JPH03171206A - Position command generation method for multi-axis machine - Google Patents

Abstract

PURPOSE:To attain highly precise orbit control by giving a specified command function being the function of time to respective axes with a certain axis as a reference when a space curve is approximated to a polygonal line. CONSTITUTION:When the space curve is approximated to the polygonal line, the interpolation command of a straight line is given by expressions I and II when an X-axis and a Y-axis are set to be x1(t) and y1(t). Here, VY/VX=K and (VX<2>+VY<2>)<1/2>:moving speed. When the gains of respective axes are set to be Kx and Ky and (m) is selected as an expression III, y(t)/x(t)=K is satisfied in spite of the values of KY and KX. Thus, the command for the other axis can previously be corrected by considering the characteristic of a servo system with the command of one axis which is approximated to the straight line as the reference, and highly precise orbit control can be realized without increasing an operation time for every sampling period.

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention is applicable to trajectory control of multi-axis machines such as NCs and robots, which have two or more axes and each axis is composed of a servo mechanism. Regarding the method by which the directive is issued. [Prior Art] To generate a free curve as a space curve in a multi-axis component machine such as an NC machine tool or a robot, a broken line approximation is performed in which a given curve is approximated by a straight line for each minute section. This straight line is given to the servo of each axis as a time function command. In order to achieve a highly accurate shape, we strive to match the servo characteristics of each axis as much as possible. However, it is impossible to exactly match the characteristics, which results in shape errors. In order to solve these problems, one reference axis is determined, and for the other axes, the reference axis command is multiplied by a pre-calculated value and a constant, and the response characteristics of the reference axis and the relevant axis are calculated. A method has been proposed in which the sum of the difference multiplied by another constant is given as a command.
3). [BM3 In the sample value control system that the invention seeks to solve, it is desirable that the sampling period be as short as possible. To achieve this, it is necessary to reduce the amount of calculation that must be performed for each sample as much as possible.

However, this method has the disadvantage that the above calculation must be performed for each sample in the sample value control system, and as the number of axes increases, the calculation time also increases. [Means for Solving the Problems] The method for generating position commands for a multi-axis machine of the present invention uses a certain axis as a reference when realizing the movement of an arbitrarily given space curve by polygonal line approximation. , f+(t), which is a function of time (t) that can realize the broken line approximation on the figure.
is given as the command function, but for other axes, x+f+(t
)+fi(t) (where, i・2.3,...,N, f+(t) is a function that is one order lower in t than r+(t).
xI is given by generating a constant〉 as a command function. [Effect] As mentioned above, since all generation functions are obtained when determining the line approximation, the amount of calculation for each sample is not affected at all even if the number of Tsumugi increases. Furthermore, differences in response characteristics between multiple axes can be completely compensated for, making highly accurate orbit control possible. [Example] Next, an example of the present invention will be described with reference to the drawings. Fig. 1 is a schematic configuration diagram of a servo system consisting of two axes, X% and Y axes, showing an embodiment of the present invention, and Fig. 2 shows a point (xo + yo
) to the point (Xr.311). A multi-axis machine will be explained here using a two-axis machine as an example. If the number of wheels is larger than that, the relationship between the first and second axes should be changed to the first, third, and so on. 1st. You can think of it as the fourth axis. (t) When performing linear interpolation by giving a speed command in steps The linear interpolation command shown in Figure 2 is as follows: ( !
), given by formula 《2》. Shame (t) = y, t - (t) y
+(t)”Vyt−κVxj
... (2) v-r five stones v1: Movement speed (given in advance). At this time, the gain K of each sleeve is set to κ8. K,
Then, the steady solution for each axis is given by the following equation (3). (4) becomes. It is. Therefore, xt(t)・V. When t, yl(t)-Vyt◆Ken-{5)-(6) The steady-state solution is the following equation (7).Here, if we set , we get .If we choose the garden in this way, then y( t)/x(t)=K
is satisfied regardless of the value of κV*KX.

Now, if we set X+ (L)'f+ (L)"Vxt, then 3
1t(t)-Kf+(t)◆1. Here is《1
0》 is given by the formula. Figure 3 shows the space curve P. P,, P, Pku+ ””+
FIG. 4 is a flowchart showing the calculation process of the position command by the position command calculation unit 1 in the case of FIG. 3. Manually set the system clock 8T, servo gain K, and KY (step 10, speed V. Step 12: Manually calculate the total score. Set the point digit to 1fj-1《Step l3
》． Point j. The speed JfVx in the X-axis direction between j◆1 and the number of interpolations N are calculated (step 14), and the value of the pitch in equation (t0) is calculated. The initial value of the number of interpolations i is l, and the initial value of the position command is δ×. 10, δy0-0 (step l6), and N position commands δX I + δy between points j and j◆1. is calculated and output to the X-axis servo mechanism 2 and Y-axis servo mechanism 3 (
Steps 17-20). Steps 14-20 are repeated for each broken line up to point Pe (step 21.22).

(2) When performing linear interpolation by giving a speed command in a ramp shape xl (t) - a t2 - (t1) yl (t) = Ka t2 + mt + n ・
- Let (t2) be the command to each axis servo system. The steady-state solutions for the response of each axis are expressed by the following equations (t3) and (t4).

therefore, becomes. (+5). The following equation is obtained from equation (+6).

Faith n=-...(t
8) K× Again, when Xt(L)-L(L)・αt2, y+(L)・Kf,(t)◆f2《0 Tatami, f2(t)=st◆n ■, n is (t7). It is given by equation (t8).

When a function is generated and a command is issued to the servo mechanism 2.3 for each of the X and Y axes, the response becomes an ideal straight line regardless of the difference in gain KX+κ7.

(3) When the acceleration is changed in a straight line The case in which the speed is a step or ramp has already been described, so the case in which the speed is accelerated in a square curve will be described.

When the speed is a square curve, the position command is Xl (t)
ma, L3m (t9).

At this time, in this method, yl (L)-Ka. t3++aL”+nt+p
-” (20) means '1-.

here. Xl(t). When y+(L) is the command to each servo mechanism 2.3, the response is desired, and the following is derived.

From these three formulas is obtained.

This means that when X▲(t)・fi(L), y. (L) =Kf, (t)+mt2+nt+p is generated, and X. It is shown that if commands are given to the Y-axis servo systems 2.3, an ideal straight line will be drawn.

The calculations shown above (Equation (5). (6). (t1).
(t2), (t9). (20)) need not be performed for every sample, but may be performed for each breaking point of the broken line approximation.

[Effects of the Invention] As explained above, the present invention makes it possible to modify in advance the commands to other axes based on the command of one linearly approximated axis in consideration of the characteristics of the servo system. By using this as a command for each axis, it is possible to realize highly reliable trajectory control of a multi-axis machine without increasing the calculation time for each sampling period.

[Brief explanation of the drawing]

FIG. 1 is an X-axis diagram showing an embodiment of the present invention. Figure 2 is a schematic configuration diagram of a servo system consisting of two axes, the Y-axis.
) to the point (XI.y+), Figure 3 shows the space curve as hat, hPs, ""PM
- A diagram showing how IPkl is approximated by a broken line, Figure 4 is the third
3 is a flowchart showing the position command calculation process of the position command calculation unit 1 in the case shown in FIG. 1...Position command calculation unit, 2-X-axis servo mechanism, 3-Y-wheel servo mechanism, 11-2 2-...Step.

Claims (1)

[Claims] In a machine having one or two or more axes, each of which is composed of a servo mechanism, when an arbitrarily given spatial curve is realized as its movement by polygonal line approximation, is the reference, and on that axis, f_i(t), which is a function of time (t) that can realize the broken line approximation on the figure, is given as a command function, but on the other axes, K_if_i(t) + f_i(t) (However, i=2
, 3, . . . , N, f_i(t) is a function one order lower in t than f_i(t), and K_i is a constant) is generated and given as a command function.