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CN112327954A - High-precision positioning method of linear motor controlled by asymmetric S-shaped speed curve - Google Patents

High-precision positioning method of linear motor controlled by asymmetric S-shaped speed curve Download PDF

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CN112327954A
CN112327954A CN202011273554.0A CN202011273554A CN112327954A CN 112327954 A CN112327954 A CN 112327954A CN 202011273554 A CN202011273554 A CN 202011273554A CN 112327954 A CN112327954 A CN 112327954A
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马建伟
左一鸣
胡国庆
王云峰
闫惠腾
司立坤
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Dalian University of Technology
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    • G05D13/62—Control of linear speed; Control of angular speed; Control of acceleration or deceleration, e.g. of a prime mover characterised by the use of electric means, e.g. use of a tachometric dynamo, use of a transducer converting an electric value into a displacement

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Abstract

本发明非对称S型速度曲线控制的直线电机高精定位方法属于高精高速运动控制领域，涉及一种非对称S型速度曲线控制的直线电机高精定位方法。该方法根据直线电机性能约束，定义比例因子并设置加减速段速度曲线形状特征，从而确定合适的运动控制参数；计算S型速度曲线时间段匹配关系，并基于点到点运行距离约束对其进行更新；根据S型速度曲线加加速度J与时间t的关系，采用逐次积分方法求解得到加速度与时间a‑t、速度与时间v‑t以及位移与时间s‑t的表达式；根据PLC扫描周期将表达式离散得到运动指令实时传送给驱动器，驱动电机按照设定指令完成动作，确保运行过程平稳性。

Figure 202011273554

The high-precision positioning method for a linear motor controlled by an asymmetric S-shaped speed curve belongs to the field of high-precision high-speed motion control, and relates to a high-precision positioning method for a linear motor controlled by an asymmetric S-shaped speed curve. According to the performance constraints of the linear motor, the method defines the scale factor and sets the shape characteristics of the speed curve of the acceleration and deceleration sections, so as to determine the appropriate motion control parameters; calculates the matching relationship of the time period of the S-shaped speed curve, and carries out the calculation based on the point-to-point running distance constraint. Update; According to the relationship between the jerk J and time t of the S-shaped velocity curve, the successive integration method is used to solve the expressions of acceleration and time a-t, velocity and time v-t, and displacement and time s-t; According to the PLC scan cycle The motion command obtained by discrete expression is transmitted to the driver in real time, and the drive motor completes the action according to the set command to ensure the stability of the running process.

Figure 202011273554

Description

High-precision positioning method for linear motor controlled by asymmetric S-shaped speed curve
Technical Field
The invention belongs to the field of high-precision high-speed motion control, and relates to a high-precision positioning method for a linear motor controlled by an asymmetric S-shaped speed curve.
Background
With the rapid development of the electronic packaging industry, high-speed packaging equipment is more and more, and advanced packaging equipment represented by a high-speed chip mounter not only puts higher requirements on precision, but also has high speed as an important index. The high-speed operation of the high-speed chip mounter from a chip taking point to a chip mounting point requires that the linear motor is frequently started and stopped at a large acceleration in a very short time, so that the vibration of equipment is caused, the chip mounting precision is reduced, and the positioning precision of point-to-point motion under the influence of high-speed operation is mainly reflected. Therefore, in the operation process, a reasonable motion curve planning algorithm and a high-precision motion control technology play a crucial role in coordinating the contradiction between the high speed and the high precision of the paster. However, most of the current drivers are packaged with motion control modules, which have low openness and are difficult to realize complex motion control forms. In order to effectively improve the impact and vibration generated by frequent starting and stopping of the linear motor in the point-to-point high-speed running process, the research of a reasonable motion control method becomes the key for realizing a high-speed high-precision motion control system.
The patent of Zhang Cheng et al, "dynamic tracking method, system and device of moving object based on S-curve acceleration and deceleration", is published under the number CN 107671859A. The patent provides a moving target dynamic tracking method based on S curve acceleration and deceleration, which is mainly applied to mechanical arm shutdown control and has lower requirements on the positioning precision of the tail end; wang King Kong et al patent "Flexible acceleration and deceleration control method and System of machine", patent publication No. CN 109656200A. The patent proposes that the S-shaped acceleration and deceleration curve is adopted to avoid the impact generated during acceleration and deceleration, the acceleration and deceleration processes are symmetrical in theoretical research, and the derivation is not carried out on the asymmetrical acceleration and deceleration process, so that the high-precision positioning of the tail end cannot be met.
Disclosure of Invention
Aiming at the defects of the prior art, the invention discloses a high-precision positioning method for a linear motor controlled by an asymmetric S-shaped speed curve. The method can freely define an S-shaped speed curve, and in the process of setting the motion parameters, the motor performance is taken as constraint, the curve shape characteristics of the acceleration and deceleration section are set by a scale factor, and the appropriate motion control parameters are determined. And dividing the S-shaped speed curve into seven time period controls, calculating a time period matching relation by combining the scale factor, and updating the time period according to the relation between the point-to-point operation displacement and the critical displacement. The continuous expressions of a-t, v-t and x-t are solved by an integral method, the continuous expressions are discretized according to a PLC scanning period, the obtained motion instructions are transmitted to a driver in real time, and the linear motor is driven to complete corresponding actions according to the instructions, so that the running stability is ensured, and the positioning accuracy of the linear motor is improved. The method realizes complex motion control, realizes the stability of the operation process by reasonably planning motion parameters, improves the point-to-point motion precision, and provides theoretical and technical support for high-speed and high-precision motion control.
The technical scheme of the invention is a high-precision positioning method of a linear motor controlled by an asymmetric S-shaped speed curve, which defines a scale factor and sets the shape characteristics of the speed curve of an acceleration section and a deceleration section according to the performance constraint of the linear motor, thereby determining proper motion control parameters; calculating the matching relation of the S-shaped speed curve time period, and updating the S-shaped speed curve time period based on the point-to-point running distance constraint; according to the relation between the acceleration J and the time t of the S-shaped speed curve, solving by adopting a successive integral method to obtain expressions of the acceleration and the time a-t, the speed and the time v-t and the displacement and the time S-t; and dispersing the expression according to the PLC scanning period to obtain a motion instruction, transmitting the motion instruction to the driver in real time, and driving the motor to complete the action according to the set instruction, so that the stability of the operation process is ensured. The method comprises the following specific steps:
step 1: determining high-speed motion control parameters under the constraint of linear motor performance;
for point-to-point motion of a high-speed chip mounter, the initial speed is 0, and in order to reduce impact caused by frequent starting and stopping of a linear motor, a traditional T-shaped speed curve is replaced by a common S-shaped speed curve. During the point-to-point acceleration and deceleration operation process, the acceleration section I, the constant speed section II and the deceleration section III can be divided. Recording the running time of the acceleration section I as taThe running time of the uniform speed section II is tconWith deceleration III for a running time td. For facilitating analysis of S-shaped velocity curvesFunction expression to accelerate segment I for time taSubdivided into acceleration periods t of rising acceleration1Acceleration period t during which acceleration is constant2And acceleration period t of acceleration drop3Deceleration time tdSubdivided into deceleration periods t of rising acceleration5Deceleration time period t with constant acceleration6And a deceleration period t during which the acceleration decreases7Then there is ta＝t1+t2+t3And td＝t5+t6+t7. In order to represent the change from the S-shaped speed curve to the T-shaped speed curve, two scaling factors 0 & ltalpha & gt & lt1 & gt and 0 & ltbeta & gt & lt1 & gt are set, the two scaling factors respectively represent the percentage of S-shaped functions of the acceleration section and the deceleration section, and the smaller the value of the scaling factor is, the closer the scaling factor is to the ideal S-shaped curve.
Thus, the seven-segment local time period t of the S-shaped speed curve can be set by the scale factoriThe relationship between i 1, 7 and the acceleration and deceleration segment time:
Figure BDA0002778418570000031
when α ═ β ═ 0, a pure S-type curve is shown, and when α ═ β ═ 1, a T-type speed curve is shown.
In practical application, parameters of the linear motor in the operation process from the point A to the point B are set according to actual working conditions. Setting the maximum speed V and the acceleration time taAnd deceleration time tdThe maximum jerk J required by the motor in actual operation can be calculated by equations (2) to (3)a,maxAnd maximum deceleration Jd,maxMaximum acceleration aa,maxMaximum deceleration ad,maxComprises the following steps:
Figure BDA0002778418570000032
Figure BDA0002778418570000041
for a given servo linear motor, the maximum acceleration a which can be achieved by the motor can be known according to motor parametersmaxWith maximum jerk Jmax. In order to meet the motor performance, the parameters (maximum speed V, acceleration period time t) set in actual operationaAnd a deceleration period time td) The jerk and acceleration calculated by the equations (2) to (3) satisfy the following conditions:
Figure BDA0002778418570000042
if the conditions are not met, the set initial parameters are invalid, and at the moment, the initial parameters need to be reset to enable the initial parameters not to exceed the maximum performance requirement of the motor.
Step 2: s-shaped speed curve time distribution and updating based on distance constraint
From step 1, the time distribution relationship between the acceleration section I and the deceleration section III of the S-shaped speed curve can be obtained, and in order to express the S-shaped speed curve, the time interval t of the uniform speed section needs to be determined4. However, due to the limitation of the distance between two points, the maximum operating speed cannot be guaranteed to reach the set value V in the actual point-to-point acceleration and deceleration operation process. Based on this, it is necessary to determine the time allocation relationship according to the relationship between the set parameter and the given distance. The calculation method is as follows:
first assume t4＝tconThe critical displacement s required to achieve the set maximum speed V during operation from point a to point B at this time can be determined according to equation (5) at 00。
Figure BDA0002778418570000043
When the running distance s from the point A to the point B satisfies s & gt s0When the temperature of the water is higher than the set temperature,
Figure BDA0002778418570000051
the running distance s > s from the point A to the point B can be obtained at the moment0Time distribution relation of S-shaped speed curve in process [ T ]]＝[t1t2t3t4t5t6t7]。
When the running distance s from the point A to the point B meets the condition that s is less than s0When the speed curve is in S-shaped speed curve displacement and time relation, S is equal to S (t)3) Therefore, the actual operation displacement s and the critical displacement s can be determined0With respect to time tiThe proportionality coefficient ε:
Figure BDA0002778418570000052
the seven-segment time t of the S-shaped speed curve can be calculated by the above formulaiThe updating is as follows:
Figure BDA0002778418570000053
thus, the running distance s from the point A to the point B is less than s0Time distribution relation of S-shaped speed curve in process [ T ]]＝[t′1 t′2 t′3 t′4 t′5 t′6 t′7]。
And step 3: establishing an S-shaped speed curve expression;
and analyzing in the step 2 to obtain seven-segment time distribution relation of the S-shaped speed curve under different displacement constraints. Then, an expression between the displacement and the time of the S-shaped velocity curve needs to be determined, and considering that the S-shaped velocity curve has a segmented first-order acceleration, the expression between the acceleration and the time can be obtained as follows:
Figure BDA0002778418570000061
wherein, T i1, 7 denotes a time coordinate, T1＝t1，T2＝T1+t2，T3＝T2+t3，T4＝T3+t4，T5＝T4+t5，T6＝T5+t6，T7＝T6+t7。
The relationship between the acceleration and the time is integrated to obtain the relationship between the speed and the time, and the relationship between the displacement and the time is obtained by integrating again, so that the values of the speed v and the displacement S corresponding to the S-shaped function at different moments t can be determined:
Figure BDA0002778418570000062
Figure BDA0002778418570000071
equations (9) - (11) give S-shaped speed curves a-t, v-t and S-t expressions, and accordingly real-time point position control of the linear motor in the operation process from the point A to the point B can be achieved.
And 4, step 4: the method is realized by the rapid point-to-point motion control of a linear motor constrained by a PLC scanning period;
from step 3, the continuous expressions for s-t, v-t and a-t can be obtained, for any given time tiThe position s corresponding to the linear motor at the moment can be calculated according to the continuous equationiV speed of movementiAnd acceleration aiInformation, for convenience of presentation, is denoted as [ t ]i,si,vi,ai]. In practical application, the PLC has the minimum scanning period tsLimitation, therefore, for the moving process from point A to point B, the continuous operation time T needs to be according to the scanning period TsThe integer multiples of which are discretized. When the PLC program is used for calculation, because the time parameter in the PLC can be expressed as the number of scanning periods and the data type is an integer, when the time variable is repeatedly iterated according to t ═ t +1, the scanning period t is expressedsAnd (3) superposition. To ensure the consistency of the calculation results, the time periods in the formulas (6) and (8) are converted toChanging the number of scanning periods, and rounding up according to a rounding mode;
Figure BDA0002778418570000072
in the formula, n _ tiRepresents a time period tiThe corresponding number of scan cycles, Round, represents the rounding function according to the rounding rule.
Then according to the scanning period tsAnd (3) updating the time distribution relation obtained in the formulas (6) and (8):
Figure BDA0002778418570000081
thereby obtaining an updated time period
Figure BDA0002778418570000082
Successive a-t equations, v-t equations and s-t equations can be calculated according to equations (9) - (11).
On the basis, the operation period T is dispersed into T ═ T according to the minimum scanning periods 2ts 3ts…T]TIn this case, the corresponding information [ t, s, v, a ] of the linear motor in each scanning cycle can be obtained from equations (9) to (11)]. The obtained displacement velocity acceleration [ s, v, a ] in each scanning period]The motion instruction is sent to a motor driver in real time through an EtherCAT network through a PLC control program, and the driver drives the linear motor to complete the rapid point-to-point motion control of the linear motor based on the S-shaped speed curve.
The invention has the obvious effects and benefits that an asymmetric S-shaped speed curve capable of customizing time parameters is provided and applied to point-to-point motion control of the linear motor, so that the problem of overlarge motor motion impact caused by unreasonable speed planning can be effectively reduced, and the method has important significance for improving the positioning precision of the motor. In the process of setting the motion parameters, the performance of a motor is taken as constraint, the curve shape characteristics of the acceleration curve of the acceleration and deceleration section are set by a scale factor, and appropriate motion control parameters are determined; dividing the S-shaped speed curve into seven time period controls, calculating a time period matching relation by combining the scale factor, and updating the time period according to the relation between the point-to-point operation displacement and the critical displacement; solving continuous expressions of a-t, v-t and x-t by using an integral method; and discretizing the continuous expression according to the PLC scanning period, transmitting the obtained motion instruction to the driver in real time, and driving the linear motor to complete corresponding actions according to the instruction, thereby ensuring the operation stability and improving the positioning precision of the linear motor. The method is suitable for various high-speed high-precision motion control occasions requiring complex motion control, particularly high-speed chip mounters, can improve the impact of a linear motor in the operation process and improve the positioning precision, and thus has important significance for improving the packaging precision and performance of electronic products.
Drawings
FIG. 1 is a general flow chart of a high-precision positioning method for a linear motor controlled by an asymmetric S-shaped speed curve.
FIG. 2 shows that the set travel distance s is 40mm (s < s)0)、s＝50mm(s＝s0) And s 60mm (s > s)0) Time-programmed displacement-time curve, s050mm is the critical displacement required to reach the maximum velocity V. Wherein, the abscissa represents the operation time in ms, and the ordinate represents the displacement in mm.
FIG. 3 shows that the travel distance s is 40mm (s < s)0)、s＝50mm(s＝s0) And s 60mm (s > s)0) Time programmed speed time curves. Wherein, the abscissa represents the operation time in ms, and the ordinate represents the speed in mm/s.
FIG. 4 shows that the travel distance s is 40mm (s < s)0)、s＝50mm(s＝s0) And s 60mm (s > s)0) Time programmed acceleration time curves. Wherein the abscissa represents the operation time in ms, and the ordinate represents the acceleration in mm/s2。
Fig. 5 shows a set displacement time curve and an actual displacement time curve when the patch distance s is 50 mm. Wherein the abscissa represents the operation time in units of s, and the ordinate represents the displacement in units of mm.
Fig. 6a) shows a displacement time curve of the driver internal control algorithm at a patch distance s of 50mm, wherein the overall operation time T is 40ms, and the settling time T is 17 ms;
fig. 6b) shows a displacement time curve of the proposed control algorithm for a patch distance s of 50mm, wherein the overall operating time T is 31ms and the settling time T is 17 ms.
Detailed Description
The detailed description of the invention will be made in conjunction with the technical solutions and the accompanying drawings
In the high-speed high-precision packaging process of the semiconductor, reasonable movement speed planning can avoid the situation that equipment generates impact or large vibration due to high-speed movement of a motor rotor so as to influence the chip mounting precision of a high-speed chip mounter, and has important significance for improving the stability of the chip mounting process and improving the chip mounting speed and precision. Based on the method, the high-precision positioning method of the linear motor controlled by the asymmetric S-shaped speed curve is invented, and the flow of the method is shown in the attached drawing 1.
The invention uses TwinCAT2 software in a Beifu industrial personal computer as a soft PLC, according to the method provided by the text, the PLC program transmits position, speed, acceleration and time instructions to an Elmo driver through an EtherCAT network cable, and the driver controls a linear motor to output corresponding instructions, thereby completing the high-speed and high-precision positioning control of the linear motor. The specific implementation process of the invention is explained in detail by taking the example of verifying the effectiveness of the method by MATLAB simulation and realizing point-to-point motion of the linear motor controlled by the S-shaped speed curve in TwinCAT2 by utilizing PLC programming.
Firstly, determining the maximum acceleration a of the linear motor according to the performance parameters of the linear motormaxAnd maximum jerk JmaxSetting the maximum speed V and the acceleration time t in the running process according to the actual running environmentaAnd a deceleration time tdAnd the scale factors alpha and beta, the acceleration time and the deceleration time of which can be further subdivided by formula (1) to obtain a time period distribution relation about the S-shaped speed curve. According to the set operation parameters, the maximum required linear motor in the acceleration section and the deceleration section under the parameters can be calculated according to the formulas (2) to (3)Jerk { Ja,max,Jd,maxAnd maximum acceleration aa,max,ad,max}. If equation (4) is satisfied, the set operating parameters can be implemented, otherwise, the parameters need to be readjusted to satisfy the constraint of equation (4).
Secondly, it is considered that a certain displacement distance s is required in order to reach the set maximum operating speed V. However, in an actual working condition, the actual running distance S is limited by the point-to-point distance, and the maximum running speed cannot be guaranteed to reach the set value, so that the time distribution relationship of each section of the S-shaped speed curve needs to be determined according to the relationship between the set parameter and the actual running distance. Firstly, the critical displacement s required for reaching the maximum speed V can be calculated according to the formula (5)0If the actual running distance satisfies s > s0The time distribution [ T ] of the S-shaped speed curve can be determined according to the formula (6)]＝[t1 t2 t3 t4t5 t6 t7](ii) a If the actual running distance satisfies s < s0The time distribution relationship of the S-shaped speed curve can be updated according to the formulas (7) to (8)
Figure BDA0002778418570000101
And then, according to the time distribution relation obtained in the step 2, by using the expressions of the jerk and the time, and calculating and deducing the expressions of the acceleration and the time, the speed and the time and the displacement and the time through integral calculation, wherein the expressions are shown in the formulas (9) to (11). According to the a-t equation, the v-t equation and the S-t equation, the operation process of the linear motor from the point A to the point B can be controlled in real time by the S-shaped speed curve.
And finally, rounding the S-shaped speed curve time distribution relation based on the scanning period in a rounding mode by using equations (12) - (13), calculating to obtain corresponding acceleration, speed and displacement in each scanning period by using equations (9) - (11), and inputting the acceleration, speed and displacement to an Elmo driver through an EtherCAT network cable, so that the linear motor is driven to reach an instruction position according to the instruction speed, and the point-to-point high-precision positioning control of the linear motor controlled by the asymmetric S-shaped speed curve is realized.
Setting the maximum speed V in the operation process to 2500mm/s and the acceleration time t according to the actual operation conditiona20ms, deceleration time tdFor example, when the scaling factor α is set to 0.2 and β is set to 0.1, t can be calculated1＝t3＝8ms，t2＝4ms，t5＝t7＝9ms，t6At this time, the critical distance s required to reach the set maximum speed V of 2500mm/s can be calculated according to the formula (5) at 2ms050 mm. In the actual chip mounter chip mounting process, the displacements from the chip taking points to the chip mounting points are different from 40-80mm, the chip displacements are 40mm, 50mm and 60mm are taken as examples, the time distribution relation calculated above is recalculated and updated according to the formulas (6) - (8) in the step 2, and the acceleration-time curve, the speed-time curve and the position-time curve in the motor operation process are obtained through simulation in the MATLAB by the formulas (9) - (11) and are shown in the figures 2, 3 and 4.
Then, a PLC control program is established in TwinCAT2 by the method, the scanning period of the system is set to be 0.5ms, S-shaped speed curve time distribution is updated by a rounding method according to formulas (12) - (13), every 0.5ms, the PLC program calculates a group of motor motion information [ t, S, v, a ] according to formulas (9) - (11) and transmits the motor motion information [ t, S, v, a ] to a driver, the driver sends out an instruction to control the linear motor to realize accurate positioning of a chip mounting process according to corresponding motion, an actual operation curve fed back by a position encoder is shown in figure 5, and the actual operation can well track a set value.
Meanwhile, in order to verify the effectiveness of the method, taking the patch distance of 50mm as an example, the algorithm proposed herein is compared with the driver internal control algorithm, and the experimental result is shown in fig. 6, fig. 6a) shows that the driver internal control algorithm shifts a time curve when the patch distance s is 50mm, wherein the set operation time T is 40ms, and the stable adjustment time T is 17 ms. Fig. 6b) shows a displacement time curve of the proposed control algorithm for a patch distance s of 50mm, wherein the set operating time T is 31ms and the settling time T is 17 ms. The experimental result shows that under the same positioning precision, the method can improve the operation set period on the premise of ensuring the positioning period, thereby shortening the operation time of the whole patch compared with the internal algorithm of the driver.
Experimental results show that the high-precision positioning method for the linear motor controlled by the asymmetric S-shaped speed curve can meet the high-precision positioning requirement of the linear motor in high-speed operation, shortens positioning time on the premise of ensuring positioning precision, and provides a guiding function for actually improving high-speed chip mounting efficiency in IC packaging.

Claims (1)

1.一种非对称S型速度曲线控制的直线电机高精定位方法，其特征在于，该方法根据直线电机性能约束，定义比例因子并设置加减速段速度曲线形状特征，从而确定合适的运动控制参数；计算S型速度曲线时间段匹配关系，并基于点到点运行距离约束对其进行更新；根据S型速度曲线加加速度J与时间t的关系，采用逐次积分方法求解得到加速度与时间a-t、速度与时间v-t以及位移与时间s-t的表达式；根据PLC扫描周期将表达式离散得到运动指令实时传送给驱动器，驱动电机按照设定指令完成动作，确保运行过程平稳性；1. A high-precision positioning method for a linear motor controlled by an asymmetric S-shaped speed curve, characterized in that the method defines a proportional factor and sets the speed curve shape characteristics of the acceleration and deceleration sections according to the performance constraints of the linear motor, so as to determine a suitable motion control parameters; calculate the time period matching relationship of the S-shaped speed curve, and update it based on the point-to-point running distance constraint; according to the relationship between the jerk J and time t of the S-shaped speed curve, the successive integration method is used to solve the acceleration and time a-t, The expression of speed and time v-t and displacement and time s-t; according to the PLC scan cycle, the expression is discrete and the motion command is sent to the driver in real time, and the drive motor completes the action according to the set command to ensure the smoothness of the running process; 方法的具体步骤如下：The specific steps of the method are as follows: 步骤1：直线电机性能约束下的高速运动控制参数确定Step 1: Determination of high-speed motion control parameters under linear motor performance constraints 对于高速贴片机点到点的运动，其初始速度为0，为了减小直线电机频繁启停带来的冲击，常用S型速度曲线代替传统的T型速度曲线；在点到点加减速运行过程中将其分为加速段I、匀速段II和减速段III；记加速段I运行时间为ta、匀速段II运行时间为tcon与减速度III运行时间为td；为了便于分析S型速度曲线的函数表达式，将加速段I运行时间ta细分为加速度上升的加速时间段t1、加速度恒定的加速时间段t2和加速度下降的加速时间段t3，同理减速度时间td细分为加速度上升的减速时间段t5、加速度恒定的减速时间段t6和加速度下降的减速时间段t7，于是有ta＝t1+t2+t3和td＝t5+t6+t7；为了表征S型速度曲线到T型速度曲线之间的变化，设置两个比例因子0≤α≤1和0≤β≤1，分别表示加速段与减速段S型函数的百分比，其比例因子值越小，越接近理想S型曲线；For the point-to-point motion of the high-speed placement machine, the initial speed is 0. In order to reduce the impact caused by the frequent start and stop of the linear motor, the S-shaped speed curve is often used to replace the traditional T-shaped speed curve; the acceleration and deceleration run from point to point. In the process, it is divided into acceleration section I, constant speed section II and deceleration section III; the running time of acceleration section I is denoted as t a , the running time of constant speed section II is t con and the running time of deceleration III is t d ; in order to facilitate the analysis of S The function expression of the speed curve, the running time ta of the acceleration segment I is subdivided into the acceleration time period t 1 of the acceleration rising, the acceleration time period t 2 of the constant acceleration and the acceleration time period t 3 of the acceleration falling, and the same is the deceleration time. The time t d is subdivided into the deceleration time period t 5 of the acceleration rising, the deceleration time period t 6 of the constant acceleration and the deceleration time period t 7 of the acceleration falling, so there are t a = t 1 +t 2 +t 3 and t d = t 5 +t 6 +t 7 ; In order to characterize the change between the S-shaped speed curve and the T-shaped speed curve, two scaling factors 0≤α≤1 and 0≤β≤1 are set, representing the acceleration section and the deceleration section S respectively The percentage of sigmoid function, the smaller the scale factor value, the closer to the ideal S-shaped curve; 通过比例因子设置S型速度曲线的七段局部时间段ti(i＝1,...,7)与加减速段时间之间的关系：The relationship between the seven local time segments t i (i=1,...,7) of the S-shaped speed curve and the acceleration and deceleration segment time is set by the proportional factor:
Figure FDA0002778418560000021
Figure FDA0002778418560000021
 当α＝β＝0时，表示纯S型曲线，当α＝β＝1时，表示T型速度曲线；When α=β=0, it represents a pure S-shaped curve, and when α=β=1, it represents a T-shaped speed curve; 根据实际工况设定直线电机从点A到点B运行过程中的参数：设置最大速度V，加速度时间ta与减速度时间td，通过公式(2)-(3)计算得到实际运行中电机所需的最大加加速度Ja,max和最大减加速度Jd,max、最大加速度aa,max、最大减速度ad,max为：According to the actual working conditions, set the parameters of the linear motor during the running process from point A to point B: set the maximum speed V, acceleration time ta and deceleration time t d , and calculate the actual running speed through formulas (2)-(3). The maximum jerk J a,max and maximum deceleration J d,max , the maximum acceleration a a,max and the maximum deceleration a d,max required by the motor are:
Figure FDA0002778418560000022
Figure FDA0002778418560000022
Figure FDA0002778418560000023
Figure FDA0002778418560000023
 对一个给定伺服直线电机，由电机参数可知电机能达到的最大加速度amax与最大加加速度Jmax；为了满足电机性能，实际运行中设定的参数：最大速度V、加速段时间ta与减速段时间td，经公式(2)-(3)计算得到的加加速度和加速度需满足以下条件：For a given servo linear motor, the maximum acceleration a max that the motor can reach and the maximum jerk J max can be known from the motor parameters; in order to meet the performance of the motor, the parameters set in actual operation: the maximum speed V, the acceleration period time t a and During the deceleration period t d , the jerk and acceleration calculated by formulas (2)-(3) must meet the following conditions:
Figure FDA0002778418560000024
Figure FDA0002778418560000024
 若不满足以上条件，则所设置的初始参数无效，此时需要重新设置初始参数，使其不超出电机最大性能要求；If the above conditions are not met, the initial parameters set are invalid, and the initial parameters need to be reset so that they do not exceed the maximum performance requirements of the motor; 步骤2：基于距离约束的S型速度曲线时间分配与更新；Step 2: Time allocation and update of S-shaped velocity curve based on distance constraints; 由步骤1，得到S型速度曲线加速段I和减速段III的时间分配关系，为了能够表达S型速度曲线，需要确定匀速段时间间隔t4；然而，受两点距离限制，实际点到点加减速运行过程中，并不能保证运行的最大速度达到设定值V；基于此，需要根据设定的参数与给定距离之间的关系确定时间分配关系；From step 1, the time distribution relationship between the acceleration section I and the deceleration section III of the S-shaped speed curve is obtained. In order to express the S-shaped speed curve, the time interval t 4 of the uniform speed section needs to be determined; however, limited by the distance between the two points, the actual point-to-point During the acceleration and deceleration operation, the maximum speed of the operation cannot be guaranteed to reach the set value V; based on this, the time distribution relationship needs to be determined according to the relationship between the set parameters and the given distance; 先假设t4＝tcon＝0，根据公式(5)确定此时由点A到点B运行过程中，为了达到设置最大速度V所需要的临界位移s0：Assuming t 4 =t con =0 first, according to formula (5), determine the critical displacement s 0 required to set the maximum speed V during the running process from point A to point B at this time:
Figure FDA0002778418560000031
Figure FDA0002778418560000031
 当点A到点B运行距离s满足s＞s0时，When the running distance s from point A to point B satisfies s>s 0 ,
Figure FDA0002778418560000032
Figure FDA0002778418560000032
 得到点A到点B运行距离s＞s0过程中，S型速度曲线的时间分配关系[T]＝[t1t2t3t4t5t6t7]；Obtain the time distribution relationship of the S-shaped speed curve in the process of running distance s>s 0 from point A to point B [T]=[t 1 t 2 t 3 t 4 t 5 t 6 t 7 ]; 当点A到点B点运行距离s满足s＜s0时，由于S型速度曲线位移与时间之间的关系满足s＝s(t3)，因此，根据实际运行位移s与临界位移s0之间的关系，设置关于时间ti的比例系数ε：When the running distance s from point A to point B satisfies s<s 0 , since the relationship between the displacement and time of the S-shaped velocity curve satisfies s=s(t 3 ), therefore, according to the actual running displacement s and the critical displacement s 0 The relationship between , set the scaling factor ε with respect to time t i :
Figure FDA0002778418560000033
Figure FDA0002778418560000033
 由上式计算S型速度曲线的七段时间ti更新为：The seven-segment time t i of the S-shaped speed curve calculated by the above formula is updated as:
Figure FDA0002778418560000041
Figure FDA0002778418560000041
 得到点A到点B运行距离s＜s0过程中，S型速度曲线的时间分配关系[T]＝[t′1t′2t′3t′4t′5t′6t′7]；In the process of obtaining the running distance from point A to point B s < s 0 , the time distribution relationship of the S-shaped speed curve [T]=[t′ 1 t′ 2 t′ 3 t′ 4 t′ 5 t′ 6 t′ 7 ] ; 步骤3：S型速度曲线表达式的确立；Step 3: Establishment of the S-shaped velocity curve expression; 由步骤2分析得到不同位移约束下的S型速度曲线七段时间分配关系；然后需要确定S型速度曲线位移与时间之间的表达式，考虑到S型速度曲线具有分段一阶加速度，得到加速度与时间之间的表达式为：The seven-segment time distribution relationship of the S-shaped velocity curve under different displacement constraints is obtained from the analysis in step 2; then the expression between the displacement and the time of the S-shaped velocity curve needs to be determined. Considering that the S-shaped velocity curve has a piecewise first-order acceleration, we get The expression between acceleration and time is:
Figure FDA0002778418560000042
Figure FDA0002778418560000042
 其中，Ti，i＝1，...，7表示时间坐标，T1＝t1，T2＝T1+t2，T3＝T2+t3，T4＝T3+t4，T5＝T4+t5，T6＝T5+t6，T7＝T6+t7；Wherein, T i , i=1,...,7 represent time coordinates, T 1 =t 1 , T 2 =T 1 +t 2 , T 3 =T 2 +t 3 , T 4 =T 3 +t 4 , T 5 =T 4 +t 5 , T 6 =T 5 +t 6 , T 7 =T 6 +t 7 ; 对加速度与时间的关系进行积分，得到速度与时间之间的关系；再次积分便可得到位移与时间之间的关系，从而可以确定S型函数在不同时刻t下所对应的速度v与位移s的值：Integrate the relationship between acceleration and time to obtain the relationship between speed and time; integrate again to obtain the relationship between displacement and time, so as to determine the speed v and displacement s corresponding to the S-shaped function at different times t The value of:
Figure FDA0002778418560000051
Figure FDA0002778418560000051
Figure FDA0002778418560000052
Figure FDA0002778418560000052
 公式(9)-(11)给出了S型速度曲线a-t，v-t以及s-t表达式，据此实现直线电机从点A到点B运行过程实时点位控制；Formulas (9)-(11) give the expressions of the S-shaped speed curves a-t, v-t and s-t, according to which the real-time point position control of the linear motor from point A to point B is realized; 步骤4：以PLC扫描周期约束的直线电机快速点到点运动控制实现；Step 4: Realize fast point-to-point motion control of linear motor constrained by PLC scan cycle; 由步骤3得到s-t、v-t与a-t的连续表达式，对于任意给定时刻ti，均可根据上述连续方程计算得到直线电机此时对应的位置si、运动速度vi与加速度ai信息，为了表示方便，记为[ti,si,vi,ai]；由于实际应用中，PLC具有最小的扫描周期ts限制，因此对于点A到点B运动过程中，需要将连续的运行时间T按照扫描周期ts的整数倍进行离散；在PLC程序进行计算时，由于PLC中时间参数表示为扫描周期的个数，其数据类型为整数，故时间变量按照t＝t+1进行重复迭代时，表示的是扫描周期ts的叠加；为保证计算结果的一致性，将公式(6)和(8)中的时间段转换为扫描周期数量，并按照四舍五入方式取整；The continuous expressions of st, vt and at are obtained from step 3. For any given time t i , the information of the position si , the motion speed vi and the acceleration a i corresponding to the linear motor at this time can be calculated according to the above continuous equation, For the convenience of expression, it is denoted as [t i , s i , v i , a i ]; because in practical applications, PLC has the minimum scan period ts limit, so for the movement process from point A to point B, it is necessary to convert the continuous The running time T is discrete according to the integer multiple of the scan period t s ; when the PLC program is calculated, since the time parameter in the PLC is expressed as the number of scan periods, and its data type is an integer, the time variable is calculated according to t=t+1 When repeated iterations, it represents the superposition of the scanning period t s ; in order to ensure the consistency of the calculation results, the time period in formulas (6) and (8) is converted into the number of scanning periods, and rounded up according to the rounding method;
Figure FDA0002778418560000061
Figure FDA0002778418560000061
 式中，n_ti表示时间段ti对应的扫描周期数量，Round表示按照四舍五入规则的取整函数；In the formula, n_t i represents the number of scan cycles corresponding to the time period t i , and Round represents the rounding function according to the rounding rule; 然后按照扫描周期ts大小，更新公式(6)和(8)中得到的时间分配关系：Then according to the size of the scanning period t s , update the time distribution relationship obtained in formulas (6) and (8):
Figure FDA0002778418560000062
Figure FDA0002778418560000062
 由此得到经过更新后的时间段
Figure FDA0002778418560000063
根据公式(9)-(11)计算得到连续的a-t方程，v-t方程以及s-t方程；This results in the updated time period
Figure FDA0002778418560000063
According to formulas (9)-(11), the continuous at equation, vt equation and st equation are obtained; 在此基础上，将其运行周期T按照最小扫描周期离散成t＝[ts 2ts 3ts…T]T，此时，由公式(9)-(11)得到直线电机在每个扫描周期下相应的信息[t,s,v,a]；在每个扫描周期内将得到的位移速度加速度[s,v,a]的运动指令通过PLC控制程序经EtherCAT网络实时发送给电机驱动器，由驱动器驱动直线电机完成直线电机基于S型速度曲线的快速点到点运动控制。On this basis, the operating period T is discretized into t=[t s 2t s 3t s ...T] T according to the minimum scan period. Under the corresponding information [t,s,v,a]; in each scan cycle, the motion command of the obtained displacement velocity acceleration [s,v,a] is sent to the motor driver in real time through the PLC control program through the EtherCAT network, and the The driver drives the linear motor to complete the fast point-to-point motion control of the linear motor based on the S-shaped speed curve.
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