CN105388782B - A kind of algorithm for the sigmoid curve generator for being used to give link - Google Patents
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Abstract
本发明涉及一种用于给定环节的S形曲线发生器的算法,其步骤为:步骤1:向函数发生器输入指令值Ak,时间参数Tnu和Tnd;步骤2:由Ak状态决定的运算;步骤3:判断输出过程是否改变正反极性;步骤4:计算S形曲线生成时间T;步骤5:计算时间t;步骤6:计算Xk;步骤7:计算输出Yk,即生成所需的S形曲线输出。本发明提供的S形曲线发生器的算法将正弦函数进行偏置,形成S形曲线,输出连续光滑,上升或下降过程中前半段与后半段对称,时间控制准确,算法简洁。
The present invention relates to a kind of algorithm for the S-shaped curve generator of given link, and its steps are: step 1: input instruction value A k to the function generator, time parameter T nu and T nd ; Step 2: by A k Operation of state determination; Step 3: Judging whether the output process changes positive or negative polarity; Step 4: Calculating the generation time T of the S-shaped curve; Step 5: Calculating the time t; Step 6: Calculating X k ; Step 7: Calculating the output Y k , that produces the desired S-curve output. The algorithm of the S-shaped curve generator provided by the invention offsets the sine function to form an S-shaped curve, the output is continuous and smooth, the first half and the second half of the rising or falling process are symmetrical, the time control is accurate, and the algorithm is simple.
Description
技术领域technical field
本发明属于电气控制技术领域,尤其是一种用于给定环节的S形曲线发生器的算法。The invention belongs to the technical field of electrical control, in particular to an algorithm for an S-shaped curve generator for a given link.
背景技术Background technique
在电气控制系统(例如电机调速系统)中,由操作者或上级自动化系统给出阶跃的工艺目标(例如速度、转矩或位置)指令信号,一般要求电气控制系统使被控对象按预设定的函数发生器参数达到工艺目标值。其目的是限制调节过程的变化率,减小电气、机械冲击,安全、稳定、快速地实现工艺控制目标。In an electrical control system (such as a motor speed control system), the operator or the superior automation system gives a step-by-step process target (such as speed, torque or position) instruction signal, and the electrical control system is generally required to make the controlled object operate according to the preset The set function generator parameters reach the process target value. Its purpose is to limit the rate of change of the adjustment process, reduce electrical and mechanical impacts, and achieve process control goals safely, stably and quickly.
目前这类用于给定环节的函数发生器函数主要有:一阶惯性函数、普通斜坡函数和带圆角的斜坡函数、以及S形函数等。At present, such function generator functions used for a given link mainly include: first-order inertial functions, ordinary ramp functions, ramp functions with rounded corners, and S-shaped functions.
一阶惯性函数发生器最简单,其特点是不论阶跃输入幅值大小,其输出响应时间相同;其次是输出变化率初始最大、随时间变化逐步降低,大致4倍惯性时间常数时间基本达到输入目标值,但理论上其输出终值为无穷大时间达到输入目标值,因此其主要应用于控制精度要求不高的场合。由于这种函数发生器初始变化率最大,对电气、机械的冲击大,一般不适合带机械传动的电气系统采用。The first-order inertial function generator is the simplest, and its characteristic is that regardless of the magnitude of the step input, its output response time is the same; secondly, the output change rate is initially the largest, gradually decreases with time, and roughly 4 times the inertial time constant time basically reaches the input The target value, but theoretically its final output value reaches the input target value in an infinite time, so it is mainly used in occasions where the control accuracy is not high. Since this kind of function generator has the largest initial change rate and has a large impact on electricity and machinery, it is generally not suitable for electrical systems with mechanical transmission.
普通斜坡函数发生器采用积分器构成斜坡输出,其特点是斜率固定、积分时间与阶跃输入幅值成正比、积分时间控制精确。这种函数发生器早期应用较普遍,但其缺点是由于输出斜率固定,起始段和末段不平滑,对电气和机械仍有一定冲击。例如,许多机械传动带有齿轮,由于齿隙的存在,当加减速度时,如果速度变化率从0阶跃到固定值、或从固定值阶跃到0,将出现打齿现象,带来系统振荡,影响机械寿命;对于长轴传动或皮带传动,由于弹性变形,如果速度变化率从0阶跃到固定值、或从固定值阶跃到0,将导致轴系振荡、或皮带打滑现象,影响设备寿命。Ordinary ramp function generators use integrators to form ramp outputs, which are characterized by fixed slope, integral time proportional to step input amplitude, and precise integral time control. This kind of function generator was widely used in the early stage, but its disadvantage is that due to the fixed output slope, the initial and final stages are not smooth, and there is still a certain impact on the electrical and mechanical. For example, many mechanical transmissions have gears. Due to the existence of backlash, when accelerating and decelerating, if the speed change rate steps from 0 to a fixed value, or from a fixed value to 0, there will be a tooth hitting phenomenon, which will bring the system Oscillation affects mechanical life; for long shaft transmission or belt transmission, due to elastic deformation, if the speed change rate steps from 0 to a fixed value, or from a fixed value to 0, it will cause shaft vibration or belt slippage, affect the life of the equipment.
带圆角的斜坡函数发生器在普通斜坡函数发生器基础上,通过一个附加的斜率积分器使起始段的斜率(变化率)从0开始积分到固定值、末段斜率从固定值积分到0,使斜坡函数发生器输出信号的起始段和终值段为圆弧状波形,中间段为固定斜率,这使得起始段和末段平滑,电气和机械冲击大大减小。这种函数发生器克服了前两种发生器的缺陷,是目前应用较为普遍的。但其算法较为复杂。The slope function generator with rounded corners is based on the ordinary slope function generator, and through an additional slope integrator, the slope (change rate) of the initial section is integrated from 0 to a fixed value, and the slope of the final section is integrated from a fixed value to a fixed value. 0, so that the initial section and final value section of the output signal of the ramp function generator are arc-shaped waveforms, and the middle section is a fixed slope, which makes the initial section and the end section smooth, and the electrical and mechanical shocks are greatly reduced. This kind of function generator overcomes the defects of the first two generators, and is currently widely used. But its algorithm is more complicated.
S形函数发生器将阶跃输入信号转变为输出终值等于输入幅值的S形光滑曲线信号,起始段与末段对称,从阶跃输入至输出终值的时间T与输入幅值成正比,时间控制准确。S形函数发生器可以有多种实现方法。从该定义看,带圆角的斜坡函数发生器也属于S形函数发生器的一种。The S-shaped function generator transforms the step input signal into an S-shaped smooth curve signal whose output final value is equal to the input amplitude. Proportional, accurate time control. The S-shaped function generator can be implemented in many ways. From this definition, the slope function generator with rounded corners is also a kind of S-shaped function generator.
以速度控制系统为例,当输入指令从某一值U1跃变至其反极性值U2(例如从50%最高速度跃变至-10%最高速度,或从-40%最高速度跃变至15%最高速度),调速系统实际需要先从U1制动到0%、再反向起动至U2,即存在2个速度调节过程。如果在该速度过零时没有制动和起动圆弧,则会对机械产生冲击,特别是对带有齿轮传动的系统有明显冲击,对弹性变形较为严重的长轴传动系统也会造成明显振荡过程,影响机械寿命。因此,从保护机械的角度出发,应以过0%点为分界点,将这种改变正反极性调速过程分解为2个S形调速过程。Taking the speed control system as an example, when the input command jumps from a certain value U1 to its opposite polarity value U2 (such as jumping from 50% of the maximum speed to -10% of the maximum speed, or from -40% of the maximum speed to 15% maximum speed), the speed control system actually needs to brake from U1 to 0%, and then reverse start to U2, that is, there are two speed adjustment processes. If there is no braking and starting arc when the speed crosses zero, it will have an impact on the machine, especially on the system with gear transmission, and it will also cause obvious oscillation on the long-axis transmission system with serious elastic deformation. process, affecting mechanical life. Therefore, from the point of view of protecting machinery, the 0% point should be taken as the dividing point, and the speed regulation process of changing positive and negative polarities should be decomposed into two S-shaped speed regulation processes.
很多电气控制场合,根据工艺控制需要,启动与制动所带负载可能有较大差别。用于给定环节的函数发生器采用启动与制动时间分别设置,可以合理充分利用电气和机械设备,提高生产效率。例如某些调速系统应用场合,工艺为带载起动、空载制动,要求给定环节的函数发生器采用较长起动时间与较短制动时间,由于起动或制动加速度与转矩成正比,在这种工艺运行下采用较长起动时间与较短制动时间的方案,使电机带载情况下加速转矩适当减小、空载情况下加速力矩适当加大,即可合理充分利用电机功率、又尽可能缩短运行时间,提高生产效率。In many electrical control occasions, according to the needs of process control, the loads carried by starting and braking may be quite different. The function generator used for a given link is set separately for starting and braking time, which can make full use of electrical and mechanical equipment and improve production efficiency. For example, in some speed regulating system applications, the process is on-load starting and no-load braking. It is required that the function generator of a given link adopts a longer starting time and a shorter braking time. Since the starting or braking acceleration is proportional to the torque Proportional, under this kind of process operation, the scheme of longer starting time and shorter braking time is adopted, so that the acceleration torque of the motor is appropriately reduced under the load condition, and the acceleration torque is appropriately increased under the no-load condition, so that the motor can be fully utilized Motor power, and shorten the running time as much as possible to improve production efficiency.
发明内容Contents of the invention
本发明的目的在于克服现有技术的不足之处,提供一种用于给定环节阶跃指令信号缓冲处理的S形曲线发生器的算法。The purpose of the present invention is to overcome the disadvantages of the prior art, and provide an algorithm for an S-shaped curve generator used for buffering and processing a step instruction signal of a given link.
本发明解决其技术问题是采取以下技术方案实现的:The present invention solves its technical problem and realizes by taking the following technical solutions:
一种用于给定环节的S形曲线发生器的算法,其步骤为:An algorithm for an S-curve generator for a given segment, the steps of which are:
步骤1:向函数发生器输入指令值Ak,时间参数Tnu和Tnd,所有变量下标k表示当前采样周期值,k-1表示前1个采样周期值,Tnu为S形曲线生成过程输出绝对值从0%增加至100%最大指令值的时间,Tnd为S形曲线生成过程输出绝对值从100%降低至0%最大指令值的时间、TA为采样周期;Step 1: Input command value A k , time parameters T nu and T nd to the function generator, all variables subscript k represents the current sampling period value, k-1 represents the value of the previous sampling period, and T nu is the generation of S-shaped curve The time when the absolute value of the process output increases from 0% to 100% of the maximum command value, T nd is the time when the absolute value of the process output of the S-curve generation decreases from 100% to 0% of the maximum command value, and TA is the sampling period;
步骤2:由Ak状态决定的运算Step 2: Operations determined by the state of A k
a.当Ak=Yk-1(输出),则运算结束;a. When A k =Y k-1 (output), the operation ends;
b.当Ak=Ak-1,令Bk=Bk-1、Ck=Ck-1;然后,如果Fk-1=1且Yk=0%,令Ck=0%、Gk=TA-tk-1,否则令Gk=TA,当F=0,执行单个S形曲线生成过程,F为标志变量,G为时间积分器的增量变量;b. When A k =A k-1 , let B k =B k-1 , C k =C k-1 ; then, if F k-1 =1 and Y k =0%, let C k =0% , G k =TA-t k-1 , otherwise let G k =TA, when F=0, execute a single S-shaped curve generation process, F is the flag variable, and G is the incremental variable of the time integrator;
c.当Ak≠Ak-1,令Bk=Ak、Ck=Yk-1、Gk=TA-tk-1,则开始新的S形曲线生成过程;c. When A k ≠A k-1 , set B k =A k , C k =Y k-1 , G k =TA-t k-1 , then start a new S-shaped curve generation process;
步骤3:判断输出过程是否改变正反极性Step 3: Determine whether the output process changes positive and negative polarity
a.当Bk×Ck<0%,令Dk=0%、Fk=1,Bk×Ck<0%时,说明输入极性发生改变,以0%为分界点,将该过程分解为:从Yk-1到0%和从0%到Ak的两个S形曲线生成算法;a. When B k × C k <0%, set D k = 0%, F k = 1, B k × C k <0%, it means that the input polarity has changed, with 0% as the cut-off point, the The process is decomposed into: two S-shaped curve generation algorithms from Y k-1 to 0% and from 0% to A k ;
b.当Bk×Ck>=0%,令Dk=Bk、Fk=0;b. When B k ×C k >=0%, set D k =B k , F k =0;
c.计算Ek=|Dk|-|Ck|;c. Calculate E k =|D k |-|C k |;
步骤4:计算S形曲线生成时间TStep 4: Calculate the S-shaped curve generation time T
a.当Ek>0%,令Tk=|Ek|×Tnu;a. When E k >0%, let T k =|E k |×T nu ;
b.当Ek<0%,令Tk=|Ek|×Tnd;b. When E k <0%, let T k =|E k |×T nd ;
c.当Ek=0%,结束。c. When E k =0%, end.
步骤5:计算时间tStep 5: Calculate time t
a.当tk=Tk,令Gk=0;a. When t k =T k , let G k =0;
b.tk=tk-1+Gk;bt k =t k-1 +G k ;
c.当tk>Tk,令tk=Tk;c. When t k >T k , let t k =T k ;
步骤6:计算Xk Step 6: Calculate Xk
Xk=50%-50%×cos[(tk/Tk)π];X k =50%-50%×cos[(t k /T k )π];
步骤7:计算输出Yk Step 7: Calculate output Y k
Yk=(Dk-Ck)×Xk+Ck,其中(Dk-Ck)为当前S形曲线的幅值,乘以单位S形曲线Xk后,再加上前一个S形曲线终值Ck,即生成所需的S形曲线输出。Y k =(D k -C k )×X k +C k , where (D k -C k ) is the amplitude of the current S-shaped curve, multiplied by the unit S-shaped curve X k , plus the previous S S-shaped curve final value C k , ie to generate the desired S-shaped curve output.
而且,在所述步骤2中,当F=1,运算执行两个S形曲线生成过程中的从Yk-1到0%的S形曲线生成算法。Moreover, in the step 2, when F=1, the operation executes the S-curve generation algorithm from Y k-1 to 0% in the two S-curve generation processes.
本发明的优点和积极效果是:Advantage and positive effect of the present invention are:
1、本发明提供的S形曲线发生器的算法将正弦函数进行偏置,形成S形曲线,输出连续光滑,上升或下降过程中前半段与后半段对称,时间控制准确,算法简洁。1. The algorithm of the S-shaped curve generator provided by the present invention offsets the sine function to form an S-shaped curve, the output is continuous and smooth, the first half and the second half of the rising or falling process are symmetrical, the time control is accurate, and the algorithm is simple.
2、本发明提供的S形曲线发生器的算法将改变正反极性的S形曲线生成过程分解为2个S形曲线生成过程,有利于保护系统和机械,延长设备寿命。2. The algorithm of the S-shaped curve generator provided by the present invention decomposes the S-shaped curve generation process of changing the positive and negative polarities into two S-shaped curve generation processes, which is beneficial to the protection of the system and machinery and prolongs the life of the equipment.
3、本发明提供的S形曲线发生器的算法从阶跃输入至S形曲线输出终值的时间T与输入幅值成正比,且输入值的绝对值增量增、减方向的时间(亦称上升时间和下降时间)T可以分别设置,有利于提高生产效率。3. The algorithm of the S-shaped curve generator provided by the present invention is directly proportional to the time T from the step input to the final value of the S-shaped curve output and the input amplitude, and the absolute value of the input value increment increases and decreases the time of the direction (also Said rise time and fall time) T can be set separately, which is conducive to improving production efficiency.
附图说明Description of drawings
图1为典型输入/输出波形图(用于对照);Figure 1 is a typical input/output waveform diagram (for comparison);
图2为本发明中Tnu和Tnd定义示意图(其中平滑曲线为输出波形图);Fig. 2 is T nu and T nd definition schematic diagram among the present invention (wherein smooth curve is the output waveform figure);
图3为本发明S形曲线发生器的算法的流程图。Fig. 3 is a flow chart of the algorithm of the S-curve generator of the present invention.
具体实施方式Detailed ways
下面结合附图并通过具体实施例对本发明作进一步详述,以下实施例只是描述性的,不是限定性的,不能以此限定本发明的保护范围。The present invention will be further described in detail below in conjunction with the accompanying drawings and through specific embodiments. The following embodiments are only descriptive, not restrictive, and cannot limit the protection scope of the present invention.
一种用于给定环节的S形曲线发生器的算法,其步骤为:An algorithm for an S-curve generator for a given segment, the steps of which are:
步骤1:向函数发生器输入指令值Ak(注:,以下所述变量如无说明均为其最大值为100%的相对值;所有变量下标k表示当前采样周期值、k-1表示前1个采样周期值)、时间参数Tnu和Tnd,其中,Tnu为S形曲线生成过程输出绝对值从0%增加至100%最大指令值的时间,Tnd为S形曲线生成过程输出绝对值从100%降低至0%最大指令值的时间、TA为采样周期;Step 1: Input the command value A k to the function generator (note: the variables mentioned below are relative values whose maximum value is 100% unless otherwise specified; all variable subscripts k represent the current sampling period value, and k-1 represents The value of the first sampling period), time parameters T nu and T nd , where T nu is the time when the absolute output value of the S-shaped curve generation process increases from 0% to 100% of the maximum command value, and T nd is the S-shaped curve generation process The time when the output absolute value decreases from 100% to 0% of the maximum command value, TA is the sampling period;
步骤2:由Ak状态决定的运算Step 2: Operations determined by the state of A k
d.当Ak=Yk-1(输出),则运算结束;d. When A k =Y k-1 (output), the operation ends;
e.当Ak=Ak-1,令Bk=Bk-1、Ck=Ck-1;然后,如果Fk-1=1且Yk=0%,令Ck=0%、Gk=TA-tk-1,否则令Gk=TA,当F=0,执行单个S形曲线生成过程,F为标志变量,G为时间积分器的增量变量;e. When A k =A k-1 , let B k =B k-1 , C k =C k-1 ; then, if F k-1 =1 and Y k =0%, let C k =0% , G k =TA-t k-1 , otherwise let G k =TA, when F=0, execute a single S-shaped curve generation process, F is the flag variable, and G is the incremental variable of the time integrator;
f.当Ak≠Ak-1,令Bk=Ak、Ck=Yk-1、Gk=TA-tk-1,则开始新的S形曲线生成过程;f. When A k ≠A k-1 , set B k =A k , C k =Y k-1 , G k =TA-t k-1 , then start a new S-shaped curve generation process;
步骤3:判断输出过程是否改变正反极性Step 3: Determine whether the output process changes positive and negative polarity
d.当Bk×Ck<0%,令Dk=0%、Fk=1,Bk×Ck<0%时,说明输入极性发生改变,以0%为分界点,将该过程分解为:从Yk-1到0%和从0%到Ak的2个S形曲线生成算法,当F=1,执行2个S形曲线生成过程中的从Yk-1到0%的S形曲线生成算法;d. When B k × C k <0%, set D k = 0%, F k = 1, B k × C k <0%, it means that the input polarity has changed, with 0% as the cut-off point, the The process is decomposed into: two S-curve generation algorithms from Y k-1 to 0% and from 0% to A k , when F=1, execute the two S-curve generation processes from Y k-1 to 0 % S-shaped curve generation algorithm;
e.当Bk×Ck>=0%,令Dk=Bk、Fk=0;e. When B k ×C k >=0%, set D k =B k , F k =0;
f.计算Ek=|Dk|-|Ck|;f. Calculate E k =|D k |-|C k |;
步骤4:计算S形曲线生成时间TStep 4: Calculate the S-shaped curve generation time T
d.当Ek>0%,令Tk=|Ek|×Tnu;d. When E k >0%, set T k =|E k |×T nu ;
e.当Ek<0%,令Tk=|Ek|×Tnd;e. When E k <0%, let T k =|E k |×T nd ;
f.当Ek=0%,结束。f. When E k =0%, end.
步骤5:计算时间tStep 5: Calculate time t
d.当tk=Tk,令Gk=0;d. When t k =T k , let G k =0;
e.tk=tk-1+Gk;et k =t k-1 +G k ;
f.当tk>Tk,令tk=Tk。f. When t k >T k , let t k =T k .
步骤6:计算Xk Step 6: Calculate X k
Xk=50%-50%×cos[(tk/Tk)π]。(该计算过程相当于将[-π/2,π/2]区间正弦函数衰减50%,再偏置为从0%~100%的单位S形曲线)。X k =50%-50%×cos[(t k /T k )π]. (This calculation process is equivalent to attenuating the sine function in the interval [-π/2, π/2] by 50%, and then offsetting it into a unit S-shaped curve from 0% to 100%).
步骤7:计算输出Yk Step 7: Calculate output Y k
Yk=(Dk-Ck)×Xk+Ck,其中(Dk-Ck)为当前S形曲线的幅值,乘以单位S形曲线Xk后,再加上前一个S形曲线终值Ck,即生成所需的S形曲线输出。Y k =(D k -C k )×X k +C k , where (D k -C k ) is the amplitude of the current S-shaped curve, multiplied by the unit S-shaped curve X k , plus the previous S S-shaped curve final value C k , ie to generate the desired S-shaped curve output.
尽管为说明目的公开了本发明的实施例和附图,但是本领域的技术人员可以理解:在不脱离本发明及所附权利要求的精神和范围内,各种替换、变化和修改都是可能的,因此,本发明的范围不局限于实施例和附图所公开的内容。Although the embodiments and drawings of the present invention are disclosed for the purpose of illustration, those skilled in the art can understand that various replacements, changes and modifications are possible without departing from the spirit and scope of the present invention and the appended claims Therefore, the scope of the present invention is not limited to what is disclosed in the embodiments and drawings.
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