CN111427308A - Error compensation comprehensive control method for trajectory planning of numerical control platform - Google Patents

Error compensation comprehensive control method for trajectory planning of numerical control platform Download PDF

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CN111427308A
CN111427308A CN202010132862.5A CN202010132862A CN111427308A CN 111427308 A CN111427308 A CN 111427308A CN 202010132862 A CN202010132862 A CN 202010132862A CN 111427308 A CN111427308 A CN 111427308A
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error
axis
speed
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contour
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CN111427308B (en
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张铁
吴彩成
邹焱飚
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South China University of Technology SCUT
Zhongshan Institute of Modern Industrial Technology of South China University of Technology
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Zhongshan Institute of Modern Industrial Technology of South China University of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/404—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

The invention discloses an error compensation comprehensive control method for trajectory planning of a numerical control platform, which comprises the following steps: (1) establishing a feed rate regulator based on chord height error constraint, and performing fifth-order polynomial speed planning by taking the maximum feed speed allowed by a large-curvature position as a constraint condition to ensure that a double shaft moves according to a specified speed rule; (2) combining a real-time contour error estimation model of a free curve of the feeding motion of the numerical control platform, obtaining contour error compensation quantity of each feeding shaft by using a cross coupling controller, and calculating position error compensation quantity of each feeding shaft by using an improved position error compensator; (3) the contour error and the position error compensation amount are used as reference position instructions at the current moment and input into a double-shaft servo system, so that the simultaneous compensation of the contour error and the tracking error is realized. The invention can obviously improve the tracking and contour control precision in the numerical control machining process while meeting the requirement of chord height error.

Description

Error compensation comprehensive control method for trajectory planning of numerical control platform
Technical Field
The invention relates to an error compensation control method in the field of numerical control machining, in particular to an error compensation comprehensive control method for trajectory planning of a numerical control platform.
Background
The application of numerical control technology makes the traditional manufacturing industry have qualitative change, especially in recent years, the development of microelectronic technology and computer technology brings new vitality to numerical control technology, and the multi-axis Computer Numerical Control (CNC) precision machining technology becomes a hotspot and difficulty problem in the industrial field. With the improvement of the requirement on the product quality, higher and higher requirements are also put forward on the tracking and contour control precision of the processed workpiece.
In the numerical control machining process, due to the fact that motion characteristics of coordinate axes of a feeding system are greatly different, the problem of contour tracking precision cannot be solved from the perspective of single-axis Servo control, a targeted contour control technology such as a cross-coupling control method must be adopted, however, the cross-coupling control method cannot reduce tracking errors remarkably, and the poor tracking performance probably causes serious machining errors, through searching existing technical documents, a novel model-referenced adaptive control strategy is provided for improving tracking performance in an academic Journal modeling and application modeling control system (2016:1-1) of Sun et al, and a novel model-referenced adaptive control strategy is provided for improving tracking performance in the International Journal modeling and application modeling control system (Wu et al, although the method has high sensitivity to the tracking precision and improves the precision of a general tracking controller, and a feedback control device (Wu et al, and a general controller) has no requirement for improving tracking precision, and no requirement for improving the tracking precision of a general tracking controller 2017,117, and no requirement for improving the tracking precision of a general controller for controlling contour.
In summary, in most cases, the cross-coupling control method is effective in reducing the profile error, but the cross-coupling control method cannot significantly reduce the tracking error. Although the cross-coupling control method and the tracking error compensation strategy are combined, the tracking and contour control accuracy can be improved at the same time, for the free curves with variable curvatures, larger contour errors still exist at the positions with large curvatures, and the requirements of chord height errors cannot be met. Therefore, there is a need in the art to develop a comprehensive control method that can significantly improve the tracking and contour control accuracy and meet the requirements of chord height error.
Disclosure of Invention
The invention aims to provide an error compensation comprehensive control method for trajectory planning of a numerical control platform, which can obviously improve the tracking and contour control accuracy and meet the requirement of chord height error, has a simple controller structure and is effective in an error compensation calculation method.
The invention is realized by at least one of the following technical schemes.
An error compensation integrated control method for numerical control platform trajectory planning comprises the following steps:
(1) establishing a feed rate regulator based on chord height error constraint, and performing fifth-order polynomial speed planning by taking the maximum feed speed allowed by a large-curvature position as a constraint condition to ensure that a double shaft moves according to a specified speed rule;
(2) combining a real-time contour error estimation model of a free curve of the feeding motion of the numerical control platform, acquiring contour error compensation quantity of each feeding shaft by using a cross coupling controller, and calculating position error compensation quantity of each feeding shaft by using an improved position error compensator;
(3) the contour error and the position error compensation amount are used as reference position instructions at the current moment and input into a double-shaft servo system, so that the simultaneous compensation of the contour error and the tracking error is realized.
Further, the step (1) specifically comprises:
(11) traversing the whole track, and collecting { P (u) at interpolation points1),P(u2),...,P(ut) Find all songs in }The rate maximum point, and this set is denoted as { P (u) }1),P(u2),...,P(un) In which utThe parameters are parameters of a parametric curve and are used for describing the position information of the interpolation points, t is an index of the number of the interpolation points and satisfies that t is more than n;
(12) assume an initial feed rate of VstartAt the curvature maximum point set { P (u) }1),P(u2),...,P(un) Find the maximum velocity V based on the chord height error constraintmaxLess than the initial feed speed VstartAnd this set is denoted as { P (u) }1),P(u2),...,P(um) And the maximum speed allowed by each point is { V }s1,Vs2,...,VsmThe parameter corresponding to the curve is { u }s1,us2,...,usmWhere n > m;
(13) assume curve parameter u ∈ [0,1 ]]Parameter set us1,us2,...,usmDivide the curve into (m +1) intervals, which correspond to { [0, u ] respectivelys1],[us1,us2],...,[usm,1]And performing speed planning by using a fifth-order polynomial in each interval, wherein the starting and stopping speed of each interval is { [ V ]start,Vs1],[Vs1,Vs2],...,[Vsm,Vend]Thus, the feed rate adjuster establishment based on the chordal height error constraint is completed.
Further, the step (2) specifically comprises:
(21) profile error E 'of the free curve according to the target command position and the actual cutting position collected by the motor encoder, and the programmed feeding speed and the actual feeding speed'cThe estimation is carried out, and the contour error estimation model is
E′c＝-Exsinφ+Eycosφ
In the above formula, E'cFor estimated profile error, φ represents the pass target instruction position r1(t) and r1Angle of inclusion of the straight line of (t') with the X-axis, ExAnd EyRespectively representing the tracking error EpComponents along the X and Y axes;
(22) the cross-coupling controller employs PI control, which is represented in the discrete domain as:
Figure BDA0002396270440000021
in the above formula, Cc(z-1) Denotes a cross-coupled controller, KcpAnd KciFor the proportional and integral gains of the cross-coupled controller, Z is a complex variable called the Z transform operator;
since the X-axis and Y-axis position and velocity loop controllers use the same gain, the two axes are considered to have matched dynamics, and at this time, the cross-coupled controller is analyzed for stability using the profile error transfer function (CETF), which is given by the equation:
Figure BDA0002396270440000031
in the above formula, KprefIndicating the position proportional gain, T, of each axissRepresents a sampling period;
further, the profile error compensation amounts distributed to the axes after the cross-coupling controller is calculated as:
C,x＝UcCx，C,y＝UcCy
in the above formula, UcRepresenting estimated contour error E'cOutput after cross-coupling controller action, CxAnd CyIs the cross-coupling coefficient of the cross-coupled controller, C,xAnd C,yThe amounts of contour error compensation in the X axis and the Y axis are shown, respectively.
Further, in step (2), the establishment of the improved position error compensator comprises the following steps:
step one, a moving coordinate system XPY is established by taking an actual cutting position P as an original point, the programming feeding speed is planned through the feeding speed regulator based on the chord height error constraint, a double shaft moves according to the planned speed rule, and the feeding speed V of the point P at the current moment is calculatedTExpressed as:
VT＝Vpxi+Vpyj
in the above formula, VpxAnd VpyRespectively representing the components of the feed speed at point P along the X-axis and Y-axis, i and j respectively representing unit vectors in the X-axis and Y-axis directions;
step two, assuming that each contour error is eliminated in one sampling period, acquiring a compensation speed V along the direction of the contour error according to the assumptionCComprises the following steps:
Figure BDA0002396270440000032
in the above formula, E'cRepresenting the contour error vector, TsIs the sampling period, VcxAnd VcyRespectively represent the compensation speed VCComponents along the X and Y axes;
step three, according to the compensation speed VCAnd the feeding speed V at the present momentTA position P' moved over one sampling period is acquired and its position vector is represented as:
P′＝(Vpx+Vcx)·Tsi+(Vpy+Vcy)·Tsj
step four, expressing the distance vector between the point P' and the target instruction position R as:
P′R＝[Ex-(Vpx+Vcx)Ts]i+[Ey-(Vpy+Vcy)Ts]j
in the above formula, ExAnd EyRespectively representing the tracking error EpComponents along the X and Y axes.
Step five, calculating the position error compensation quantity along the X-axis and Y-axis directions:
Pecx＝Ex-(Vpx+Vcx)Ts，Pecy＝Ey-(Vpy+Vcy)Ts
further, the amount of position error compensation distributed to each axis after the improved position error compensator is operated is calculated as:
Pe,x＝PecxKpcx，Pe,y＝PecyKpcy
in the above formula, KpcxAnd KpcyIs a corresponding gain constant, Pe,xAnd Pe,yThe X-axis and Y-axis position error compensation amounts are shown, respectively.
Further, the step (3) specifically comprises the following steps:
(31) according to the contour error and the position error compensation quantity, the output control law of the X axis and the Y axis is obtained as follows:
Ux＝Rx+PecxKpcx+UcCx，Uy＝Ry+PecyKpcy+UcCy
in the above formula, RxAnd RyIs a reference position command generated by a non-uniform ratio B-spline (NURBS) curve interpolator;
(32) updating the control input quantity of the double-shaft servo system once every sampling period, and updating the real-time obtained UxAnd UyThe reference position command is input into a double-shaft servo system as a reference position command at the current moment, namely the simultaneous compensation of the contour error and the tracking error is realized.
Compared with the prior art, the invention has the advantages that:
1. the method can obviously improve the tracking and contour control precision in the numerical control machining process and meet the requirement of chord height error.
2. The controller has simple structure and effective error compensation amount calculation method.
Drawings
FIG. 1 is a velocity segment schematic of a feed rate regulator of the present embodiment based on a chordal height error constraint;
FIG. 2 is a schematic diagram of a contour error estimation method for a free curve according to the present embodiment;
FIG. 3 is a schematic diagram of an improved position error compensator of the present embodiment;
FIG. 4 is a structural diagram of an error compensation comprehensive control method for trajectory planning of a numerical control platform according to the embodiment;
FIG. 5 is a flowchart of an error compensation integrated control method for trajectory planning of a numerical control platform according to the present embodiment;
FIG. 6 is a hardware structure diagram of the numerical control platform according to the present invention;
FIG. 7 is a parametric curve tool path described in this example section using a NURBS curve;
FIG. 8 is a comparison graph of profile errors when interpolating and tracking the tool path of the parameter curve shown in FIG. 7 according to the present embodiment;
fig. 9 is a graph showing a comparison of tracking errors when the tool path of the parameter curve shown in fig. 7 is interpolated and tracked according to the present embodiment.
Detailed Description
The invention is further described with reference to the following figures and embodiments.
An error compensation integrated control method for numerical control platform trajectory planning as shown in fig. 5 and 4 comprises the following steps:
(1) establishing a feed rate regulator based on chord height error constraint, and performing fifth-order polynomial speed planning by taking the maximum feed speed allowed by a large-curvature position as a constraint condition to ensure that a double shaft moves according to a specified speed rule;
the step (1) specifically comprises the following steps:
(11) traversing the whole track, and collecting { P (u) at interpolation points1),P(u2),...,P(ut) Find all the curvature maxima points in this set and label this set as { P (u) }1),P(u2),...,P(un) In which utThe parameters are parameters of a parametric curve and are used for describing the position information of the interpolation points, t is an index of the number of the interpolation points and satisfies that t is more than n;
(12) assume an initial feed rate of VstartAt the curvature maximum point set { P (u) }1),P(u2),...,P(un) Find the maximum velocity V based on the chord height error constraintmaxLess than the initial feed speed VstartAnd this set is denoted as { P (u) }1),P(u2),...,P(um) Each point pair conforms toAllowable maximum speed is Vs1,Vs2,...,VsmThe parameter corresponding to the curve is { u }s1,us2,...,usmWhere n > m;
(13) assume curve parameter u ∈ [0,1 ]]Parameter set us1,us2,...,usmDivide the curve into (m +1) intervals, which correspond to { [0, u ] respectivelys1],[us1,us2],...,[usm,1]And performing speed planning by using a fifth-order polynomial in each interval, wherein the starting and stopping speed of each interval is { [ V ]start,Vs1],[Vs1,Vs2],...,[Vsm,Vend]Thus, the feed rate adjuster establishment based on the chordal height error constraint is completed. A schematic diagram of the planned segment speeds is shown in fig. 1.
(2) Combining a real-time contour error estimation model of a free curve of the feeding motion of the numerical control platform, acquiring contour error compensation quantity of each feeding shaft by using a cross coupling controller, and calculating position error compensation quantity of each feeding shaft by using an improved position error compensator;
specifically, the step (2) specifically includes:
(21) according to the target instruction position and the actual cutting position p collected by the motor encoder1(t), and profile error E 'of programmed and actual feed speeds versus free curve'cThe estimation is carried out, specifically, as shown in FIG. 2, the contour error estimation model is
E′c＝-Exsinφ+Eycosφ
In the above formula, E'cFor estimated profile error, φ represents the pass target instruction position r1(t) and r1(t') angle of the straight line with the X-axis, ExAnd EyRespectively representing the tracking error EpComponents along the X and Y axes;
more specifically, a point r on the target reference path1(t') is expressed as:
Figure BDA0002396270440000051
in the above formula, Vx1(t) and Vy1(t) represents the components of the programmed feed rate along the X-axis and Y-axis, respectively, and, correspondingly, Vx2(t) and Vy2(t) represents the components of the actual feed rate along the X-axis and Y-axis, respectively, and Δ t represents the value from r1(t') move to r1(t) total time;
(22) the cross-coupling controller employs PI control, which is represented in the discrete domain as:
Figure BDA0002396270440000061
in the above formula, Cc(z-1) Denotes a cross-coupled controller, KcpAnd KciFor the proportional and integral gains of the cross-coupled controller, Z is a complex variable called the Z transform operator;
since the X-axis and Y-axis position and velocity loop controllers use the same gain, the two axes are considered to have nearly matched dynamics. At this time, the cross-coupled controller may be subjected to a stability analysis using a profile error transfer function (CETF) having the equation
Figure BDA0002396270440000062
In the above formula, KprefIndicating the position proportional gain, T, of each axissRepresenting the sampling period.
Further, the amount of profile error compensation assigned to each axis after the cross-coupled controller is applied can be obtained as
C,x＝UcCx，C,y＝UcCy
In the above formula, UcRepresenting estimated contour error E'cOutput after cross-coupling controller action, CxAnd CyIs the cross-coupling coefficient of the cross-coupled controller and satisfies Cx＝-sinφ，Cy＝cosφ，C,xAnd C,yRespectively representing the contour error compensation quantity of an X axis and a Y axis;
the improved position error compensator essentially comprises the steps of:
step one, a moving coordinate system XPY is established by taking an actual cutting position P as an original point, the programming feeding speed is planned through the feeding speed regulator based on the chord height error constraint, a double shaft moves according to the planned speed rule, and the feeding speed V of the point P at the current moment is calculatedTExpressed as:
VT＝Vpxi+Vpyj
in the above formula, VpxAnd VpyRespectively representing the components of the feed speed at point P along the X-axis and Y-axis, i and j respectively representing unit vectors in the X-axis and Y-axis directions;
step two, assuming that each contour error is eliminated in one sampling period, acquiring a compensation speed V along the direction of the contour error according to the assumptionCComprises the following steps:
Figure BDA0002396270440000063
in the above formula, E'cRepresenting the contour error vector, TsIs the sampling period, VcxAnd VcyRespectively represent the compensation speed VCComponents along the X and Y axes;
step three, according to the compensation speed VCAnd the feeding speed V at the present momentTA position P' moved over one sampling period is acquired and its position vector is represented as:
P′＝(Vpx+Vcx)·Tsi+(Vpy+Vcy)·Tsj
step four, expressing the distance vector between the point P' and the target instruction position R as:
P′R＝[Ex-(Vpx+Vcx)Ts]i+[Ey-(Vpy+Vcy)Ts]j
in the above formula, ExAnd EyRespectively representing the tracking error EpComponents along the X and Y axes.
Step five, calculating the position error compensation quantity along the X-axis and Y-axis directions:
Pecx＝Ex-(Vpx+Vcx)Ts，Pecy＝Ey-(Vpy+Vcy)Ts
further, the amount of position error compensation distributed to each axis after the improved position error compensator is operated is calculated as:
Pe,x＝PecxKpcx，Pe,y＝PecyKpcy
in the above formula, KpcxAnd KpcyIs a corresponding gain constant, Pe,xAnd Pe,yThe X-axis and Y-axis position error compensation amounts are shown, respectively.
A schematic diagram of the improved position error compensator is shown in figure 3.
(3) The contour error and the position error compensation amount are used as reference position instructions of the current moment and input into a double-shaft servo system, so that the simultaneous compensation of the contour error and the tracking error is realized, and the method specifically comprises the following steps:
(31) according to the contour error and the position error compensation quantity, the output control law of the double-shaft servo system to the X shaft and the Y shaft is obtained as follows:
Ux＝Rx+PecxKpcx+UcCx，Uy＝Ry+PecyKpcy+UcCy
in the above formula, RxAnd RyIs a reference position command generated by a non-uniform ratio B-spline (NURBS) curve interpolator;
(32) the control input quantity of the system is updated once every sampling period, and the real-time updated U is obtainedxAnd UyThe reference position command as the current time is input into the double-shaft servo actuator, namely the simultaneous compensation of the contour error and the tracking error is realized, and the error compensation integrated control structure is shown in FIG. 4. K in FIG. 4pxAnd KpyIs a position loop feedback controller of a servo system, GvxAnd GvyIs X, Y axle bagLinks including the speed loop, the current loop and the actuating mechanism can be obtained through model identification. PxAnd PyIs the actual position of the motor output by each shaft and can be obtained by sampling the photoelectric encoder signal, and F represents the feeding speed.
The invention is realized in the numerical control platform shown in fig. 6: the test objects are a high-order AC servo driver of the Taida ASDA A2-E series and a servo motor of the ECMA series. NURBS interpolation is implemented in a computer and the actual position of each axis is obtained by sampling the photoelectric encoder signals of the motor. The calculation and compensation of the real-time contour error are realized by programming on Kithara software, an industrial personal computer sends compensation quantity to a servo unit through an EtherCAT bus, and the system control period is T s1 ms. Further, the X, Y feed shaft was composed of two ball screws (pitch 20mm/rev and 10mm/rev, respectively) and each ball screw was provided with a grating scale having a resolution of 1 μm. The values of the gain constants used are: kpx＝35，Kpy＝35，Kcp＝2.0，Kci＝0.001， Kpcx＝1.0，Kpcy1.0; the maximum allowable chord height error is set to 0.001 mm.
Fig. 7 is a parametric curve tool path described by NURBS curves. Wherein the content of the first and second substances,
the control peaks are ① (0.0 ), ② (-4.99420, -3.24613), ③ (-16.91645, -10.99536), ④ (20.95161, -18.41546), ⑤ (-24.97704, -23.46105), ⑥ (23.20926, -38.53194), ⑦ (-30.24880, -42.11590), ⑧ (18.47811, -53.82904), ⑨ (-37.67975, -64.20412), ⑩ (-3.54279, -69.02725),
Figure RE-GDA0002525260550000081
(17.88210,-72.05432)；
the node vector is: (0,0,0,0,0.0776395399490701,0.185342496081936,0.292366084595116,
0.409866448276429,0.536057475002697,0.650968691324137,0.780942625933166,1,1, 1,1)；
the weight factors are: (1,1,1,1,1,1,1,1,1,1,1).
Fig. 8 is a graph showing a comparison of profile errors when the tool path of the parameter curve shown in fig. 7 is interpolated and tracked. The solid line in the figure represents the absolute profile error without error compensation, with a maximum value of 1572.20 μm for profile error and 414.34 μm for root mean square profile error. The dotted line in the figure indicates the absolute profile error when the error compensation integrated control method is used, and the maximum value of the profile error is 662.51 μm, and the root mean square profile error is 143.38 μm.
Fig. 9 is a graph showing a comparison of tracking errors when the tool path of the parameter curve shown in fig. 7 is interpolated and tracked. The solid line in the figure represents the tracking error without the error compensation method, and the maximum value of the tracking error is 2227.10 μm, and the root mean square tracking error is 1866.80 μm. The dotted line in the figure indicates the tracking error when the error compensation integrated control method is used, and the maximum value of the tracking error is 1238.30 μm, and the root mean square tracking error is 916.93 μm.
By contrast, the error compensation comprehensive control method for the trajectory planning of the numerical control platform can obviously improve the tracking and contour control precision and meet the requirement of chord height errors, and the controller is simple in structure and the error compensation amount calculation method is effective. The method can be applied and popularized in a numerical control system and a numerical control machine tool, and is particularly significant to numerical control machining of free curves with variable curvatures, which needs to consider chord height error constraint and machining tracks.
The above-mentioned embodiments are merely preferred embodiments of the present invention, and the scope of the present invention is not limited thereto, so that the changes in the shape and principle of the present invention should be covered by the protection scope of the present invention.

Claims (5)

1. An error compensation integrated control method for numerical control platform trajectory planning is characterized by comprising the following steps:
(1) establishing a feed rate regulator based on chord height error constraint, and performing fifth-order polynomial speed planning by taking the maximum feed speed allowed by a large-curvature position as a constraint condition to ensure that a double shaft moves according to a specified speed rule;
(2) combining a real-time contour error estimation model of a free curve of the feeding motion of the numerical control platform, obtaining contour error compensation quantity of each feeding shaft by using a cross coupling controller, and calculating position error compensation quantity of each feeding shaft by using an improved position error compensator;
(3) the contour error and the position error compensation amount are used as reference position instructions at the current moment and input into a double-shaft servo system, so that the simultaneous compensation of the contour error and the tracking error is realized.
2. The error compensation comprehensive control method for numerical control platform trajectory planning according to claim 1, wherein the step (1) specifically comprises:
(11) traversing the whole track, and collecting { P (u) at interpolation points1),P(u2),...,P(ut) Find all the curvature maxima points in this set and label this set as { P (u) }1),P(u2),...,P(un) In which utThe parameters are parameters of a parametric curve and are used for describing the position information of the interpolation points, t is an index of the number of the interpolation points and satisfies that t is more than n;
(12) assume an initial feed rate of VstartAt the curvature maximum point set { P (u) }1),P(u2),...,P(un) Find the maximum velocity V based on the chord height error constraintmaxLess than the initial feed speed VstartAnd this set is denoted as { P (u) }1),P(u2),...,P(um) The maximum speed allowed by each point is { V }s1,Vs2,...,VsmThe parameter corresponding to the curve is { u }s1,us2,...,usmWhere n > m;
(13) assume curve parameter u ∈ [0,1 ]]Parameter set us1,us2,...,usmDivide the curve into (m +1) intervals, which correspond to { [0, u ] respectivelys1],[us1,us2],...,[usm,1]And performing speed planning by using a fifth-order polynomial in each interval, wherein the starting and stopping speed of each interval is { [ V ]start,Vs1],[Vs1,Vs2],...,[Vsm,Vend]Thus, the feed rate adjuster establishment based on the chordal height error constraint is completed.
3. The error compensation comprehensive control method for numerical control platform trajectory planning according to claim 1, wherein the step (2) specifically comprises:
(21) profile error E 'of the free curve according to the target command position and the actual cutting position collected by the motor encoder, and the programmed feeding speed and the actual feeding speed'cThe estimation is carried out, and the contour error estimation model is
E′c＝-Exsinφ+Eycosφ
In the above formula, E'cFor estimated profile error, φ represents the pass target instruction position r1(t) and r1(t') angle of the straight line with the X-axis, ExAnd EyRespectively representing the tracking error EpComponents along the X and Y axes;
(22) the cross-coupling controller adopts PI control, and the representation form of the PI control in a discrete domain is as follows:
Figure FDA0002396270430000021
in the above formula, Cc(z-1) Denotes a cross-coupled controller, KcpAnd KciFor the proportional and integral gains of the cross-coupled controller, Z is a complex variable called the Z transform operator;
since the X-axis and Y-axis position and velocity loop controllers use the same gain, the two axes are considered to have matched dynamics, and at this time, the cross-coupled controller is analyzed for stability using the profile error transfer function (CETF), which is given by the equation:
Figure FDA0002396270430000022
in the above formula, KprefIndicating the position proportional gain, T, of each axissRepresents a sampling period;
further, the profile error compensation amounts distributed to the axes after the cross-coupling controller is calculated as:
C,x＝UcCx，C,y＝UcCy
in the above formula, UcRepresenting estimated contour error E'cOutput after cross-coupling controller action, CxAnd CyIs the cross-coupling coefficient of the cross-coupling controller, C,xAnd C,yThe amounts of contour error compensation in the X axis and the Y axis are shown, respectively.
4. The method of claim 1, wherein the step (2) of establishing the improved position error compensator comprises the steps of:
step one, a moving coordinate system XPY is established by taking an actual cutting position P as an origin, the programmed feeding speed is planned through the feeding rate regulator based on the chord height error constraint, a double shaft moves according to the planned speed rule, and the feeding speed V at the current moment of the point P is calculatedTExpressed as:
VT＝Vpxi+Vpyj
in the above formula, VpxAnd VpyRespectively representing the components of the feed speed at point P along the X-axis and Y-axis, i and j respectively representing unit vectors in the X-axis and Y-axis directions;
step two, assuming that each contour error is eliminated in one sampling period, calculating the compensation speed V along the direction of the contour error according to the assumptionCComprises the following steps:
Figure FDA0002396270430000023
in the above formula, E'cRepresenting the contour error vector, TsIs the sampling period, VcxAnd VcyRespectively represent the compensation speed VCComponents along the X and Y axes;
step three, according to the compensation speed VCAnd the feeding speed V at the present momentTAcquiring a position P 'moved to over one sampling period'And its position vector is represented as:
P′＝(Vpx+Vcx)·Tsi+(Vpy+Vcy)·Tsj
step four, expressing the distance vector between the point P' and the target instruction position R as:
P′R＝[Ex-(Vpx+Vcx)Ts]i+[Ey-(Vpy+Vcy)Ts]j
in the above formula, ExAnd EyRespectively representing the tracking error EpComponents along the X and Y axes;
step five, obtaining position error compensation along the X-axis and Y-axis directions:
Pecx＝Ex-(Vpx+Vcx)Ts，Pecy＝Ey-(Vpy+Vcy)Ts
further, the amount of position error compensation distributed to each axis after the improved position error compensator is operated is calculated as:
Pe,x＝PecxKpcx，Pe,y＝PecyKpcy
in the above formula, KpcxAnd KpcyIs a corresponding gain constant, Pe,xAnd Pe,yThe X-axis and Y-axis position error compensation amounts are shown, respectively.
5. The error compensation comprehensive control method for numerical control platform trajectory planning according to claim 1, wherein the step (3) specifically comprises the following steps:
(31) according to the contour error and the position error compensation quantity, the output control law of the X axis and the Y axis is obtained as follows:
Ux＝Rx+PecxKpcx+UcCx，Uy＝Ry+PecyKpcy+UcCy
in the above formula, RxAnd RyIs generated by a non-uniform proportional B-spline (NURBS) curve interpolatorA reference position command;
(32) updating the control input quantity of the double-shaft servo system once every sampling period, and updating the real-time obtained UxAnd UyThe reference position command as the current moment is input into a double-shaft servo system, namely the simultaneous compensation of the contour error and the tracking error is realized.
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