KR100249354B1 - Method of contour error modeling for cross-coupled control of cnc machines - Google Patents

Abstract

The contour error modeling method according to the present invention generates a knot point on a reference trajectory at every sampling time by interpolating a given curve in a computer numerical control device, and it is regarded as a straight line between the knot points. A window of the reference trajectory is defined by storing a window with a moderate size, and the distance between the current position of the reference trajectory and the current position of the actual trajectory is found. The contour error is calculated as the closest distance between the current position of the trajectory and any point between the two points. In the present invention, since the variable window is used, real time calculation of the contour error can be performed in real time without worrying about the calculation time by calculating many points and distances on the reference trajectory, thereby real-time monitoring of the mutual coupling control and the contour control performance of the CNC system. Can be used effectively.

Description

Real-Time Contour Error Modeling Method in 2D Plane of Computer Numerical Control Unit

The present invention relates to a contour error modeling method for cross coupled control of a Computer Numerical Control (CNC) system.

Machining precision of a workpiece using a CNC machine tool is directly related to the quality of the workpiece, and efforts for higher precision machining continue. In conventional multi-axis CNC machine tools, each axis was controlled independently of each other in a completely separate form. However, with this separate control method, it is impossible to expect good control performance without accurate consideration of the influences between the axes in the controller design process, and different driver dynamics, external disturbances, changes in system parameters, system Inevitably, contour errors occur due to nonlinearity.

In order to solve this problem, conventionally, a method of adding a mutual coupling controller to consider contour errors separately from the tracking controller of each axis has been proposed, and since then, in the field of control of CNC machine tools, it is possible to directly As a method of reducing or eliminating contour errors, interest in controlling a plurality of axes simultaneously is increasing. The mutual coupling controller calculates the contour error every sampling period and adds a correction input to each axis according to the error, and is used in parallel to the tracking controller of each axis.

However, the contour error according to the prior art can be easily calculated in the case of a linear path, but when processing a nonlinear path such as an arc and an involute, the tracking is the difference between the position of the reference trajectory and the actual trajectory of each axis. The error can be known accurately by information about the actual position and the position of the reference trajectory. However, since the contour error is defined as the distance between the current position of the actual trajectory and the position P _c ^* closest to the reference trajectory, it is necessary to know P _c ^* to calculate the exact contour error.

However, since P _c ^* is not known in real time, it is difficult to accurately calculate the contour error, and it is important to accurately calculate the contour error because how accurately the contour error model approximates the actual error is directly related to the performance of the mutual coupling control.

Conventionally known methods for calculating the contour error include using a tracking error and the instantaneous slope of the reference trajectory, approximating the reference trajectory with a circle, or using the speed of the reference trajectory and the actual trajectory. have.

However, these prior arts do not use any information about the past reference trajectories that are available, but use only the information about the reference trajectory and the actual trajectory at the present moment to find an approximate contour error that is somewhat far from the actual contour error. One thing.

The present invention is to solve the problems of the prior art as described above, an object of the present invention is to calculate the contour error in real time for the mutual coupling control in the dynamic system of the two-dimensional plane feed movement, such as CNC system It is to propose a contour error modeling method that makes it possible.

1 shows the contouring characteristics of the X-Y table of a CNC system;

2 is a view for explaining a contour error modeling method according to the present invention;

3 is a flowchart for finding P ₁ ^* and P ₂ ^* in the method according to the present invention;

4 is a diagram showing a relationship between two points P ₁ ^* and P ₂ ^* obtained from FIG. 3 and a contour error;

In order to achieve the above object, the contour error modeling method for the mutual coupling control of the computer numerical control system according to the present invention is defined by knot points generated at every sampling time by interpolating a given curve. Defining a variable window for the reference trajectory to be stored and storing a past value of the reference trajectory in a memory; Find the distance between the past value of the reference trajectory and the current position of the actual trajectory, and P ₁ ^* and P ₂ ^* (P ₁ ^* and P ₂ ^* are _two consecutive notes on the reference trajectory, which are the shortest points in the past trajectory of the reference trajectory. Finding as a point P ₁ ^* is a point ahead of P ₂ ^* ; And calculating a contour error as the closest distance to the current position of the actual trajectory and the straight line connecting the two points.

In the contour error modeling method according to the present invention, the start of the variable window is P ₁ ^* at the previous sampling time, and the end of the variable window starts from the start point of the variable window and the note point and the current position on the reference trajectory. It is characterized in that it is a note point on the reference trajectory which increases and decreases the distance to the distance.

Hereinafter, with reference to the accompanying drawings will be described in detail the contour error modeling method according to the present invention.

Machining work with CNC machine tools is accomplished by moving a table or tool along a continuous trajectory in two- or three-dimensional space, and how exactly the movement path of the actual table or tool controls the desired trajectory is followed by Machining precision is determined.

1 is a diagram illustrating contouring characteristics of an X-Y table.

In FIG. 1, the dotted line arrow indicates tracking error, and the solid line arrow indicates contour error. The tracking error is defined as the difference between the current position of the reference trajectory of each axis and the current position of the actual trajectory, while the contour error is defined as the shortest distance between the reference trajectory and the current actual position. Therefore, reducing the tracking error does not necessarily reduce the contour error. Also, for CNC systems, contour error is an important characteristic parameter that determines machining accuracy.

2 is a view for explaining a contour error modeling method according to the present invention.

When machining any curve in a CNC machine tool, the interpolator interpolates a given curve to generate note points on the reference trajectory at every sampling time, as shown in FIG. 2, between which points are considered straight lines. Therefore, it is possible to approximate linearly between each interpolation period.

Referring to the case of Fig. 2 by way of example, since the X-Y table of the CNC machine tool has a time delay amount, P is always the current position of the reference trajectory.^*(t) is the position delayed by the amount of time delay P (t) is the actual position. Therefore, two points having the shortest distance from the past points of the reference trajectory exist at P (t) which is the current position of the actual trajectory. P these two points respectively_One ^*And P₂ ^*When set to, contour error ε_cIs P (t) and any point between two points P_c ^*It can be defined as the closest distance to (t).

In order to find the two points closest to the current position on the reference trajectory, calculating a lot of points and distances on the reference trajectory may require a lot of calculation time. In other words, by defining a window of a suitable size and storing the past value of the reference trajectory in the memory and obtaining a distance from the current position of the actual trajectory, two points having the shortest distance can be found among the past data of the reference trajectory. If the actual position of the next moment is called P (t + 1), the start of the window at this moment is P ₁ ^* as shown in Fig. 2, and the distance from this point to the current position decreases. Will increase again. Therefore, the end of the window is to increase the distance again.

In this way, it is possible to minimize the amount of calculation and reduce the execution time by repeatedly defining the window. The method of finding the two points P ₁ ^* and P ₂ ^* closest to the actual position is shown in the flowchart shown in FIG. 3.

Step 0: Initialization Step

In this method, the distance (d) between the current position of the actual trajectory P (t) and the points on the reference trajectory (d) is calculated, and the closest two points P ₁ ^* and P ₂ ^* When t = 0, which is the start time of machining, and t = T, which is the next time, there is no comparison, so the change of distance Δd cannot be obtained. So, P ₁ ^* and P ₂ ^* are initially expressed as Equation 1 below. Set it.

In Equation 1, T is a sampling time. And store k = 1 in memory. Where k is the location where P ₁ ^* is stored in memory.

First step

Store the position P ^* (t) of the reference trajectory in memory at current moment t, then read k at time t-1, k = k + 1, and then distance to the actual position as shown in Equation 2 below. Find d.

d (k) = ∥P ^* (k) -P (t) ∥

Second step

As shown in Equation 3 below, the distance is reduced by calculating k to calculate the distance Δd.

Third step

If the change Δd of the distance is greater than or equal to '0', go to the second step, otherwise go to the next fourth step.

Fourth Step

If the change Δd of the distance is smaller than '0', the point closest to the actual position becomes P ^* (k + 1), and the next closest point is found. If d (k) < d (k + 2), go to the next fifth step; otherwise, go to the next sixth step.

5th step

As shown in Equation 4 below, the two points closest to P ₁ ^* and P ₂ ^* are substituted, and the position k where P ₁ ^* is stored in the memory is finished.

Sixth step

As shown in Equation 5 below, the two points closest to P ₁ ^* and P ₂ ^* are substituted, and the position k where P ₁ ^* is stored in the memory is finished.

The above method saves the past values of the reference trajectories, calculates the distance between these values and the current position, then looks at the change in distance and, if there is a change in distance, saves the value of k at that time, which is the two points closest to the current position. To find P ₁ ^* and P ₂ ^* .

Thus, in the transition state, the size of the window changes every moment, but as the system enters the normal state, the size of the window is fixed.

The two points found in this way can be shown in FIG. 4, and as shown in FIG. 4, the coordinate of P ₁ ^* is (x ₁ , y ₁ ) and the coordinate of P ₂ ^* is (x ₂ , y _2). Θ in FIG. 4 is a value to be calculated for each interpolation period, and can be expressed by Equation 6 below.

FIG. 4 is a diagram showing the relationship between the two points P ₁ ^* and P ₂ ^* obtained as described above and the contour error. FIG. 4A is a case where x ₂ ≧ x ₁ , and FIG. 4B is a case where x ₂ <x ₁ . In Figure 4 e _x 'is the error of the X-axis of P (t) and P ₂ ^* , e _y ' is the error of the Y-axis. Therefore, the contour error ε _c of the current moment due to the geometric shape can be expressed by Equation 7 below.

The above-described method can be applied to any reference trajectory since only the position P ₁ ^* and P ₂ ^{*, which} are the positions of the reference trajectories closest to the actual position, can calculate the contour error.

As described above, the contour error modeling method according to the present invention generates a note point on a reference trajectory at every sampling time by interpolating a given curve in the CNC system, and it is regarded as a straight line between the note points. A window of the reference trajectory is defined by storing a window with a moderate size, and the distance between the current position of the reference trajectory and the current position of the actual trajectory is found. The contour error is calculated as the closest distance between the current position of the trajectory and any point between the two points. In the present invention, since the variable window is used, real time calculation of the contour error can be performed in real time without worrying about the calculation time by calculating many points and distances on the reference trajectory, thereby real-time monitoring of the mutual coupling control and the contour control performance of the CNC system. Can be used effectively.

Claims (3)

A contour error modeling method for mutual coupling control of a computer numerical control system, comprising: a reference trajectory defined by a note point generated at every sampling time by interpolating a given curve Defining a variable window to store a past value of a reference trajectory in a memory; Find the distance between the past value of the reference trajectory and the current position of the actual trajectory, and P ₁ ^* and P ₂ ^* (P ₁ ^* and P ₂ ^* are _two consecutive notes on the reference trajectory, which are the shortest points in the past trajectory of the reference trajectory. Finding as a point P ₁ ^* is a point ahead of P ₂ ^* ; And And calculating the contour error as the closest distance to the current position of the actual trajectory and any point between the two points. The method of claim 1, wherein the start of the variable window is P ₁ ^* at a previous sampling time, and the end of the variable window is obtained by determining a distance from a start point of the variable window to a current point and a note point on a reference trajectory. Contour error modeling method characterized in that the point is a note point on the reference trajectory increases with decreasing distance. 3. The method of claim 2, wherein the calculating of P1 ^* and P2 ^* is performed by the following method; Step 0: Initialization Step In this method, the distance (d) between the current position of the actual trajectory P (t) and the points on the reference trajectory (d) is calculated, and the closest two points P ₁ ^* and P ₂ ^* When t = 0, which is the start time of machining, and t = T, which is the next time, there is no comparison, so the change of distance Δd cannot be obtained. So, P ₁ ^* and P ₂ ^* are initially expressed as Equation 1 below. Set it. Equation 1

In Equation 1, T is a sampling time. And store k = 1 in memory. Where k is the location where P ₁ ^* is stored in memory. First step Store the position P ^* (t) of the reference trajectory in memory at current moment t, then read k at time t-1, k = k + 1, and then distance to the actual position as shown in Equation 2 below. Find d. Equation 2 d (k) = ∥P ^* (k) -P (t) ∥ Second step As shown in Equation 3 below, the distance is reduced by calculating k to calculate the distance Δd. Equation 3

Third step If the change Δd of the distance is greater than or equal to '0', go to the second step, otherwise go to the next fourth step. Fourth Step If the change Δd of the distance is smaller than '0', the point closest to the actual position becomes P ^* (k + 1), and the next closest point is found. If d (k) &lt; d (k + 2), go to the next fifth step; otherwise, go to the next sixth step. 5th step As shown in Equation 4 below, the two points closest to P ₁ ^* and P ₂ ^* are substituted, and the position k where P ₁ ^* is stored in the memory is finished. Equation 4

Sixth step As shown in Equation 5 below, the two points closest to P ₁ ^* and P ₂ ^* are substituted, and the position k where P ₁ ^* is stored in the memory is finished. Equation 5

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