CN105929791B - The direct contour outline control method of plane rectangular coordinates kinematic system - Google Patents
The direct contour outline control method of plane rectangular coordinates kinematic system 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
- G05B19/19—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 positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
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- G—PHYSICS
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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
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Abstract
The invention discloses a kind of direct contour outline control methods of rectangular co-ordinate kinematic system, calculate to complete by 11 modular logical process, specific steps are in this way：Motion planning；Profile Stateful Inspection；Speed transformation by reciprocal direction；Tangential velocity generates；Tangential velocity controls；Profile errors control；Controlled quentity controlled variable positive-going transition；X, the characteristics match of Y-axis；And the single shaft control of X, Y-axis.This method can monitor contour motion state in real time, according to physical location and the analytic expression of programming profile, calculate actual profile error.Profile errors direction realizes the double-closed-loop control of profile errors and profile errors speed, meets the physics law of rectangular co-ordinate kinematic system, improves profile control effect.Rectangular co-ordinate and the characteristics match of speed, the real-time transform of controlled quentity controlled variable and reference axis under profile coordinate so that each rectangular axes are harmonious when different directions carry out contour motion.Profile errors can fully be reduced, realize high-precision profile control.
Description
Technical field
The invention belongs to numerical controlled machinery manufacture fields, and in particular to the computer numerical control of plane rectangular coordinates contour motion
Technical method.
Background technology
In numerical controlled machinery process, profile errors are the important indicators for evaluating multi-shaft motion control system precision.Mesh
The basic principle of preceding rectangular co-ordinate kinetic control system computer numerical control (CNC) is, control system is to profile mobile route into line number
According to sampling interpolation, interpolation obtains the coordinate under each moment rectangular coordinate system, then interpolation coordinate is distributed according to interpolation cycle interval
To the servo-drive system of each shifting axle, the position command as each shifting axle servo-drive system.Each axis servo-drive system to position command into
Row follows, and is compared the location of instruction that the data of the shaft position are exported with the moment interpolation in each servo period, obtains
To site error (i.e. the tracking error of the axis).Then, which is calculated according to certain control law according to site error
Controlled quentity controlled variable is exported as control.Repeat above-mentioned measurement, the work compared, calculate and exported every fixed servo period,
The servo motor and transmission mechanism of the axis can be driven, the position command time series that interpolator exports is followed continuously to be transported
It is dynamic.Practical contour motion track is that the movement of each axis of rectangular co-ordinate motion is synthesized.
Since in motion control, the tracking error of each axis exists always, therefore the contour motion synthesized is there is also error,
Lead to actual motion profile and instruct the deviation of profile.On the other hand, since each axis is different to the response characteristic of instruction and each
The states such as nonlinear normal modes, load disturbance that axis is subject to are different so that the movement of each axis cannot be coordinated completely, can also generate wheel
Wide error.In order to reduce profile errors, current kinetic control system uses two different strategies.The first is to reduce single shaft
Tracking error, including using location/velocity/electric current Three-loop control, feedforward control, disturbance observation with compensation etc..This method
It is disadvantageous in that, due to response characteristic, unknown disturbance, Parameters variation and model accuracy etc., tracking error is not
It may completely eliminate, so the ability for reducing profile errors is limited.In addition, since each axis is independent position control, do not have
There is the mismatch considered between each axis tracking error, cause multi-shaft interlocked uncoordinated, there is actual motion profile and desired profile
Relatively large deviation.In order to improve multi-shaft interlocked harmony, profile errors are reduced, propose second reduction profile errors in recent years
Control strategy -- cross-coupling control.Direction and size of the cross-couplings profile control by real-time estimation profile errors, generate
Outline compensation control output quantity, is superimposed upon the control of original uniaxiality controller by one compensation controlled quentity controlled variable after coordinate transform
In output quantity.By being modified to practical resultant motion, its sports coordination is improved, to reduce profile errors.It is but this
Method is still established on the basis of traditional uniaxial position tracking.Each axis controller, which needs to take into account simultaneously, reduces location following error
In terms of profile errors two, by the way that different control gains is set to weigh two indices.Since the control instruction of these two aspects exists
It is not orthogonal under rectangular co-ordinate, therefore position tracking is coupled with the presence of profile errors control room.Position Tracking Control amount can be cut
Weak profile errors controlled quentity controlled variable still is possible to generate larger profile errors in this way, this at a high speed, on the motion path of higher curvature
It embodies more obvious.In addition, in this controller, since location following controls the controller gain phase mutual coupling controlled with profile
It closes, restrain, make its adjustment difficult, thus can not be widely used in Computerized Numerical Control processing technology.
Invention content
It is an object of the present invention to provide a kind of direct contour outline control methods of plane rectangular coordinates kinematic system, can solve
The difficult point that certainly existing control method precision is low, adjustment is difficult.
To solve the above problems, the direct contour outline control method of the plane rectangular coordinates kinematic system proposed, passes through 11
A modular logical process calculates to complete, and is as follows：
(1) motion planning：Generate the instruction planning of contour motion tangential velocity；According to programming profile input by userWith
Motion planning constraints plans contour motion process generation contour motion tangential velocity instructs vtcJoin with contour curve
The relation function f, v of number utc=f (u) is used for follow-up controlling unit in real time.
(2) profile Stateful Inspection：According to current X-Y axis physical location Px、PyAnd programming profileWheel is calculated in real time
Wide error ec, profile errors directionThe parameter u of the corresponding programming contour curve of current actual positions, physical location are corresponding
Tangential motion directionWhereinIt is unit direction vector.
(3) speed transformation by reciprocal direction：According to two axle speed V of X-Yx、VyAnd currentCalculate the reality along programming profile
Border tangential velocity vtaWith profile errors direction speed vca。
(4) tangential velocity generates：Calculate current time tangential admission speed；The song calculated according to profile state monitoring module
The line parameter u and f of motion planning module generation, calculates current time tangential admission speed command v in real timetc。
(5) tangential velocity controls：Calculate the output of Tangents Control amount；According to instruction tangential velocity vtcWith practical tangential velocity
vtaCalculate tangential velocity error evt, wherein evt=vtc-vta, then by evtIt is defeated that Tangents Control amount is calculated according to Feedback Control Law
Go out.
(6) profile errors control：The e calculated according to profile Stateful InspectioncAnd the v that speed transformation by reciprocal direction calculatesca, according to anti-
It presents control law and calculates profile errors direction controlling amount output UC。
(7) controlled quentity controlled variable positive-going transition：It is calculated according to current outline state monitoring moduleBy Tangents Control amount UT
With profile errors direction controlling amount UC, it is transformed into the controlled quentity controlled variable U of X-axis under rectangular co-ordinatexWith the controlled quentity controlled variable U of Y-axisy。
(8) X-axis control characteristic matches：The characteristic of X single shaft control module input/output is compensated, makes the characteristic of X-Y axis
Match； UxAfter the resume module, practical X-axis controlled quentity controlled variable is generated
(9) X-axis single shaft control：According to X-axis controlled quentity controlled variableServo motor is converted to by signal processing and power amplification
Torque exports, and the X-axis under X-Y rectangular co-ordinates is driven to move by machine driving link；
(10) Y-axis control characteristic matches：The characteristic of Y single shaft control module input/output is compensated, makes the characteristic of X-Y axis
Match；UyAfter the resume module, practical Y-axis controlled quentity controlled variable is generated
(11) Y-axis single shaft control：According to Y-axis controlled quentity controlled variableServo motor is converted to by signal processing and power amplification
Torque output, by machine driving link drive X-Y rectangular co-ordinates under Y-axis move,
Within each SERVO CONTROL period, kinetic control system repeats the above steps the processes of (2)~(11), can realize
Continuous high-accurate outline movement.
The control of profile errors in above-mentioned steps (6) is controlled in profile errors direction using Dual-loop feedback control, and outer shroud is
Profile errors control ring；Inner ring is profile errors speed control ring.Step (6) further can be analyzed to following steps：
(6-1) profile errors feedback control：The e calculated according to profile Stateful InspectioncCalculate the speed in profile errors direction
Instruct vcc。
(6-2) calculates the velocity error in profile errors direction：According to vccAnd the v that speed transformation by reciprocal direction calculatesca, calculate wheel
The velocity error e of wide direction of errorvc, wherein evc=vcc-vca。
(6-3) profile errors speed feedback control：According to evcCalculate profile errors direction controlling amount output UC。
Advantages of the present invention and the advantageous effect generated are：
(1) directly plane rectangular coordinates contour motion state can be monitored in real time, according to physical location and programming
The analytic expression of profile calculates actual profile error, has very high precision.Profile errors direction realizes profile errors and wheel
The double-closed-loop control of wide error speed meets the physics law of plane rectangular coordinates kinematic system, improves profile control effect.
Rectangular co-ordinate and the characteristics match of speed, the real-time transform of controlled quentity controlled variable and reference axis under profile coordinate so that rectangular co-ordinate
X-Y axis is harmonious when different directions carry out contour motion.Therefore, this method can fully reduce profile errors, realize high
Accuracy contour controls.
(2) the method for the present invention no longer carries out profile control indirectly by the position tracking of X-Y axis, eliminates position tracking
After link, there is no profile errors ingredient caused by two axis tracking errors, thus profile control accuracy is improved.
(3) by face profile direction of error and the tangential orthogonality of contour motion it is found that controlled quentity controlled variable UCWith UTBe it is orthogonal,
Controlled quentity controlled variable is independent of each other, and tangential motion can be separately adjustable with profile errors control section, and control parameter has specific physics
Meaning simplifies the adjustment process of system.
(4) in occasions such as digital control processings, the tangential velocity of contour motion has a major impact suface processing quality.Tradition control
Device processed can not directly carry out tangential velocity closed-loop control, and the uncoordinated and position tracking lag of each axis leads to tangential velocity precision
Difference, especially in the high-speed motion of deep camber and angular position.The method of the present invention can according to tangential velocity plan function f and in real time
The parameter of curve u of detection quickly, accurately obtains real-time tangential velocity instruction.And it is controlled by tangential velocity and carries out closed loop
Control improves the accuracy of tangential velocity.
(5) implementation of the method for the present invention can be based on existing kinetic control system hardware facility, without increasing hardware i.e.
It can implement, convenient for having the upgrading of kinetic control system, reduce cost.
Description of the drawings
Fig. 1 is direct contour outline control method logical process computing block diagram in the present invention.
Fig. 2 is profile state monitoring principle figure in the present invention.
Fig. 3 is motion planning module principle figure in the present invention.
Fig. 4 is controlled quentity controlled variable vector and velocity vector transformation relation figure in the present invention.
Fig. 5 is tangential velocity control principle drawing in the present invention.
Fig. 6 is profile errors control principle drawing 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 following embodiments be narrative, be not limited, the content that the present invention is covered is not limited to following embodiments.
The direct contour outline control method of plane rectangular coordinates kinematic system passes through following 11 modular logical process meters
It calculates to complete, be as follows：
(1) motion planning：Generate the instruction planning of contour motion tangential velocity；According to programming profile input by userWith
Motion planning constraints plans contour motion process generation contour motion tangential velocity instructs vtcJoin with contour curve
The relation function f, v of number utc=f (u) is used for follow-up controlling unit in real time.
(2) profile Stateful Inspection：According to current X-Y axis physical location Px、PyAnd programming profileProfile is calculated in real time
Error ec, profile errors directionThe parameter u of the corresponding programming contour curve of current actual positions, physical location is corresponding cuts
To the direction of motionWhereinIt is unit direction vector.
(3) speed transformation by reciprocal direction：According to two axle speed V of X-Yx、VyAnd currentCalculate the reality along programming profile
Border tangential velocity vtaWith profile errors direction speed vca。
(4) tangential velocity generates：Calculate current time tangential admission speed；The song calculated according to profile state monitoring module
The line parameter u and f of motion planning module generation, calculates current time tangential admission speed command v in real timetc。
(5) tangential velocity controls：Calculate the output of Tangents Control amount；According to instruction tangential velocity vtcWith practical tangential velocity
vtaCalculate tangential velocity error evt, wherein evt=vtc-vta, then by evtThe output of Tangents Control amount is calculated according to Feedback Control Law
UT。
(6) profile errors control：The e calculated according to profile Stateful InspectioncAnd the v that speed transformation by reciprocal direction calculatesca, according to anti-
It presents control law and calculates profile errors direction controlling amount output UC。
(7) controlled quentity controlled variable positive-going transition：It is calculated according to current outline state monitoring moduleBy Tangents Control amount UT
With profile errors direction controlling amount UC, it is transformed into X-axis controlled quentity controlled variable U under rectangular co-ordinatexWith the controlled quentity controlled variable U of Y-axisy。
(8) X-axis control characteristic matches：The characteristic of X single shaft control module input/output is compensated, makes the characteristic of X-Y axis
Match；UxAfter the resume module, practical X-axis controlled quentity controlled variable is generated
(9) X-axis single shaft control：According to X-axis controlled quentity controlled variableServo motor is converted to by signal processing and power amplification
Torque exports, and the X-axis under X-Y rectangular co-ordinates is driven to move by machine driving link.
(10) Y-axis control characteristic matches：The characteristic of Y single shaft control module input/output is compensated, makes the characteristic of X-Y-axis
Match；UyAfter the resume module, practical Y-axis controlled quentity controlled variable is generated
(11) Y-axis single shaft control：According to Y-axis controlled quentity controlled variableServo motor is converted to by signal processing and power amplification
Torque output, by machine driving link drive X-Y rectangular co-ordinates under Y-axis move.
Within each SERVO CONTROL period, kinetic control system repeats the above steps the processes of (2)~(11), can realize
Continuous high-accurate outline movement.
The control of profile errors in above-mentioned steps (6) is controlled in profile errors direction using Dual-loop feedback control, and outer shroud is
Profile errors control ring；Inner ring is profile errors speed control ring.Step (6) further can be analyzed to following steps：
(6-1) profile errors feedback control：The e calculated according to profile Stateful InspectioncCalculate the speed in profile errors direction
Instruct vcc。
(6-2) calculates the velocity error in profile errors direction：According to vccAnd the v that speed transformation by reciprocal direction calculatesca, calculate wheel
The velocity error e of wide direction of errorvc, wherein evc=vcc-vca。
(6-3) profile errors speed feedback control：According to evcCalculate profile errors direction controlling amount output UC。
Fig. 1 shows the logical relation of contouring control system operation.The plane rectangular coordinates motion of the present embodiment contains
There are two vertical control shafts of X-Y.
In Fig. 1, single shaft control module is by the driver of each kinematic axis servo motors of X-Y, servo motor, transmission mechanism, position
It puts and is formed with speed feedback device.Other modules in Fig. 1 can in real time count on the microprocessor of contour motion controller
The mode of word control program is realized, the signal in program is controlled to be transmitted in the form of program variable.Microprocessor and single shaft control mould
It is communicated between block by electric signal and interface circuit.
In the present embodiment, using AC synchronous servo motor and its driver, driver works in direct torque for X and Y-axis
Mode, according to each axis controlled quentity controlled variable(wherein, i=x, y, similarly hereinafter), servo motor is converted to by signal processing and power amplification
Torque output.Using shaft coupling, ball screw assembly, guideway, X-Y table movement is driven, completes contour motion.Installation
Position and velocity sensor on X and Y-axis can obtain X and the respective physical location of Y-axis and speed signal in real time.
Motion planning principle such as Fig. 3, the programming profile of user are stored inside control system in the form of parametric equation.It is false
If the parametric equation of programming contour curve handled isIts parameter area is [us,ue], then move initial position pair
It is u to answer parameter of curves, movement end position homologous thread parameter is ue.The constraints of motion planning includes rising for tangential motion
Beginning speed vs, maximum speed vmax, maximum end speed vemax, peak acceleration amaxWith maximum acceleration JmaxDeng.Planning
As a result requirement generation contour motion tangential velocity instruction vtcWith the relation function f of contour curve parameter u.
Routinely planing method generates v under constraints for specific implementationtcWith the relationship f of time ttAnd contour curve
The relationship S of displacement S and time tt, while basisIt can obtain the relation function S of S and uu.According to ft, StAnd Su, sample can be passed through
The method of interpolation, by the planning f of time domaintParameter of curve domain is mapped to, obtains using u as independent variable, is represented with spline function
Motion planning f.Since f can be acquired before movement, motion planning be not take up real time kinematics control when microprocessor when
Between resource.
The principle of profile Stateful Inspection is as shown in Figure 2.Due to disturbance etc., actual motion profile will deviate from programming wheel
It is wide.During exercise sometime, it is assumed that the current actual positions that position feedback device is readIt can basisWithPosition relationship solve contour motion state.Due to profile errors ecSize be defined asIt arrivesThe shortest distance,
Therefore the point that this shortest distance is corresponded on programming curve can be foundIt may know that simultaneouslyDirection and profile errors
Direction overlaps.
On the other hand, it can be calculated by curve parametric equationPlace leads vectorThenDirection be song
Line tangential direction.It is defined according to profile errors it is found that pointLocate curve tangential direction withVertically, therefore equation can be obtainedThe solution equation can acquire the parameter u of corresponding programming contour curve.Profile errors can further be acquired
Absolute valueThe unit vector in the corresponding tangential motion direction of physical location
Profile errors direction unit vectorIt is defined asIt is rotated by 90 ° counterclockwise, thenec
Symbol definition beWithIn the same direction when be it is negative,WithFor just when reversely.
Speed transformation by reciprocal direction principle is with reference to 4 left side of figure.VxAnd VyIt is X respectively, the X that Y-axis single shaft control module measures, Y-axis is real
Border speed, therefore aggregate velocity vector can be obtainedIt willIt projects to respectivelyWithDirection is obtained along programming profile
Practical tangential velocity vtaWith profile errors direction speed vca.It is defined, can obtain according to inner product of vectorWith
The generation of tangential velocity is the parameter of curve u and the generation of motion planning module calculated according to profile state monitoring module
F, calculate current time tangential admission speed command vtc, i.e. vtc=f (u) (reference can be made to Fig. 3).
Tangential velocity control calculates controlled quentity controlled variable output U using Feedback Control LawT, reference can be made to Fig. 5.According to the tangential speed of instruction
Spend vtcWith practical tangential velocity vtaCalculate tangential velocity error evt=vtc-vta.Feedback rate control (is compared using PI in the present embodiment
Example+integration) control, to reduce steady-state error.If ratio and storage gain are respectively KPTAnd KIT, then
Profile errors control is using Dual-loop feedback control control law (referring to Fig. 6), and outer shroud is profile errors control ring, inner ring
For profile errors speed control ring.
The present embodiment outer shroud is controlled using P (ratio), by profile errors ecCalculate the speed command v in profile errors directioncc,
To compensate profile errors.If outer shroud proportional gain is KPCO, then vcc=KPCOec.Inner ring is controlled using PI (proportional+integral), according to
vccAnd the v that speed transformation by reciprocal direction module calculatescaCalculate the velocity error e in profile errors directionvc=vcc-vca.If inner ring ratio
It is respectively K with storage gainPCIAnd KICI, then controlled quentity controlled variable output
Controlled quentity controlled variable positive-going transition principle is with reference to 4 right side of figure.In order to by UTAnd UCIt transforms under X-Y plane rectangular co-ordinate, by UT
And UCIt projects on X and Y-axis respectively, then the control component projected on each axis is superimposed.Due toIt is unit vector,
Therefore Ux=UTTx+UCNx, Uy=UTTy+UCNy。
The matching of reference axis control characteristic-and for compensating the characteristic of single shaft control module input/output, make the characteristic of each axis
Matching improves the harmony of multi-shaft interlocked control.X, Y-axis control characteristic matching module are proportional component in the present embodiment, than
Example gain is KMi, then in Fig. 1Assuming that the output torque M of single shaft controliTo controlling signalGain be
Kai, load rotating inertia Ji.Ignore axis dynamic characteristic and friction, disturbance when factors when, in order to realize the coordination of movement,
Wish that the overall gain of each axis is equal, that is, meetTherefore, by setting each axis KMiWanting for above formula can be met
It asks, realizes when all directions move, to profile control signal UTAnd UCResponse it is consistent.
According to the logic flow in Fig. 1, after motion planning, each real-time operation module is in each servo period by letter
Number processing sequence is called, you can is realized the direct contour outline control method, is completed continuous high-accurate outline movement.
Claims (2)
1. the direct contour outline control method of plane rectangular coordinates kinematic system, it is characterised in that the control method passes through 11 moulds
The logical process of block calculates to complete, and is as follows：
(1) motion planning：Generate the instruction planning of contour motion tangential velocity；According to programming profile input by userAnd movement
Plan constraint condition plans contour motion process generation contour motion tangential velocity instructs vtcWith contour curve parameter u
Relation function f, vtc=f (u) is used for follow-up controlling unit in real time；
(2) profile Stateful Inspection：According to current X-Y axis physical location Px、PyAnd programming profileProfile errors are calculated in real time
ec, profile errors directionThe parameter u of the corresponding programming contour curve of current actual positions, the corresponding tangential fortune of physical location
Dynamic directionWhereinIt is unit direction vector；
(3) speed transformation by reciprocal direction：According to two axle speed V of X-Yx、VyAnd currentCalculate actually cutting along programming profile
To speed vtaWith profile errors direction speed vca；
(4) tangential velocity generates：Calculate current time tangential admission speed；Joined according to the curve that profile state monitoring module calculates
The number u and f of motion planning module generation calculates the speed command v of current time tangential admission in real timetc；
(5) tangential velocity controls：Calculate the output of Tangents Control amount；According to instruction tangential velocity vtcWith practical tangential velocity vtaIt calculates
Tangential velocity error evt, wherein evt=vtc-vta, then by evtTangents Control amount output U is calculated according to Feedback Control LawT；
(6) profile errors control：The e calculated according to profile Stateful InspectioncAnd the v that speed transformation by reciprocal direction calculatesca, controlled according to feedback
Rule processed calculates profile errors direction controlling amount output UC；
(7) controlled quentity controlled variable positive-going transition：It is calculated according to current outline state monitoring moduleBy Tangents Control amount UTAnd wheel
Wide direction of error controlled quentity controlled variable UC, it is transformed into the controlled quentity controlled variable U of X-axis under rectangular co-ordinatexWith the controlled quentity controlled variable U of Y-axisy；
(8) X-axis control characteristic matches：The characteristic of X single shaft control module input/output is compensated, makes the characteristics match of X-Y axis；UxThrough
After crossing the resume module, practical X-axis controlled quentity controlled variable is generated
(9) X-axis single shaft control：According to X-axis controlled quentity controlled variableThe torque of servo motor is converted to by signal processing and power amplification
Output drives the X-axis under X-Y rectangular co-ordinates to move by machine driving link；
(10) Y-axis control characteristic matches：The characteristic of Y single shaft control module input/output is compensated, makes the characteristics match of X-Y axis；Uy
After the resume module, practical Y-axis controlled quentity controlled variable is generated
(11) Y-axis single shaft control：According to Y-axis controlled quentity controlled variableTurning for servo motor is converted to by signal processing and power amplification
Square exports, and the Y-axis under X-Y rectangular co-ordinates is driven to move by machine driving link,
Within each SERVO CONTROL period, kinetic control system repeats the above steps the processes of (2)~(11), can realize continuous
High-accurate outline movement.
2. the direct contour outline control method of plane rectangular coordinates kinematic system described in accordance with the claim 1, it is characterized in that：It is described
Profile errors control in step (6) is controlled in profile errors direction using Dual-loop feedback control, and outer shroud is profile errors control ring；
Inner ring is profile errors speed control ring；Step (6) further can be analyzed to following steps：
(6-1) profile errors feedback control：The e calculated according to profile Stateful InspectioncCalculate the speed command in profile errors direction
vcc；
(6-2) calculates the velocity error in profile errors direction：According to vccAnd the v that speed transformation by reciprocal direction calculatesca, calculate profile errors
The velocity error e in directionvc, wherein evc=vcc-vca；
(6-3) profile errors speed feedback control：According to evcCalculate profile errors direction controlling amount output UC。
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| CN106774163B (en) * | 2016-12-08 | 2019-02-05 | 哈尔滨工业大学深圳研究生院 | High-precision three-dimensional contour outline control method and device |
| CN109828534B (en) * | 2019-01-03 | 2020-10-30 | 浙江工业大学 | Real-time contour error compensation method of embedded cutting bed controller |
| CN112327752A (en) * | 2020-11-16 | 2021-02-05 | 大连理工大学 | Double-ring compensation method for contour error of four-axis turning track |
| CN114356255B (en) * | 2021-12-31 | 2022-09-06 | 东莞市启思达智能技术有限公司 | Interpolation table application method and system based on printing process |
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