A multi-axis contour error control method based on time delay synchronization

Abstract

The application discloses a multi-axis linkage contour error control method based on time delay synchronization, position data of initial reference trajectories and actual trajectories is acquired in the axis coordinate system, the synchronization delay time is calculated according to the position data of the reference trajectories and the actual trajectories, the coupling error is calculated based on the synchronization delay time, the initial trajectory is compensated according to the coupling error, the ideal reference trajectory is obtained to make the delay time synchronization, the new reference trajectory is run, the operation of steps S1-S3 is repeated until the accuracy requirement is met. The application does not need to perform the contour error estimation, avoids the accuracy decline caused by the estimation error, does not need to perform the coordinate transformation of the axis coordinate system and the workpiece coordinate system, and directly performs the compensation in the machine tool coordinate system, so that the application has wide applicability.

Description

Technical Field

[0001] This invention belongs to the field of multi-axis linkage servo control technology, specifically relating to a multi-axis linkage contour error control method based on time delay synchronization. Background Technology

[0002] In contour tracking tasks, due to servo system response delays and dynamic coupling between different axes, a certain deviation occurs between the actual running trajectory and the reference trajectory. Contour error is typically used to describe the accuracy of contour tracking tasks; it is defined as the shortest distance from the actual position point to the reference trajectory. Improving the trajectory tracking accuracy of a single axis through trajectory tracking control methods, such as zero-phase error tracking control and sliding mode control, can indirectly improve contour accuracy to some extent. However, due to the limited control bandwidth of feedback drivers and the incompatibility of dynamics between different axes, simply improving the trajectory tracking performance of each axis cannot effectively suppress contour error. In complex contour machining scenarios with large curvature and high feed rates, contour machining performance is significantly reduced. Therefore, direct control of contour error has been extensively studied. However, contour error cannot be measured in real time by sensors. Furthermore, the reference trajectory is usually a free-form curve, and the contour error in it cannot be represented analytically. Therefore, previous studies have required accurate estimation of contour error before implementing contour error control.

[0003] In existing contour error control methods, one type approximates the reference trajectory using circular arcs or straight lines, derives the conversion relationship between contour error and tracking errors of each axis, and compensates for the reference trajectory based on the decomposed axis errors, such as cross-coupling control. Another type is model-based pre-compensation methods, which compensate for the reference trajectory by finding the perpendicular point on the reference trajectory. However, most existing five-axis contour control research is based on the assumption that the desired tool path is sufficiently smooth, and few studies consider improving contour performance under machining tasks with large curvature and sharp corner trajectories. Furthermore, existing contour control methods require forward and inverse kinematic calculations for each position point to achieve coordinate transformation between the axis coordinate system and the workpiece coordinate system. The requirements of kinematic calculation limit the versatility of contour error control methods because it depends on the structural parameters of different machine tools. In addition, the kinematic transformation process is not always solvable, and the calculation process may encounter singularity problems. Therefore, it is necessary to propose a new method. Summary of the Invention

[0004] To address the aforementioned technical problems, the present invention aims to provide a multi-axis linkage contour error control method based on time delay synchronization. This method eliminates the need for contour error estimation, thus avoiding the decrease in accuracy caused by estimation errors. It also eliminates the need for coordinate transformation between the axis coordinate system and the workpiece coordinate system, and compensation is performed directly in the machine tool coordinate system. Therefore, it has wide applicability.

[0005] To achieve the above-mentioned objectives, the technical solution adopted by the present invention is as follows:

[0006] A multi-axis linkage contour error control method based on time delay synchronization includes the following steps:

[0007] S1: Obtain the position data of the initial reference trajectory and the actual trajectory in the axis coordinate system;

[0008] S2: The synchronization delay time is calculated based on the position data of the reference trajectory and the actual trajectory;

[0009] S3: Calculate the coupling error based on the synchronization delay time, and compensate the initial trajectory according to the coupling error to obtain an ideal reference trajectory;

[0010] S4: Run the new reference trajectory and repeat steps S1-S3 until the accuracy requirements are met.

[0011] Preferably, step S2 includes the following steps:

[0012] S2.1: Based on the position data collected in step S1, calculate the reference trajectory velocity and actual trajectory velocity of each motion axis;

[0013] S2.2: Calculate the delay time of each motion axis based on the position data collected in step S1 and the velocity data calculated in step S2.1;

[0014] S2.3: Based on the speed data obtained in step S2.1 and the delay time obtained in step S2.2, calculate the synchronization delay time, where the synchronization delay time refers to the time taken for the reference trajectory point to reach the point where the delay time of each axis is consistent.

[0015] Preferably, in step S1, the reference trajectory is represented as {q} ref (0),q ref (T),...,q ref (kT)}, the actual trajectory is represented as {q act (0),q act (T),...q act (kT)}, where k represents the number of interpolation cycles and T represents the sampling period.

[0016] Preferably, in step S2.1, the reference trajectory velocity and actual trajectory velocity of each motion axis are calculated by the center difference method.

[0017] More preferably, in step S2.1, the first point is calculated using backward difference, the last point is calculated using forward difference, and the calculation formulas for the remaining points are as follows:

[0018] Where j represents the calculation process of the j-th axis.

[0019] Preferably, in step S2.2, the entire delay process is treated as uniformly accelerated motion, using the average velocity v. d,j To calculate the delay time, the average of the reference trajectory velocity and the actual trajectory velocity is used as the average velocity v. d,j The calculation formula is: The delay time t is calculated using the reference trajectory, the actual trajectory, and the average velocity. d,j .

[0020] More preferably, in step S2.2, a speed threshold is set when the average speed v d,j When the speed exceeds the threshold, calculate the delay time t. d,j When the average velocity v d,j When the speed is less than or equal to the speed threshold, the delay time t will be applied. d,j It is considered as 0.

[0021] More preferably, in step S2.2, the delay time t d,j Through average velocity v d,j Calculate and set the velocity threshold to 0.005 mm / s. The calculation formula is:

[0022] Preferably, in step S2.3, the synchronization delay time The calculation formula is:

[0023] Where n represents the number of motion axes.

[0024] Preferably, in step S3, the position points on the reference trajectory where the delay time of each axis is synchronized are taken as the contour error points q. comp Based on the synchronization delay time, the contour error point q comp The calculation formula is: At this point, the tracking error of each axis is expressed as: e j (kT)=(q ref,j (kT)-q comp,j (kT))+(q comp,j (kT)-q act,j (kT))=e 1,j (kT)+e 2,j (kT), where e j (kT) is divided into synchronization error e 1,j (kT) and coupling error e 2,j (kT);

[0025] Based on coupling error e 2,j (kT) compensates for the reference trajectory, that is:

[0026] At this point, the reference trajectory has a synchronization delay on the compensated actual trajectory. Since the delay processes before and after compensation are not completely consistent, the position point of the compensated actual trajectory is approximately on the reference trajectory, that is: At this point, the contour error can be effectively reduced.

[0027] Beneficial effects:

[0028] This invention compensates for a reference trajectory in axial space, avoiding compensation deviations caused by spatial geometric features such as large curvature and sharp angles of the trajectory. Furthermore, since the entire compensation process is implemented in the axial space coordinate system, it eliminates the need for contour error estimation and coordinate transformation, thus possessing extremely wide applicability.

[0029] This invention operates on a reference trajectory without affecting the stability of the closed-loop controller. It is also compatible with other types of controllers, such as cascaded PI controllers and speed feedforward controllers, and has the advantage of wide applicability. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the experimental platform according to an embodiment of the present invention;

[0031] Figure 2 This is a schematic diagram illustrating the definition of synchronization delay time in an embodiment of the present invention;

[0032] Figure 3 This is a schematic diagram illustrating compensation in an embodiment of the present invention;

[0033] Figure 4 This is a flowchart of the contour error control method based on time delay synchronization of the present invention. Detailed Implementation

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the specific implementation methods of the present invention will be described below with reference to the accompanying drawings. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings and other implementation methods can be obtained based on these drawings without any creative effort.

[0035] The technical solution of the present invention will be described in detail below with specific embodiments.

[0036] This invention proposes a multi-axis linkage contour error control method based on time-delay synchronization. It estimates the synchronization delay time in the axis coordinate system, finds the coupling error under the time-delay synchronization, and compensates for the reference trajectory based on the coupling error to obtain an ideal reference trajectory. The method includes the following steps:

[0037] S1: Run the initial reference trajectory and collect the location data of planned points and actual points based on the sampling period.

[0038] The reference trajectory and the actual trajectory can be represented as {q} ref (0),q ref (T),...,q ref (kT)} and {q act (0),q act (T),...q act (kT)}, where k represents the number of interpolation cycles and T is the sampling period of the sensor or encoder.

[0039] like Figure 1 As shown, the experimental platform is a BC-type dual rotary table five-axis CNC machine tool equipped with a Googol CNC system. The machining contour can be specified through the host computer, and the reference trajectory and actual running trajectory information after CNC system interpolation can be output.

[0040] Preferred, Figure 1 In this experiment, the three linear axis drives are Yaskawa SGDM-10ADA-V, and the two rotary axis drives are Sanyo RS1A03AAWA. Sampling is performed at a frequency of 500Hz on the controller panel. During the experiment, the CNC machine tool receives G-codes based on G01 and simultaneously acquires the reference and actual position information of each axis at sampling intervals.

[0041] S2: The synchronization delay time is calculated based on the position data of the reference trajectory and the actual trajectory, as follows:

[0042] S2.1: Estimate the velocities of the reference trajectory and the actual trajectory using the central difference method. The first point is calculated using backward difference, and the last point is calculated using forward difference, i.e.:

[0043] Where j represents the calculation process of the j-th axis.

[0044] S2.2: Calculate the delay time of each motion axis based on the position data collected in step S1 and the velocity data calculated in step S2.1.

[0045] In step S2.2, since the sampling time is relatively small, the entire delay process can be approximated as uniformly accelerated motion, and the average velocity v can be used. d,j To calculate the time of the delay process;

[0046] The formula for calculating average speed is:

[0047] Delay time t d,jThe speed can be calculated using the average speed. To avoid excessive delay when the shaft motion is extremely small, this invention sets a speed threshold of 0.005 mm / s, i.e.:

[0048]

[0049] S2.3: such as Figure 2 As shown, the synchronization delay time is defined as the time taken for a point with consistent delay times on each axis to reach the reference trajectory. The synchronization delay time is expressed by the following formula. Make an estimate:

[0050] Where n represents the number of motion axes.

[0051] S3: Calculate the coupling error based on the synchronization delay time, compensate the initial trajectory according to the coupling error, and obtain the ideal reference trajectory, as follows:

[0052] The contour error point q comp Defined as the position point where the delay time of each axis on the reference trajectory is synchronized, the contour error point is calculated based on the synchronization delay time.

[0053] Specifically, the calculation formula is as follows: At this point, the tracking error of each axis is expressed as: e j (kT)=(q ref,j (kT)-q comp,j (kT))+(q comp,j (kT)-q act,j (kT))=e 1,j (kT)+e 2,j (kT);

[0054] The above formula represents the tracking error e of each axis. j (kT) is divided into synchronization error e 1,j (kT) and coupling error e 2,j (kT). Synchronization error e 1,j (kT) is due to the system's response characteristics on each axis, reflecting the overall response delay of the system; coupling error e 2,j (kT) originates from the lack of coordination in the motion of each axis, that is, the time delay of each axis in the time domain is not synchronized.

[0055] The reference trajectory is compensated based on coupling error, as illustrated in the following diagram. Figure 3As shown, due to the inconsistent delay times of each axis, the actual positions of each axis are distributed at different times on the reference trajectory. By estimating the synchronization delay time, the contour error points under synchronized delay times are obtained. The contour error points are distributed at the same time on the reference trajectory. At this time, the tracking error can be divided into synchronization error and coupling error. The reference trajectory is compensated based on the coupling error, that is:

[0056]

[0057] Therefore, the reference trajectory has a synchronization delay on the compensated actual trajectory. Since the delay processes before and after compensation are not completely consistent, the position point of the compensated actual trajectory is approximately on the reference trajectory, and the contour error can be effectively reduced.

[0058] S4: Run the new reference trajectory and repeat the operations in steps S1-S3 until the accuracy requirements are met.

[0059] The embodiments provided by the present invention have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of the present invention, and the descriptions of the embodiments above are only for the purpose of helping to understand the core ideas of the present invention. It should be noted that those skilled in the art can make several improvements and modifications to the present invention without departing from the principles of the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A multi-axis linkage contour error control method based on time-delay synchronization, characterized in that, Includes the following steps: S1: Obtain the initial reference trajectory and actual trajectory position data in the axis coordinate system; S2: The synchronization delay time is calculated based on the position data of the reference trajectory and the actual trajectory. S3: Calculate the coupling error based on the synchronization delay time, compensate the initial trajectory according to the coupling error, and obtain a new reference trajectory; S4: Run the new reference trajectory and repeat steps S1-S3 until the accuracy requirements are met; Step S2 includes the following steps: S2.1: Based on the position data collected in step S1, calculate the reference trajectory velocity and actual trajectory velocity of each motion axis; S2.2: Calculate the delay time of each motion axis based on the position data collected in step S1 and the velocity data calculated in step S2.1; S2.3: Based on the speed data obtained in step S2.1 and the delay time obtained in step S2.2, calculate the synchronization delay time, where the synchronization delay time refers to the time taken for the reference trajectory point to reach the point where the delay time of each axis is consistent. In step S2.2, the entire delay process is treated as uniformly accelerated motion, using the average velocity v. d,j To calculate the delay time, the average of the reference trajectory velocity and the actual trajectory velocity is used as the average velocity v. d,j The delay time t is calculated using the reference trajectory, the actual trajectory, and the average velocity. d,j ; In step S2.3, the synchronization delay time The calculation formula is: Where n represents the number of motion axes.

2. The multi-axis linkage contour error control method based on time delay synchronization according to claim 1, characterized in that, In step S2.1, the reference trajectory velocity and actual trajectory velocity of each motion axis are calculated by the center difference method.

3. The multi-axis linkage contour error control method based on time delay synchronization according to claim 2, characterized in that, In step S1, the reference trajectory is represented as {q} ref (0),q ref (T),...,q ref (kT)}, the actual trajectory is represented as {q act (0),q act (T),...q act (kT)}, where k represents the number of interpolation cycles and T represents the sampling period; In step S2.1, the first point is calculated using backward differencing, the last point is calculated using forward differencing, and the calculation formulas for the remaining points are as follows: Where j represents the calculation process of the j-th axis.

4. The multi-axis linkage contour error control method based on time delay synchronization according to claim 1, characterized in that, In step S2.2, a speed threshold is set when the average speed v d,j When the speed exceeds the threshold, calculate the delay time t. d,j .

5. The multi-axis linkage contour error control method based on time delay synchronization according to claim 4, characterized in that, In step S2.2, the delay time t d,j Through average velocity v d,j Calculate and set the velocity threshold to 0.005 mm / s. The calculation formula is:

6. The multi-axis linkage contour error control method based on time delay synchronization according to claim 3, characterized in that, In step S3, the position points on the reference trajectory where the delay time of each axis is synchronized are taken as the contour error points q. comp Based on the synchronization delay time, the contour error point q comp The calculation formula is: At this point, the tracking error of each axis is expressed as: e j (kT)=(q ref,j (kT)-q comp,j (kT))+(q comp,j (kT)-q act,j (kT))=e 1,j (kT)+e 2,j (kT), where e j (kT) is divided into synchronization error e 1,j (kT) and coupling error e 2,j (kT); Based on coupling error e 2,j (kT) compensates for the reference trajectory, that is: The compensated actual trajectory position point is on the reference trajectory, that is: At this point, the contour error can be effectively reduced.

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