CN105929791A - Direct contour control method of plane rectangular coordinate motion system - Google Patents
Direct contour control method of plane rectangular coordinate motion 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
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- 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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- 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 direct contour control method of a plane rectangular coordinate motion system. The method is completed through eleven modular logic processing calculations and comprises the following concrete steps: motion planning; contour state monitoring; speed inverse transformation; tangential speed generation; tangential speed control; contour error control; control amount forward transformation; feature matching of an X axis and a Y axis; and single-axis control of the X axis and the Y axis. According to the method, a contour motion state can be monitored in real time, and real contour errors are calculated according to analysis formulas of an actual position and a programming contour. Dual-closed-loop control of the contour errors and a contour error speed is realized in a contour error direction, a physical rule of a right angle coordinate motion system is observed, and the contour control effect is improved. Through real-time transformation of the speed and a control amount under right angle coordinates and contour coordinates and feature matching of the coordinate axes, each right angle coordinate axis coordinates consistently during contour motion in different directions. The contour errors can be fully reduced, and high-precision contour control is realized.
Description
Technical field
The invention belongs to numerical controlled machinery manufacture field, be specifically related to the computer numerical control technology method of plane rectangular coordinates contour motion.
Background technology
In the numerical controlled machinery course of processing, profile errors is the important indicator evaluating multi-shaft motion control system precision.The ultimate principle of rectangular coordinate kinetic control system computer numerical control (CNC) at present is, control system carries out Sampled-data interpolation to profile mobile route, interpolation obtains the coordinate under each moment rectangular coordinate system, interpolation coordinate is assigned to the servosystem of each shifting axle again, as the position command of each shifting axle servosystem according to interpolation cycle interval.Position command is followed by each axle servosystem, the location of instruction that the data of this shaft position and this moment interpolation export is compared in each servo period, obtains site error (i.e. the tracking error of this axle).Then, calculate the controlled quentity controlled variable in this moment according to certain control law according to site error, as controlling output.Repeating above-mentioned measurement, the work compared, calculate and export every fixing servo period, can drive servomotor and the drive mechanism of this axle, the position command time series following interpolator output is moved continuously.Actual contour motion track is that the motion of axle each to rectangular coordinate motion synthesizes and obtains.
Owing to, in motor control, the tracking error of each axle exists all the time, the contour motion therefore synthesized there is also error, causes the deviation of actual motion profile and instruction profile.On the other hand, owing to each axle is different to the response characteristic of instruction, and the nonlinear normal modes that is subject to of each axle, the state such as load disturbance are different so that the motion of each axle can not be coordinated completely, also can produce profile errors.In order to reduce profile errors, current kinetic control system uses two kinds of different strategies.The first is the tracking error reducing single shaft, including using location/velocity/electric current Three-loop control, the feedforward, disturbance observation and compensation etc..The method is disadvantageous in that, due to reasons such as response characteristic, unknown disturbance, Parameters variation and model accuracies, tracking error can not be completely eliminated, so reducing the limited in one's ability of profile errors.Further, since each axle is independent position control, do not account for not mating between each axle tracking error, cause multi-shaft interlocked inharmonious, make actual motion profile and desired profile have relatively large deviation.In order to improve multi-shaft interlocked harmony, reduce profile errors, in recent years propose the second and reduce control strategy--the cross-coupling control of profile errors.Cross-couplings profile controls direction and size by estimating profile errors in real time, produces one and compensates controlled quentity controlled variable, outline compensation controls after coordinate transform output and is superimposed upon on the control output of original uniaxiality controller.By actual resultant motion is modified, improve its sports coordination, to reduce profile errors.But this method is still set up on the basis of traditional single shaft position is followed the tracks of.Each axis controller needs to take into account reduction location following error and profile errors two aspect simultaneously, by arranging different control gain balance two indices.Owing to the control instruction of these two aspects is not orthogonal under rectangular coordinate, therefore position is followed the tracks of and is coupled with existing between profile errors control.Position Tracking Control amount can weakened outline error control amount, still so be possible to produce bigger profile errors, this at a high speed, embody on the motion path of higher curvature and become apparent from.Additionally, in this controller, the controller gain controlling to control with profile due to location following intercouples, pins down so that it is adjusts difficulty, thus cannot be widely used in Computerized Numerical Control processing technology.
Summary of the invention
It is an object of the present invention to provide the direct contour outline control method of a kind of plane rectangular coordinates motor system, the difficult point that existing control method precision is low, adjust difficulty can be solved.
For solving the problems referred to above, the direct contour outline control method of the plane rectangular coordinates motor system proposed, calculated by 11 modular logical process, specifically comprised the following steps that
(1) motion planning: generate the instruction planning of contour motion tangential velocity；Programming profile according to user's inputWith motion planning constraints, contour motion process is planned, generate contour motion tangential velocity instruction vtcRelation function f, v with contour curve parameter utc=f (u), for follow-up real-time controlling unit.
(2) profile Stateful Inspection: according to current X-Y axle physical location Px、PyAnd programming profileCalculate profile errors e in real timec, profile errors directionThe tangential motion direction that programming parameter u of contour curve, physical location that current actual positions is corresponding are correspondingWhereinIt is unit direction vector.
(3) speed transformation by reciprocal direction: according to X-Y two axle speed Vx、VyAnd it is currentCalculate actual tangential velocity v along programming profiletaWith profile errors direction speed vca。
(4) tangential velocity produces: calculate current time tangential admission speed；The f that parameter of curve u calculated according to profile state monitoring module and motion planning module generate, 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 actual 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.
(6) profile errors controls: the e calculated according to profile Stateful InspectioncAnd the v that speed transformation by reciprocal direction calculatesca, calculate profile errors direction controlling amount output U according to Feedback Control LawC。
(7) controlled quentity controlled variable positive-going transition: calculate according to current outline state monitoring moduleBy Tangents Control amount UTWith profile errors direction controlling amount UC, it is transformed into controlled quentity controlled variable U of X-axis under rectangular coordinatexControlled quentity controlled variable U with Y-axisy。
(8) X-axis control characteristic coupling: compensate the characteristic of X single shaft control module input/output, make the characteristics match of X-Y axle；UxAfter this resume module, produce actual X-axis controlled quentity controlled variable
(9) X-axis single shaft control: according to X-axis controlled quentity controlled variableChange into the torque output of servomotor through signal processing and power amplification, the X-axis under machine driving link drives X-Y rectangular coordinate moves；
(10) Y-axis control characteristic coupling: compensate the characteristic of Y single shaft control module input/output, make the characteristics match of X-Y axle；UyAfter this resume module, produce actual Y-axis controlled quentity controlled variable
(11) Y-axis single shaft control: according to Y-axis controlled quentity controlled variableChange into the torque output of servomotor through signal processing and power amplification, the Y-axis under machine driving link drives X Y rectangular coordinate moves,
Within each SERVO CONTROL cycle, kinetic control system repeat the above steps (2)～the process of (11), the motion of continuous print high-accurate outline can be realized.
The control of the profile errors in above-mentioned steps (6) uses Dual-loop feedback control to control in profile errors direction, and outer shroud is that profile errors controls ring；Internal ring is profile errors speed controlling ring.Step (6) can be analyzed to following steps further:
(6-1) profile errors feedback control: the e calculated according to profile Stateful InspectioncCalculate the speed command v in profile errors directioncc。
(6-2) velocity error in profile errors direction is calculated: according to vccAnd the v that speed transformation by reciprocal direction calculatesca, calculate velocity error e in profile errors directionvc, wherein evc=vcc-vca。
(6-3) profile errors speed feedback control: according to evcCalculate profile errors direction controlling amount output UC。
Having the beneficial effects that of advantages of the present invention and generation:
(1) directly plane rectangular coordinates contour motion state can be monitored in real time, according to physical location and the analytic expression of programming profile, calculate actual profile error, there is the highest precision.Profile errors direction achieves the double-closed-loop control of profile errors and profile errors speed, meets the physics law of plane rectangular coordinates motor system, improves profile and controls effect.Rectangular coordinate and speed, the real-time transform of controlled quentity controlled variable and the characteristics match of coordinate axes under profile coordinate so that the X-Y axle of rectangular coordinate is harmonious when different directions carries out contour motion.Therefore, the method can fully reduce profile errors, it is achieved high-accurate outline controls.
(2) the inventive method is no longer followed the tracks of by the position of X-Y axle and is indirectly carried out profile control, after eliminating position tracking link, there is not the profile errors composition that two axle tracking errors cause, thus improves profile control accuracy.
(3) from the orthogonality that face profile direction of error and contour motion are tangential, controlled quentity controlled variable UCWith UTBeing orthogonal, controlled quentity controlled variable is independent of each other, tangential motion and profile errors control part can independent regulation, and control parameter there is clear and definite physical significance, simplify the adjustment process of system.
(4) in occasions such as digital control processings, suface processing quality is had a major impact by the tangential velocity of contour motion.Traditional controller directly cannot carry out closed loop control to tangential velocity, and the inharmonious and position tracking lag of each axle causes tangential velocity low precision, especially when the high-speed motion of deep camber and angle position.The inventive method can obtain the instruction of real-time tangential velocity quickly, accurately according to tangential velocity planning function f and parameter of curve u of detection in real time.And control to carry out closed loop control by tangential velocity, improve the accuracy of tangential velocity.
(5) enforcement of the inventive method can be based on existing kinetic control system hardware facility, it is not necessary to increasing hardware can implement, it is simple to the upgrading of existing kinetic control system, reduces cost.
Accompanying drawing explanation
Fig. 1 is direct contour outline control method logical process computing block diagram in the present invention.
Fig. 2 is profile status monitoring schematic diagram 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 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
Detailed description of the invention
Below in conjunction with accompanying drawing and by embodiment, the enforcement step of the inventive method is further described.It should be noted that following embodiment is narrative, be not determinate, the content that the present invention is contained is not limited to following embodiment.
The direct contour outline control method of plane rectangular coordinates motor system, has been calculated by following 11 modular logical process, has specifically comprised the following steps that
(1) motion planning: generate the instruction planning of contour motion tangential velocity；Programming profile according to user's inputWith motion planning constraints, contour motion process is planned, generate contour motion tangential velocity instruction vtcRelation function f, v with contour curve parameter utc=f (u), for follow-up real-time controlling unit.
(2) profile Stateful Inspection: according to current X-Y axle physical location Px、PyAnd programming profileCalculate profile errors e in real timec, profile errors directionThe tangential motion direction that programming parameter u of contour curve, physical location that current actual positions is corresponding are correspondingWhereinIt is unit direction vector.
(3) speed transformation by reciprocal direction: according to X-Y two axle speed Vx、VyAnd it is currentCalculate actual tangential velocity v along programming profiletaWith profile errors direction speed vca。
(4) tangential velocity produces: calculate current time tangential admission speed；The f that parameter of curve u calculated according to profile state monitoring module and motion planning module generate, 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 actual tangential velocity vtaCalculate 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 controls: the e calculated according to profile Stateful InspectioncAnd the v that speed transformation by reciprocal direction calculatesca, calculate profile errors direction controlling amount output U according to Feedback Control LawC。
(7) controlled quentity controlled variable positive-going transition: calculate according to current outline state monitoring moduleBy Tangents Control amount UTWith profile errors direction controlling amount UC, it is transformed into X-axis controlled quentity controlled variable U under rectangular coordinatexControlled quentity controlled variable U with Y-axisy。
(8) X-axis control characteristic coupling: compensate the characteristic of X single shaft control module input/output, make the characteristics match of X-Y axle； UxAfter this resume module, produce actual X-axis controlled quentity controlled variable
(9) X-axis single shaft control: according to X-axis controlled quentity controlled variableChange into the torque output of servomotor through signal processing and power amplification, the X-axis under machine driving link drives X-Y rectangular coordinate moves.
(10) Y-axis control characteristic coupling: compensate the characteristic of Y single shaft control module input/output, make the characteristics match of X Y-axis；UyAfter this resume module, produce actual Y-axis controlled quentity controlled variable
(11) Y-axis single shaft control: according to Y-axis controlled quentity controlled variableChange into the torque output of servomotor through signal processing and power amplification, the Y-axis under machine driving link drives X Y rectangular coordinate moves.
Within each SERVO CONTROL cycle, kinetic control system repeat the above steps (2)～the process of (11), the motion of continuous print high-accurate outline can be realized.
The control of the profile errors in above-mentioned steps (6) uses Dual-loop feedback control to control in profile errors direction, and outer shroud is that profile errors controls ring；Internal ring is profile errors speed controlling ring.Step (6) can be analyzed to following steps further:
(6-1) profile errors feedback control: the e calculated according to profile Stateful InspectioncCalculate the speed command v in profile errors directioncc。
(6-2) velocity error in profile errors direction is calculated: according to vccAnd the v that speed transformation by reciprocal direction calculatesca, calculate velocity error e in profile errors directionvc, 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 that contouring control system runs.The plane rectangular coordinates motion of the present embodiment contains the control axle that X-Y two is vertical.
In Fig. 1, single shaft control module is made up of driver, servomotor, drive mechanism, position and the speed feedback device of X-Y each kinematic axis servomotor.Other modules in Fig. 1 can realize on the microprocessor of contour motion controller in the way of realtime digital control program, and the signal in control program transmits with program variable form.Microprocessor and single shaft control intermodule are by electric signal and interface circuit communication.
In the present embodiment, X and Y-axis use AC synchronous servomotor and driver thereof, and driver works in direct torque mode, according to each axle controlled quentity controlled variable(wherein, i=x, y, lower same), the torque output of servomotor is changed into through signal processing and power amplification.Again through shaft coupling, ball screw assembly, guideway, drive X-Y table to move, complete contour motion.It is arranged on the position in X and Y-axis and velocity sensor can obtain X and the respective physical location of Y-axis and rate signal in real time.
Motion planning principle such as Fig. 3, the profile form with parametric equation inside control system that programs of user stores.Assume that the parametric equation programming contour curve processed isIts parameter area is [us,ue], then motion original position homologous thread parameter is us, motion end position homologous thread parameter is ue.The constraints of motion planning includes starting velocity v of tangential motions, maximal rate vmax, maximum end speed vemax, peak acceleration amaxWith maximum acceleration JmaxDeng.The result of planning requires to generate contour motion tangential velocity instruction vtcRelation function f with contour curve parameter u.
It is embodied as planing method routinely under constraints, generates vtcRelation f with time tt, and relation S of contour curve displacement S and time tt, basis simultaneouslyThe relation function S of available S Yu uu.According to ft, StAnd Su, can be by the method for spline interpolation, by the planning f of time domaintIt is mapped to parameter of curve territory, it is thus achieved that with u as independent variable, the motion planning f represented by spline function.Owing to f can try to achieve before motion, therefore motion planning is not take up the time resource of microprocessor when real time kinematics controls.
The principle of profile Stateful Inspection is as shown in Figure 2.Due to reasons such as disturbances, actual motion profile will deviate from programming profile.The most sometime, it is assumed that the current actual positions that position feedback device readsCan basisWithPosition relationship solve contour motion state.Due to profile errors ecSize be defined asArriveBeeline, therefore can find the point of this beeline corresponding on programming curveMay know that simultaneouslyDirection overlap with profile errors direction.
On the other hand, curve parametric equation can calculatePlace leads vectorThenDirection be curve tangential direction.Understand according to profile errors definition, pointPlace curve tangential direction withVertically, equation can therefore be obtainedSolve parameter u that the equation can try to achieve the programming contour curve of correspondence.The absolute value of profile errors can be tried to achieve furtherThe unit vector in the tangential motion direction that physical location is corresponding
Profile errors direction unit vectorIt is defined as90-degree rotation counterclockwise, thenecSymbol be defined asWithIt is negative time in the same direction,WithJust it is time reversely.
Speed transformation by reciprocal direction principle is with reference on the left of Fig. 4.VxAnd VyIt is X respectively, the X that Y-axis single shaft control module is measured, Y-axis actual speed, therefore can obtain aggregate velocity vectorWillProject to respectivelyWithDirection, obtains actual tangential velocity v along programming profiletaWith profile errors direction speed vca.Define according to inner product of vector, availableWith
The generation of tangential velocity is parameter of curve u calculated according to profile state monitoring module and the f of motion planning module generation, calculates current time tangential admission speed command vtc, i.e. vtc=f (u) (can be found in Fig. 3).
Tangential velocity controls to use Feedback Control Law to calculate controlled quentity controlled variable output UT, can be found in Fig. 5.According to instruction tangential velocity vtcWith actual tangential velocity vtaCalculate tangential velocity error evt=vtc-vta.In the present embodiment, feedback rate control uses PI (proportional+integral) to control, to reduce steady-state error.If ratio and storage gain are respectively KPTAnd KIT, then
Profile errors controls to use Dual-loop feedback control control law (seeing Fig. 6), and outer shroud is that profile errors controls ring, and internal ring is profile errors speed controlling ring.
The present embodiment outer shroud uses P (ratio) to control, 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.Internal ring uses PI (proportional+integral) to control, according to vccAnd the v that speed transformation by reciprocal direction module calculatescaCalculate velocity error e in profile errors directionvc=vcc-vca.If internal ring ratio and storage gain are respectively KPCIAnd KICI, then controlled quentity controlled variable output
Controlled quentity controlled variable positive-going transition principle is with reference on the right side of Fig. 4.In order to by UTAnd UCTransform under X-Y plane rectangular coordinate, by UTAnd UCProject to respectively in X and Y-axis, then the control component superposition that will project on each axle.Due toIt is unit vector, therefore Ux=UTTx+UCNx, Uy=UTTy+UCNy。
Coordinate axes control characteristic coupling, for compensating the characteristic of single shaft control module input/output, makes the characteristics match of each axle, improves the harmony of multi-shaft interlocked control.In the present embodiment, X, Y-axis control characteristic matching module are proportional component, and proportional gain is KMi, then in Fig. 1Assume the output torque M of single shaft controliTo control signalGain be Kai, load rotating inertia is Ji.When ignoring dynamic characteristic and the factor such as friction, disturbance of axle, in order to realize the coordination of motion, it is desirable to the overall gain of each axle is equal, the most satisfiedTherefore, by setting each axle KMiThe requirement of above formula can be met, it is achieved that when all directions are moved, to profile control signal UTAnd UCResponse consistent.
According to the logic flow in Fig. 1, after motion planning, each real-time operation module is called by signal processing sequence in each servo period, can realize described direct contour outline control method, completes the motion of continuous print high-accurate outline.
Claims (2)
1. the direct contour outline control method of plane rectangular coordinates motor system, it is characterised in that described control method passes through 11 modules
The logical process changed has calculated, and specifically comprises the following steps that
(1) motion planning: generate the instruction planning of contour motion tangential velocity；Programming profile according to user's inputAnd fortune
Contour motion process is planned by dynamic plan constraint condition, generates contour motion tangential velocity instruction vtcWith contour curve parameter u
Relation function f, vtc=f (u), for follow-up real-time controlling unit；
(2) profile Stateful Inspection: according to current X-Y axle physical location Px、PyAnd programming profileCalculate profile in real time
Error ec, profile errors directionProgramming parameter u of contour curve, corresponding the cutting of physical location that current actual positions is corresponding
To the direction of motionWhereinIt is unit direction vector；
(3) speed transformation by reciprocal direction: according to X-Y two axle speed Vx、VyAnd it is currentCalculate the reality along programming profile
Border tangential velocity vtaWith profile errors direction speed vca；
(4) tangential velocity produces: calculate current time tangential admission speed；The curve ginseng calculated according to profile state monitoring module
The f that number u and motion planning module generate, 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 actual tangential velocity vtaMeter
Calculate 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 controls: the e calculated according to profile Stateful InspectioncAnd the v that speed transformation by reciprocal direction calculatesca, according to feedback
Control law calculates profile errors direction controlling amount output UC；
(7) controlled quentity controlled variable positive-going transition: calculate according to current outline state monitoring moduleBy Tangents Control amount UTWith
Profile errors direction controlling amount UC, it is transformed into controlled quentity controlled variable U of X-axis under rectangular coordinatexControlled quentity controlled variable U with Y-axisy；
(8) X-axis control characteristic coupling: compensate the characteristic of X single shaft control module input/output, make the characteristics match of X-Y axle；
UxAfter this resume module, produce actual X-axis controlled quentity controlled variable
(9) X-axis single shaft control: according to X-axis controlled quentity controlled variableServomotor is changed into through signal processing and power amplification
Torque exports, and the X-axis under machine driving link drives X-Y rectangular coordinate moves；
(10) Y-axis control characteristic coupling: compensate the characteristic of Y single shaft control module input/output, make the characteristic of X-Y axle
Join；UyAfter this resume module, produce actual Y-axis controlled quentity controlled variable
(11) Y-axis single shaft control: according to Y-axis controlled quentity controlled variableServomotor is changed into through signal processing and power amplification
Torque exports, and the Y-axis under machine driving link drives X-Y rectangular coordinate moves,
Within each SERVO CONTROL cycle, kinetic control system repeat the above steps (2)～the process of (11), continuous print can be realized
High-accurate outline moves.
2., according to the direct contour outline control method of the plane rectangular coordinates motor system described in claim 1, it is characterized in that: described
Profile errors in step (6) controls to use Dual-loop feedback control to control in profile errors direction, and outer shroud is that profile errors controls ring；
Internal ring is profile errors speed controlling ring；Step (6) can be analyzed to following steps further:
(6-1) profile errors feedback control: the e calculated according to profile Stateful InspectioncCalculate the speed command in profile errors direction
vcc；
(6-2) velocity error in profile errors direction is calculated: according to vccAnd the v that speed transformation by reciprocal direction calculatesca, calculate profile by mistake
Velocity error e in difference 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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| CN106774163A (en) * | 2016-12-08 | 2017-05-31 | 哈尔滨工业大学深圳研究生院 | High-precision three-dimensional contour outline control method and device |
| 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 |
| CN109828534A (en) * | 2019-01-03 | 2019-05-31 | 浙江工业大学 | A kind of real time profile error compensating method of embedded cutting controller |
| 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 |
| CN114356255A (en) * | 2021-12-31 | 2022-04-15 | 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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