Feed system position feed-forward quantity compression method

Abstract

The invention discloses a feed system position feed-forward quantity compression method, which comprises the following steps of: (1) acquiring operation data of a numerical control machine tool, and calculating a feed-forward quantity of an impulse response model by adopting the operation data; (2) acquiring the motion state of the numerical control machine tool at the current moment, wherein the motion state of the numerical control machine tool at the current moment is selected from constant speed, uniform variable speed, variable acceleration or low speed; the low speed is specifically that the speed ranges from-0.03 mm / ms to 0.03 mm / ms; fitting the feed-forward quantity in each motion state with the operation data to obtain a polynomial; and (3) selecting a corresponding polynomial according to the current motion state, and substituting the operation data of the current numerical control machine tool into the corresponding polynomial to calculate the compression feed-forward quantity. According to the feed-forward quantity compression method, the technical problems that when an existing convolution type speed impulse response model feed-forward method is used for contour error control, loss of calculation time is too high, and contour error compensation precision is low are solved.

Description

Technical Field

[0001] The present invention belongs to the field of numerical control technology, and more specifically, relates to a method for compressing the position feedforward amount of a feed system. Background Art

[0002] For the feed system model based on traditional mathematical methods, the model itself has low accuracy and difficult parameter identification. The complexity of the model itself is relatively low, and the final contour error compensation accuracy is poor. Different from the feed system model based on traditional mathematical methods, the convolutional speed pulse response model has a high model complexity, can accurately reflect the response characteristics of the actual feed system, has a high model prediction accuracy, and finally has a higher accuracy after feedforward compensation using the convolutional speed pulse response model. Currently, the main steps for calculating the feedforward amount using the feedforward function of the convolutional speed pulse response model are as follows:

[0003] The first step: Use two sets of command speed sequences to obtain the speed pulse response model of the feed system and save it;

[0004] The second step: Import the model into the numerical control system. After enabling the feedforward function, the system reads the speed pulse response model matrix;

[0005] The third step: In each control cycle (1 ms), the command of the previous cycle is superimposed with the speed pulse response model and the feedforward amount of the current control cycle is calculated by back-calculation and sent down.

[0006] However, the above-mentioned feedforward method of the convolutional speed pulse response model has the problem of too high computational complexity. The speed pulse response model matrix generally contains 200 data points, and the feedforward compensation function has strong real-time requirements. Therefore, calculating the feedforward amount will occupy a large amount of CPU time. If the multi-axis convolutional speed pulse response model feedforward function is enabled, the time consumption will double. On the one hand, it will squeeze the time allocated by the CPU to other functions. On the other hand, if the feedforward amount is not calculated within the current control cycle (1 ms), there will be a problem of incorrect feedforward amount sending, seriously affecting the machining accuracy; in a more serious situation, it will directly cause the inter-process communication (IPC) to crash, with a certain potential safety hazard.

[0007] When using the convolution-based contour error control technology based on the velocity pulse response model for contour error control, excessive matrix operations and floating-point operations are used, resulting in a too high computational complexity. At the same time, in order to ensure the contour error compensation accuracy, the numerical control system needs to calculate the feedforward amount of convolution-based contour error compensation once in each control cycle (usually 1ms), which causes the time allocated by the system for convolution-based contour error compensation to be too long, significantly squeezing the time of other functions with high real-time requirements. In addition, within each fixed interpolation cycle (1ms), the numerical control system will preferentially execute tasks with higher priorities such as the interpolation thread and the velocity planning thread, resulting in limited CPU time allocated to the remaining tasks. If, in a certain interpolation cycle (1ms), the numerical control system spends too much time on high-priority tasks, it will cause the feedforward amount of convolution-based contour error compensation for this interpolation cycle (1ms) to not be calculated within the remaining time of this interpolation cycle (1ms), resulting in a large error in the feedforward amount calculation for this interpolation cycle (1ms) and failing to achieve the expected compensation effect.

[0008] Therefore, when using the existing feedforward method of the convolution-based velocity pulse response model for contour error control, there is a problem of excessive time consumption in calculation, and there is a certain probability that it will affect the final compensation accuracy. Summary of the Invention

[0009] In view of the above defects or improvement requirements of the prior art, the present invention provides a method for compressing the position feedforward amount of a feed system, thereby solving the technical problems of high time consumption and high space resource consumption in the real-time calculation of the feedforward amount by the existing feedforward method of the convolution-based velocity pulse response model.

[0010] To achieve the above object, according to one aspect of the present invention, there is provided a method for compressing the position feedforward amount of a feed system, including the following steps:

[0011] (1) Obtain the operating data of the numerically controlled machine tool, and calculate the feedforward amount of the pulse response model using the operating data;

[0012] (2) Obtain the motion state of the numerically controlled machine tool at the current moment, and the motion state of the numerically controlled machine tool at the current moment is selected from uniform motion, uniformly variable motion, variable acceleration or low speed; the low speed is specifically a speed of -0.03 to 0.03 mm / ms; respectively fit the feedforward amount in each motion state with the operating data to obtain a polynomial;

[0013] (3) Select the corresponding polynomial according to the current motion state, and substitute the operating data of the current numerically controlled machine tool into the corresponding polynomial to calculate the compressed feedforward amount.

[0014] Preferably, the operating data includes command speed and command acceleration data.

[0015] Preferably, when the motion state of the CNC machine tool at the current moment is uniform, the specific method for compressing the feedforward amount is as follows:

[0016] S1 Design a machining code for uniform motion, run the machining code for uniform motion on the CNC machine tool, collect the commanded speed of the CNC machine tool, and calculate the corresponding feedforward amount T for uniform motion through the impulse response model uv ; Fit the feedforward amount T for uniform motion uv linearly with the commanded speed to obtain the first polynomial fitting curve f uv ;

[0017] S2 Substitute the commanded speed v1 at a certain moment into the first polynomial fitting curve f uv to obtain the corresponding feedforward amount for uniform motion at the current moment The feedforward amount for uniform motion at the current moment is the compressed feedforward amount.

[0018] Preferably, the first polynomial fitting curve f uv is a linear function, specifically f v = kv, where v is the commanded speed of the CNC machine tool and k is the fitting coefficient.

[0019] Preferably, when the motion state of the CNC machine tool at the current moment is uniformly variable, the specific method for compressing the feedforward amount is as follows:

[0020] T1 Design a machining code for uniform motion, run the machining code for uniform motion on the CNC machine tool, collect the commanded speed of the CNC machine tool, and calculate the corresponding feedforward amount T for uniform motion through the impulse response model v ; Fit the feedforward amount T for uniform motion v linearly with the commanded speed to obtain the second polynomial fitting curve f v ;

[0021] T2 Design machining codes for different fixed acceleration motions respectively, run the machining codes for different fixed accelerations on the CNC machine tool respectively, and collect the commanded acceleration of the CNC machine tool. Calculate the corresponding feedforward amount T for acceleration through the impulse response model at each commanded acceleration respectively a ; Fit the feedforward amount T for acceleration corresponding to different commanded accelerations a linearly to obtain the third polynomial fitting curve f a ;

[0022] T3 Substitute the commanded speed v2 corresponding to a certain moment into the second polynomial fitting curve f v to obtain the corresponding feedforward amount for uniform motion at the current moment Substitute the commanded acceleration a2 into the third polynomial fitting curve f aObtain the corresponding acceleration feedforward value at the current moment The compression feedforward value T2 at the current moment satisfies:

[0023] Preferably, the second polynomial fitting curve f v is a linear function, specifically f v = dv; the third polynomial fitting curve f a is a cubic function, specifically f a = m*a 3 + n*a 2 + l*a + h; where v is the commanded speed of the CNC machine tool, a is the commanded acceleration of the CNC machine tool, and d, m, n, l, h are fitting coefficients.

[0024] Preferably, when the motion state of the CNC machine tool at the current moment is variable acceleration, the feedforward value compression method is specifically:

[0025] M1 Design the machining code for variable acceleration motion, run the machining code for variable acceleration motion on the CNC machine tool, collect the commanded acceleration and commanded speed of the CNC machine tool, and calculate the variable acceleration feedforward value T va sequence in the time domain t through the impulse response model;

[0026] M2 Obtain the first-order differential sequence of the variable acceleration feedforward value T va sequence by differentiating the variable acceleration feedforward value T va sequence, and perform polynomial fitting on the first-order differential sequence of the variable acceleration feedforward value T va and the commanded acceleration to obtain where a is the commanded acceleration, and p, c are fitting coefficients;

[0027] M3 Integrate the formula (1) in step M2 to obtain the fourth polynomial fitting curve f(v, t), f(v, t) = pv + ct + q, where v is the commanded speed, t is the time, and q is the fitting coefficient; substitute the commanded speed corresponding to a certain moment into the fourth polynomial fitting curve f(v, t) to obtain the compression feedforward value at the current moment.

[0028] Preferably, when the motion state of the CNC machine tool at the current moment is low-speed motion, the feedforward value compression method is specifically:

[0029] N1 Design the low-speed motion machining code, run the machining code on the CNC machine tool, collect the commanded speed v3 data of the CNC machine tool, and calculate the low-speed feedforward value T l sequence in the time domain t using the impulse response model;

[0030] N2 Compare the commanded speed v3 with the low-speed feedforward value Tl Perform linear fitting and adopt a piecewise modeling method. When the speed is -0.03 ≤ v3 < 0 mm / ms and 0.01 ≤ v3 ≤ 0.03 mm / ms, a first-order polynomial is used for fitting; when the speed is 0 ≤ v3 < 0.01 mm / ms, a second-order polynomial is used for fitting.

[0031] N3 Substitute the command speed at a certain current moment into the first-order polynomial or the second-order polynomial, and the pre-compression amount at the current moment can be obtained.

[0032] Generally speaking, compared with the prior art, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

[0033] (1) By adopting the pre-feed amount compression method of the present invention, during the process of using the contour error control of the convolutional speed pulse response model, only a small number of floating-point operations need to be performed in the numerical control system to obtain the convolutional pre-feed amount of the current control cycle (1 ms), and there is no need to perform complex matrix operations, which greatly reduces the computational complexity of using the convolutional speed pulse response pre-feed, so that the numerical control system can allocate more CPU time to other functions, leaving a large space for further expanding the strong real-time functions inside the numerical control system, and can solve the problem of high time consumption for calculating the pre-feed amount of the convolutional speed pulse response model pre-feed function.

[0034] (2) By adopting the pre-feed amount compression method of the present invention, during the operation of the numerical control system, only a small amount of space needs to be allocated in the stack area to store the necessary expression control parameters, which greatly reduces the space complexity of the convolutional speed pulse response pre-feed compensation module; during the calculation of the convolutional speed pulse response pre-feed without using the pre-feed amount compression method, a large amount of stack area space is required to store the intermediate values calculated in each cycle and the speed pulse response matrix; reducing the use of the stack area space can leave a good foundation for subsequent expansion of other functions of the numerical control system. Description of the Drawings

[0035] Figure 1 It is the pre-feed amount when the acceleration is fixed after separating the speed in Embodiment 1.

[0036] Figure 2 It is the fitting curve of the acceleration and the pre-feed amount after separating the speed in Embodiment 1.

[0037] Figure 3 It is the comparison of the first-order differential curve of the command acceleration and the pre-feed amount in Embodiment 2 (the acceleration is magnified 7 times)

[0038] Figure 4 It is the scatter plot of the first-order differential of the pre-feed amount under different accelerations in Embodiment 2.

[0039] Figure 5It is the first-order function expression fitting instruction for acceleration and the first-order differential of the feedforward quantity in Embodiment 2.

[0040] Figure 6 It is the relationship curve graph of the instruction speed and the feedforward quantity in the low-speed range in Embodiment 3.

[0041] Figure 7 It is the enlarged graph of the relationship curve of the instruction speed and the feedforward quantity in the low-speed range in Embodiment 3.

[0042] Figure 8 It is the segmented graph of the relationship curve of the instruction speed and the feedforward quantity in the low-speed range in Embodiment 3.

[0043] Figure 9 It is the segmented graph of the relationship curve of the instruction speed and the feedforward quantity with the low-speed range of -0.03 to 0 mm / ms in Embodiment 3.

[0044] Figure 10 In Embodiment 3, it is the segmented graph of the relationship curve of the instruction speed and the feedforward quantity with the low-speed range of 0 to 0.01 mm / ms.

[0045] Figure 11 In Embodiment 3, it is the segmented graph of the relationship curve of the instruction speed and the feedforward quantity with the low-speed range of 0.01 to 0.03 mm / ms. Specific implementation manners

[0046] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0047] Embodiment 1

[0048] A feedforward quantity compression method in a fixed acceleration motion state of a feed system, including the following steps:

[0049] S1: Feedforward quantity compression method in a fixed acceleration motion state

[0050] Split the current feedforward quantity to be calculated into the sum of the feedforward quantity in the current constant speed state and the feedforward quantity generated by the current acceleration, that is:

[0051] f cur = f v + f a (1)

[0052] f cur : The feedforward quantity to be calculated at the current moment; f v: Feedforward of the speed corresponding to the constant speed state at the current moment; f a : Feedforward generated by the acceleration at the current moment

[0053] In formula (1), f a Can be calculated according to the feedforward compression algorithm under a fixed acceleration; f v Is linearly related to the speed, so it can be calculated according to the feedforward corresponding to any constant speed. When the command speed is 0.3 mm / ms, the feedforward corresponding to the current command speed is 2.5 mm calculated through the impulse response model,

[0054]

[0055] f v : Feedforward of the speed corresponding to the constant speed section at the current moment; v: Command speed at the current moment; v sta : Speed at a known constant speed moment; f v_sta : Feedforward of a known constant speed section.

[0056] An experiment was carried out using a Gaoke GS200 vertical five-axis machining center machine tool, Figure 1 Is the feedforward under a fixed acceleration after separating the speed; Figure 2 The figure shows the result of summarizing the common command acceleration-feedforward data in the machining process. The acceleration is measured from -0.001 to 0.001 mm / ms 2 The feedforward is calculated through the impulse response model, and the command acceleration-feedforward in the figure is fitted with a third-order polynomial. The expression of the fitted curve is:

[0057] vf a =1.015*10 5 *a 3 +36.25*a 2 -18.87*a + 0.0001779 (3)

[0058] vf a : Feedforward only caused by acceleration; a: Acceleration at the current moment.

[0059] Substitute formula (2) and formula (3) into formula (1). The input variables are the command speed and command acceleration at the current moment, and the feedforward at the current moment can be calculated.

[0060] Example 2

[0061] A method for compressing the position feedforward in the variable acceleration motion state of a feed system includes the following steps:

[0062] M1 designs a machining code for variable acceleration motion. Run the machining code for variable acceleration motion on a numerically controlled machine tool, collect the commanded acceleration and commanded speed of the numerically controlled machine tool, and calculate the variable acceleration feedforward quantity T at time domain t through a pulse response model va sequence;

[0063] M2 obtains the first-order differential sequence of the variable acceleration feedforward quantity T va by differentiating the sequence of the variable acceleration feedforward quantity T va and polynomially fits the first-order differential sequence of the variable acceleration feedforward quantity T va and the commanded acceleration to obtain where a is the commanded acceleration, and p and c are fitting coefficients; in the acceleration range of 0 to 0.001 mm / ms 2 , Equation (1) is obtained by Figure 5 fitting the polynomial as

[0064] M3 integrates Equation (1) in step M2 to obtain the fourth polynomial fitting curve f(v, t), f(v, t)=6.358v + 0.0004032t, where v is the commanded speed and t is the time; substituting the commanded speed corresponding to a certain moment into the fourth polynomial fitting curve f(v, t), the compression feedforward quantity at the current moment can be obtained.

[0065] Figure 3 In, within the variable acceleration range in the time domain, the acceleration range is 0 to 0.001 mm / ms 2 , and the first-order differential curve of the feedforward quantity basically coincides with the amplified commanded acceleration curve; Figure 4 Taking the commanded acceleration as the horizontal axis and the first-order differential of the feedforward quantity as the vertical axis, a commanded acceleration - first-order differential of the feedforward quantity relationship diagram is shown, and the data points basically show a linear relationship; Figure 5 The relationship between the commanded acceleration and the first-order differential of the feedforward quantity is polynomially fitted using a linear function.

[0066] In the actual application process, only the coefficients p and c in Equation (1) need to be fitted. The first-order differential of the feedforward quantity is calculated through Equation (1) and the acceleration, and then the first-order differential values of the feedforward quantity per millisecond are accumulated, that is, the first-order differential of the feedforward quantity is integrated; at the same time, when using this method in the variable acceleration motion state, the feedforward quantity at the starting position of the variable acceleration section needs to be recorded, and the feedforward quantity at the starting position is used as the starting value of the final integration; finally, the compressed feedforward quantity can be obtained. According to Figures 3 - 5 shown, in the variable acceleration motion state, there is a relatively obvious linear relationship between the first-order differential of the feedforward quantity and the commanded acceleration.

[0067] Example 3

[0068] A method for compressing the position feedforward amount of a feed system, a feedforward amount compression scheme under low-speed conditions where non-linear friction has a major impact, including the following steps:

[0069] (1) Design a low-speed motion processing code, run the processing code on a numerically controlled machine tool, collect the command speed data of the numerically controlled machine tool, and calculate the low-speed feedforward amount T l sequence in the time domain t; the low speed specifically refers to a speed of -0.03 to 0.03 mm / ms;

[0070] (2) Perform linear fitting on the command speed and the low-speed feedforward amount T l using a piecewise modeling method. When the speed is -0.03 to 0 mm / ms and 0.01 to 0.03 mm / ms, a first-degree polynomial is used for fitting; when the speed is 0 to 0.01 mm / ms, a second-degree polynomial is used for fitting;

[0071] (3) Substitute the command speed at a certain current moment into the first-degree polynomial or the second-degree polynomial to obtain the compressed feedforward amount at the current moment.

[0072] The feedforward amount compression under low-speed conditions where non-linear friction has a major impact adopts a piecewise fitting method. For example, Figures 6 - 7 in the case shown, the complete low-speed segment data is divided into three segments. The data after segmentation is as Figure 8 shown. The data from the starting point to the starting position point in the figure is the first segment, the starting position point to the ending position point is the second segment, and the ending position point to the end of the data is the third segment.

[0073] An experiment was conducted using a Gaoke GS200 vertical five-axis machining center machine tool. The fitting effect of the first segment of data is as Figure 9 shown. When the speed is -0.03 to 0 mm / ms, it is represented by a first-degree polynomial, and the expression is as follows:

[0074] vf = 7.379*v cmd -0.01416 (8)

[0075] The fitting effect of the second segment of data is as Figure 10 shown. When the speed is 0 to 0.01 mm / ms, it is represented by a second-degree polynomial, and the expression is as follows:

[0076] vf = -198.3*v cmd 2 + 8.911*v cmd -0.007393 (9)

[0077] The fitting effect of the third segment of data is as Figure 11As shown, when the speed is 0.01 - 0.03 mm / ms, a first-degree polynomial is still used for representation, and the expression is as follows:

[0078] vf = 6.626 * v cmd -0.04324 (10)

[0079] v cmd : command speed; vf: feedforward amount

[0080] From equations (8), (9), and (10), the feedforward amount at the current moment can be obtained based on the command speed at the current moment.

[0081] It is easy for those skilled in the art to understand that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for compressing the position feedforward amount of a feed system, characterized in that, It includes the following steps: (1) Obtain the operation data of the numerically controlled machine tool, and calculate the feedforward amount of the impulse response model by using the operation data; (2) Obtain the motion state of the numerically controlled machine tool at the current moment. The motion state of the numerically controlled machine tool at the current moment is selected from uniform motion, uniformly variable motion, variable acceleration or low speed; the low speed is specifically a speed of -0.03 to 0.03 mm / ms; Fit the feedforward amount in each motion state with the operation data respectively to obtain a polynomial; (3) Select the corresponding polynomial according to the current motion state, and substitute the operation data of the current numerically controlled machine tool into the corresponding polynomial to calculate the compressed feedforward amount.

2. The method for compressing the position feedforward amount of a feed system according to claim 1, characterized in that, The operation data includes command speed and command acceleration data.

3. A method for compressing the position feedforward amount of a feed system according to claim 2, characterized in that, When the motion state of the numerically controlled machine tool at the current moment is uniform motion, the specific feedforward amount compression method is: S1 Design the machining code for uniform motion, run the machining code for uniform motion on the numerical control machine tool, collect the commanded speed of the numerical control machine tool, and calculate the corresponding uniform feedforward amount T through the impulse response model uv ; Linearly fit the constant feedforward amount T uv with the commanded speed to obtain a first polynomial fitting curve f uv ; S2 substitutes the command speed v1 at a certain moment into the first polynomial fitting curve f uv to obtain the corresponding constant-speed feedforward amount at the current moment The constant-speed feedforward amount at the current moment is the compression feedforward amount.

4. A method for compressing the position feedforward amount of a feed system according to claim 3, characterized in that, The first polynomial fitting curve f uv is a linear function, specifically f v = kv, where v is the command speed of the CNC machine tool and k is the fitting coefficient.

5. A method for compressing the position feedforward amount of a feed system according to claim 2, characterized in that, When the motion state of the numerically controlled machine tool at the current moment is uniformly variable motion, the specific feedforward amount compression method is: The machining code for uniform motion is designed for T1. The machining code for uniform motion is run on a numerically controlled machine tool, the commanded speed of the numerically controlled machine tool is collected, and the corresponding uniform feedforward amount T is calculated through a pulse response model. v ; The uniform feedforward amount T v is linearly fitted with the commanded speed to obtain a second polynomial fitting curve f v ; Design machining codes for different fixed accelerations of T2 respectively, run the machining codes under different fixed accelerations on a numerical control machine tool, collect the commanded acceleration of the numerical control machine tool, and calculate the corresponding acceleration feedforward amount T under each commanded acceleration respectively through a pulse response model a ; The acceleration feedforward amounts T corresponding to different commanded accelerations a are linearly fitted to obtain a third-degree polynomial fitting curve f a ; T3 substitutes the command speed v2 corresponding to a certain moment into the second polynomial fitting curve f v to obtain the corresponding constant-speed feedforward amount at the current moment Substitute the command acceleration a2 into the third polynomial fitting curve f a to obtain the corresponding acceleration feedforward amount at the current moment The compression feedforward amount T2 at the current moment satisfies:

6. A method for compressing the position feedforward amount of a feed system according to claim 5, characterized in that The second polynomial fitting curve f v is a linear function, specifically f v = dv; The third polynomial fitting curve f a is a cubic function, specifically f a = m * a 3 + n * a 2 + l * a + h; Wherein, v is the command speed of the numerically controlled machine tool, a is the command acceleration of the numerically controlled machine tool, and d, m, n, l, h are fitting coefficients.

7. A method for compressing the position feedforward amount of a feed system according to claim 2, characterized in that When the motion state of the numerically controlled machine tool at the current moment is variable acceleration, the specific feedforward amount compression method is: The machining code for variable acceleration motion is designed by M1. The machining code for variable acceleration motion is run on a numerically controlled machine tool, and the commanded acceleration and commanded speed of the numerically controlled machine tool are collected. The variable acceleration feedforward quantity T at time domain t is calculated through a pulse response model va sequence; M2 obtains the feedforward quantity T of the variable acceleration by va performing sequence difference on the feedforward quantity T of the variable acceleration to obtain va the first-order differential sequence of the feedforward quantity T of the variable acceleration, and performing polynomial fitting on the first-order differential sequence of the feedforward quantity T of the variable acceleration and the command acceleration to obtain va where a is the command acceleration, and p and c are fitting coefficients; ​ M3 Integrates Equation (1) in Step M2 to obtain the fourth polynomial fitting curve f(v, t), f(v, t)=pv+ct+q, where v is the command speed, t is the time, and q is the fitting coefficient; Substitute the command speed corresponding to a certain moment into the fourth polynomial fitting curve f(v, t), and the compressed feedforward amount at the current moment can be obtained.

8. A method for compressing the position feedforward amount of a feed system according to claim 2, characterized in that When the motion state of the numerically controlled machine tool at the current moment is low-speed motion, the specific feedforward amount compression method is: The N1 designs a low-speed motion processing code, runs the processing code on a numerical control machine tool, collects the instruction speed v3 data of the numerical control machine tool, and calculates the low-speed feedforward quantity T in the time domain t by using a pulse response model l sequence; N2 compares the command speed v3 with the low-speed feedforward amount T l Performs a linear fit and adopts a piecewise modeling method. When the speed is -0.03 ≤ v3 < 0 mm / ms and 0.01 ≤ v3 ≤ 0.03 mm / ms, a first-degree polynomial is used for fitting; when the speed is 0 ≤ v3 < 0.01 mm / ms, a second-degree polynomial is used for fitting; N3 Substitute the command speed at a certain current moment into the first-degree polynomial or the second-degree polynomial, and the compressed feedforward amount at the current moment can be obtained.

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