CN113885443A - Linear acceleration and deceleration control method based on segmented filtering and acceleration limiting - Google Patents

Linear acceleration and deceleration control method based on segmented filtering and acceleration limiting Download PDF

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CN113885443A
CN113885443A CN202010637796.7A CN202010637796A CN113885443A CN 113885443 A CN113885443 A CN 113885443A CN 202010637796 A CN202010637796 A CN 202010637796A CN 113885443 A CN113885443 A CN 113885443A
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acceleration
maximum
deceleration
speed
filtering
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CN113885443B (en
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王家恒
封雨鑫
高云峰
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Shenzhen Han's Smart Control Technology Co ltd
Han s Laser Technology Industry Group Co Ltd
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Shenzhen Han's Smart Control Technology Co ltd
Han s Laser Technology Industry Group Co Ltd
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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
    • G05B19/416—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 of velocity, acceleration or deceleration
    • G05B19/4166—Controlling feed or in-feed
    • 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
    • G05B19/41—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 interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and the rate of travel along that 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
    • G05B2219/30—Nc systems
    • G05B2219/43—Speed, acceleration, deceleration control ADC
    • G05B2219/43001—Speed, feed, infeed, acceleration, stopping problems
    • 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 embodiment of the application belongs to the technical field of numerical control, and relates to a linear acceleration and deceleration control method based on segmented filtering and acceleration limiting. The technical scheme provided by the application comprises the following steps: acquiring a filtering compensation increment according to the motion condition; obtaining interpolation increment under boundary conditions; judging the time state of the movement according to conditions, and acquiring the maximum speed, the maximum acceleration and the maximum deceleration which can be achieved in the actual movement process; acquiring a filtering length in the acceleration and deceleration process by using the acceleration in a segmentation manner; and discretizing the continuous speed plan by using a linear acceleration and deceleration method to improve the interpolation precision of the motion. Through calculation planning of linear acceleration and deceleration, the motion process is easy to discretize; through the sectional filtering, the smooth transition of the acceleration is realized, the impact vibration is prevented from occurring during the motion transition, the motion is more reasonable, and the transition filtering phenomenon can not occur even if the difference between the acceleration time and the deceleration time is larger.

Description

Linear acceleration and deceleration control method based on segmented filtering and acceleration limiting
Technical Field
The application relates to the technical field of numerical control, in particular to a linear acceleration and deceleration control method based on segmented filtering and acceleration limiting.
Background
The numerical control machine tool needs to move according to a preset track in the working process, and in order to reduce the impact or oscillation phenomenon at the corner or at the start-stop position, reasonable acceleration and deceleration control must be performed on the machine tool, so that the machining efficiency and the service life of the machine tool are improved.
The acceleration and deceleration control method applied to the numerical control system has a plurality of control methods, such as the conventional linear deceleration, seven-segment S-shaped acceleration and deceleration, trigonometric function acceleration and deceleration and the like. The conventional linear deceleration model has small calculated amount and obvious acceleration and deceleration effects, so the motion efficiency is higher, but the generated acceleration has a jump phenomenon and larger impact force on a machine tool, so the linear deceleration model is only suitable for a low-speed motion control process. The seven-segment S-shaped acceleration and deceleration control model is relatively complex in structure, the acceleration is gradually increased or decreased by the method, the effect of continuous acceleration is achieved, the impact force generated in the motion process is well reduced, the calculated motion time is usually not integral multiple of an interpolation period, if the interpolation integral time in the last period is less than the displacement of one period, the motion is suddenly changed, if the last interpolation period is ignored, the motion is not accurate enough, and the phenomenon is difficult to eliminate due to the fact that the model has more parameter limitation in structure. The acceleration and the jerk of the trigonometric function acceleration and deceleration control method are continuous, so the smoothness of the movement is good, but the calculation is realized by a table look-up mode, the calculation efficiency is not high enough, the model only reaches the maximum acceleration at one time point, the movement response is not rapid enough, and the acceleration and deceleration efficiency is relatively low. The linear acceleration and deceleration model based on the filtering technology has good motion characteristics, but a general model uses a filtering length to carry out filtering smoothing on the acceleration and deceleration processes, and when the difference between the acceleration time and the deceleration time is increased, the effect after filtering is poor.
Disclosure of Invention
The invention aims to provide a linear acceleration and deceleration control method based on segmented filtering and acceleration limiting, and solves the technical problem that the effect is poor after filtering in the conventional filtering technology.
In order to solve the above-mentioned problems, embodiments of the present invention provide the following technical solutions:
a linear acceleration and deceleration control method based on segmented filtering and acceleration limiting is characterized by comprising the following steps:
acquiring a filtering compensation increment according to the motion condition;
obtaining interpolation increment under boundary conditions;
judging the time state of the movement according to conditions, and acquiring the maximum speed, the maximum acceleration and the maximum deceleration which can be achieved in the actual movement process;
acquiring a filtering length in the acceleration and deceleration process by using the acceleration in a segmentation manner;
and discretizing the continuous speed plan by using a linear acceleration and deceleration method to improve the interpolation precision of the motion.
Further, the step of obtaining a filter compensation increment according to the motion condition comprises:
acquiring data parameters during linear acceleration and deceleration filtering according to motion conditions of a motion path, a maximum allowable speed, a starting speed and a tail speed of a machine tool, wherein in the process of single-segment motion, when the single-segment motion comprises acceleration or deceleration, the initial instantaneous speed and the tail instantaneous speed are respectively VsAnd VeThe maximum acceleration is a, and the target displacement is StargetFiltering linear acceleration and deceleration by using a sliding mean filtering method to enable the acceleration to gradually rise or fall and eliminate acceleration mutation, and filtering the speed of the ith interpolation period
Figure BDA0002565935410000021
Can be expressed as:
Figure BDA0002565935410000022
in the formula, FiFor interpolating speed after dispersion
Figure BDA0002565935410000031
Where L is the filter length, TsFor interpolating the period, taking the period time as a unit quantity, TsT is the number of interpolation cycles before filtering, and the total number of interpolation cycles after filtering is TLT + L-1, A is the interpolated acceleration after dispersion, if the deceleration process is the formula
Figure BDA0002565935410000032
Where a is-D, D is the interpolated deceleration after dispersion;
respectively interpolating the increment with the same instantaneous speed at the beginning and the end, and then adding all the interpolation increments after the linear filtering to obtain the total displacement Sf：
Figure BDA0002565935410000033
Wherein,
Figure BDA0002565935410000034
order to
Figure BDA0002565935410000035
The filtered total displacement Sf＝Starget+Sp，SpCompensating for the delta for filtering;
after filtering, the acceleration obtained by interpolation planning is continuous in a segmented manner, and the acceleration A and the Jerk are as follows:
Figure BDA0002565935410000036
further, the step of obtaining the interpolation increment under the boundary condition includes:
calculating the filtering length L of different stages according to the maximum jerk value J1、L2Wherein L is1For the filter length of the acceleration phase, L2For the filtering length in the deceleration stage, before interpolation dispersion, the maximum allowable speed is VmMaximum acceleration and maximum deceleration is au、adThe total target displacement amount is S,
in the rising phase, its displacement increment Starget1Comprises the following steps:
Figure BDA0002565935410000041
in the descending phase, its displacement is increased by an amount Starget2Comprises the following steps:
Figure BDA0002565935410000042
according to the formula
Figure BDA0002565935410000043
Can be provided with
Figure BDA0002565935410000044
The total displacement amount S is:
Figure BDA0002565935410000045
maximum speed V due to limitation of motion condition parametersmMaximum acceleration auAnd maximum deceleration adThe maximum speed which can be actually achieved after filtering is Vm' the maximum acceleration and deceleration that can be actually achieved is au' and ad', can be divided into case pair formula
Figure BDA0002565935410000046
Solving is carried out when the tail speed is greater than the initial speed, i.e. Vs≤VeThe calculation process of (a) is as follows; when the final speed is less than the initial speed, i.e. Vs>VeThe calculation process of (2) is consistent with the solving method,
when V iss≤VeWhen the temperature of the water is higher than the set temperature,
speed at which maximum deceleration is achievable
Figure BDA0002565935410000047
Substituting into formula
Figure BDA0002565935410000048
Then obtaining:
Figure BDA0002565935410000049
speed at which maximum acceleration is achievable
Figure BDA0002565935410000051
Substituting into formula
Figure BDA0002565935410000052
Then obtaining:
Figure BDA0002565935410000053
in the formula
Figure BDA0002565935410000054
In order of Vm1＝VmTo obtain Sk1(ii) a In the formula
Figure BDA0002565935410000055
In order of Vm2＝VmTo obtain Sk2When the maximum acceleration is not reached and the maximum deceleration is not reached, the actual acceleration is
Figure BDA0002565935410000056
The actual deceleration is
Figure BDA0002565935410000057
Make into a formula
Figure BDA0002565935410000058
Then obtain Sk3。
Further, the step of judging the time state of the movement through the condition and acquiring the maximum speed, the maximum acceleration and the maximum deceleration which can be achieved in the actual movement process comprises the following steps:
let the time of acceleration, uniform speed and deceleration stage be t1、t2And t3，
When V ism2>VeWhen the temperature of the water is higher than the set temperature,
case 1.1: vm≥Vm1，
If S is greater than or equal to Sk1To obtain a result 1: can reach the maximum set maximum speed, and the maximum acceleration and deceleration can reach SK＝Sk1，
If Sm1≤S<Sk1To obtain a result 2: the set maximum speed can not be reached, the maximum acceleration and deceleration can be reached,
if Sm2≤S<Sm1To obtain a result 3: the set maximum speed, the maximum deceleration, the maximum acceleration,
if S is less than or equal to Sm2To obtain a result 4: the set maximum speed, the maximum deceleration and the maximum acceleration cannot be reached;
case 1.2: vm2≤Vm<Vm1，
If S is greater than or equal to Sk2To obtain a result of 5: a set maximum speed is reached, a maximum deceleration cannot be reached, a maximum acceleration can be reached, SK＝Sk2，
If Sm2≤S<Sk2To obtain a result of 6: the set maximum speed, the maximum deceleration, the maximum acceleration,
if S<Sm2To obtain a result 7: the set maximum speed and the maximum deceleration cannot be reachedDegree, maximum acceleration cannot be achieved;
case 1.3: vm<Vm2，
If S is greater than or equal to Sk3To obtain a result of 8: can reach the set maximum speed, can not reach the maximum deceleration, can not reach the maximum acceleration, SK＝Sk3，
If S<Sk3To obtain a result of 9: the set maximum speed, maximum deceleration, maximum acceleration,
when V ism2≤VeWhen the temperature of the water is higher than the set temperature,
case 2.1: vm≥Vm1，
If S is greater than or equal to Sk1To obtain the results 1 which were obtained,
if Sm1≤S<Sk1To obtain the result 2,
if S<Sm1To obtain a result 3;
case 2.2: vm<Vm1，
If S is greater than or equal to Sk2And a solution was obtained in which, as a result 5,
if S<Sk2Obtaining a result 6;
if the above results reach the maximum set speed and the maximum acceleration and the maximum deceleration can be reached, the parameters that can be reached and the time t for rising, uniform speed and falling are obtained1,t2,t3Respectively as follows:
Figure BDA0002565935410000071
for the case that the maximum acceleration is not reached, let
Figure BDA0002565935410000072
For the case that the maximum deceleration is not reached, let
Figure BDA0002565935410000073
Then bring it into the formula
Figure BDA0002565935410000074
Solution V by dichotomymIf the set maximum speed is not reached, let SKSubstituted into formula S
Figure BDA0002565935410000075
The actual arriving parameters and the rising, uniform and falling time.
Further, the step of acquiring the filter length in the acceleration and deceleration process by using the jerk segment includes:
the obtained filter length is:
Figure BDA0002565935410000076
wherein [. cndot. ] represents rounding.
Further, the discretizing the continuous speed plan by the linear acceleration and deceleration method to improve the interpolation accuracy of the motion includes:
discrete interpolation time, fine tuning maximum speed;
and (5) sliding filtering processing.
Further, the step of interpolating the time discrete interpolation and fine-tuning the maximum speed comprises:
the interpolation time of each stage after dispersion is T1、T2And T3The process is as follows:
Figure BDA0002565935410000077
recalculate the maximum speed that can be actually reached after fine tuning:
Figure BDA0002565935410000078
the acceleration and deceleration after fine adjustment are:
Figure BDA0002565935410000081
further, the sliding filter processing step includes:
substituting the discretized parameters into a formula
Figure BDA0002565935410000082
I is not less than 1 but not more than T + L-1, L is not less than 1 and
Figure BDA0002565935410000083
and performing interpolation calculation.
Further, after the sliding filter processing step, the method further includes:
and outputting the feed amount of each interpolation period.
Compared with the prior art, the embodiment of the invention mainly has the following beneficial effects:
a linear acceleration and deceleration control method based on segmented filtering and acceleration limiting is easy to discretize a motion process through calculation planning of linear acceleration and deceleration; by means of segmented filtering, smooth transition of acceleration is achieved, impact vibration during motion transition is prevented, filtering lengths during acceleration and deceleration can be calculated according to specific motion conditions, motion is more reasonable, and transition filtering is avoided even if the difference between acceleration time and deceleration time is large; the acceleration generated in the motion process is limited, and the mechanical characteristics of the machine tool can be exerted to the maximum extent in the motion process through the maximum acceleration.
Drawings
In order to illustrate the solution of the invention more clearly, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are some embodiments of the invention, and that other drawings may be derived from these drawings by a person skilled in the art without inventive effort.
FIG. 1 is a block diagram of a flow chart of a linear acceleration/deceleration control method based on segmented filtering and jerk limiting according to an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating the planning effect of interpolation speed and acceleration of 5-segment continuous motion according to an embodiment of the present invention;
fig. 3 is a schematic diagram illustrating the effect of jerk planning for 5-segment continuous motion in the embodiment of the present invention.
Detailed Description
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The terms "comprising" and "having," and any variations thereof, in the description and claims of the present invention and the description of the above figures are intended to cover non-exclusive inclusions. The terms "first," "second," and the like in the description and in the claims, or in the drawings, are used for distinguishing between different objects and not necessarily for describing a particular sequential order.
Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the invention. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. It is explicitly and implicitly understood by one skilled in the art that the embodiments described herein can be combined with other embodiments.
In order to make the technical solutions of the present invention better understood by those skilled in the art, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the relevant drawings.
Examples
A linear acceleration and deceleration control method based on segmented filtering and acceleration limiting comprises the following steps:
acquiring a filtering compensation increment according to the motion condition;
obtaining interpolation increment under boundary conditions;
judging the time state of the movement according to conditions, and acquiring the maximum speed, the maximum acceleration and the maximum deceleration which can be achieved in the actual movement process;
acquiring a filtering length in the acceleration and deceleration process by using the acceleration in a segmentation manner;
and discretizing the continuous speed plan by using a linear acceleration and deceleration method to improve the interpolation precision of the motion.
The invention utilizes the characteristic that the linear acceleration and deceleration is convenient to calculate, and uses the interpolation period time to reversely deduce the acceleration, so that the motion process is discretized; the head-tail interpolation speed can be different from zero, so that continuous processing operation of multiple tracks is facilitated; the acceleration in the acceleration and deceleration process is smoothly transited by using a segmented filtering method, the filtering length in the acceleration and deceleration process is calculated by the segmented filtering according to specific parameters in the motion, and a good motion effect can be achieved after the filtering even if the difference between the acceleration time and the deceleration time is large; the maximum acceleration of the motion after filtering is limited, so that the machine tool can exert the mechanical performance to the maximum extent within an allowable range.
The step of obtaining a filter compensation increment according to the motion condition comprises the following steps:
acquiring data parameters during linear acceleration and deceleration filtering according to motion conditions of a motion path, a maximum allowable speed, a starting speed and a tail speed of a machine tool, wherein in the process of single-segment motion, when the single-segment motion comprises acceleration or deceleration, the initial instantaneous speed and the tail instantaneous speed are respectively VsAnd VeThe maximum acceleration is a, and the target displacement is StargetFiltering linear acceleration and deceleration by using a sliding mean filtering method to enable the acceleration to gradually rise or fall and eliminate acceleration mutation, and filtering the speed of the ith interpolation period
Figure BDA0002565935410000101
Can be expressed as:
Figure BDA0002565935410000102
1≤i≤T+L-1,1≤L
in the formula, FiFor interpolating speed after dispersion
Figure BDA0002565935410000103
Where L is the filter length, TsFor interpolating the period, taking the period time as a unit quantity, TsT is the number of interpolation cycles before filtering, and the total number of interpolation cycles after filtering is TLT + L-1, A is the interpolated acceleration after dispersion, if the deceleration process is the formula
Figure BDA0002565935410000111
Where a is-D, D is the interpolated deceleration after dispersion;
respectively interpolating the increment with the same instantaneous speed at the beginning and the end, and then adding all the interpolation increments after the linear filtering to obtain the total displacement Sf：
Figure BDA0002565935410000112
Wherein,
Figure BDA0002565935410000113
order to
Figure BDA0002565935410000114
The filtered total displacement Sf＝Starget+Sp，SpCompensating for the delta for filtering;
after filtering, the acceleration obtained by interpolation planning is continuous in a segmented manner, and the acceleration A and the Jerk are as follows:
Figure BDA0002565935410000115
the step of obtaining the interpolation increment under the boundary condition comprises the following steps:
according to maximum accelerationThe value J is used for calculating the filtering length L of different stages1、L2Wherein L is1For the filter length of the acceleration phase, L2For the filtering length in the deceleration stage, before interpolation dispersion, the maximum allowable speed is VmMaximum acceleration and maximum deceleration is au、adThe total target displacement amount is S,
in the rising phase, its displacement increment Starget1Comprises the following steps:
Figure BDA0002565935410000116
in the descending phase, its displacement is increased by an amount Starget2Comprises the following steps:
Figure BDA0002565935410000121
according to the formula
Figure BDA0002565935410000122
Can be provided with
Figure BDA0002565935410000123
The total displacement amount S is:
Figure BDA0002565935410000124
it should be noted that the maximum speed V is limited by the motion condition parametersmMaximum acceleration auAnd maximum deceleration adNot all can be reached during the movement. The maximum speed which can be actually reached after filtering is Vm' the maximum acceleration and deceleration that can be actually achieved is au' and ad'. Can be divided into a formula
Figure BDA0002565935410000125
The solution is carried out, only when the tail speed is larger than the initial speed, i.e. V, will be discusseds≤VeThe calculation process of (2); if the final speed is smaller than the initial speed, the solving method is consistent.
Maximum speed V due to limitation of motion condition parametersmMaximum acceleration auAnd maximum deceleration adThe maximum speed which can be actually achieved after filtering is Vm' the maximum acceleration and deceleration that can be actually achieved is au' and ad', can be divided into case pair formula
Figure BDA0002565935410000126
Solving is carried out when the tail speed is greater than the initial speed, i.e. Vs≤VeThe calculation process of (a) is as follows; when the final speed is less than the initial speed, i.e. Vs>VeThe calculation process of (2) is consistent with the solving method,
when V iss≤VeWhen the temperature of the water is higher than the set temperature,
speed at which maximum deceleration is achievable
Figure BDA0002565935410000127
Substituting into formula
Figure BDA0002565935410000131
Then obtaining:
Figure BDA0002565935410000132
speed at which maximum acceleration is achievable
Figure BDA0002565935410000133
Substituting into formula
Figure BDA0002565935410000134
Then obtaining:
Figure BDA0002565935410000135
at publicFormula (II)
Figure BDA0002565935410000136
In order of Vm1＝VmTo obtain Sk1(ii) a In the formula
Figure BDA0002565935410000137
In order of Vm2＝VmTo obtain Sk2When the maximum acceleration is not reached and the maximum deceleration is not reached, the actual acceleration is
Figure BDA0002565935410000138
The actual deceleration is
Figure BDA0002565935410000139
Make into a formula
Figure BDA00025659354100001310
Then obtain Sk3。
The step of judging the time state of the movement according to the conditions and acquiring the maximum speed, the maximum acceleration and the maximum deceleration which can be achieved in the actual movement process comprises the following steps of:
let the time of acceleration, uniform speed and deceleration stage be t1、t2And t3，
When V ism2>VeWhen the temperature of the water is higher than the set temperature,
case 1.1: vm≥Vm1，
If S is greater than or equal to Sk1To obtain a result 1: can reach the maximum set maximum speed, and the maximum acceleration and deceleration can reach SK＝Sk1，
If Sm1≤S<Sk1To obtain a result 2: the set maximum speed can not be reached, the maximum acceleration and deceleration can be reached,
if Sm2≤S<Sm1To obtain a result 3: the set maximum speed, the maximum deceleration, the maximum acceleration,
if S is less than or equal to Sm2To obtain a result 4: cannot reach the set maximum speed, does notThe maximum deceleration can be reached, and the maximum acceleration cannot be reached;
case 1.2: vm2≤Vm<Vm1，
If S is greater than or equal to Sk2To obtain a result of 5: a set maximum speed is reached, a maximum deceleration cannot be reached, a maximum acceleration can be reached, SK＝Sk2，
If Sm2≤S<Sk2To obtain a result of 6: the set maximum speed, the maximum deceleration, the maximum acceleration,
if S<Sm2To obtain a result 7: the set maximum speed, the maximum deceleration and the maximum acceleration cannot be reached;
case 1.3: vm<Vm2，
If S is greater than or equal to Sk3To obtain a result of 8: can reach the set maximum speed, can not reach the maximum deceleration, can not reach the maximum acceleration, SK＝Sk3，
If S<Sk3To obtain a result of 9: the set maximum speed, maximum deceleration, maximum acceleration,
when V ism2≤VeWhen the temperature of the water is higher than the set temperature,
case 2.1: vm≥Vm1，
If S is greater than or equal to Sk1To obtain the results 1 which were obtained,
if Sm1≤S<Sk1To obtain the result 2,
if S<Sm1To obtain a result 3;
case 2.2: vm<Vm1，
If S is greater than or equal to Sk2And a solution was obtained in which, as a result 5,
if S<Sk2Obtaining a result 6;
if the above results reach the maximum set speed and the maximum acceleration and the maximum deceleration can be reached, the parameters that can be reached and the time t for rising, uniform speed and falling are obtained1,t2,t3Are respectively as：
Figure BDA0002565935410000151
For the case that the maximum acceleration is not reached, let
Figure BDA0002565935410000152
For the case that the maximum deceleration is not reached, let
Figure BDA0002565935410000153
Then bring it into the formula
Figure BDA0002565935410000154
Solution V by dichotomymIf the set maximum speed is not reached, let SKSubstituted into formula S
Figure BDA0002565935410000155
The actual arriving parameters and the rising, uniform and falling time.
Further, the step of acquiring the filter length in the acceleration and deceleration process by using the jerk segment includes:
the obtained filter length is:
Figure BDA0002565935410000156
wherein [. cndot. ] represents rounding.
The step of carrying out discretization processing on the continuous speed plan by using a linear acceleration and deceleration method to improve the interpolation precision of the motion comprises the following steps:
discrete interpolation time, fine tuning maximum speed;
and (5) sliding filtering processing.
The step of fine tuning the maximum speed by the discrete interpolation time comprises the following steps:
the interpolation time of each stage after dispersion is T1、T2And T3The process is as follows:
Figure BDA0002565935410000157
recalculate the maximum speed that can be actually reached after fine tuning:
Figure BDA0002565935410000161
the acceleration and deceleration after fine adjustment are:
Figure BDA0002565935410000162
the sliding filter processing step includes:
substituting the discretized parameters into a formula
Figure BDA0002565935410000163
I is not less than 1 but not more than T + L-1, L is not less than 1 and
Figure BDA0002565935410000164
and performing interpolation calculation. After the sliding filter processing step, the method further comprises:
and outputting the feed amount of each interpolation period.
Simulation verification: the machine tool parameters in the numerical control system are set as follows: interpolation period Ts1ms, the maximum acceleration and deceleration is au＝2000mm/s2,ad＝2000mm/s2Converted into periodic unitsu＝2μm/ms2,ad＝2μm/ms2The maximum Jerk value J is 0.2 μm/ms3。
The motion process is divided into 5 sections, and the target distance S and the initial instantaneous speed V of each sectionsEnd instantaneous velocity VeAnd a reference maximum speed VmAs shown in the upper part of table 1, the end instantaneous speed of each segment is the same as the initial instantaneous speed of the next segment to ensure continuity of motion. After calculation, the trueMaximum speed V of real arrivalm', rise stage filter length L1Filter length L in the falling phase2Discrete acceleration uniform speed and deceleration time T1、T2、T3As shown in the lower portion of table 1. The data show that the actual maximum speed that can be achieved is within the maximum allowed value, and the actual maximum speed after discrete fine adjustment is occasionally slightly larger than the allowed value, but the movement effect is not influenced. After the filtering length is calculated in a segmented mode, the filtering lengths in the acceleration process and the deceleration process are not necessarily equal, and the phenomenon of transition filtering caused by the fact that the same filtering length is used in the whole acceleration and deceleration movement process is avoided. The discrete acceleration and deceleration time is integral multiple of the interpolation period, and accurate interpolation can be carried out.
TABLE 1 initialization conditions and calculation results for each motion process
Figure BDA0002565935410000171
The speed change and the acceleration change of 5 sections in the operation process are shown in FIG. 2, and the speed curve is smooth and can be guided; the acceleration of the machine tool is continuously changed within an allowable range, so that the jumping phenomenon does not exist, and the impact on the machine tool is reduced. The variation of the jerk in the motion process is as shown in fig. 3, and the jerk is kept at the maximum value in the uneven acceleration or uneven deceleration stage, so that the jerk does not exceed the maximum value excessively, and the mechanical performance of the machine tool is exerted to the maximum extent within the condition allowable range.
According to the linear acceleration and deceleration control method based on the segmented filtering and the acceleration limiting, provided by the embodiment of the invention, through calculation planning of linear acceleration and deceleration, a motion process is easy to discretize; by means of segmented filtering, smooth transition of acceleration is achieved, impact vibration during motion transition is prevented, filtering lengths during acceleration and deceleration can be calculated according to specific motion conditions, motion is more reasonable, and transition filtering is avoided even if the difference between acceleration time and deceleration time is large; the acceleration generated in the motion process is limited, and the mechanical characteristics of the machine tool can be exerted to the maximum extent in the motion process through the maximum acceleration.
It is to be understood that the above-described embodiments are merely illustrative of some, but not restrictive, of the broad invention, and that the appended drawings illustrate preferred embodiments of the invention without limiting its scope. This invention may be embodied in many different forms and, on the contrary, these embodiments are provided so that this disclosure will be thorough and complete. Although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that various changes in the embodiments and modifications can be made, and equivalents may be substituted for elements thereof. All equivalent structures made by using the contents of the specification and the attached drawings of the invention can be directly or indirectly applied to other related technical fields, and are also within the protection scope of the patent of the invention.

Claims (9)

1. A linear acceleration and deceleration control method based on segmented filtering and acceleration limiting is characterized by comprising the following steps:
acquiring a filtering compensation increment according to the motion condition;
obtaining interpolation increment under boundary conditions;
judging the time state of the movement according to conditions, and acquiring the maximum speed, the maximum acceleration and the maximum deceleration which can be achieved in the actual movement process;
acquiring a filtering length in the acceleration and deceleration process by using the acceleration in a segmentation manner;
and discretizing the continuous speed plan by using a linear acceleration and deceleration method to improve the interpolation precision of the motion.
2. The linear acceleration/deceleration control method based on segmented filtering and jerk limiting of claim 1,
the step of obtaining a filter compensation increment according to the motion condition comprises the following steps:
according to the movement path, maximum allowable speed, starting speed and ending speed of the machine toolThe motion condition of the degree, data parameters when obtaining straight line acceleration and deceleration filtering, in the single-stage motion process, when the single-stage motion includes acceleration or deceleration, its initial instantaneous speed and end instantaneous speed are respectively VsAnd VeThe maximum acceleration is a, and the target displacement is StargetFiltering linear acceleration and deceleration by using a sliding mean filtering method to enable the acceleration to gradually rise or fall and eliminate acceleration mutation, and filtering the speed of the ith interpolation period
Figure FDA0002565935400000013
Can be expressed as:
Figure FDA0002565935400000011
1≤i≤T+L-1,1≤L
in the formula, FiFor interpolating speed after dispersion
Figure FDA0002565935400000012
Where L is the filter length, TsFor interpolating the period, taking the period time as a unit quantity, TsT is the number of interpolation cycles before filtering, and the total number of interpolation cycles after filtering is TLT + L-1, A is the interpolated acceleration after dispersion, if the deceleration process is the formula
Figure FDA0002565935400000021
Where a is-D, D is the interpolated deceleration after dispersion;
respectively interpolating the increment with the same instantaneous speed at the beginning and the end, and then adding all the interpolation increments after the linear filtering to obtain the total displacement Sf：
Figure FDA0002565935400000022
Wherein，
Figure FDA0002565935400000023
Order to
Figure FDA0002565935400000024
The filtered total displacement Sf＝Starget+Sp，SpCompensating for the delta for filtering;
after filtering, the acceleration obtained by interpolation planning is continuous in segments, and the acceleration is
Figure FDA0002565935400000027
And Jerk is Jerk:
Figure FDA0002565935400000025
3. the linear acceleration/deceleration control method based on segmented filtering and jerk limiting of claim 2,
the step of obtaining the interpolation increment under the boundary condition comprises the following steps:
calculating the filtering length L of different stages according to the maximum jerk value J1、L2Wherein L is1For the filter length of the acceleration phase, L2For the filtering length in the deceleration stage, before interpolation dispersion, the maximum allowable speed is VmMaximum acceleration and maximum deceleration is au、adThe total target displacement amount is S,
in the rising phase, its displacement increment Starget1Comprises the following steps:
Figure FDA0002565935400000026
in the descending phase, its displacement is increased by an amount Starget2Comprises the following steps:
Figure FDA0002565935400000031
according to the formula
Figure FDA0002565935400000032
Can be provided with
Figure FDA0002565935400000033
The total displacement amount S is:
Figure FDA0002565935400000034
maximum speed V due to limitation of motion condition parametersmMaximum acceleration auAnd maximum deceleration adThe maximum speed which can be actually achieved after filtering is Vm' the maximum acceleration and deceleration that can be actually achieved is au' and ad', can be divided into case pair formula
Figure FDA0002565935400000035
Solving is carried out when the tail speed is greater than the initial speed, i.e. Vs≤VeThe calculation process of (a) is as follows; when the final speed is less than the initial speed, i.e. Vs>VeThe calculation process of (2) is consistent with the solving method,
when V iss≤VeWhen the temperature of the water is higher than the set temperature,
speed at which maximum deceleration is achievable
Figure FDA0002565935400000036
Substituting into formula
Figure FDA0002565935400000037
Then obtaining:
Figure FDA0002565935400000038
speed at which maximum acceleration is achievable
Figure FDA0002565935400000039
Substituting into formula
Figure FDA00025659354000000310
Then obtaining:
Figure FDA0002565935400000041
in the formula
Figure FDA0002565935400000042
In order of Vm1＝VmTo obtain Sk1(ii) a In the formula
Figure FDA0002565935400000043
In order of Vm2＝VmTo obtain Sk2When the maximum acceleration is not reached and the maximum deceleration is not reached, the actual acceleration is
Figure FDA0002565935400000044
The actual deceleration is
Figure FDA0002565935400000045
Make into a formula
Figure FDA0002565935400000046
Then obtain Sk3。
4. The linear acceleration/deceleration control method based on segmented filtering and jerk limiting of claim 3,
the step of judging the time state of the movement according to the conditions and acquiring the maximum speed, the maximum acceleration and the maximum deceleration which can be achieved in the actual movement process comprises the following steps of:
let the time of acceleration, uniform speed and deceleration stage be t1、t2And t3，
When V ism2>VeWhen the temperature of the water is higher than the set temperature,
case 1.1: vm≥Vm1，
If S is greater than or equal to Sk1To obtain a result 1: can reach the maximum set maximum speed, and the maximum acceleration and deceleration can reach SK＝Sk1，
If Sm1≤S<Sk1To obtain a result 2: the set maximum speed can not be reached, the maximum acceleration and deceleration can be reached,
if Sm2≤S<Sm1To obtain a result 3: the set maximum speed, the maximum deceleration, the maximum acceleration,
if S is less than or equal to Sm2To obtain a result 4: the set maximum speed, the maximum deceleration and the maximum acceleration cannot be reached;
case 1.2: vm2≤Vm<Vm1，
If S is greater than or equal to Sk2To obtain a result of 5: a set maximum speed is reached, a maximum deceleration cannot be reached, a maximum acceleration can be reached, SK＝Sk2，
If Sm2≤S<Sk2To obtain a result of 6: the set maximum speed, the maximum deceleration, the maximum acceleration,
if S<Sm2To obtain a result 7: the set maximum speed, the maximum deceleration and the maximum acceleration cannot be reached;
case 1.3: vm<Vm2，
If S is greater than or equal to Sk3To obtain a result of 8: can reach the set maximum speed, can not reach the maximum deceleration, can not reach the maximum acceleration, SK＝Sk3，
If S<Sk3To obtain a result of 9: the set maximum speed, maximum deceleration, maximum acceleration,
when V ism2≤VeWhen the temperature of the water is higher than the set temperature,
case 2.1: vm≥Vm1，
If S is greater than or equal to Sk1To obtain the results 1 which were obtained,
if Sm1≤S<Sk1To obtain the result 2,
if S<Sm1To obtain a result 3;
case 2.2: vm<Vm1，
If S is greater than or equal to Sk2And a solution was obtained in which, as a result 5,
if S<Sk2Obtaining a result 6;
if the above results reach the maximum set speed and the maximum acceleration and the maximum deceleration can be reached, the parameters that can be reached and the time t for rising, uniform speed and falling are obtained1,t2,t3Respectively as follows:
Figure FDA0002565935400000061
for the case that the maximum acceleration is not reached, let
Figure FDA0002565935400000062
For the case that the maximum deceleration is not reached, let
Figure FDA0002565935400000063
Then bring it into the formula
Figure FDA0002565935400000064
Solution V by dichotomymIf the set maximum speed is not reached, let SKSubstituted into formula S
Figure FDA0002565935400000065
The actual arriving parameters and the rising, uniform and falling time.
5. The linear acceleration/deceleration control method based on segmented filtering and jerk limiting as claimed in claim 4,
the step of acquiring the filter length in the acceleration and deceleration process by using the acceleration segmentation comprises the following steps:
the obtained filter length is:
Figure FDA0002565935400000066
wherein [. cndot. ] represents rounding.
6. The linear acceleration/deceleration control method based on segmented filtering and jerk limiting of claim 1,
the step of carrying out discretization processing on the continuous speed plan by using a linear acceleration and deceleration method to improve the interpolation precision of the motion comprises the following steps:
discrete interpolation time, fine tuning maximum speed;
and (5) sliding filtering processing.
7. The linear acceleration/deceleration control method based on segmented filtering and jerk limiting of claim 6,
the step of fine tuning the maximum speed by the discrete interpolation time comprises the following steps:
the interpolation time of each stage after dispersion is T1、T2And T3The process is as follows:
Figure FDA0002565935400000071
recalculate the maximum speed that can be actually reached after fine tuning:
Figure FDA0002565935400000072
the acceleration and deceleration after fine adjustment are:
Figure FDA0002565935400000073
8. the linear acceleration/deceleration control method based on segmented filtering and jerk limiting of claim 6,
the sliding filter processing step includes:
substituting the discretized parameters into a formula
Figure FDA0002565935400000074
I is not less than 1 but not more than T + L-1, L is not less than 1 and
Figure FDA0002565935400000075
and performing interpolation calculation.
9. The linear acceleration/deceleration control method based on segmented filtering and jerk limiting of claim 6,
after the sliding filter processing step, the method further comprises:
and outputting the feed amount of each interpolation period.
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