CN113885443B - Linear acceleration and deceleration control method based on piecewise filtering and jerk limiting - Google Patents
Linear acceleration and deceleration control method based on piecewise filtering and jerk limiting Download PDFInfo
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/416—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
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- 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
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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 piecewise filtering and jerk 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 motion by the condition, and acquiring the maximum speed, the maximum acceleration and the maximum deceleration which can be achieved in the actual motion process; acquiring a filtering length in the acceleration and deceleration process by utilizing the jerk segment; and discretizing continuous speed planning by using a linear acceleration and deceleration method so as to improve the interpolation precision of the motion. Through calculation planning of linear acceleration and deceleration, discretization is easy to carry out on the motion process; through sectional filtering, smooth transition of acceleration is realized, impact vibration is prevented from occurring during motion transition, so that motion is more reasonable, and transition filtering phenomenon can not occur even if the acceleration time and the deceleration time differ greatly.
Description
Technical Field
The application relates to the technical field of numerical control, in particular to a linear acceleration and deceleration control method based on piecewise filtering and limiting jerk.
Background
In order to reduce the impact or vibration phenomenon at the corner or the start-stop position, the numerical control machine tool needs to be reasonably accelerated and decelerated so as to improve the machining efficiency and the service life of the machine tool.
The acceleration and deceleration control methods applied to the numerical control system are many, such as conventional linear deceleration, seven-segment S-shaped acceleration and deceleration, trigonometric function acceleration and deceleration and other control methods. The conventional linear deceleration model has small calculated amount and obvious acceleration and deceleration effects, so that the motion efficiency is higher, but the generated acceleration has a jump phenomenon, and the impact force on a machine tool is larger, so that the method 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, so that the continuous acceleration effect is achieved, the impact force generated in the motion process is reduced, the calculated motion time is not an integral multiple of the interpolation period generally, if the interpolation integral time is smaller than the displacement of one period in the last period, the motion is suddenly changed, if the last interpolation period is ignored, the motion is inaccurate, and the model has more parameter limitations in construction, so that the phenomenon is difficult to eliminate. The acceleration and deceleration control method of the trigonometric function is continuous in acceleration and deceleration, so that the smoothness of movement is good, calculation is realized in a table look-up mode, the calculation efficiency is not high enough, the model reaches the maximum acceleration only 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 the general model uses a filtering length to carry out filtering smoothing on 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 application aims to provide a linear acceleration and deceleration control method based on piecewise filtering and jerk limiting, which solves the technical problem of poor filtering effect of the existing filtering technology.
In order to solve the above-mentioned problems, the embodiment of the present application provides the following technical solutions:
a linear acceleration and deceleration control method based on piecewise filtering and jerk 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 motion by the condition, and acquiring the maximum speed, the maximum acceleration and the maximum deceleration which can be achieved in the actual motion process;
acquiring a filtering length in the acceleration and deceleration process by utilizing the jerk segment;
and discretizing continuous speed planning by using a linear acceleration and deceleration method so as to improve the interpolation precision of the motion.
Further, the step of obtaining the filter compensation increment according to the motion condition includes:
according to the motion conditions of the motion path, the maximum allowable speed, the initial speed and the final speed of the machine tool, acquiring data parameters during linear acceleration and deceleration filtering, wherein in the single-segment motion process, when the single-segment motion comprises acceleration or deceleration, the initial instantaneous speed and the final instantaneous speed are respectively V s And V is equal to e Maximum acceleration is a, target displacement is S target The linear acceleration and deceleration is filtered by a sliding average filtering method, so that the acceleration is gradually increased or decreased, the acceleration mutation is eliminated, and the speed after the i-th interpolation period is filteredCan be expressed as:
wherein F is i Is the interpolation speed after the discretization
Wherein L is the filtering length, T s For interpolation period, T is calculated by taking period time as unit quantity s =1, T is the number of interpolation cycles before filtering, and the total number of interpolation cycles after filtering is T L The value of =T+L-1, A is the interpolation speed after the discretization, if the value is the deceleration process, the formula is given byA= -D, D being the discrete interpolated deceleration;
inserted at the beginning and end respectivelyThe increment which is the same as the initial and final instantaneous speeds is added to all the interpolation increments after the linear filtering to obtain the total displacement S f ：
Wherein,order the
The filtered total displacement S f ＝S target +S p ，S p Compensating the delta for filtering;
after filtering, the acceleration obtained by interpolation planning is piecewise continuous, and the acceleration A and the Jerk are Jerk:
further, the step of obtaining interpolation increment under the boundary condition includes:
calculating the filtering length L of different stages according to the maximum jerk value J 1 、L 2 Wherein L is 1 To accelerate the filtering length of the stage, L 2 For the filtering length of the deceleration stage, the maximum allowable speed is V before interpolation dispersion m Maximum acceleration and maximum deceleration of a u 、a d The total target displacement amount is S,
in the rising phase, its displacement increment S target1 The method comprises the following steps:
in the descent phase, its displacement increment S target2 The method comprises the following steps:
according to the formulaCan be provided with +.>The total displacement S is:
maximum speed V due to limitation of motion condition parameters m Maximum acceleration a u Maximum deceleration a d Not all can be reached in the motion process, so that the maximum speed which can be actually reached after filtering is V m ' the maximum acceleration and deceleration actually achievable is a u ' and a d ' the formula can be divided into case pairsSolving, when the end speed is greater than the initial speed, i.e. V s ≤V e The calculation process of (1) is as follows; when the final speed is less than the initial speed, i.e. V s >V e Is consistent with the method of solving,
when V is s ≤V e In the time-course of which the first and second contact surfaces,
speed at which maximum deceleration is achievableCarry-over formulaThe following steps are obtained:
speed at which maximum acceleration is achievableCarry-over formulaThe following steps are obtained:
in the formulaIn order V m1 ＝V m Obtaining S k1 The method comprises the steps of carrying out a first treatment on the surface of the In formula->In order V m2 ＝V m Obtaining S k2 When the maximum acceleration is not reachable and the maximum deceleration is not reachable, the actual acceleration is +.>The actual deceleration is->Let bring in formula->Obtaining S k3 。
Further, the step of judging the time state of the motion through the condition and obtaining the maximum speed, the maximum acceleration and the maximum deceleration which can be achieved in the actual motion process comprises the following steps:
the time of acceleration, uniform speed and deceleration stage is respectively t 1 、t 2 And t 3 ，
When V is m2 >V e In the time-course of which the first and second contact surfaces,
case 1.1: v (V) m ≥V m1 ，
If S is greater than or equal to S k1 Result 1: can reach the maximum set maximum speed and the maximum acceleration and deceleration, S K ＝S k1 ，
If S m1 ≤S<S k1 Result 2: the maximum speed cannot be set, the maximum acceleration and deceleration can be achieved,
if S m2 ≤S<S m1 Result 3: the set maximum speed cannot be reached, the maximum deceleration cannot be reached, the maximum acceleration can be reached,
if S is less than or equal to S m2 Results 4 were obtained: the maximum speed cannot be set, the maximum deceleration cannot be reached, and the maximum acceleration cannot be reached;
case 1.2: v (V) m2 ≤V m <V m1 ，
If S is greater than or equal to S k2 Result 5: up to a set maximum speed, not up to a maximum deceleration, up to a maximum acceleration, S K ＝S k2 ，
If S m2 ≤S<S k2 Result 6: the set maximum speed cannot be reached, the maximum deceleration cannot be reached, the maximum acceleration can be reached,
if S<S m2 Result 7: the maximum speed cannot be set, the maximum deceleration cannot be reached, and the maximum acceleration cannot be reached;
case 1.3: v (V) m <V m2 ，
If S is greater than or equal to S k3 Result 8: can reach the set maximum speed, can not reach the maximum deceleration, can not reach the maximum acceleration, S K ＝S k3 ，
If S<S k3 Result 9: the set maximum speed, the maximum deceleration, the maximum acceleration are not reached,
when V is m2 ≤V e In the time-course of which the first and second contact surfaces,
case 2.1: v (V) m ≥V m1 ，
If S is greater than or equal to S k1 A result 1 was obtained, which was obtained,
if S m1 ≤S<S k1 The result was obtained as a result 2,
if S<S m1 Obtaining a result 3;
case 2.2: v (V) m <V m1 ，
If S is greater than or equal to S k2 The result was obtained as a result 5,
if S<S k2 Obtaining a result 6;
for the above results, if the maximum set speed is reached and the maximum acceleration and the maximum deceleration are both reached, the parameters which can be actually reached and the time t of rising, uniform speed and falling are obtained 1 ,t 2 ,t 3 The method comprises the following steps of:
for the case of not reaching the maximum acceleration, letFor the case where the maximum deceleration is not reached, +.>Then bring it into the formula +.>Solving V by dichotomy m ' if the set maximum speed is not reached, let S K =s, bring in formula->Parameters that can be actually reached and the time of rising, uniform speed and falling.
Further, the step of obtaining the filter length in the acceleration and deceleration process by using the jerk segment includes:
the obtained filter length is as follows:
wherein [ (DEG ] represents rounding).
Further, the discrete processing is performed on the continuous speed plan by using a linear acceleration and deceleration method, so as to improve the interpolation precision of the motion, and the method comprises the following steps:
discrete interpolation time, fine tuning maximum speed;
and (5) sliding filtering treatment.
Further, the discrete interpolation time, the step of fine tuning the maximum speed includes:
the interpolation time of each stage after the discretization is T 1 、T 2 And T 3 The process comprises the following steps:
recalculating the actual maximum speed that can be reached after trimming:
the acceleration and deceleration after fine tuning are:
further, the sliding filter processing step includes:
the discrete parameters are put into a formulaI is more than or equal to 1 and less than or equal to T+L-1, and L and>interpolation calculation is performed.
Further, after the sliding filter processing step, the method further includes:
the feed amount per interpolation period is output.
Compared with the prior art, the embodiment of the application has the following main beneficial effects:
a linear acceleration and deceleration control method based on piecewise filtering and limiting jerk is easy to discretize a motion process through calculation planning of linear acceleration and deceleration; the smooth transition of acceleration is realized through sectional filtering, impact vibration is prevented from occurring during motion transition, and the filtering length during acceleration and deceleration can be calculated respectively according to specific motion conditions, so that the motion is more reasonable, and the phenomenon of transition filtering does not occur even if the acceleration time and the deceleration time differ greatly; the jerk occurring in the motion process is limited, and the mechanical characteristics of the machine tool can be furthest exerted in the motion process by maximizing the jerk.
Drawings
In order to more clearly illustrate the solution of the present application, a brief description will be given below of the drawings required for the description of the embodiments, it being apparent that the drawings in the following description are some embodiments of the present application and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a linear acceleration and deceleration control method based on piecewise filtering and jerk limitation in an embodiment of the application;
FIG. 2 is a schematic diagram showing the effect of interpolation speed and acceleration of 5-segment continuous motion in the embodiment of the present application;
fig. 3 is a schematic diagram showing the effect of jerk of 5-segment continuous motion in accordance with an embodiment of the present application.
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 application belongs. The terminology used herein in the description of the application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The terms "comprising" and "having" and any variations thereof in the description of the application and the claims and the foregoing description of the drawings are intended to cover non-exclusive inclusions. The terms first, second and the like in the description and in the claims or in the above-described figures, are used for distinguishing between different objects and not necessarily for describing a sequential or chronological order.
Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment may be included in at least one embodiment of the application. The appearances of such phrases 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. Those of skill in the art will explicitly and implicitly appreciate that the embodiments described herein may be combined with other embodiments.
In order to enable those skilled in the art to better understand the present application, a technical solution of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.
Examples
A linear acceleration and deceleration control method based on piecewise filtering and jerk 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 motion by the condition, and acquiring the maximum speed, the maximum acceleration and the maximum deceleration which can be achieved in the actual motion process;
acquiring a filtering length in the acceleration and deceleration process by utilizing the jerk segment;
and discretizing continuous speed planning by using a linear acceleration and deceleration method so as to improve the interpolation precision of the motion.
The application utilizes the characteristic of convenient calculation of linear acceleration and deceleration and uses interpolation cycle time to reversely push acceleration, so as to discretize the motion process; the head-tail interpolation speed is not zero, so that continuous processing operation of multi-section tracks is facilitated; the acceleration in the acceleration and deceleration processes is smoothly transited by a sectional filtering method, the filtering length in the acceleration and deceleration processes is calculated by the sectional filtering according to specific parameters in the motion process, and even if the difference between the acceleration time and the deceleration time is large, the better motion effect can be achieved after the filtering; by limiting the maximum jerk of the filtered motion, the machine tool is allowed to exert its mechanical properties to a maximum extent within the allowable range.
The step of obtaining the filtering compensation increment according to the motion condition comprises the following steps:
according to the motion conditions of the motion path, the maximum allowable speed, the initial speed and the final speed of the machine tool, acquiring data parameters during linear acceleration and deceleration filtering, wherein in the single-segment motion process, when the single-segment motion comprises acceleration or deceleration, the initial instantaneous speed and the final instantaneous speed are respectively V s And V is equal to e Maximum acceleration is a, target displacement is S target The linear acceleration and deceleration is filtered by a sliding average filtering method, so that the acceleration is gradually increased or decreased, the acceleration mutation is eliminated, and the speed after the i-th interpolation period is filteredCan be expressed as:
1≤i≤T+L-1,1≤L
wherein F is i Is the interpolation speed after the discretization
Wherein L is the filtering length, T s For interpolation period, T is calculated by taking period time as unit quantity s =1, T is the number of interpolation cycles before filtering, and the total number of interpolation cycles after filtering is T L The value of =T+L-1, A is the interpolation speed after the discretization, if the value is the deceleration process, the formula is given byA= -D, D being the discrete interpolated deceleration;
the increment which is the same as the starting and ending instantaneous speed is interpolated at the initial and ending, and then added with all the interpolation increments after the linear filtering to obtain the total displacement S f ：
Wherein,order the
The filtered total displacement S f ＝S target +S p ，S p Compensating the delta for filtering;
after filtering, the acceleration obtained by interpolation planning is piecewise continuous, and the acceleration A and the Jerk are Jerk:
the step of obtaining interpolation increment under the boundary condition comprises the following steps:
calculating the filtering length L of different stages according to the maximum jerk value J 1 、L 2 Wherein L is 1 To accelerate the filtering length of the stage, L 2 For the filtering length of the deceleration stage, the maximum allowable speed is V before interpolation dispersion m Maximum acceleration and maximum deceleration of a u 、a d The total target displacement amount is S,
in the rising phase, its displacement increment S target1 The method comprises the following steps:
in the descent phase, its displacement increment S target2 The method comprises the following steps:
according to the formulaCan be provided with +.>The total displacement S is:
it should be noted that, due to limitation of motion condition parameters, maximum speed V m Maximum acceleration a u Maximum deceleration a d Not all can be reached during the movement. The maximum speed which can be actually achieved after filtering is V m ' the maximum acceleration and deceleration actually achievable is a u ' and a d '. Can be divided into case-to-case formulasSolving, only when the end speed is greater than the initial speed, i.e. V s ≤V e Is calculated according to the calculation process of (1); if the final speed is smaller than the initial speed, the solving method is consistent.
Maximum speed V due to limitation of motion condition parameters m Maximum acceleration a u Maximum deceleration a d Not all can be reached in the motion process, so that the maximum speed which can be actually reached after filtering is V m ' the maximum acceleration and deceleration actually achievable is a u ' and a d ' the formula can be divided into case pairsSolving, when the end speed is greater than the initial speed, i.e. V s ≤V e The calculation process of (1) is as follows; when the final speed is less than the initial speed, i.e. V s >V e Is consistent with the method of solving,
when V is s ≤V e In the time-course of which the first and second contact surfaces,
speed at which maximum deceleration is achievableCarry-over formulaThe following steps are obtained:
speed at which maximum acceleration is achievableCarry-over formulaThe following steps are obtained:
in the formulaIn order V m1 ＝V m Obtaining S k1 The method comprises the steps of carrying out a first treatment on the surface of the In formula->In order V m2 ＝V m Obtaining S k2 When the maximum acceleration is not reachable and the maximum deceleration is not reachable, the actual acceleration is +.>The actual deceleration is->Let bring in formula->Obtaining S k3 。
The step of judging the time state of the motion through the conditions and obtaining the maximum speed, the maximum acceleration and the maximum deceleration which can be achieved in the actual motion process comprises the following steps:
the time of acceleration, uniform speed and deceleration stage is respectively t 1 、t 2 And t 3 ，
When V is m2 >V e In the time-course of which the first and second contact surfaces,
case 1.1: v (V) m ≥V m1 ，
If S is greater than or equal to S k1 Result 1: can reach the maximum set maximum speed and the maximum acceleration and deceleration, S K ＝S k1 ，
If S m1 ≤S<S k1 Result 2: the maximum speed cannot be set, the maximum acceleration and deceleration can be achieved,
if S m2 ≤S<S m1 Result 3: the set maximum speed cannot be reached, the maximum deceleration cannot be reached, the maximum acceleration can be reached,
if S is less than or equal to S m2 Results 4 were obtained: the maximum speed cannot be set, the maximum deceleration cannot be reached, and the maximum acceleration cannot be reached;
case 1.2: v (V) m2 ≤V m <V m1 ，
If S is greater than or equal to S k2 Result 5: up to a set maximum speed, not up to a maximum deceleration, up to a maximum acceleration, S K ＝S k2 ，
If S m2 ≤S<S k2 Result 6: the set maximum speed cannot be reached, the maximum deceleration cannot be reached, the maximum acceleration can be reached,
if S<S m2 Result 7: cannot reach the set maximum speedMaximum deceleration is reached and maximum acceleration cannot be reached;
case 1.3: v (V) m <V m2 ，
If S is greater than or equal to S k3 Result 8: can reach the set maximum speed, can not reach the maximum deceleration, can not reach the maximum acceleration, S K ＝S k3 ，
If S<S k3 Result 9: the set maximum speed, the maximum deceleration, the maximum acceleration are not reached,
when V is m2 ≤V e In the time-course of which the first and second contact surfaces,
case 2.1: v (V) m ≥V m1 ，
If S is greater than or equal to S k1 A result 1 was obtained, which was obtained,
if S m1 ≤S<S k1 The result was obtained as a result 2,
if S<S m1 Obtaining a result 3;
case 2.2: v (V) m <V m1 ，
If S is greater than or equal to S k2 The result was obtained as a result 5,
if S<S k2 Obtaining a result 6;
for the above results, if the maximum set speed is reached and the maximum acceleration and the maximum deceleration are both reached, the parameters which can be actually reached and the time t of rising, uniform speed and falling are obtained 1 ,t 2 ,t 3 The method comprises the following steps of:
for the case of not reaching the maximum acceleration, letFor the case where the maximum deceleration is not reached, +.>Then bring it into the formula +.>Solving V by dichotomy m ' if the set maximum speed is not reached, let S K =s, bring in formula->Parameters that can be actually reached and the time of rising, uniform speed and falling.
Further, the step of obtaining the filter length in the acceleration and deceleration process by using the jerk segment includes:
the obtained filter length is as follows:
wherein [ (DEG ] represents rounding).
The discrete processing is carried out on the continuous speed planning by using the linear acceleration and deceleration method so as to improve the interpolation precision of the motion, and the method comprises the following steps:
discrete interpolation time, fine tuning maximum speed;
and (5) sliding filtering treatment.
The discrete interpolation time, the step of fine tuning the maximum speed includes:
the interpolation time of each stage after the discretization is T 1 、T 2 And T 3 The process comprises the following steps:
recalculating the actual maximum speed that can be reached after trimming:
the acceleration and deceleration after fine tuning are:
the sliding filter processing step comprises the following steps:
the discrete parameters are put into a formulaI is more than or equal to 1 and less than or equal to T+L-1, and L and>interpolation calculation is performed. After the sliding filter processing step, further comprising:
the feed amount per interpolation period is output.
Simulation verification: the machine tool parameters in the numerical control system are set as follows: interpolation period T s =1 ms, maximum acceleration and maximum deceleration of a u ＝2000mm/s 2 ,a d ＝2000mm/s 2 Converted into a periodic unit u ＝2μm/ms 2 ,a d ＝2μm/ms 2 The maximum Jerk has a value of j=0.2 μm/ms 3 。
The movement process is divided into 5 sections, and the target distance S and the initial instantaneous speed V of each section are respectively carried out s End instantaneous speed V e Reference maximum speed V m As shown in the upper part of table 1, the last 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 obtained true maximum speed V m ' rising stage filter length L 1 Length of downset filtering L 2 Discrete acceleration uniform speed and deceleration time T 1 、T 2 、T 3 As shown in the lower part of table 1. The data shows that the actual maximum speed that can be achieved is within the allowable maximum value range, and the actual maximum speed after discrete trimming is occasionally slightly larger than the allowable value, but the movement effect is not affected. After the filtering length is calculated in a sectionalized way, the filtering lengths in the acceleration and deceleration processes 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 motion process is avoided. Acceleration and deceleration after dispersionThe time is an integer multiple of the interpolation period, and accurate interpolation can be performed.
TABLE 1 initialization conditions for each motion process and calculation results
The speed change and the acceleration change of the 5 sections in the running process are shown in figure 2, and the speed curve is smooth and conductive; the acceleration of the machine tool is continuously changed within an allowable range, so that the jump phenomenon is avoided, and the impact on the machine tool is reduced. As shown in figure 3, the jerk change in the motion process is kept at the maximum value in the non-uniform acceleration or non-uniform deceleration stage, and the condition that the jerk exceeds the maximum value is avoided, so that the mechanical performance of the machine tool is exerted to the maximum extent within the allowable range of conditions.
According to the linear acceleration and deceleration control method based on the piecewise filtering and the jerk limitation, the motion process is easy to discretize through the calculation planning of linear acceleration and deceleration; the smooth transition of acceleration is realized through sectional filtering, impact vibration is prevented from occurring during motion transition, and the filtering length during acceleration and deceleration can be calculated respectively according to specific motion conditions, so that the motion is more reasonable, and the phenomenon of transition filtering does not occur even if the acceleration time and the deceleration time differ greatly; the jerk occurring in the motion process is limited, and the mechanical characteristics of the machine tool can be furthest exerted in the motion process by maximizing the jerk.
It is apparent that the above-described embodiments are only some embodiments of the present application, but not all embodiments, and the preferred embodiments of the present application are shown in the drawings, which do not limit the scope of the patent claims. This application may be embodied in many different forms, but rather, embodiments are provided in order to provide a thorough and complete understanding of the present disclosure. Although the application has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that modifications may be made to the embodiments described in the foregoing description, or equivalents may be substituted for elements thereof. All equivalent structures made by the content of the specification and the drawings of the application are directly or indirectly applied to other related technical fields, and are also within the scope of the application.
Claims (9)
1. A linear acceleration and deceleration control method based on piecewise filtering and jerk 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 motion by the condition, and acquiring the maximum speed, the maximum acceleration and the maximum deceleration which can be achieved in the actual motion process;
acquiring a filtering length in the acceleration and deceleration process by utilizing the jerk segment;
discretizing continuous speed planning by using a linear acceleration and deceleration method to improve the interpolation precision of motion;
the step of obtaining the filtering compensation increment according to the motion condition comprises the following steps:
according to the motion conditions of the motion path, the maximum allowable speed, the initial speed and the final speed of the machine tool, acquiring data parameters during linear acceleration and deceleration filtering, and when single-stage motion comprises acceleration or deceleration in the single-stage motion process, filtering the linear acceleration and deceleration by using a sliding average filtering method to gradually increase or decrease the acceleration and eliminate the acceleration mutation;
respectively interpolating the increment which is the same as the starting and ending instantaneous speed at the initial and ending, and then adding the increment with all the interpolation increments after linear filtering to obtain the total displacement;
after filtering, the acceleration obtained by interpolation planning is piecewise continuous.
2. The linear acceleration and deceleration control method based on piecewise filtering and jerk limiting of claim 1, wherein during a single motion, the single motion includes acceleration or deceleration, at its beginningThe starting instantaneous speed and the ending instantaneous speed are V respectively s And V is equal to e Maximum acceleration is a, target displacement is S target The i-th interpolation period filtered speedCan be expressed as:
wherein F is i Is the interpolation speed after the discretization
Wherein L is the filtering length, T s For interpolation period, T is calculated by taking period time as unit quantity s =1, T is the number of interpolation cycles before filtering, and the total number of interpolation cycles after filtering is T L The value of =T+L-1, A is the interpolation speed after the discretization, if the value is the deceleration process, the formula is given byA= -D, D being the discrete interpolated deceleration;
total displacement S f ：
Wherein,order the
Then after filteringIs the total displacement S of (2) f ＝S target +S p ，S p Compensating the delta for filtering;
interpolation planning derived accelerationAnd Jerk of Jerk:
3. the linear acceleration and deceleration control method based on piecewise filtering and jerk limiting of claim 2, wherein,
the step of obtaining interpolation increment under the boundary condition comprises the following steps:
calculating the filtering length L of different stages according to the maximum jerk value J 1 、L 2 Wherein L is 1 To accelerate the filtering length of the stage, L 2 For the filtering length of the deceleration stage, the maximum allowable speed is V before interpolation dispersion m Maximum acceleration and maximum deceleration of a u 、a d The total target displacement amount is S,
in the rising phase, its displacement increment S target1 The method comprises the following steps:
S P1 for filtering compensation increment of rising stage, in falling stage its displacement increment S target2 The method comprises the following steps:
S P2 the increment is compensated for filtering in the falling phase according to the formulaSetting upThe total displacement S is:
maximum allowable speed V due to limitation of motion condition parameters m Maximum acceleration a u Maximum deceleration a d Not all can be reached in the motion process, so that the maximum speed which can be actually reached after filtering is V m ' the maximum acceleration and deceleration actually achievable is a u ' and a d ' the formula can be divided into case pairsSolving, when the end speed is greater than the initial speed, i.e. V s ≤V e The calculation process of (1) is as follows; when the final speed is less than the initial speed, i.e. V s >V e Is consistent with the method of solving,
when V is s ≤V e In the time-course of which the first and second contact surfaces,
speed at which maximum deceleration is achievableCarry formula->The following steps are obtained:
S m1 for displacement when maximum deceleration is reached, speed when maximum acceleration is reachedCarry-over formulaThe following steps are obtained:
S m2 for displacement when maximum acceleration is reached, the formula is thatIn order V m1 ＝V m Obtaining S k1 ，S k1 To reach the maximum allowable speed V m The deceleration section is displaced during the time; in the formulaIn order V m2 ＝V m Obtaining S k2 ，S k2 To reach the maximum allowable speed V m The displacement of the acceleration section when the maximum acceleration is not reached and the maximum deceleration is not reached, the actual acceleration is +.>The actual deceleration is->Will->Carry formula->Obtaining S k3 ，S k3 The displacement of the acceleration section when the maximum acceleration is not reached.
4. The linear acceleration and deceleration control method based on piecewise filtering and jerk limiting of claim 3, wherein,
the step of judging the time state of the motion through the conditions and obtaining the maximum speed, the maximum acceleration and the maximum deceleration which can be achieved in the actual motion process comprises the following steps:
the time of acceleration, uniform speed and deceleration stage is respectively t 1 、t 2 And t 3 ，
When V is m2 >V e In the time-course of which the first and second contact surfaces,
case 1.1: v (V) m ≥V m1 ，
If S is greater than or equal to S k1 Result 1: can reach the maximum set maximum speed and the maximum acceleration and deceleration, S K ＝S k1 ，S K Displacement amount for movement;
if S m1 ≤S<S k1 Result 2: the maximum speed cannot be set, the maximum acceleration and deceleration can be achieved,
if S m2 ≤S<S m1 Result 3: the set maximum speed cannot be reached, the maximum deceleration cannot be reached, the maximum acceleration can be reached,
if S is less than or equal to S m2 Results 4 were obtained: the maximum speed cannot be set, the maximum deceleration cannot be reached, and the maximum acceleration cannot be reached;
case 1.2: v (V) m2 ≤V m <V m1 ，
If S is greater than or equal to S k2 Result 5: up to a set maximum speed, not up to a maximum deceleration, up to a maximum acceleration, S K ＝S k2 ，
If S m2 ≤S<S k2 Result 6: the set maximum speed cannot be reached, the maximum deceleration cannot be reached, the maximum acceleration can be reached,
if S<S m2 Result 7: the maximum speed cannot be set, the maximum deceleration cannot be reached, and the maximum acceleration cannot be reached;
case 1.3: v (V) m <V m2 ，
If S is greater than or equal to S k3 Result 8: can reach the set maximum speed, can not reach the maximum deceleration, can not reach the maximum acceleration, S K ＝S k3 ，
If S<S k3 Result 9: the set maximum speed, the maximum deceleration, the maximum acceleration are not reached,
when V is m2 ≤V e In the time-course of which the first and second contact surfaces,
case 2.1: v (V) m ≥V m1 ，
If S is greater than or equal to S k1 A result 1 was obtained, which was obtained,
if S m1 ≤S<S k1 The result was obtained as a result 2,
if S<S m1 Obtaining a result 3;
case 2.2: v (V) m <V m1 ，
If S is greater than or equal to S k2 The result was obtained as a result 5,
if S<S k2 Obtaining a result 6;
as to the above results, if the maximum set speed is reached and the maximum acceleration and the maximum deceleration are both reached, the parameters which can be actually reached and the time t of rising, uniform speed and falling are obtained 1 ,t 2 ,t 3 The method comprises the following steps of:
for the case of not reaching the maximum acceleration, letFor the case of not reaching the maximum deceleration, letThen bring it into the formula +.>Solving by dichotomyV m ' if the set maximum speed is not reached, let S K =s, bring in formula->Parameters that can be actually reached and the time of rising, uniform speed and falling.
5. The linear acceleration and deceleration control method based on piecewise filtering and jerk limiting of claim 4, wherein,
the step of obtaining the filtering length in the acceleration and deceleration process by utilizing the jerk segment comprises the following steps:
the obtained filter length is as follows:
wherein [ (DEG ] represents rounding).
6. The linear acceleration and deceleration control method based on piecewise filtering and jerk limiting of claim 4, wherein,
the discrete processing is carried out on the continuous speed planning by using the linear acceleration and deceleration method so as to improve the interpolation precision of the motion, and the method comprises the following steps:
discrete interpolation time, fine tuning maximum speed;
and (5) sliding filtering treatment.
7. The linear acceleration and deceleration control method based on piecewise filtering and jerk limiting of claim 6, wherein,
the discrete interpolation time, the step of fine tuning the maximum speed includes:
the interpolation time of each stage after the discretization is T 1 、T 2 And T 3 The process comprises the following steps:
recalculating the actual maximum speed that can be reached after trimming:
the acceleration and deceleration after fine tuning are:
8. the linear acceleration and deceleration control method based on piecewise filtering and jerk limiting of claim 6, wherein,
the sliding filter processing step comprises the following steps:
the discrete parameters are put into a formula
I is more than or equal to 1 and less than or equal to T+L-1, and L and>interpolation calculation is performed.
9. The linear acceleration and deceleration control method based on piecewise filtering and jerk limiting of claim 6, wherein,
after the sliding filter processing step, further comprising:
the feed amount per interpolation period is output.
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