CN108062071A - The real-time assay of parameter curve trace track profile errors - Google Patents
The real-time assay of parameter curve trace track profile errors Download PDFInfo
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- 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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Abstract
The invention discloses a kind of real-time assay of parameter curve trace track profile errors, the physical location of each axis servomotor is read by controller.Classification judgement is carried out according to the situation of relation pair servo profile errors of the corresponding parameter of curve of current instruction position, last moment foot point parameter, the tangent vector of each position, distance vector.Nonlinear verticality function is defined, is classified situation according to profile errors, the solution section of verticality function is determined using interval endpoint searching method.The solution of verticality function is calculated by Nonlinear Numerical solution, so as to calculate the exact value of profile errors.The present invention is realized to the real-time tracking of servo profile error solution scope and accurately defined, computational accuracy and efficient, the real-time high-precision for realizing servo profile errors measures, complexity, the technique on-line optimization in the production process of high speed, error compensation control, equipment condition monitoring etc. are can be applied to, promotes production precision and efficiency.
Description
Technical field
The invention belongs to Mechatronic Systems SERVO CONTROL fields, and in particular to the slave wheel into parameter curve tracking control system
The real time measure technology of wide error.
Background technology
Multiaxis contour motion servo-control system is widely used in numerically-controlled machine tool, robot, lithographic equipment etc..In multiaxis
In servo-control system, had by the profile errors that system control sytsem introduces to path accuracy and directly affected.In order to servo
Profile errors are monitored so as to modified technique and parameter or are corrected control to error, it is necessary to be carried out to profile errors
Accurate Determining.Generally require the mathematical table of each moment position coordinates of each axis and theory locus according to each servomotor feedback
Up to formula, profile errors are calculated.With the application increasingly complex of multiple-axis servo kinetic control system, movement locus by
The tracks such as simple straight line, circular arc are gradually transitions free parameter curvilinear path.However, the mathematical expression phase of parameter curve track
To complexity, the difficulty in computation of profile errors is larger, it is more difficult to realize and is measured in real time in control.
Servo profile errors are defined as servo-drive system physical location to the distance of theory locus curve.This distance is typically nothing
Method is measured directly, and generally by the physical location for the servomotor for measuring each kinematic axis, profile errors are counted indirectly
It calculates.It can be divided into two class method of off-line calculation and the real time measure for the profile errors measure of servo track.Off-line calculation can basis
The definition of profile errors lists in actual path each point to the range equation of theoretical parameter track, and by seeking extreme value or most
The methods of optimization, is calculated.Since range equation is usually nonlinear high-order equation, analytic solutions can not be obtained, it is necessary to using number
Value calculating method iterates.The equation obtained according further to definition contains multiple solutions, it is necessary to solve multiple candidate solutions simultaneously
It is accepted or rejected, calculation amount is very big.Real-time assay generally use approximate processing, by carrying out geometry or generation to profile errors
Approximate processing on number, and the information of each axis tracking error in servo-drive system is utilized, the calculating of profile errors is simplified, so as to
Enough it is applied to the online the real time measure of servo profile errors.But existing approximate calculation method high speed, higher curvature complicated track
In the case of computational accuracy it is generally poor, therefore, it is difficult to realize accurate profile errors the real time measure.With digitlization servo control
The promotion of system computing capacity processed and high-speed, high precision motion controller demand it is growing, be badly in need of in real-time servo wheel
Wide error realizes more accurate, perfect computational methods in measuring, but currently still lacks effective real-time high-precision assay method.
The content of the invention
The purpose of the invention is to overcome deficiency of the prior art, a kind of parameter curve trace track profile is provided and is missed
The real-time assay of difference, the shortcomings of low existing assay method precision, inefficient can be solved.
The purpose of the present invention is what is be achieved through the following technical solutions：
The real-time assay of parameter curve trace track profile errors, it is assumed that the parameter curve equation of track is
The corresponding parameter u scopes in track are [us,ue], algorithm is initialized before starting, by foot point parametric variable u0It is initialized as curveThe parameter value u of starting points, concurrently set neighborhood search bound variable ε1、ε2、ε3(being all higher than 0), interval endpoint Searching point
Number N (N>1), for given position vectorIt is vector to define verticality function f (u)Arrow is cut with curveIt is interior
Product (u ∈ [us,ue]), afterwards within each SERVO CONTROL cycle, current outline error is calculated, is as follows：
(1) current each axis servomotor position feedback is read, determines current actual positionsFoot point is set to lose flag bit
Lost is 0；
(2) u is compared0Parameter of curve u corresponding with the current servo location of instructionCIf u0≥uC, make the foot point region of search left
Endpoint variables ua=uC, foot point region of search right end point variable ub=min (ua+ε1,ue), it enters step (9)；Otherwise, into step
Suddenly (3)；
(3) u is calculated0And uCThe curve at place cuts arrowWith
(4) calculateWithInner productIf d<0, it enters step (5)；Otherwise, enter step
(6)；
(5) u is madeb=uC,ua0=max (u0-ε2,us), call interval endpoint searching method search ua, i.e. ua=UEPS (ub,
ua0), it enters step (9)；
(6) if f (u0)>0, make ua=u0, call interval endpoint searching method search ub, i.e. ub=UEPS (ua,uc), enter
Step (9)；Otherwise, enter step (7)；
(7) if f (u0)<0, make ub=u0,ua1=max (u0-ε3,us) call interval endpoint searching method search ua, i.e. ua
=UEPS (ub,ua1), it enters step (9)；Otherwise, enter step (8)；
(8) u is made0It remains unchanged, enters step (12)；
(9) f (u are calculateda) and f (ub)；If f (ua)·f(ub)>0, it enters step (10)；Otherwise, enter step (11)；
(10) it is 1 to put lost flag bits, if | f (ua)|<|f(ub) |, make u0=ua；Otherwise, u is made0=ub；It enters step
(12)；
(11) Nonlinear-Equations Numerical Solution method is called in section [ua,ub] in search verticality Functional Equation f (u)=0 rootIt makes updated
(12) servo profile error size is calculated
During motion control, controller repeats the above steps (1)~(12) within each SERVO CONTROL cycle, you can real
The real-time high-precision of servo profile errors measures in existing parameter curve track movement.
Interval endpoint searching method u in step (5), (6), (7)ep=UEPS (uss,use) comprise the following steps：
(A1) f (u are calculatedss)。
(A2) if f (uss)=0 makes search result variable uep=uss, return；Otherwise, enter step (A3)；
(A3) step-size in search Δ u=(u are madese-uss)/N, search point counting variable i=1；
(A4) f (u are calculatedss+i×Δu)；
(A5) if f (uss+i×Δu)·f(uss)≤0, makes uep=f (uss+ i × Δ u) is returned；
(A6) i=i+1 is made, if i<N, return to step (A4)；Otherwise, enter step (A7)；
(A7) u is madeep=use, return.
Compared with prior art, advantageous effect caused by technical scheme is：
(1) servo profile error calculation precision is high.In real-time calculate, employ numerical solution and replace at traditional approximation
Reason method can realize that high-precision servo profile errors measure by setting iterations.
(2) computational efficiency is high, realizes real-time high-precision profile errors measure.Take full advantage of the current servo location of instruction
Corresponding parameter of curve uC, last moment u0The controllers internal information such as parameter carries out the interval range of profile errors solution
It real-time tracking and accurately defines, numerical solution is enable to rapidly converge to current time true servo profile errors.
(3) adaptable this method is directed to the different situations being likely to occur and is classified processing, and this method is enable to fit
The various profile errors in reality is answered to calculate primary condition.Classification handles the quantity for also greatly reducing solution of equation, improves effect
Rate.
(4) real-time high-precision of parameter curve trace track profile errors is measured, it can be in complicated, high speed production process
In on-line optimization is carried out to technical process, promote precision and efficiency；It can also realize that machining state is monitored on-line, find to set in time
The problem of standby or technique, avoids losing.It is also to realize that error accurately compensates control that servo profile errors real-time high-precision, which measures,
Premise.
(5) implementation of the method for the present invention can be based on existing servo-control system hardware facility, without increasing new biography
Sensor can be implemented, and convenient for having the upgrading of control system, reduce cost.
Description of the drawings
Fig. 1 is servo profile the real time measure flow chart in the present invention.
Fig. 2 is interval endpoint searching method flow chart in the present invention.
Fig. 3 is control system principle schematic in the present invention.
Fig. 4 is that profile measures 1 schematic diagram of situation in the present invention.
Fig. 5 is that profile measures 2 schematic diagram of situation in the present invention.
Fig. 6 is that profile measures 3 schematic diagram of situation in the present invention.
Fig. 7 is that profile measures 4 schematic diagram of situation in the present invention.
Fig. 8 is that profile measures 5 schematic diagram of situation in the present invention.
Fig. 9 is solution interval schematic diagram in the present invention.
Specific embodiment
Below in conjunction with attached drawing and pass through embodiment the implementation steps of the method for the present invention are further described.It needs to illustrate
Be that following embodiments are narrative, be not limited, the content that is covered of the present invention is not limited to following embodiments.
Control system principle described in this example is as shown in Figure 3.The control system contains X and Y totally 2 kinematic axis.Control
Parametric curve interpolator device in system is realized to parameter curve equationCarry out time sampling interpolation (the corresponding parameter u in track
Scope is [us,ue]), interpolator can export the corresponding parameter of curve u in servo instruction position when each controlling cycle arrivesC、
X-axis location of instruction Cx(uC) and Y-axis location of instruction Cy(uC).X, Y-axis servo-drive system is each independent position-force control, X, Y
Axis physical location is respectively PxAnd Py, the open-loop transfer function difference G of each axisx(s) and Gy(s).More than physical location can be by installing
Encoder on servomotor is detected, and feeds back to controller, according to motor physical location and the deviation of the location of instruction
It generates control signal and through amplifying driving motor, realizes position-force control.Servo profile errors the real time measure module connects in Fig. 3
Receive the parameter of curve u from parametric curve interpolator deviceCThe physical location P of signal and each axis servo feedbackxAnd PySignal.It should
Module calculates output profile errors letter in real time using the real-time assay of this invention parameter curve trace track profile errors
Number ec。
Before movement starts, servo profile errors the real time measure module carries out algorithm initialization, by foot point variable u0Initially
Turn to curveThe parameter value u of starting points, concurrently set neighborhood search bound variable ε1,ε2,ε3, interval endpoint search point
N.In addition, for given position vectorIt is vector to define verticality function f (u)Arrow is cut with curveInner product
(u∈[us,ue]), it is used in assay method.
After movement starts, within each SERVO CONTROL cycle, missed by the profile at following steps the real time measure current time
Difference：
(1) control system reads X, Y-axis encoder for servo motor count value, obtains current each shaft position feedback, determines to work as
Preceding physical locationIt is 0 that foot point is set, which to lose flag bit lost,.
(2) u is compared0Parameter of curve u corresponding with the current servo location of instructionC.If u0≥uC, make the foot point region of search left
Endpoint variables ua=uC, foot point region of search right end point variable ub=min (ua+ε1,ue), it enters step (9)；Otherwise, into step
Suddenly (3).
(3) u is calculated0And uCThe curve at place cuts arrowWith
(4) calculateWithInner productIf d<0, it enters step (5)；Otherwise, into step
Suddenly (6).
(5) u is madeb=uC,ua0=max (u0-ε2,us), call interval endpoint searching method search ua, i.e. ua=UEPS (ub,
ua0), it enters step (9).
(6) if f (u0)>0, make ua=u0, call interval endpoint searching method search ub, i.e. ub=UEPS (ua,uc), enter
Step (9)；Otherwise, enter step (7).
(7) if f (u0)<0, make ub=u0,ua1=max (u0-ε3,us) call interval endpoint searching method search ua, i.e. ua
=UEPS (ub,ua1), it enters step (9)；Otherwise, enter step (8).
(8) u is made0It remains unchanged, enters step (12).
(9) f (u are calculateda) and f (ub).If f (ua)·f(ub)>0, it enters step (10)；Otherwise, enter step (11).
(10) it is 1 to put lost flag bits, if | f (ua)|<|f(ub) |, make u0=ua；Otherwise, u is made0=ub.It enters step
(12)。
(11) Nonlinear-Equations Numerical Solution method is called in section [ua,ub] in search verticality Functional Equation f (u)=0 rootIt makes updated
(12) servo profile error size is calculated
Interval endpoint searching method u involved in above-mentioned profile errors stepep=UEPS (uss,use) specific implementation step
It is rapid as follows：
(A1) f (u are calculatedss)。
(A2) if f (uss)=0, makes uep=uss, return；Otherwise, enter step (A3).
(A3) Δ u=(u are madese-uss)/N, i=1.
(A4) f (u are calculatedss+i×Δu)。
(A5) if f (uss+i×Δu)·f(uss)≤0, makes uep=f (uss+ i × Δ u) is returned.
(A6) i=i+1 is made, if i<N, return to step (A4)；Otherwise, enter step (A7).
(A7) u is madeep=use, return.
Fig. 4 is u in step (2)0≥uCSituation, such case illustrates current uCLag behind a moment foot point variable
u0.Under the action of servo feedback control, this moment foot point variableIt will be to uCIt moves in direction.Therefore foot point variable is set
The left and right endpoint of the region of search of solution is ua=uC,ub=min (ua+ε1,ue)。
Fig. 5 is in step (4), (5)WithInner product d<0 situation.There is such case and illustrate that position refers to
Make corresponding uCPoint direction of feed and the corresponding foot point u of last moment physical location0Direction of feed angle be more than 90 degree, the two
Direction differs greatly.At this time in position vector2 foot points for meeting f (u)=0 nearby are likely to occur, respectively close toWithAccording to the requirement for reducing contour motion tracking error, answer prioritizing selection closeFoot point solve profile errors.Cause
This, sets the right endpoint u of the region of searchb=uC, left end point is with interval endpoint searching method from right endpoint to ua0=max (u0-ε2,
us) direction search, it can preferentially find closeFoot point variableSolution section.
Fig. 6 is f (u in step (6)0)>0 situation, this is common scenario the most, represents physical locationCorresponding foot
Point variableThan last moment foot point variable u0Closer to the corresponding parameter of curve u of the current servo location of instructionC.Setting is searched at this time
Rope section left end point is ua=u0, call interval endpoint searching method since left end point to uCDirection search right endpoint ub, i.e. ub
=UEPS (ua,uc)。
Fig. 7 is f (u in step (7)0)<0 situation.Such case illustrates physical locationCorresponding foot point variable is to position
Instruct corresponding uCOpposite direction moves.Therefore, region of search right endpoint is set as ub=u0, left end point interval endpoint
Searching method is from right endpoint to ua1=max (u0-ε3,us) direction search.Step (8) is only in f (u0In the case of)=0
Into.Such case illustrates physical locationIt does not change, therefore foot point variable is also constant.
Fig. 8 is f (u in step (9), (10)a)·f(ub)>0 situation, illustrate foot point should not in the region of search, if
It puts foot point and loses flag bit lost=1.Such case is often as physical locationCorresponding foot point has exceeded movement locus pair
Parameter area [the u answereds,ue], some endpoint of the region of search has reached the limit of and usOr ueIt overlaps.Profile errors are curve at this time
Upper distanceNearest endpoint, can be by according to step (10) | f (ua) | and | f (ub) | relation judge.
Fig. 9 is using the numerical method section [u that step gives in front in step (11)a,ub] in solve nonlinear equation
The root of f (u)=0Schematic diagram.It can be seen from the figure that, due to f (ua) and f (ub) symbol is on the contrary, therefore in [ua,ub] in it is inevitable
There is the root for meeting f (u)=0Numerical Methods Solve may be employed.In the present embodiment, numerical solution uses Brent methods, tool
There is the advantages of fast convergence rate.The iterations of numerical method determines that iterations gets over Gao Ze according to the required precision of controller
The servo profile error precision of measure is higher.Step (12) is according to the definition of profile errors, by calculating updated foot point
To physical locationDistance calculate profile errors size.Search range variable ε1,ε2,ε3, interval endpoint search point N can make
The customer parameter of device in order to control, they determine to understand the operation time of section search and the precision in section.
During motion control, controller performs above-mentioned step within each SERVO CONTROL cycle according to the flow in Fig. 1, Fig. 2
Suddenly (1)~(12), you can calculate the exact value of current time servo profile errors and exported, realize parameter curve rail
The real-time high-precision of servo profile errors measures in mark high-speed motion.
The present invention is not limited to embodiments described above.The description of specific embodiment is intended to describe and be said above
Bright technical scheme, above-mentioned specific embodiment is only schematical, is not restricted.This is not being departed from
In the case of invention objective and scope of the claimed protection, those of ordinary skill in the art may be used also under the enlightenment of the present invention
The specific conversion of many forms is made, within these are all belonged to the scope of protection of the present invention.
Claims (2)
1. the real-time assay of parameter curve trace track profile errors, which is characterized in that assuming that the parameter curve side of track
Cheng WeiThe corresponding parameter u scopes in track are [us,ue], algorithm is initialized before starting, by foot point parametric variable u0Just
Beginning turns to curveThe parameter value u of starting points, concurrently set neighborhood search bound variable ε1、ε2、ε3(being all higher than 0), section
Endpoint search point N (N>1), for given position vectorIt is vector to define verticality function f (u)It is cut with curve
ArrowInner product (u ∈ [us,ue]), afterwards within each SERVO CONTROL cycle, current outline error is calculated, specific steps are such as
Under：
(1) current each axis servomotor position feedback is read, determines current actual positionsFoot point is set to lose flag bit lost
For 0；
(2) u is compared0Parameter of curve u corresponding with the current servo location of instructionCIf u0≥uC, foot point region of search left end point is made to become
Measure ua=uC, foot point region of search right end point variable ub=min (ua+ε1,ue), it enters step (9)；Otherwise, enter step (3)；
(3) u is calculated0And uCThe curve at place cuts arrowWith
(4) calculateWithInner productIf d<0, it enters step (5)；Otherwise, enter step (6)；
(5) u is madeb=uC,ua0=max (u0-ε2,us), call interval endpoint searching method search ua, i.e. ua=UEPS (ub,ua0),
It enters step (9)；
(6) if f (u0)>0, make ua=u0, call interval endpoint searching method search ub, i.e. ub=UEPS (ua,uc), it enters step
(9)；Otherwise, enter step (7)；
(7) if f (u0)<0, make ub=u0,ua1=max (u0-ε3,us) call interval endpoint searching method search ua, i.e. ua=UEPS
(ub,ua1), it enters step (9)；Otherwise, enter step (8)；
(8) u is made0It remains unchanged, enters step (12)；
(9) f (u are calculateda) and f (ub)；If f (ua)·f(ub)>0, it enters step (10)；Otherwise, enter step (11)；
(10) it is 1 to put lost flag bits, if | f (ua)|<|f(ub) |, make u0=ua；Otherwise, u is made0=ub；It enters step (12)；
(11) Nonlinear-Equations Numerical Solution method is called in section [ua,ub] in search verticality Functional Equation f (u)=0 root
It makes updated
(12) servo profile error size e is calculatedc,
During motion control, controller repeats the above steps (1)~(12) within each SERVO CONTROL cycle, you can realizes ginseng
The real-time high-precision of servo profile errors measures in the movement of number curve track.
2. the real-time assay of parameter curve trace track profile errors described in accordance with the claim 1, it is characterized in that, step
(5), the interval endpoint searching method u in (6), (7)ep=UEPS (uss,use) comprise the following steps：
(A1) f (u are calculatedss)。
(A2) if f (uss)=0 makes search result variable uep=uss, return；Otherwise, enter step (A3)；
(A3) step-size in search Δ u=(u are madese-uss)/N, search point counting variable i=1；
(A4) f (u are calculatedss+i×Δu)；
(A5) if f (uss+i×Δu)·f(uss)≤0, makes uep=f (uss+ i × Δ u) is returned；
(A6) i=i+1 is made, if i<N, return to step (A4)；Otherwise, enter step (A7)；
(A7) u is madeep=use, return.
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| CN113441598A (en) * | 2021-06-30 | 2021-09-28 | 武汉重型机床集团有限公司 | High-precision recording method for spinning machine |
| CN114740800A (en) * | 2022-03-09 | 2022-07-12 | 天津大学 | Double-sliding-mode direct contour control method for parameter curve machining path |
| CN114740800B (en) * | 2022-03-09 | 2024-05-24 | 天津大学 | Double-sliding-mode direct contour control method of parameter curve processing path |
| CN115657608A (en) * | 2022-10-26 | 2023-01-31 | 英孚康（浙江）工业技术有限公司 | Global asymmetric S-shaped flexible speed curve planning method based on Brent iteration method |
| CN115657608B (en) * | 2022-10-26 | 2023-09-08 | 英孚康（浙江）工业技术有限公司 | Global asymmetric S-shaped flexible speed curve planning method based on Brent iteration method |
| CN118707894A (en) * | 2024-08-29 | 2024-09-27 | 成都飞机工业（集团）有限责任公司 | Method, device, medium and equipment for acquiring contour error of machining plane of numerical control machine tool |
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