accuracy depends on the output data of encoder and the maximum difference of real angle.Current main-stream diameter 58
Resolution ratio is the electromechanical encoder accuracy of 16 at 0.16 ° or so.The type encoder applies this method precision can be brought up to
0.016.Within.
As described above, encoder accuracy is much larger than encoder minimum resolving accuracy, such encoder is referred to as differentiating
The encoder that rate is high, precision is low.This method can be used to improve encoder accuracy for this encoder.
Compared with prior art, the inventive method can be on the premise of hardware cost not be improved, while improves encoder
Precision and resolution ratio, it is portable strong, applied widely, and the encoder data available for various occasions is handled.
Brief description of the drawings
Fig. 1 is the exact value mapping function of encoder；
Fig. 2 is encoder fitting function schematic diagram；
Fig. 3 is coder transitions block diagram；
Fig. 4 is digital processing unit program flow diagram.
Embodiment
Concrete technical scheme of the invention described further below, in order to which those skilled in the art is further understood that
The present invention, without forming the limitation to its right.
Embodiment 1, a kind of method that encoder accuracy is improved based on collimation technique, this method is for high resolution, precision
Low encoder is improved by polynomial calibration algorithm and encoded on the premise of hardware is not increased, do not reduce encoder resolution
The precision of device；Polynomial calibration algorithm and calibration parameter are stored in the programmable digital processor of decoder internal, coding
When device works, polynomial calibration algorithm calls calibration parameter to calibrate encoder angular and improves encoder accuracy.
The programmable digital processor is selected from single-chip microcomputer, DSP, FPGA or PLD.
Described polynomial calibration algorithm carries out data calibration using single order fitting of a polynomial algorithm, and calibration parameter is segmentation
The single order fitting of a polynomial parameter of formula, encoder work when, programmable processor call a rank multinomial school fitting algorithm according to
Single order fitting of a polynomial parameter, which calculates, obtains high-precision encoder angular.
The input of this method is the original angle of encoder, is exported as final precise angle after processing；This method is by making
Encoder original angle is obtained to the mapping function f (x) of High-precision angle with high precision turntable, and the function is saved in coding
In device；When encoder works, the mapping function is called to obtain mapping angle to improve encoder accuracy；According to encoder history angle
Angle value, and the motor pattern of encoder are predicted to obtain encoder prediction angle；By original angle, mapping angle and pre- measuring angle
Fusion calculation is carried out, the intensive reading for improving the resolution ratio of angle and further improving encoder obtains final accurate angle.
Pre- measuring angle determines according to encoder velocity and acceleration, it is assumed that velocity and acceleration is permanent in the encoder short time
Fixed, then short time inner encoder motion model is as follows：
Wherein t is time quantum, and a is amount of acceleration, and v is speed amount, and β is angle constant, and α is encoder current angle value；
Using one-step prediction, i.e., calculate the state of+1 point of kth in known k-th point of state；This pattern (1) does following simplification：
Wherein αpFor pre- measuring angle；αaFor final accurate angle, k moment encoder angulars are substituted with it here；T is number
According to the sampling period.
The method for obtaining mapping function f (x) comprises the following steps that：
(1) turntable zero-bit is alignd with the original zero-bit of encoder first；
(2) turntable is incrementally rotated fixed angle every time, record encoder original angle, be rotated by 360 ° rear stop recording,
This angle is encoder and turntable zero-bit；
(3) in each data segment, the f (x) of each data segment is obtained using polynomial fitting method, it is whole so as to obtain
F (x) in the range of 360 °；
(4) record of turntable angle is completed in decoder internal programmable digital chip, and is solidified in the form of program
Mapping function f (x).
The specific method of wherein fitting of a polynomial algorithm is as follows：
Assuming that mapping function meets the expression of n-order polynomial：
Wherein ajFor undetermined coefficient, calculated and obtained by equation below：
Wherein xiTo be fitted the continuous n encoder initial data of section, f (x)iIt is encoder mapping function value, used here as
Turntable data are approximate, i=1,2...n.
The method for obtaining mapping function f (x), step in detail below can also be used：
(1) first turntable zero-bit is alignd with the original zero-bit of encoder；
(2) turntable is incrementally rotated fixed angle every time, record encoder original angle, be rotated by 360 ° rear stop recording,
This angle is encoder and turntable zero-bit；
(3) turntable angle and corresponding encoder original angle are recorded, the encoder corresponding to turntable angle subtracts is original
Angle obtains the error array of encoder, obtains error curve e (x) using sine curve fitting, wherein x is encoder rudimentary horn
Degree, unit are degree；
E (x)=Asin (x+ θ)+B (5)
(4) mapping function f (x)=x+e (x) is obtained.
Method during error curve e (x) is obtained, is repeatedly measured for batch production encoder of fixed production line, technique for fixing
Sum up consistent error curve e (x).
When encoder works, predict to obtain encoder according to the motor pattern of encoder historical point view value, and encoder
Predict angle [alpha]p；Mapping function f (x) is called to obtain mapping angle αf；And encoder original angle alphao；Obtain encoder most
Whole precise angle αaCalculation formula：
αa=kp·αp+kf·αf+ko·αo (6)
Wherein kp, kf, koFor blending weight coefficient, respectively pre- measuring angle weight coefficient, mapping angle weight coefficient and original
Beginning angle weight coefficient kp+kf+ko=1.
The computational methods of data fusion weight coefficient are specific as follows in fusion calculation：
(1) the weight coefficient k in final precise angle shared by pre- measuring anglepGained speed is calculated by encoder historical point view
Determined with acceleration；Formula is as follows：
Wherein akFor kth point encoder acceleration, vkFor kth point encoder speed；
(2) weight coefficient k shared by mapping angle in final precise anglefBy acquisition mapping function f (x) errors r.m.s. with
All error r.m.s. accountings determine；Formula is as follows：
Wherein εfError is obtained for mapping function, is determined by rotary table error, installation axial system error, curve fit error；εoFor
Encoder original angle error, determined by the initial precision of encoder；
(3) weight coefficient k shared by encoder original angle in final precise angleoBy encoder original angle error Fang Jun
Root determines with all error r.m.s. accountings；Formula is as follows：
Embodiment 2, a kind of method that encoder accuracy is improved based on collimation technique：
For each encoder, the mapping of its output valve to exact value is referred to as the exact value mapping function of encoder such as
Fig. 1, hereinafter referred to as mapping function f (x), this function contain the information such as the axial system error of encoder, transformed error.To mapping
Function carries out n-order polynomial fitting, and expression formula is as follows：
Wherein ajFor undetermined coefficient, it can be calculated and obtained by equation below：
Wherein xi(i=1,2...n) be fitting section continuous n encoder output data, f (x)i(i=1,2...n) is
Corresponding exact value.X is obtained by measurement meansiWith f (x)iUndetermined coefficient a can be obtained to calculate afterwardsjSo as to obtain
The n-order polynomial fitting function f (x) of mapping function.
To simplify computing, multistage single order fitting of a polynomial is selected here.Single order fitting of a polynomial is also referred to as linear fit, compiles
Code device output angle can be approximated to be straight line in the range of 2 °.Therefore it is as follows for each section of f (x) formula：
F (x)=a1x+a0(xn≤ x ＜ xn+1) (10)
360 ° of angular ranges are divided intoSection, obtain every section of starting point coordinate (x by measuring as shown in Figure 2n, f
(x)n) and terminal point coordinate (xn+1, f (x)n+1), it is as follows to substitute into formula (4) calculating this section of matched curve parameter value of acquisition by 2 points：
Each section of curve of 360 ° of angular ranges, which links up, just obtains complete f (x) as shown in Figure 2.
Such as Fig. 3 coder transitions block diagrams, encoder mainly angled sensor unit, angle solving unit, data processing
Unit, bus unit and DC/DC power units.Wherein angular transducer and angle solving unit is completed mechanical angle and arrived jointly
The conversion of digital angle.Bus unit is completed encoder and communicated with the data of outside.DC/DC power units complete Power convert.
Wherein encoder calibration algorithm is realized in digital processing element.
Digital processing element prestores the beginning and end of every section of experiment curv totally 180 groups of end-point datas.Such as Fig. 4 numerals
Processor program flow chart.Shown in encoder when encoder works, digital processing element is read first after completing system initialization
180 groups of single order fitting of a polynomial parameters are taken, then complete the calculating of 180 sections of mapping function parameters.Angle is read in cyclic program
After spending data signal, the section according to belonging to angle numeral signal search needs the mapping function that calls, a rank multinomial is called
Fitting algorithm completes data calibration, finally completes the transmission of encoder angular.
Embodiment 3, a kind of method that encoder accuracy is improved based on collimation technique：
Mapping function f (x) of the encoder by output original angle to actual angle is obtained by measurement means.By turntable with
Encoder is coaxially connected, reads turntable data Z1, and record the encoder output B of same position1, turntable is rotated into certain angle
Spend and it is static after, record turntable data Z2And encoder data B2.Obtain turntable angle number group Z and corresponding encoder
Array B.Array Z and array B is fitted using the cftool instruments in matlab, obtains mapping function f (x).
Assuming that the motor pattern of encoder is movement at the uniform velocity, encoder prediction angle can be obtained according to historical point view.It is public
Formula is as follows：
αp=2 αa(n)+αa(n-1) (12)
It can be calculated more than and obtain encoder mapping angle αf, predict angle [alpha]pAnd original angle alphao.Substituted into
Formula (6), while take kp=0.1, kf=0.8, ko=0.1.By above-mentioned algorithm in the electromechanical coding of single speed using a diameter of 58mm
Realized on the inside single-chip microcomputer of device.By original 10 ' encoder accuracy is brought up into 60, and " resolution ratio brings up to 16 by 14.
Wherein mapping function f (x) acquisition can use following method.
A) encoder is arranged on turntable, adjustment revolving table position makes encoder output be zero.Revolving table position is arranged to
Zero-bit.Turntable is completed with the zero-bit of encoder to aliging；
B) set turntable to be rotated forward according to 2 ° every time, the original angle of encoder is recorded afterwards in place every time, by what is obtained
Data are saved in array B successively.Turntable is rotated 180 times in the method and obtains 180 encoder original angle data；
C) data are divided into 3 one group in order, carry out 2 rank fittings, the wherein first data of the group of kth+1 are the data
K group data last data.For example, first group of data sequence number is (1,2,3), second group of data sequence number is (3,4,5),
To the last one group of data sequence number is (179,180,1).Data are substituted into formula (3), (4) can obtain mapping function f (x).
The programmable digital that the mapping function parameter of all data segments is saved in encoder by this method according to order is handled
In device.While in order to retrieve the sequence number of each data correspondence mappings function, it is necessary to which the Origin And Destination of every group of data is recorded in
In encoder.The segmentation of this way function is more, it is necessary to which the parameter of storage is more, retrieval time is also longer, the benefit brought
Be mapping function confidence level it is higher.
The angular segments of each group of covering are first angle-data of the group and the angle model in last angle-data value
Enclose.
Wherein mapping function f (x) acquisition can also use following method：
A) encoder is arranged on turntable, adjustment revolving table position makes encoder output be zero.Revolving table position is arranged to
Zero-bit.Turntable is completed with the zero-bit of encoder to aliging；
B) set turntable to be rotated forward according to 2 ° every time, the original angle of encoder is recorded afterwards in place every time, by what is obtained
Data are saved in array B successively.Turntable is rotated 180 times in the method and obtains 180 encoder original angle data；
C) the encoder original angle corresponding to turntable angle subtracts, obtains error array E.Its is big for encoder
Most error curves are in Sine distribution in the range of 360, therefore encoder errors curve can be fitted according to formula (5),
Obtain parameter A, B, θ.Mapping function is obtained according to formula f (x)=x+e (x).
The characteristics of this method is only to need to store parameter A, B, θ, you can to obtain mapping function.Therefore storage parameter is few,
Without retrieval.It is similar if it is desired to obtaining the mapping function of higher precision, error fit curve can increase spatially high order
Harmonic wave.Equally bring high-precision while need to consume more memory spaces and calculation resources.
In this method, wherein code device predicts angle [alpha]p, mapping angle αf, original angle alphaoAmalgamation mode can be according to formula
(6) carry out.Wherein weight coefficient kpCalculated according to formula (7).Wherein vkApproximate formula is as follows：
Wherein T is the encoder sampling period, αa(k) k-th of history precise angle is represented.Wherein akApproximate formula is such as
Under：
Because the formula is based on the assumption that encoder velocity and acceleration is constant.Need to ensure when acceleration changeReduce, therefore for akWith ak+1The situation of contrary sign is, it is necessary to which the entry value is taken；Same vkWith vk+1Contrary sign, thenEntry value takes 0.The k when encoder speed, acceleration are constant can so be ensuredpWith maximum occurrences 0.5.
For weight coefficient kf、koThen need according to formula (8), (9) calculating.Wherein εfMapping function error is represented, can be with
Calculated according to deviation accumulation law.Such as the error included in the mapping function acquisition methods in example 2 has error of fitting εf1、
Turntable measurement error εf2And alignment error εf3.Then mapping function error calculation formula is as follows：
Claims (10)
- A kind of 1. method that encoder accuracy is improved based on collimation technique, it is characterised in that this method is for high resolution, precision Low encoder is improved by polynomial calibration algorithm and encoded on the premise of hardware is not increased, do not reduce encoder resolution The precision of device；Polynomial calibration algorithm and calibration parameter are stored in the programmable digital processor of decoder internal, coding When device works, polynomial calibration algorithm calls calibration parameter to calibrate encoder angular, and encoder accuracy is improved.
- 2. a kind of method that encoder accuracy is improved based on collimation technique according to claim 1, it is characterised in that described Programmable digital processor be selected from single-chip microcomputer, DSP, FPGA or PLD.
- 3. a kind of method that encoder accuracy is improved based on collimation technique according to claim 1, it is characterised in that described Polynomial calibration algorithm using single order fitting of a polynomial algorithm carry out data calibration, calibration parameter for segmented single order it is multinomial Formula fitting parameter, when encoder works, programmable processor calls a rank multinomial school fitting algorithm to be intended according to a rank multinomial Close parameter and calculate the high-precision encoder angular of acquisition.
- A kind of 4. method that encoder accuracy is improved based on collimation technique according to claim 3, it is characterised in that：The party The input of method is the original angle of encoder, is exported as final precise angle after processing；This method is by using high precision turntable Encoder original angle is obtained to the mapping function f (x) of High-precision angle, and the function is saved in encoder；Encoder During work, the mapping function is called to obtain mapping angle；It is pre- according to encoder historical point view value, and the motor pattern of encoder Measure encoder prediction angle；Original angle, mapping angle and pre- measuring angle are subjected to fusion calculation, improve the resolution of angle Rate and further improve encoder precision obtain final accurate angle.
- A kind of 5. method that encoder accuracy is improved based on collimation technique according to claim 4, it is characterised in thatPre- measuring angle determines according to encoder velocity and acceleration, it is assumed that velocity and acceleration is constant in the encoder short time, then Short time inner encoder motion model is as follows：<mrow> <mi>&alpha;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msup> <mi>at</mi> <mn>2</mn> </msup> </mrow> <mn>2</mn> </mfrac> <mo>+</mo> <mi>v</mi> <mi>t</mi> <mo>+</mo> <mi>&beta;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>Wherein t is time quantum, and a is amount of acceleration, and v is speed amount, and β is angle constant, and α is encoder current angle value；Use One-step prediction, i.e., calculate the state of+1 point of kth in known k-th point of state；This pattern (1) does following simplification：<mrow> <msub> <mi>&alpha;</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>&CenterDot;</mo> <mi>T</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msup> <mi>aT</mi> <mn>2</mn> </msup> </mrow> <mn>2</mn> </mfrac> <mo>+</mo> <mi>v</mi> <mi>T</mi> <mo>+</mo> <msub> <mi>&alpha;</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>&CenterDot;</mo> <mi>T</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>Wherein αpFor pre- measuring angle；αaFor final accurate angle, k moment encoder angulars are substituted with it here；T adopts for data The sample cycle.
- 6. a kind of method that encoder accuracy is improved based on collimation technique according to claim 4, it is characterised in that obtain Mapping function f (x) method comprises the following steps that：(1) turntable zero-bit is alignd with the original zero-bit of encoder first；(2) turntable is incrementally rotated fixed angle every time, record encoder original angle, be rotated by 360 ° rear stop recording, this angle Spend for encoder and turntable zero-bit；(3) in each data segment, the f (x) of each data segment is obtained using polynomial fitting method, so as to obtain whole 360 ° of models Enclose interior f (x)；(4) record of turntable angle is completed in decoder internal programmable digital chip, and solidifies mapping in the form of program Function f (x).
- 7. a kind of method that encoder accuracy is improved based on collimation technique according to claim 4, it is characterised in that wherein The specific method of fitting of a polynomial algorithm is as follows：Assuming that mapping function meets the expression of n-order polynomial：<mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>j</mi> <mo>=</mo> <mi>n</mi> </mrow> </munderover> <msub> <mi>a</mi> <mi>j</mi> </msub> <msup> <mi>x</mi> <mi>j</mi> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>Wherein ajFor undetermined coefficient, calculated and obtained by equation below：<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>x</mi> <mi>n</mi> <mi>n</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mi>n</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <msub> <mi>x</mi> <mi>n</mi> </msub> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>x</mi> <mn>2</mn> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mn>2</mn> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <msub> <mi>x</mi> <mn>2</mn> </msub> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>x</mi> <mn>1</mn> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mn>1</mn> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <msub> <mi>x</mi> <mn>1</mn> </msub> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mi>n</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mn>0</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>f</mi> <msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mi>n</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>f</mi> <msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>f</mi> <msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mn>2</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>f</mi> <msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mn>1</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>Wherein xiTo be fitted the continuous n encoder initial data of section, f (x)iIt is encoder mapping function value, used here as turntable Data are approximate, i=1,2...n.
- 8. a kind of method that encoder accuracy is improved based on collimation technique according to claim 4, it is characterised in that obtain Mapping function f (x) method, is comprised the following steps that：(1) first turntable zero-bit is alignd with the original zero-bit of encoder；(2) turntable is incrementally rotated fixed angle every time, record encoder original angle, be rotated by 360 ° rear stop recording, this angle Spend for encoder and turntable zero-bit；(3) turntable angle and corresponding encoder original angle are recorded, the encoder original angle corresponding to turntable angle subtracts The error array of encoder is obtained, error curve e (x) is obtained using sine curve fitting, wherein x is encoder original angle, Unit is degree；(4) mapping function f (x)=x+e (x) is obtained.
- A kind of 9. method that encoder accuracy is improved based on collimation technique according to claim 8, it is characterised in that：Obtain Method during error curve e (x), the multiple measurement of batch production encoder for fixed production line, technique for fixing are summed up with one The error curve e (x) of cause property.
- 10. a kind of method that encoder accuracy is improved based on collimation technique according to claim 4, it is characterised in that compile During code device work, predict to obtain encoder prediction angle [alpha] according to the motor pattern of encoder historical point view value, and encoderp； Mapping function f (x) is called to obtain mapping angle αf；And encoder original angle alphao；Obtain the final precise angle α of encodera Calculation formula：αa=kp·αp+kf·αf+ko·αo (6)Wherein kp, kf, koFor blending weight coefficient, respectively pre- measuring angle weight coefficient, mapping angle weight coefficient and rudimentary horn Spend weight coefficient kp+kf+ko=1；The computational methods of data fusion weight coefficient are specific as follows in fusion calculation：(1) the weight coefficient k in final precise angle shared by pre- measuring anglepGained speed is calculated with adding by encoder historical point view Speed determines；Formula is as follows：<mrow> <msub> <mi>k</mi> <mi>p</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>a</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&CenterDot;</mo> <msub> <mi>a</mi> <mi>k</mi> </msub> </mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>a</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>v</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&CenterDot;</mo> <msub> <mi>v</mi> <mi>k</mi> </msub> </mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>v</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>v</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>Wherein akFor kth point encoder acceleration, vkFor kth point encoder speed；(2) weight coefficient k shared by mapping angle in final precise anglefBy acquisition mapping function f (x) errors r.m.s. with owning Error r.m.s. accounting determines；Formula is as follows：<mrow> <msub> <mi>k</mi> <mi>f</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mfrac> <mrow> <mo>|</mo> <msub> <mi>&epsiv;</mi> <mi>o</mi> </msub> <mo>|</mo> </mrow> <msqrt> <mrow> <msubsup> <mi>&epsiv;</mi> <mi>f</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&epsiv;</mi> <mi>o</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>Wherein εfError is obtained for mapping function, is determined by rotary table error, installation axial system error, curve fit error；εoFor coding Device original angle error, determined by the initial precision of encoder；(3) weight coefficient k shared by encoder original angle in final precise angleoBy encoder original angle error r.m.s. with All error r.m.s. accountings determine；Formula is as follows：<mrow> <msub> <mi>k</mi> <mi>o</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mfrac> <mrow> <mo>|</mo> <msub> <mi>&epsiv;</mi> <mi>f</mi> </msub> <mo>|</mo> </mrow> <msqrt> <mrow> <msubsup> <mi>&epsiv;</mi> <mi>f</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&epsiv;</mi> <mi>o</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
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