JP3608587B2 - Linear interpolation method - Google Patents

Description

すなわち、式（１）のΔｘ_ｍで割ることによる余りＢを、次のスキャンで式（１）の演算に再度含めることにより、余りによる丸め誤差が全く生じない。なお、これは整数型積分演算を行う際の常套手段である。
【００１３】
このコントローラ１では、位置パターン発生器１４にＸ座標の目標値ｘmを与え、所定の速度パターンにすべく、加速時間、減速時間及び定常移動速度を位置パターン発生器１４に設定して、Ｘ軸についての位置パターンを生成する。そして、スキャンごとに、微分回路２１によって、位置パターンから求められた位置指令ｘ(ｎ)から１スキャン前の値ｘ（ｎ−１）を減算して位置指令の増分値（差分値）δｘ(ｎ)を算出し、積分回路２４によって、増分値δｘ(ｎ)にΔｙm／Δｘmの比率を乗じて積分すると、Ｘ軸方向の移動量ｘ(ｎ)−ｘm-1に対応したＹ軸方向の移動量ｙ(ｎ)−ｙm-1が積分値Ｉ(ｎ)として求められることになる。この積分値Ｉ(ｎ)を加算器２５によって、直前のサイクルの目標値ｙm-1に加算することにより、各スキャンごとのＹ軸についての位置指令ｙ(ｎ)が算出される。上述したように、移動量の比ｘ(ｎ)−ｘm-1：ｙ(ｎ)−ｙm-1は、Δｘm：Δｙmに等しく、このようなｘ(ｎ),ｙ(ｎ)を用いることにより、一直線の軌跡を描かせることが可能になっている。
【００１４】
なお、上述した処理を｜Δｘ_m｜≧｜Δｙ_m｜の場合に行えば、Ｘ軸の加減速度以下に、Ｙ軸の加減速度を抑えることができる。したがって、過大加速度を防ぐ観点から、図５に示すようにＸ軸の目標値ｘ_mから位置指令ｙ(ｎ)を生成するのは｜Δｘ_m｜≧｜Δｙ_m｜の場合とし、｜Δｘ_m｜＜｜Δｙ_m｜の場合には、図６に示すように、Ｙ軸の目標値ｙ_mからＸ軸の位置指令ｘ(ｎ)を求めるようにすることが好ましい。図６に示すコントローラ１は、図５に示すものと同様のものであるが、位置パターン発生器１４、微分回路２１、積分回路２４及び加算器２５の配置がＸ軸とＹ軸に関して入れ替わっており、ｘ_mとｙ_m、ｘ _m-1 とｙ_m-1、ｘ(ｎ)とｙ(ｎ)、Δｘ_mとΔｙ_m、δｘ(ｎ)とδｙ(ｎ)が相互に入れ替わった構成となっている。ＸＹプロッタなどでは、｜Δｘ_m｜と｜Δｙ_m｜の大小関係は随時変化し得るものであるから、コントローラ１としては、｜Δｘ_m｜と｜Δｙ_m｜の大小関係に応じて図５の構成によって制御を行うか図６の構成によって制御を行うかを自動的に切り替えるようなものを使用することが望ましい。定周期スキャン方法によるデジタル制御を行うコントローラは一般にソフトウェアで実現されるから、このような自動的な切り替えを行える構成とすることは容易である。
【００１５】
以上説明したようにして、各位置決めサイクルにおいて、正確に一直線の軌跡を描く位置指令を生成することが可能になり、これをもとに各軸の剛性の高い位置制御を実施すれば、一直線軌跡を実現できることになる。
【００１６】
【発明の効果】
以上説明したように本発明は、Ｘ軸とＹ軸の一方の位置指令を位置パターンから求め、位置決めサイクルごとの移動距離の比に基づいた積分演算を行って他方の位置指令を算出することにより、各位置決めサイクルにおいて過大加速度を伴わずに、自動的に、正確な一直線の軌跡を描く制御系を実現することができるという効果がある。
【図面の簡単な説明】
【図１】ポイント・ツー・ポイント制御による位置決めを説明する図である。
【図２】ポイント・ツー・ポイント制御による通常の位置決め制御系を示すブロック線図である。
【図３】従来のＸＹ軸位置決めシステムの構成を示すブロック線図である。
【図４】一直線の軌跡を描かせるときの各軸の速度指令と位置指令との関係を示すグラフである。
【図５】本発明の実施の一形態の直線補間方法（｜Δｘ_ｍ｜≧｜Δｙ_ｍ｜の場合）が適用されるＸＹ軸位置決めシステムの構成を示すブロック線図である。
【図６】本発明の実施の一形態の直線補間方法（｜Δｘ_ｍ｜＜｜Δｙ_ｍ｜の場合）が適用されるＸＹ軸位置決めシステムの構成を示すブロック線図である。
【符号の説明】
１ コントローラ
２，２_１，２_２ サーボドライバ
３，３_１，３_２ サーボモータ
４，４_１，４_２ パルスジェネレータ
１０，１０_１，１０_２，２３ 減算器
１１，１１_１，１１_２ 乗算器
１２，１２_１，１２_２ Ｄ／Ａ変換器
１３，１３_１，１３_２ カウンタ
１４，１４_１，１４_２ 位置パターン発生器
２０ 目標位置データ
２１ 微分回路
２２ 遅延素子
２４ 積分回路
２５ 加算器
Ｋ_ｐ，Ｋ_ｐ１，Ｋ_ｐ２ 位置制御ゲイン
ｘ（ｎ），ｙ（ｎ） スキャンごとの位置指令
δｘ（ｎ），δｙ（ｎ） 位置指令の増分値[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a control method such as an XY plotter that drives a X- and Y-axis by a servomotor to perform point-to-point (PTP) positioning, and in particular, uses a controller based on a periodic scan method to add a servomotor. The present invention relates to a linear interpolation method capable of obtaining a straight track including a deceleration section.
[0002]
[Prior art]
Some XY plotters use step motors for both the X and Y axes and perform open loop control based on the number of pulses that drive the step motor, but depending on the application, size, and required performance, There is a configuration in which a servo motor is provided for each of the X-axis and the Y-axis, and the servo motors are closed-loop controlled according to a target value input from the outside. In many XY plotters, as shown in FIG. 1, the target position is given as a point sequence {P _i (x _i , y _i ), i = 0, 1, 2,. It is required to connect two adjacent points with a straight line (movement locus L). Note that control in the case where a target position is given by a point sequence is referred to as point-to-point control.
[0003]
In the XY plotter, when the target value of the X axis and the Y axis can be separated, such as when the target position is given by an XY coordinate value, conventionally, point-to-point control is performed independently for each of the X axis and the Y axis. It is common. FIG. 2 is a block diagram showing a configuration of a normal control system (for one axis) in which point-to-point control is performed by the fixed scan method. Connected to the servo motor 3 are a pulse generator 4 that generates a position feedback pulse, and a servo driver 2 that drives the servo motor 3 based on the speed command N _ref from the controller 1 and the position feedback pulse from the pulse generator 4. Yes. The controller 1 is intended to realize a digital control by periodic scanning method, a counter 13 for outputting a position feedback by counting the position feedback pulse, the target position x according to the _m position command x for each scan ( a position pattern generator 14 for generating n), multiplies the subtractor 10 for calculating a position deviation between a position feedback and position command x (n), the position control gain K _p to the position deviation of the subtracter 10 outputs The multiplier 11 and the D / A converter 12 for outputting the output of the multiplier 11 as the speed command N _ref described above are configured.
[0004]
Position pattern generator 14, together with the target position x _m is input, such that the desired speed pattern as shown in FIG. 2, (time to reach from 0 to 100% speed) acceleration time, deceleration time (100% The time from the speed to zero) and the steady movement speed (speed when moving at a constant speed from the completion of acceleration to the start of deceleration) are set, and position patterns corresponding to these input values and set values are generated. . The value of the position pattern for each scan time in the controller 1 becomes the position command x (n) for each scan time. The position command x (n) obtained in this way is matched with the position feedback by the subtracter 10, and the position control is performed by the controller 1 so that the resulting position deviation is zero.
Providing a control system as described above the X-axis and Y-axis, the target position command x _m of each positioning cycle obtained from the previously prepared target position group _for y _m, by performing each positioning control, Movements such as an XY plotter can be realized. FIG. 3 shows a configuration of a conventional XY axis positioning system configured as described above. In the drawing, the subscript 1 corresponds to the X axis, and the subscript 2 represents the Y axis. The target position in each positioning cycle is given as target position data 20.
[0005]
[Problems to be solved by the invention]
In the positioning system shown in FIG. 3, each of the position pattern generators 14 ₁ and 14 ₂ is given an acceleration time, a deceleration time, and a steady moving speed with respect to the corresponding axis. Here, assuming that Δx _m = x _m −x _m−1 and Δy _m = y _m −y _m−1 , the acceleration time, deceleration time and steady movement speed given to the X axis and Y axis, respectively, However, if | Δx _m | = | Δy _m |, since the acceleration completion time and the deceleration start time coincide with each other on the X axis and the Y axis, respectively, as shown in FIG. A straight movement trajectory is obtained from the start of movement to the completion of positioning. However, in the case of | Δx _m | ≠ | Δy _m |, since the acceleration completion time and the deceleration start time are different from each other on the X axis and the Y axis, it is impossible to draw a straight line locus. In order to obtain a linear trajectory even if | Δx _m | ≠ | Δy _m |, the steady movement speed of each axis is set in proportion to | Δx _m | and | Δy _m | Acceleration / deceleration time may be set in inverse proportion to | Δx _m | and | Δy _m |, but acceleration / deceleration time is not an integer ratio between the X axis and Y axis, or for reasons such as setting resolution, In many cases, the acceleration time and deceleration time cannot be set accurately. For this reason, an error occurs in the acceleration time and the deceleration time, and this error causes a deviation from the straight line locus. Therefore, when a linear trajectory is required between target positions for each positioning cycle, a desired result cannot be obtained by the method described above.
[0006]
An object of the present invention is to provide a linear interpolation method capable of accurately drawing a straight line between target positions without excessive acceleration when a target position group is given.
[0007]
[Means for Solving the Problems]
Linear interpolation method of the present invention related to an XY plotter for servo-driving the X-axis and Y-axis with the periodic scan method, the target position in the immediately preceding positioning cycle _{P m-1 (x m-} 1, y m target position in the current positioning cycle from _-1) P _m (x _m, in the linear interpolation method for performing a positioning control to y _m), the moving distance [Delta] x _m of the X-axis and Y-axis direction, the [Delta] y _m Are defined as Δx _m = x _m −x _m−1 and Δy _m = y _m −y _m−1 , respectively, and a position pattern from the target position in the previous positioning cycle and the target position in the current positioning cycle. generate, for each scan, a difference .delta.x (n) between the position position command value at the time of the previous scan with respect to the position command x for the X-axis obtained from the pattern (n) x (n-1 ) determined by the differentiating circuit, the moving distance of the X-axis and Y-axis direction by the integration circuit The ratio Δy _m / Δx _m integrated by multiplying the difference δx (n), for the Y-axis by adding the the integrating value to the target value y _m-1 Y coordinate in the immediately preceding positioning cycle by adder The position command y (n) is obtained, and the position control of the X axis and the Y axis is executed from time to time based on the position commands x (n) and y (n). Get.
[0008]
In the present invention, the method of determining the X axis and the Y axis is arbitrary and is not limited to the X axis in the right direction from the origin and the Y axis in the upward direction from the origin. For example, the right direction from the origin may be defined as the Y axis, and the upward direction from the origin may be defined as the X axis. However, in order to prevent occurrence of excessive acceleration, in the invention described in claim 1, it is preferable to select the X axis and the Y axis so that | Δx _m | ≧ | Δy _m |. From this point of view, in the invention described in claim 2, the processing for the X axis and the Y axis depends on whether | Δx _m | ≧ | Δy _m | or | Δx _m | <| Δy _m |. The contents have been changed.
Further, as the position pattern, it is preferable to use a position pattern obtained by setting an acceleration time, a deceleration time, and a steady movement speed so as to obtain a predetermined speed pattern.
Hereinafter, the principle of the present invention will be described.
[0009]
FIG. 4 shows an ideal relationship between the speed command and the position command for the X and Y axes for drawing a straight locus in the positioning from the point P _m−1 to the point P _m as shown in FIG. The value A of the speed command N _x for the X axis and the value B of the speed command N _y for the Y axis have a relationship of A: B = Δx _m : Δy _m at every time in one positioning cycle. Then, in the position command that is an integral value thereof, C: D = Δx _m : Δy _m holds for the position command values C and D on the X and Y axes. Therefore, for each scan, for example, the position command x (n) is sampled from the position pattern for the X axis, the difference δx (n) from the position command value at the previous scan is obtained, and the ratio of the movement distance in each axis direction The difference δx (n) is multiplied by Δy _m / Δx _m and integrated. Then, at any time within one cycle, a movement amount in the Y-axis direction having a ratio of Δy _m / Δx _{m with} respect to the movement amount in the X-axis direction is obtained. Here, the moving amount refers to a difference from the target value (x _m−1 , y _m−1 ) in the previous cycle. When the amount of movement in the Y-axis direction is obtained in this way, the position command y for the Y-axis at _every moment in the current cycle is added to the target value ym _-1 of the Y-coordinate in the previous cycle. (N) is obtained.
[0010]
DETAILED DESCRIPTION OF THE INVENTION
Next, an embodiment of the present invention will be described. FIG. 5 is a block diagram showing the configuration of the X and Y axis control system based on the linear interpolation method according to the embodiment of the present invention. A servo motor 3 ₁ corresponding to the X axis and a servo motor 3 ₂ corresponding to the Y axis are provided, and each servo motor 3 ₁ , 3 ₂ has a pulse generator 4 ₁ , 4 that generates a position feedback pulse, respectively. _2, the servo driver 2 is connected to drive the servo motor 3 _1, 3 ₂ based speed command N _ref1, N _ref2 from the controller 1 to the position feedback pulse from the pulse generator 4 _1, 4 _2. The controller 1 is intended to realize a digital control by periodic scanning method, a counter 13 _1, 13 ₂ to output as position feedback by counting the position feedback pulse of each axis, and position feedback of each axis position Subtractors 10 ₁ and 10 _{2 for} calculating position deviations from commands x (n) and y (n), respectively, and position control gains K _p1 and K _p2 are _added to the position deviations output by subtracters 10 ₁ and 10 ₂ , respectively. Multipliers 11 ₁ and 11 ₂ for multiplication, and D / A converters 12 ₁ and 12 ₂ for outputting the outputs of the multipliers 11 ₁ and 11 ₂ as speed commands N _ref1 and N _ref2 for the respective axes, respectively. ing. More controller 1, a position pattern generator 14 for outputting a position command x (n) for each scanned target value x _m is the input of the X-axis, and when the last scan the position command x (n) A differential circuit 21 for calculating a difference δx (n) with respect to the position command value x (n−1) , an integration circuit 24 for multiplying the difference δx (n) by the moving distance ratio Δy _m / Δx _m and integrating. An adder 25 is provided which adds the integrated value I (n) output from the integrating circuit 24 to the Y-axis target value ym _-1 in the previous positioning cycle to obtain a position command y (n) for the Y-axis. ing. The differentiating circuit 21 includes a delay element 22 for holding a position command at the previous scan, and a subtractor 23 for subtracting the position command x (n−1) at the previous scan from the position command x (n). ,include.
[0011]
In the integration circuit 24, integral calculation including division is performed as represented by Δy _m / Δx _m , but in order to prevent a slight rounding error, an integer type subjected to the following remainder correction processing is performed. An operation is to be performed. However, “→” represents a storing instruction, and “MOD” represents an instruction for obtaining a remainder.
[0012]
[Expression 1]

That is, the remainder B by dividing by [Delta] x _m of formula (1), by including again the calculation of formula (1) in the next scan, it does not occur at all rounding errors due to too. This is a conventional means for performing integer type integral operation.
[0013]
In this controller 1, the target value xm of the X coordinate is given to the position pattern generator 14, the acceleration time, the deceleration time, and the steady movement speed are set in the position pattern generator 14 to obtain a predetermined speed pattern, and the X axis Generate a position pattern for. Then, for each scan, the differential circuit 21 subtracts the value x (n−1) from the previous scan from the position command x (n) obtained from the position pattern to increment the position command increment value (difference value) δx ( n) is calculated and integrated by multiplying the increment value δx (n) by the ratio Δym / Δxm by the integration circuit 24, the Y-axis direction corresponding to the movement amount x (n) −xm−1 in the X-axis direction is obtained. The movement amount y (n) -ym-1 is obtained as the integral value I (n). By adding this integrated value I (n) to the target value ym-1 of the immediately preceding cycle by the adder 25, a position command y (n) for the Y axis for each scan is calculated. As described above, the ratio x (n) −xm−1: y (n) −ym−1 of the movement amount is equal to Δxm: Δym, and by using such x (n), y (n) It is possible to draw a straight locus.
[0014]
If the above-described processing is performed when | Δx _m | ≧ | Δy _m |, the acceleration / deceleration of the Y axis can be suppressed below the acceleration / deceleration of the X axis. Therefore, from the viewpoint of preventing excessive acceleration, as shown in FIG. 5, the position command y (n) is generated from the X-axis target value x _{m when} | Δx _m | ≧ | Δy _m |, and | Δx _m In the case of | <| Δy _m |, it is preferable to obtain the X-axis position command x (n) from the Y-axis target value y _m as shown in FIG. The controller 1 shown in FIG. 6 is the same as that shown in FIG. 5, but the arrangement of the position pattern generator 14, the differentiation circuit 21, the integration circuit 24, and the adder 25 is interchanged with respect to the X axis and the Y axis. , X _m and y _m , x _m−1 and y _m−1 , x (n) and y (n), Δx _m and Δy _m , δx (n) and δy (n) are interchanged. ing. In an XY plotter or the like, the magnitude relationship between | Δx _m | and | Δy _m | can be changed at any time. Therefore, the controller 1 in FIG. 5 corresponds to the magnitude relationship between | Δx _m | and | Δy _m | It is desirable to use a device that automatically switches between control according to the configuration and control according to the configuration of FIG. Since a controller that performs digital control by the periodic scan method is generally realized by software, it is easy to adopt a configuration that can perform such automatic switching.
[0015]
As described above, in each positioning cycle, it is possible to generate a position command that accurately draws a straight line trajectory. Based on this, if position control with high rigidity of each axis is performed, a straight line trajectory is generated. Can be realized.
[0016]
【The invention's effect】
As described above, the present invention obtains one position command for the X-axis and the Y-axis from the position pattern, calculates the other position command by performing an integration operation based on the ratio of the movement distance for each positioning cycle. There is an effect that it is possible to realize a control system that automatically draws an accurate straight line trajectory without excessive acceleration in each positioning cycle.
[Brief description of the drawings]
FIG. 1 is a diagram illustrating positioning by point-to-point control.
FIG. 2 is a block diagram showing a normal positioning control system based on point-to-point control.
FIG. 3 is a block diagram showing a configuration of a conventional XY axis positioning system.
FIG. 4 is a graph showing a relationship between a speed command and a position command for each axis when a straight locus is drawn.
FIG. 5 is a block diagram showing a configuration of an XY axis positioning system to which a linear interpolation method (in the case of | Δx _m | ≧ | Δy _m |) according to an embodiment of the present invention is applied.
FIG. 6 is a block diagram illustrating a configuration of an XY axis positioning system to which a linear interpolation method (in the case of | Δx _m | <| Δy _m |) according to an embodiment of the present invention is applied.
[Explanation of symbols]
1 controller 2, 2 ₁ , 2 ₂ servo driver 3, 3 ₁ , 3 ₂ servo motor 4, 4 ₁ , 4 ₂ pulse generator 10, 10 ₁ , 10 ₂ , 23 subtractor 11, 11 ₁ , 11 ₂ multiplier 12 , ₁₂ 1, ₁₂ 2 D / A converter 13 _1, 13 ₂ counters 14, 14 _1, 14 ₂ position pattern generator 20 the target position data 21 differentiating circuit 22 the delay element 24 integrating circuit 25 adders _K p, K _p1 , K _p2 Position control gain x (n), y (n) Position command δx (n), δy (n) increment value for each scan

Claims (3)

And about the XY plotter for servo-driving the X-axis and Y-axis with the periodic scan method, the target position in the immediately preceding positioning cycle _{P m-1 (x m-} 1, y m-1) (m: natural number) In the linear interpolation method when performing positioning control from to the target position P _m (x _m , y _m ) in the current positioning cycle,
The moving distance [Delta] x _m of the X-axis and Y-axis direction, the [Delta] y _m, respectively, defined by _{Δx m = x m -x m-} 1, Δy m = y m -y m-1,
A position pattern is generated from the target position in the previous positioning cycle and the target position in the current positioning cycle,
For each scan, the position command x for the X-axis obtained from the position pattern (n): position command value at the time of the previous scan on (n is a natural number) x (n-1) difference between .delta.x (n) Is obtained by a differentiating circuit , integrated by multiplying the difference δx (n) by the ratio Δy _m / Δx _m of the movement distance in the X-axis and Y-axis directions by an integrating circuit, and the integrated value is integrated by the adder. and added to the target value y _m-1 Y coordinate of a cycle to acquire the position command y (n) for the Y axis, the respective position command x (n), based on the y (n), sometimes A linear interpolation method characterized in that a linear trajectory is obtained by executing the position control of the X axis and the Y axis every moment. And about the XY plotter for servo-driving the X-axis and Y-axis with the periodic scan method, the target position in the immediately preceding positioning cycle _{P m-1 (x m-} 1, y m-1) (m: natural number) In the linear interpolation method when performing positioning control from to the target position P _m (x _m , y _m ) in the current positioning cycle,
The moving distance [Delta] x _m of the X-axis and Y-axis direction, the [Delta] y _m, respectively, defined by _{Δx m = x m -x m-} 1, Δy m = y m -y m-1,
If | Δx _m | ≧ | Δy _m |
Generates a position pattern for the X-axis from the target position at the target position and the current positioning cycle in the immediately preceding positioning cycle,
For each scan, the position command x for the X-axis obtained from the position pattern (n): position command value at the time of the previous scan on (n is a natural number) x (n-1) difference between .delta.x (n) Is obtained by a differentiating circuit , integrated by multiplying the difference δx (n) by the ratio Δy _m / Δx _m of the movement distance in the X-axis and Y-axis directions by an integrating circuit, and the integrated value is integrated by the adder. and added to the target value y _m-1 Y coordinate of a cycle to acquire the position command y (n) for the Y axis, the respective position command x (n), based on the y (n), sometimes The position control of the X axis and the Y axis is executed every moment,
If | Δx _m | <| Δy _m |
Generates a position pattern for the Y-axis from the target position at the target position and the current positioning cycle in the immediately preceding positioning cycle,
For each scan, by the differentiation circuit differential .delta.y (n) with the obtained from the position pattern Y position command value at the time of the previous scan with respect to the position command y (n) for the axis y (n-1) determined, wherein a ratio Δx _m / Δy _m of moving distance of the X-axis and Y-axis direction by integrating by multiplying the difference .delta.y (n) by the integrating circuit, the integrating component value by the adder in the immediately preceding positioning cycle of was added to the target value x _m-1 of X-coordinate to get the position command x (n) for the X axis, the respective position command x (n), based on the y (n), moment to moment, A linear interpolation method characterized in that a linear trajectory is obtained by executing position control of the X axis and the Y axis . The linear interpolation method according to claim 1, wherein the position pattern is obtained by setting an acceleration time, a deceleration time, and a steady movement speed so as to obtain a predetermined speed pattern.

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