CN110703683B - Numerical control system single-axis error adjusting algorithm based on speed step - Google Patents

Numerical control system single-axis error adjusting algorithm based on speed step Download PDF

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CN110703683B
CN110703683B CN201910917517.XA CN201910917517A CN110703683B CN 110703683 B CN110703683 B CN 110703683B CN 201910917517 A CN201910917517 A CN 201910917517A CN 110703683 B CN110703683 B CN 110703683B
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刘清建
解润海
张�杰
董罡
曹立波
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Tianjin Tiansen Intelligent Equipment Co ltd
Tianjin 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
    • G05B19/19—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
    • 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
    • G05B2219/00—Program-control systems
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Abstract

The invention relates to a numerical control system single-axis error adjusting algorithm based on speed steps, which is mainly technically characterized in that: calculating the maximum speed step value of the shaft; calculating an expected speed in a current servo period, an error value in the current servo period and an error variable quantity in the current servo period; if the error variation in the current servo period is a positive value, the feedback speed in the previous servo period is equal to the error variation, otherwise, the feedback speed in the previous servo period is 0; correcting the expected speed in the current servo period according to the feedback speed in the previous servo period; and multiplying the expected speed in the current servo period by one servo period to obtain an output expected value. The invention has the characteristics of reasonable design, easy adjustment, strong applicability, simple algorithm, high operation efficiency and the like.

Description

Numerical control system single-axis error adjustment algorithm based on speed step
Technical Field
The invention belongs to the technical field of motion control of numerical control systems, and particularly relates to a single-axis error adjusting algorithm of a numerical control system based on speed steps.
Background
At present, PID and PID-based respective optimization algorithms are generally adopted for motion control closed-loop regulation, or a targeted closed-loop control algorithm is constructed and modeled for specific motion control. For closed-loop control of a numerical control system, the majority of the closed-loop control modes adopt PID (proportion integration differentiation) control modes, and the closed-loop control method has the characteristics of simplicity in debugging, strong applicability and the like, but the PID control method needs to be combined with the performance of controlled equipment, so that the PID control method has more adjusted parameters and poor applicability.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a single-axis error adjusting algorithm of a numerical control system based on speed steps, which is reasonable in design, flexible in adjustment and high in applicability.
The technical problem to be solved by the invention is realized by adopting the following technical scheme:
a numerical control system single-axis error adjusting algorithm based on speed steps comprises the following steps:
step 1, calculating a maximum speed step value delta V of a shaft;
step 2, calculating the expected speed Req _ V in the current servo periodc+1；
Step 3, calculating an error value error in the current servo period;
step 4, calculating the error variation d _ error in the current servo period;
step 5, if the error variation d _ error in the current servo period is a positive value, the feedback speed feedback _ V in the previous servo periodcD _ error, if d _ error is negative, feedback _ Vc＝0；
Step 6, feedback _ V is fed according to the feedback speed in the previous servo periodcFor the desired speed Req _ V in the current servo cyclec+1Correcting;
step 7, obtaining the expected speed Req _ V in the current servo period obtained in the step 6c+1Multiplied by one servo period T to obtain the output desired value ReqS.
Further, the step 1 calculates the maximum speed step value Δ V of the shaft according to the following formula:
ΔV＝Amax×0.1×eε×T
wherein e epsilon is an error correction coefficient of the axis, and Amax is a maximum acceleration value.
Further, the value range of the error correction coefficient e epsilon of the axis is as follows: e epsilon is more than or equal to 0.1 and less than or equal to 2.
Further, the step 2 calculates the expected speed Req _ V in the current servo period according to the following formulac+1：
Figure BDA0002216545670000011
Wherein S isc+1The difference between the command position and the feedback position is cut off until the current servo period, the value is a positive value, but the direction is required to be positive by pointing to the direction of the expected position point; n is a variable, and the value of n is as follows:
Figure BDA0002216545670000021
Figure BDA0002216545670000022
further, the step 3 calculates an error value error in the current servo period according to the following formula:
error＝Sc-Sc+1
wherein S iscBy the difference between the commanded position and the feedback position of the previous servo cycle, Sc+1The difference between the command position and the feedback position of the current servo cycle is obtained.
Further, the step 4 calculates the error variation d _ error in the current servo period according to the following formula:
d_error＝error/T。
further, the specific processing method in step 6 is as follows:
if abs (feedback _ V)c-Req_Vc+1)Δ V ≦ the desired speed Req _ V in the current servo cyclec+1No correction is made;
if abs (feedback _ V)c-Req_Vc+1)Δ V, the following is performed:
when the Req _ Vc+1＞feedback_VcThen Δ V does not need to be corrected and the desired speed Req _ V in the current servo cycle is adjustedc+1Corrected to feedback _ Vc+ΔV；
When the feedback _ Vc＞Req_Vc+1Then, Δ V is corrected to Δ V' ═ a × T, and the desired speed Req _ V in the current servo cycle is corrected to Δ V ═ a × Tc+1Corrected to feedback _ Vc- Δ V', in the above formula,
Figure BDA0002216545670000023
in the above formula, Sc+1The difference between the command position and the feedback position of the current servo cycle is obtained.
The invention has the advantages and positive effects that:
the invention has reasonable design, obtains the output expected value by calculating the maximum speed step value of the axis, the expected speed in the current servo period, the error value in the current servo period, the error variation in the current servo period and the feedback speed in the previous servo period and correcting the expected speed in the current servo period according to the error variation, can well combine the controlled equipment performances together, and has the characteristics of easy adjustment, strong applicability, simple algorithm, high operation efficiency and the like.
Detailed Description
The technical scheme of the invention is further explained by combining specific examples.
A numerical control system single-axis error adjusting algorithm based on speed steps comprises the following steps:
step 1, calculating the maximum speed step value delta V of the shaft according to the following formula:
ΔV＝Amax×0.1×eε×T (1)
wherein e epsilon is an error correction coefficient of the axis, e epsilon is more than or equal to 0.1 and less than or equal to 2, T is a servo period, and Amax is a maximum acceleration value.
Here, we explain the concept of the present axis:
in the numerical control system control, the method adopts pid algorithm for error regulation control, the regulated control object is for each motion control axis of the coordinate system in each control system, such as XYZ/ABC, the error regulation control algorithm for each axis is the same, but the specific application object of each algorithm is a control axis, which generally corresponds to a servo driver + a servo motor, and the feedback mode can be that the encoder of the servo driver can also be the final raster ruler feedback position of the actuator. This axis is to say a coordinate axis within the coordinate system under control of the numerical control system. The feedback position source can be a servo driver encoder or the position feedback of the final linear mechanism.
Step 2, calculating the period in the current servo periodHope velocity Req _ Vc+1The specific method comprises the following steps:
substituting the delta V obtained in the step 1 into a formula (2), calculating to obtain an intermediate solution value temp,
Figure BDA0002216545670000031
wherein S isc+1The value of the difference between the commanded position and the feedback position for the current servo cycle is positive, but the direction is required to be positive in the direction pointing to the desired position point.
Setting a variable n, n being an integer,
Figure BDA0002216545670000032
substituting the n into a formula (3), and calculating to obtain the expected speed Req _ V in the current servo periodc+1，
Figure BDA0002216545670000033
Step 3, calculating an error value error in the current servo period according to the following formula, wherein the specific method comprises the following steps:
let ScTo stop until the difference between the command position and the feedback position of the previous servo cycle, ScAnd Sc+1Substituting into formula (4) to obtain the error value error in the current servo period,
error＝Sc-Sc+1 (4)
step 4, calculating the error variation d _ error in the current servo period, wherein the specific method comprises the following steps:
calculating an error variation d _ error in the current servo period according to a servo period T and the error value error in the current servo period obtained in the step 3 by a formula (5),
d_error＝error/T (5)
step 5, setting the feedback speed in the previous servo period as feedback _ VcIf d _ error is positive, feedback _ VcD _ error; feedback _ V if d _ error is negativec＝0。
Step 6, obtaining the feedback speed feedback _ V in the previous servo period according to the step 5cFor the desired speed Req _ V in the current servo cyclec+1The correction is carried out by the specific method:
such as abs (feedback _ V)c-Req_Vc+1)If Δ V is less than or equal to Δ V, then Req _ Vc+1No correction is made;
such as abs (feedback _ V)c-Req_Vc+1)Δ V, the following is performed:
case 1: when the Req _ Vc+1＞feedback_VcThen Δ V does not need to be corrected, and Req _ V is setc+1Corrected to feedback _ Vc+ΔV；
Case 2: when the feedback _ Vc＞Req_Vc+1If so, the feedback _ V is usedcAnd Sc+1Substituting into the formula (6) to obtain a,
Figure BDA0002216545670000041
correcting the maximum speed step value Δ V to Δ V' ═ a × T, and then correcting the Req _ Vc+1Corrected to feedback _ Vc-ΔV'；
Step 7, obtaining the expected speed Req _ V in the current servo period obtained in the step 6c+1Substituting the formula (7) to obtain the output expected value ReqS,
ReqS＝Req_Vc+1×T (7)
the final output expected value ReqS is obtained through the steps. The output desired value ReqS is used to correct the error. Since the error is the position that the control system expects the current control axis to reach, and there is a difference between the position that it actually feedbacks now and the position that we require to reach for various reasons, this difference is finally a distance value, therefore, by adding the expected value ReqS additionally to the position command value that it expects to reach in a certain servo cycle, it is the distance that we expect the axis to eventually travel in the servo cycle. The expected value is then solved for a value which is positive with the expected position pointing up one servo cycle, and if it is consistent with the expected position direction of this servo cycle, it is added directly, and if it is not consistent, it is subtracted.
For example: if the current ReqS is 1mm, the positive direction of the current ReqS refers to the expected position facing to the previous servo cycle, namely the positive direction of the X axis, and the expected moving position in the servo cycle is 5mm in the positive direction of the X, the finally output command instruction is 6mm in the positive direction of the X; if the expected moving position in the servo period is X negative direction 5mm, the final output command is X negative direction 4 mm.
Several examples are given below to illustrate the practice of the invention:
example 1
Step 1, the error correction coefficient e epsilon of the axis is 0.1, the servo period T is 1ms (millisecond), and the maximum acceleration value Amax is 0.1m/s2(m/s)2)＝1×102mm/ms2(mm/ms)2) The maximum acceleration Δ V of the present axis is calculated as follows:
ΔV＝Amax×0.1×eε×T＝1×102×0.1×0.1×1＝1mm/ms
step 2, at a certain time m1, stopping until the difference S between the current servo cycle command position and the feedback positionc+1At 7mm, T, Δ V and S obtained in step 1c+1Substituting the formula to obtain an intermediate solution value temp of 3.27,
Figure BDA0002216545670000051
setting a variable n as an integer, substituting temp and n into
Figure BDA0002216545670000052
N is 3;
will Sc+1Substituting n into the following formula, and calculating to obtain the expected speed Req _ V in the current servo periodc+1，Req_Vc+1＝3.25mm/ms，
Figure BDA0002216545670000053
Step 3, ScIs the difference between the commanded position and the feedback position by the previous servo cycle at a time m1, ScEqual to 10; will ScAnd Sc+1Substituting the following formula to obtain the error value error in the current servo period,
error＝Sc-Sc+1＝10-7＝3mm
step 4, according to T and the error obtained in the step 3, calculating by the following formula to obtain the error variation d _ error of 3mm/ms in the current servo period,
d_error＝error/T＝3mm/ms
step 5, setting the feedback speed in the previous servo period as feedback _ VcBecause d _ error is positive, feedback _ Vc＝d_error＝3mm/ms；
Step 6, feedback _ V obtained according to the step 5cBecause abs (feedback _ V)c-Req_Vc+1) When abs (3-3.25) is 0.25mm/ms ≦ Δ V is 1mm/ms, Req _ Vc+1Without modification, i.e. Req _ Vc+1＝3.25mm/ms；
Step 7, the Req _ V obtained in the step 6c+1Substituting the formula to obtain the output expected value ReqS,
ReqS＝Req_Vc+1×T＝3.25mm。
example 2
Step 1, the error correction coefficient e epsilon of the axis is 0.1, the servo period T is 1ms (millisecond), and the maximum acceleration value Amax is 0.1m/s2(m/s)2)＝1×102mm/ms2(mm/ms)2) Calculating the maximum acceleration of the shaft as delta V: Δ V ═ Amax × 0.1 × e ∈ × T ═ 1 × 102×0.1×0.1×1＝1mm/ms；
Step 2, at a certain time m2, stopping until the difference S between the current servo cycle command position and the feedback positionc+1At 7mm, T, Δ V and S obtained in step 1c+1Substituting the formula to obtain an intermediate solution value temp of 3.27,
Figure BDA0002216545670000061
setting a variable n, n being an integer, substituting temp and n into
Figure BDA0002216545670000062
N is 3;
will Sc+1Substituting n into the following formula, and calculating to obtain the expected speed Req _ V in the current servo periodc+1，Req_Vc+1＝3.25mm/ms，
Figure BDA0002216545670000063
Step 3, ScIs the difference between the commanded position and the feedback position by the previous servo cycle at a time m2, ScEqual to 9; will ScAnd Sc+1Substituting the following formula to obtain the error value error in the current servo period,
error＝Sc-Sc+1＝9-7＝2mm
step 4, according to T and the error obtained in the step 3, calculating to obtain the error variation d _ error of 2mm/ms in the current servo period through the following formula,
d_error＝error/T＝2mm/ms
step 5, setting the feedback speed in the previous servo period as feedback _ VcBecause d _ error is positive, feedback _ Vc＝d_error＝2mm/ms；
Step 6, feedback _ V obtained according to the step 5cBecause abs (feedback _ V)c-Req_Vc+1)＝abs(2-3.25)＝1.25mm/ms>Δ V is 1mm/ms, and Req _ Vc+1＞feedback_VcThen Δ V does not need to be corrected and Req _ V will be appliedc+1Corrected to feedback _ Vc+ Δ V, i.e. Req _ Vc+1Corrected to feedback _ Vc+ΔV＝2+1＝3mm/ms
Step 7, the Req _ V obtained in the step 6c+1Substituting the formula to obtain the output periodThe value of the return is the value of ReqS,
ReqS＝Req_Vc+1×T＝3mm。
example 3
Step 1, the error correction coefficient e epsilon of the axis is 0.1, the servo period T is 1ms (millisecond), and the maximum acceleration value Amax is 0.1m/s2(m/s)2)＝1×102mm/ms2(mm/ms)2) Calculating the maximum acceleration of the shaft as delta V: Δ V ═ Amax × 0.1 × e ∈ × T ═ 1 × 102×0.1×0.1×1＝1mm/ms；
Step 2, at a certain time m3, stopping until the difference S between the current servo cycle command position and the feedback positionc+1At 7mm, T, Δ V and S obtained in step 1c+1Substituting the formula to obtain an intermediate solution value temp of 3.27,
Figure BDA0002216545670000071
setting a variable n, n being an integer, substituting temp and n into
Figure BDA0002216545670000072
N is 3;
will Sc+1Substituting n into the following formula, and calculating to obtain the expected speed Req _ V in the current servo periodc+1，Req_Vc+1＝3.25mm/ms，
Figure BDA0002216545670000073
Step 3, ScIs the difference between the commanded position and the feedback position by the previous servo cycle at a time m3, ScEqual to 12; will ScAnd Sc+1Substituting the following formula to obtain an error value error in one servo period,
error＝Sc-Sc+1＝12-7＝5mm
step 4, according to T and the error obtained in the step 3, calculating by the following formula to obtain the error variation d _ error of 5mm/ms in the current servo period,
d_error＝error/T＝5mm/ms (5)
step 5, setting the feedback speed in the previous servo period as feedback _ VcIf d _ error is positive, feedback _ Vc＝d_error＝5mm/ms；
Step 6, obtaining feedback _ V according to the step 5cBecause abs (feedback _ V)c-Req_Vc+1)＝abs(5-3.25)＝1.75mm/ms>ΔV＝1mm/ms，
And feedback _ Vc＞Req_Vc+1Then the feedback _ V is usedcAnd Sc+1Substituting the formula into the formula to obtain a,
Figure BDA0002216545670000074
correcting the Δ V to Δ V' ═ a × T ═ 1.79mm/ms, and then correcting the Req _ Vc+1Corrected to feedback _ Vc- Δ V'; i.e. Req _ Vc+1Corrected to feedback _ Vc-ΔV'＝5-1.79＝3.21mm/ms
Step 7, the Req _ V obtained in the step 6c+1Substituting the formula to obtain the output expected value ReqS,
ReqS＝Req_Vc+1×T＝3.21mm。
example 4
Step 1, the error correction coefficient e epsilon of the axis is 0.1, the servo period T is 1ms (millisecond), and the maximum acceleration value Amax is 0.1m/s2(m/s)2)＝1×102mm/ms2(mm/ms)2) Calculating the maximum acceleration of the shaft as delta V: Δ V ═ Amax × 0.1 × e ∈ × T ═ 1 × 102×0.1×0.1×1＝1mm/ms；
Step 2, at a certain time m4, stopping until the difference S between the current servo cycle command position and the feedback positionc+1At 7mm, T, Δ V and S obtained in step 1c+1Substituting the formula to obtain an intermediate solution value temp of 3.27,
Figure BDA0002216545670000081
setting a variable n, n being an integer, substituting temp and n into
Figure BDA0002216545670000082
N is 3;
will Sc+1Substituting n into the following formula, and calculating to obtain the expected speed Req _ V in the current servo periodc+1，Req_Vc+1＝3.25mm/ms，
Figure BDA0002216545670000083
Step 3, ScIs the difference between the commanded position and the feedback position by the previous servo cycle at a time m4, ScEqual to 5; will ScAnd Sc+1Substituting the following formula to obtain an error value error in one servo period,
error＝Sc-Sc+1＝5-7＝-2mm
step 4, according to T and the error obtained in the step 3, calculating to obtain the error variation d _ error of-2 mm/ms in the current servo period by the following formula,
d_error＝error/T＝-2mm/ms
step 5, setting the feedback speed in the previous servo period as feedback _ VcIf d _ error is negative, feedback _ VcValue 0, feedback _ Vc＝0mm/ms；
Step 6, feedback _ V obtained according to the step 5cBecause abs (feedback _ V)c-Req_Vc+1)＝abs(0-3.25)＝3.25mm/ms>ΔV＝1mm/ms，
And Req _ Vc+1＞feedback_VcThen Δ V does not need to be corrected and Req _ V will be usedc+1Corrected to feedback _ Vc+ Δ V, i.e. Req _ Vc+1Corrected to feedback _ Vc+ΔV＝0+1＝1mm/ms
Step 7, the Req _ V obtained in the step 6c+1Substituting the formula to obtain the output expected value ReqS,
ReqS＝Req_Vc+1×T＝1mm。
nothing in this specification is said to apply to the prior art.
It should be emphasized that the embodiments described herein are illustrative rather than restrictive, and thus the present invention is not limited to the embodiments described in the detailed description, but also includes other embodiments that can be derived from the technical solutions of the present invention by those skilled in the art.

Claims (3)

1. The utility model provides a numerical control system unipolar error adjustment algorithm based on speed step which characterized in that: the method comprises the following steps:
step 1, calculating a maximum speed step value delta V of a shaft;
step 2, calculating the expected speed Req _ V in the current servo periodc+1；
Step 3, calculating an error value error in the current servo period;
step 4, calculating the error variation d _ error in the current servo period;
step 5, if the error variable d _ error in the current servo period is a positive value, the feedback speed feedback _ V in the previous servo periodcD _ error, if d _ error is negative, feedback _ Vc＝0；
Step 6, according to the feedback speed feedback _ V in the previous servo periodcFor the desired speed Req _ V in the current servo cyclec+1Correcting;
step 7, obtaining the expected speed Req _ V in the current servo period obtained in the step 6c+1Multiplying the servo period T to obtain an output expected value ReqS;
said step 2 calculates the expected speed Req _ V in the current servo cycle according to the following formulac+1：
Figure FDA0003629375220000011
Wherein S isc+1To the difference between the command position and the feedback position of the current servo cycleA value, the value of which is positive, but the direction is required to be positive in a direction pointing to the desired location point; n is a variable, and the value of n is as follows:
Figure FDA0003629375220000012
Figure FDA0003629375220000013
the error value error in the current servo period is calculated in the step 3 according to the following formula:
error＝Sc-Sc+1
wherein S iscBy the difference between the commanded position and the feedback position of the previous servo cycle, Sc+1The difference value between the command position and the feedback position of the current servo period is obtained;
and 4, calculating the error variation d _ error in the current servo period according to the following formula:
d_error＝error/T；
the specific processing method of the step 6 comprises the following steps:
if abs (feedback _ V)c-Req_Vc+1)Δ V ≦ the desired speed Req _ V in the current servo cyclec+1No correction is made;
if abs (feedback _ V)c-Req_Vc+1)Δ V, the following is performed:
when the Req _ Vc+1＞feedback_VcThen Δ V does not need to be corrected and the desired speed Req _ V in the current servo cycle is adjustedc+1Corrected to feedback _ Vc+ΔV；
When the feedback _ Vc＞Req_Vc+1Then, Δ V is corrected to Δ V' ═ a × T, and the desired speed Req _ V in the current servo cycle is corrected to Δ V ═ a × Tc+1Corrected to feedback _ Vc- Δ V', in the above formula,
Figure FDA0003629375220000021
in the above formula, Sc+1The difference between the command position and the feedback position of the current servo cycle is obtained.
2. The numerical control system single-axis error adjustment algorithm based on speed steps as claimed in claim 1, characterized in that: step 1 is to calculate the maximum speed step value Δ V of the shaft according to the following formula:
ΔV＝A max×0.1×eε×T
wherein e epsilon is an error correction coefficient of the axis, and A max is a maximum acceleration value.
3. The numerical control system single-axis error adjustment algorithm based on speed steps as claimed in claim 2, characterized in that: the value range of the error correction coefficient e epsilon of the axis is as follows: e epsilon is more than or equal to 0.1 and less than or equal to 2.
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