Ultra-precision turning feedforward control method, medium and equipment based on frequency response data

Abstract

The present invention relates to the field of ultra-precision turning optimization control, and in particular to an ultra-precision turning feedforward control method, medium and equipment based on frequency response data. It includes: obtaining the expected frequency band range and cutoff frequency according to the frequency response data of the servo axis to be optimized in the machine tool; using a feedforward controller composed of an FIR filter and a low-pass filter in series, and establishing an inverse model of the servo axis to be optimized in the expected frequency band range according to the frequency response data; inputting the initial processing trajectory into the inverse model to generate the optimized processing trajectory corresponding to the servo axis to be optimized. The present invention adopts a flexible-order FIR filter in series with a low-pass filter as a feedforward controller, and based on the frequency response data of the servo axis to be optimized, obtains the inverse model of the servo axis to be optimized of the machine tool within the expected frequency band range. Therefore, through the compensation of the feedforward controller, the frequency response of the overall system can be made flat, so as to reduce the tracking error of the servo axis of the machine tool and thus improve the processing accuracy of the workpiece.

Description

Background Art

[0002] Ultra-precision machining is a manufacturing technology that aims to achieve extremely high accuracy (usually at the sub-micron or even nanometer level) and surface quality (usually surface roughness can reach the nanometer level). It is usually used to manufacture high-precision parts and is widely used in optics, aerospace, semiconductors, and medical fields. Ultra-precision machining is a core technology of modern manufacturing and is crucial to many high-precision fields.

[0003] Ultra-precision machining machines are the core equipment for ultra-precision machining. In existing ultra-precision machining machines (such as ultra-precision turning machines), multiple mutually cooperating machining axes (such as rotating axes and reciprocating translation axes) are usually set up to achieve machining requirements for different workpieces and surface shapes. In order to ensure higher precision, not only are there higher precision requirements on the hardware structure of the axis, such as the servo axis, but a control feedback system with higher precision (such as a servo system) is also set up to control the movement of each axis. In order to make the machine tool more universal, the parameters of its control strategy are usually set conservatively, and the system stability is higher, but it will cause the servo axis's follow-up ability (response ability) to not be optimal, thereby reducing the machining accuracy. At the same time, the original control system of existing commercial machine tools is generally not open after production, so it is impossible to improve the machining accuracy of the machine tool by adjusting the control system. As a result, the machining accuracy of the machine tool cannot be further improved and optimized. Summary of the invention

[0004] In view of one of the above technical problems, the technical solution adopted by the present invention is:

[0005] According to one aspect of the present invention, there is provided an ultra-precision turning feedforward control method based on frequency response data, the method comprising the following steps:

[0006] According to the frequency response data of the servo axis to be optimized in the machine tool, the expected frequency band range and cutoff frequency of the servo axis to be optimized are obtained; the expected frequency band range is from 0 Hz to the frequency when the gain drops to +3 dB or -3 dB;

[0007] A feedforward controller composed of a FIR filter and a low-pass filter connected in series is used to establish an inverse model of the servo axis to be optimized in the desired frequency band according to the frequency response data of the servo axis to be optimized in the machine tool; the FIR filter is used to fit the inverse model of the servo axis to be optimized in the desired frequency band, and the low-pass filter is used to filter out the inverse model data greater than the cutoff frequency in the inverse model fitted by the FIR filter; the cutoff frequency is the maximum frequency value in the desired frequency band;

[0008] The initial machining trajectory corresponding to the servo axis to be optimized is input into the inverse model to generate the optimized machining trajectory corresponding to the servo axis to be optimized.

[0009] According to a second aspect of the present invention, a non-transitory computer-readable storage medium is provided, which stores a computer program. When the computer program is executed by a processor, the above-mentioned ultra-precision turning feedforward control method based on frequency response data is implemented.

[0010] According to a third aspect of the present invention, there is provided an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned ultra-precision turning feedforward control method based on frequency response data when executing the computer program.

[0011] The present invention has at least one of the following beneficial effects:

[0012] The present invention adopts a flexible-order FIR filter in series with a low-pass filter as a feedforward controller, and based on the frequency response data of the servo axis to be optimized, obtains the inverse model of the servo axis to be optimized of the machine tool within the expected frequency band. Thus, through the compensation of the feedforward controller, the frequency response of the overall system can be made flat, so as to reduce the tracking error of the servo axis of the machine tool and thus improve the machining accuracy of the workpiece (such as an optical free-form surface).

[0013] At the same time, by adopting a feedforward control strategy, a corresponding adjustment model can be established according to the frequency response characteristics of the servo axis, and the control system can respond to known changes by pre-calculating and adjusting the input, thereby improving the following ability of the ultra-precision lathe servo axis system within the desired frequency band. This method does not require modifying the original parameters of the internal controller of the machine tool and does not affect its stability and bandwidth. It overcomes the problems of phase lag of the feedback controller and limited use on existing commercial machine tools, and can be widely used in commercial machine tools in industrial production.

[0014] In addition, by designing the feedforward controller of the servo axis system based on the frequency response data, the parameters of the feedforward controller can be adjusted directly according to the frequency response characteristics of the actual controlled object, thereby achieving the optimal control effect within the desired frequency band. This avoids the negative impact on system performance caused by the difficult-to-eliminate modeling error between the system model and the controlled object when designing the feedforward controller using the existing model method, and can also avoid the instability problem that may be caused by the inverse model of the non-minimum phase system. It has wide applicability in the industrial field, especially for precision motion control systems with complex dynamic characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0016] Figure 1 A flow chart of an ultra-precision turning feedforward control method based on frequency response data provided by an embodiment of the present invention;

[0017] Figure 2 A schematic structural diagram of an ultra-precision lathe provided in an embodiment of the present invention;

[0018] Figure 3 A schematic diagram of an overall system using a feedforward control method provided by an embodiment of the present invention, wherein H(z) is a FIR filter, G(z) is a low-pass filter, and P(z) is a servo axis control system to be optimized;

[0019] Figure 4 A single-sided frequency spectrum diagram of a reference tool trajectory provided by an embodiment of the present invention;

[0020] Figure 5 A schematic diagram of a Z-axis frequency response (part (a) thereof), a schematic diagram of a FIR filter frequency response (part (b) thereof), and a schematic diagram of a Z-axis frequency response (part (c) thereof) after adding a feedforward controller to improve the frequency response provided by an embodiment of the present invention;

[0021] Figure 6 A schematic diagram of the convergence trend of the optimization solution process of g(Q) in the feasible domain F corresponding to Q based on the differential evolution algorithm provided in an embodiment of the present invention;

[0022] Figure 7 Schematic diagram of comparison of servo Z-axis tracking errors of different controllers provided in an embodiment of the present invention, wherein the original trajectory in (a) is a single-frequency reference signal (40 Hz); the original trajectory in (b) is a composite reference signal (30, 35, 40 Hz);

[0023] Figure 8 A schematic diagram comparing the Z-axis tracking error before and after the tool reference trajectory is corrected according to an embodiment of the present invention; wherein (a) is the situation corresponding to the reference tool trajectory before correction; (b) is the situation corresponding to the tool trajectory after correction by the feedforward controller;

[0024] Fig. 9 A schematic diagram of the comparison of the three-dimensional morphology and the two-dimensional profile of the machined surface before and after the tool reference trajectory is corrected according to an embodiment of the present invention; wherein (a) is the situation corresponding to the reference tool trajectory before correction; (b) is the situation corresponding to the tool trajectory after correction;

[0025] Fig.10A schematic diagram of the comparison of the roughness of the machined surface before and after the reference tool trajectory is corrected according to an embodiment of the present invention; wherein (a) is the situation corresponding to the reference tool trajectory before correction; (b) is the situation corresponding to the corrected tool trajectory; (c) is the situation of the surface roughness value of the evaluation area;

[0026] Fig.11 A flow chart of a method for acquiring an inverse model of an ultra-precision turning axis based on frequency is provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.

[0028] As a possible embodiment of the present invention, Figure 1 As shown, an ultra-precision turning feedforward control method based on frequency response data is provided, and the method comprises the following steps:

[0029] S100: According to the frequency response data of the servo axis to be optimized in the machine tool, the expected frequency band range and cutoff frequency of the servo axis to be optimized are obtained. The expected frequency band range is from 0 Hz to the frequency when the gain drops to +3 dB or -3 dB.

[0030] The frequency response data of the servo axis is data describing the dynamic characteristics of the servo system at different frequencies, usually including amplitude-frequency characteristics and phase-frequency characteristics. These data are useful for analyzing the dynamic characteristics, stability, bandwidth and other indicators of the servo system. In this embodiment, it is usually possible to determine which axis's following ability will have an important impact on the machining accuracy based on the motion state of each servo axis in the machine tool during the machining process, and determine it as the corresponding servo axis to be optimized. By analyzing the frequency response data of the servo axis to be optimized, the expected frequency band range of the servo axis to be optimized can be determined.

[0031] Take the following ultra-precision lathe as an example to illustrate. Figure 2As shown, the ultra-precision lathe includes: a base, a servo Z-axis 1, a servo X-axis 2, a servo C-axis 3, a workpiece fixture 4 and a tool assembly 5; the servo Z-axis 1 and the servo X-axis 2 are both used to realize reciprocating translational motion along a straight line direction, and the servo C-axis 3 is used to realize rotational motion around a central axis; the servo Z-axis 1 and the servo X-axis 2 are installed on the base, and the moving direction of the servo Z-axis 1 is perpendicular to the moving direction of the servo X-axis 2, and the servo Z-axis 1 and the servo X-axis 2 are arranged in a T shape; the servo C-axis 3 is installed on the slide surface of the servo X-axis 2 along a direction parallel to the moving direction of the servo Z-axis 1; the workpiece fixture 4 is fixed on the servo C-axis 3; the tool assembly 5 is fixedly arranged on the slide surface of the servo Z-axis 1.

[0032] During the surface processing of this ultra-precision lathe, the servo axis C axis 3 maintains stable operation, the servo axis X axis 2 realizes the smooth feeding of the tool from the edge of the workpiece to the center, and the cutting edge profile is adjusted by the servo Z axis 1 to always be tangent to the target surface shape. Therefore, the following ability of the servo Z axis 1 has an important influence on the processing accuracy, and then the servo Z axis 1 is determined as the servo axis to be optimized. It is necessary to design a feedforward controller to reduce the tracking error of the servo Z axis 1. In addition, the high-frequency reciprocating motion in the processing process can be concentrated on the axial servo axis (Z axis) that adjusts the cutting depth of the tool by reasonably planning the tool trajectory generation method.

[0033] When determining the expected frequency band range of the servo axis to be optimized through frequency response data, a Bode plot can be drawn based on the frequency response data of the corresponding servo axis. Usually, the amplitude-frequency characteristic diagram (such as Figure 5 As shown in Figure a), the frequency at which the gain drops to +3dB or -3dB is used as the maximum value of the desired frequency band, and the minimum value of the desired frequency band is 0Hz. Figure 5 As shown in Figure a, the frequency when the gain drops to +3dB is 100Hz, that is, the corresponding desired frequency band range is [0Hz, 100Hz], and the cutoff frequency of the low-pass filter in the corresponding feedforward controller is 100Hz.

[0034] The above-mentioned +3dB or -3dB limit values ​​can be adaptively adjusted according to actual needs. Usually, in existing commercial ultra-precision slow-tool servo lathes, the hardware limit is usually within 100Hz. Therefore, even if the part after the operating frequency exceeds 100Hz is optimized, the machine tool hardware and the corresponding driver cannot reach the corresponding capabilities. Therefore, for existing commercial ultra-precision slow-tool servo lathes, the maximum value of the expected frequency band range does not exceed 100Hz.

[0035] S200: Use a feedforward controller composed of a FIR filter and a low-pass filter in series, and establish an inverse model of the servo axis to be optimized in the expected frequency band according to the frequency response data of the servo axis to be optimized in the machine tool. The FIR filter (Finite Impulse Response Filter) is used to fit the inverse model of the servo axis to be optimized in the expected frequency band, and the low-pass filter is used to filter out the inverse model data greater than the cutoff frequency in the inverse model fitted by the FIR filter. The cutoff frequency is the maximum frequency value in the expected frequency band. For example, the cutoff frequency is 100Hz.

[0036] In this step, the FIR filter is the core of the feedforward controller. By establishing an approximate inverse model of the servo axis to be optimized within the expected frequency band, the required input can be directly calculated according to the expected output, and then the control signal can be adjusted in advance to achieve the purpose of optimizing the system response. The order of the FIR filter affects both the approximate accuracy of the servo axis inverse model and the number of optimization variables. It is necessary to balance the computational efficiency while meeting the approximate accuracy requirements, so as to select a suitable order for the FIR filter. The low-pass filter is mainly used to intercept the data in the expected frequency band [0Hz, 100Hz] of the inverse model data fitted by the FIR filter, so as to filter out the influence of the data after 100Hz, and further limit the adjustment of the reference tool trajectory by the FIR filter to the expected frequency band.

[0037] S300: Inputting the initial machining trajectory corresponding to the servo axis to be optimized into the inverse model to generate the optimized machining trajectory corresponding to the servo axis to be optimized.

[0038] The initial machining trajectory in this embodiment is the reference tool trajectory, which can be obtained by using a tool trajectory generation method based on geometric analysis. The cutting edge profile of the diamond tool is controlled to scan along a spiral path from the edge of the workpiece to the center, traversing the workpiece surface, while ensuring that the cutting edge profile is always tangent to the target free-form surface in the cutting plane, so that the cutting edge profile envelope forms a machining surface. In the tool trajectory generation method, the reference tool trajectory is obtained by equal-angle discretization and stable X-axis tool tip arc radius compensation. Figure 2 Taking the ultra-precision lathe shown in the figure as an example, the reference tool trajectory in the polar coordinate system, the corresponding motion trajectory components θ(k), ρ(k), z(k) of the servo axis C axis 3, servo axis X axis 2 and servo Z axis 1 are shown as follows:

[0039] ;

[0040] Among them, n c is the rotation speed of the ultra-precision lathe spindle (i.e., servo axis C axis 3), k is the discrete point number in the reference tool trajectory, Δt is the time interval between adjacent discrete points, and Dw is the workpiece diameter corresponding to the target free-form surface, f t is the feed rate of the radial servo axis, and L represents the tool tip arc radius compensation function determined by the geometric parameters of the diamond tool and the target surface shape.

[0041] In this embodiment, the feedforward controller is used to pre-process the reference tool trajectory of the ultra-precision lathe before machining, and to adjust the input reference tool trajectory in advance according to the target tool trajectory output as needed by establishing an approximate inverse model of the servo axis to be optimized for the ultra-precision lathe. The tracking error caused by the bandwidth limitation of the servo axis during machining is suppressed, so that the output response of the servo axis accurately follows the change of the input command, thereby improving the machining accuracy of the machine tool in a targeted manner.

[0042] As another possible embodiment of the present invention, S200 includes:

[0043] S201: Based on the collected frequency response data of the servo axis to be optimized in the machine tool, the frequency response information of the servo axis to be optimized is obtained by discrete Fourier transform. .

[0044] In this step, the frequency response data is used to reflect the dynamic response performance of the servo axis to be optimized, that is, to measure whether its output response can accurately follow the changes in the input command. The frequency response data is obtained as follows:

[0045] The linear frequency sweep signal is selected as the reference signal to drive the servo Z axis 1 to move along a given trajectory. At the same time, the data acquisition device is used to synchronously obtain the command position information r(k) of the servo Z axis 1 and the actual position information y(k) detected by the displacement sensor on the servo axis; the frequency domain representation of the time domain discrete signals r(k) and y(k) can be obtained by discrete Fourier transform:

[0046] ;

[0047] ;

[0048] ;

[0049] Where R(m) and Y(m) represent the sampled values ​​of signals r(k) and y(k) on the unit circle of their Z transform results R(z) and Y(z), respectively. m is the frequency component number, N is the number of sampling points of the discrete time domain signal, and f m is a series of discrete frequency components in the frequency domain after discrete Fourier transform, T s represents the sampling time, j is the definition of an imaginary number, j 2 =-1.

[0050] In this embodiment, the frequency range of the linear sweep signal is 0.0001 Hz to 100 Hz, the amplitude is 0.5 μm, and the signal duration is 75 s. By setting the above parameters, the signal can cover the frequency components of the desired frequency band as evenly as possible, so as to capture the dynamic performance of the servo axis as fully as possible.

[0051] Usually, because the sampling frequency of the servo system is usually high (for example, several thousand Hz to tens of kHz), a large amount of frequency response data can be collected through the control of the above linear sweep signal, resulting in a very large amount of data. Therefore, in order to reduce the subsequent calculation amount and improve the calculation efficiency, the data will be downsampled after the Fourier transform (FFT).

[0052] Specifically, in this step, the frequency response data sequence length is set to 200, the corresponding frequency sampling interval is 0.5 Hz, and the frequency response data of the servo Z axis 1 is further calculated according to the discrete Fourier transform result as follows:

[0053] ;

[0054] Among them, P(m) represents the sampled value of the axial servo axis discrete system P(z) on the unit circle, from which the frequency response information of the servo axis to be optimized can be obtained . In this step, N=200.

[0055] S202: According to the preset order of the FIR filter, the frequency response information of the FIR filter obtained by discrete Fourier transform .

[0056] The representation of the FIR filter in the Z domain is:

[0057] ;

[0058] Among them, N f Represents the order of the FIR filter. For the selection of the order of the FIR filter, the larger the order, the higher the fitting accuracy, that is, the higher the accuracy of the inverse model, the greater the corresponding calculation overhead and the lower the calculation efficiency. Therefore, when using it, it is necessary to balance the calculation efficiency while meeting the approximate accuracy requirements, so as to select a suitable order for the FIR filter. Usually, the selection range of the FIR filter order can be [15,25]. Preferably, the order of the FIR filter is 20, under which the accuracy can be guaranteed and the corresponding calculation efficiency is also high.

[0059] h 0 ,h 1 ,h 2 ,…,h Nfrepresents the coefficient of the FIR filter; after the order of the FIR filter is determined, its structure is also determined accordingly, and the coefficient of the FIR filter can be adjusted to change the FIR filter frequency response characteristics to compensate for the frequency response characteristics of the servo axis to be optimized. Therefore, the process of generating the inverse model in this embodiment is to 0 ,h 1 ,h 2 ,…,h Nf The optimization process is to determine the FIR filter by finding a set of optimal solutions in the feasible domain of coefficient values, that is, to determine the inverse model. Z domain represents a method of converting discrete time signals or systems from the time domain to the complex frequency domain through Z-transform. H(z) is the frequency response information of the FIR filter in this step. .

[0060] S203: According to and , which generates the optimal cost function of the FIR filter coefficients .

[0061] in, for In the filter corresponding coefficient Q = (h 0 ,h 1 ,h 2 ,…,h Nf ), . N f is the order of the FIR filter. Nf For FIR filter N f The coefficient of the order. d Indicates the highest frequency component within the desired frequency band. m is the discrete frequency component in the frequency domain after discrete Fourier transform, T s Indicates the sampling time.

[0062] S204: Optimize and solve g(Q) in the feasible region F corresponding to Q. The corresponding Q is used as the coefficient information of the FIR filter, and the target filter is generated. is the minimum value of g(Q) in the feasible domain F corresponding to Q.

[0063] S205: Using the target filter, construct an initial inverse model of the servo axis to be optimized in the desired frequency band range.

[0064] S206: Using a low-pass filter to filter out the inverse model data of the initial inverse model that is greater than the cutoff frequency, so as to generate an inverse model of the servo axis to be optimized within a desired frequency band.

[0065] In this embodiment Represents the dynamic characteristics of the servo axis at different frequencies, usually including amplitude-frequency response and phase-frequency response. Indicates the gain and phase characteristics of the filter at different frequencies. In this embodiment, a feedforward control strategy is used to compensate for the dynamic characteristics of the servo axis by an inverse model. Therefore, if the frequency response data of the FIR filter and the servo axis are reciprocal, the dynamic characteristics of the servo axis can be offset, thereby improving the control accuracy and response speed of the system.

[0066] Therefore, if Figure 5 As shown in (c) in the figure, in order to make the overall system composed of the feedforward controller and the servo axis to be optimized have flat amplitude-frequency characteristics and phase-frequency characteristics in the desired frequency band, it is necessary to require the frequency response of the overall system at different frequency components to be as close to 1 as possible, and then the optimization cost function of the FIR filter coefficient can be constructed as follows: .

[0067] In the subsequent solution calculation, the feasible domain of the coefficients is continuously iterated to find the optimal solution. Specifically, the existing heuristic algorithm can be used to optimize g(Q) in the feasible domain F corresponding to Q. , then the set of coefficients is used as the optimal solution of the coefficients of the FIR filter, and then the initial inverse model formed by the FIR filter is determined. Then, the part from 0 Hz to 100 Hz is cut out through a low-pass filter as the inverse model of the servo axis to be optimized in the desired frequency band. In this embodiment, the order of the low-pass filter can be 3000.

[0068] A feasible implementation of S204 is as follows:

[0069] S214: Based on the differential evolution algorithm, g(Q) is optimized and solved in the feasible domain F corresponding to Q.

[0070] In S204, a heuristic algorithm is used to solve the constrained optimization problem. A feasible solution is constructed and continuously iterated to improve the problem so as to approach the global optimal solution. The heuristic algorithm is suitable for solving optimization problems with high complexity that cannot be effectively solved by precise algorithms. Preferably, in this embodiment, a differential evolution algorithm is used to obtain an approximate global optimal solution of the optimization variable Q.

[0071] The steps to use the differential evolution algorithm to calculate the optimal solution to a given constrained optimization problem are as follows:

[0072] The population in the differential evolution algorithm consists of multiple candidate solutions, each of which represents a potential optimal solution. First, we establish the candidate solution X of the given constrained optimization problem. i,G ={x 1 i,G , x 2i,G , x 3 i,G , …, x 21 i,G} i=1,2,…,N P , where N P is the population size, G is the number of population iterations; the individuals in the initial population are randomly generated and must meet the value range restrictions of the optimization variables (FIR filter coefficients), and the upper and lower limits of the value range are set to Q max =10 7 [1] 21 and Q max =10 7 ·[-1] 21 , the value of the nth parameter of the i-th individual in the initial population is as follows:

[0073] ;

[0074] Among them, x n max and x n min They represent the upper and lower bounds of the nth parameter in the optimization variable Q respectively; further, the candidate solution X can be obtained according to the following calculation formula: i,G The corresponding mutation vector M i,G ={m 1 i,G , m 2 i,G , m 3 i,G ,…,m 21 i,G} i=1,2,…,N P ,

[0075] ;

[0076] Among them, r i 1 and r i 2 Indicates that in [1,N P ] are two mutually exclusive integers randomly selected from 1 represents the variation factor, X best,G represents the candidate solution with the best fitness in the Gth generation; then, the candidate solutions in the population are crossed with the corresponding mutation vectors to generate a trial vector T i,G ={t 1 i,G , t 2 i,G , t 3 i,G ,…,t21 i,G} , as shown below:

[0077] ;

[0078] Among them, C R is the crossover rate, n rand is a random integer, if t n i,G The value of x exceeds n max and x n min If the given range is n i,G Initialize; according to the formula Calculate the trial vector T i,G and the corresponding candidate solution X i,G The objective function value is compared with the value of the trial vector T. i,G The objective function value of is smaller, then the trial vector T i,G Will replace candidate solution X i,G Enter the G+1 generation population, otherwise, the candidate solution X i,G will continue to be retained in the G+1 generation population; finally, after G end After iterations, the global optimal solution X is obtained. best,Gend , which are the coefficients of the designed FIR filter.

[0079] Specifically, in this embodiment, the maximum number of iterations of the differential evolution algorithm is set to 300, and the population size N P is 100, and the final objective function value after iteration is 174. The detailed parameters and frequency response of the obtained FIR filter are shown in Table 1 and Figure 5 As shown in (b) in the figure, the convergence trend during the optimization process is as follows Figure 6 shown.

[0080] Table 1

[0081]

[0082] The component z(k) corresponding to the servo Z axis 1 in the reference tool trajectory is extracted and input into the feedforward controller, and the filtered corrected tool trajectory is obtained according to the output r(k); then, the filtered corrected tool trajectory is converted into a NC program input as follows Figure 2 The machine tool shown executes the machining; after the machining is completed, the machined surface topography is measured.

[0083] In this embodiment, the ultra-precision turning feedforward control system based on frequency response data includes an FIR filter, a low-pass filter and an ultra-precision lathe control system (specifically, it can be a certain servo axis to be optimized): the FIR filter and the low-pass filter are connected in series to form a feedforward controller, which is used to pre-process the reference tool trajectory generated by the traditional geometric analysis method before processing; the coefficients of the FIR filter can be obtained by constructing and solving the constrained optimization problem, and the filter is used to simulate the inverse model of the ultra-precision lathe servo axis, so as to directly calculate the required input according to the expected output to obtain the corrected tool trajectory; the low-pass filter is used to suppress the high-frequency components in the corrected tool trajectory that exceed the expected frequency band range; the filtered corrected tool trajectory is used to generate a CNC program and input it into the ultra-precision lathe control system for execution, so as to control the machine tool to complete product processing.

[0084] Specifically, by performing a trajectory tracking experiment on the servo Z-axis 1 of the ultra-precision lathe, the effectiveness of the feedforward controller designed in the above embodiment is verified. The reference signal of the servo Z-axis 1 is as follows:

[0085] ;

[0086] Among them, A 1 , A 2 and A 3 is the amplitude of each sine wave, A 4 is the bias coefficient, f 1 、f 2 and f 3 is the frequency component of each sine wave, and all frequency components are within the expected frequency band. Table 2 compares the tracking results of different controllers, and selects the tracking errors corresponding to the single-frequency reference signal with a frequency component of 40 Hz and the composite reference signal containing 30, 35 and 40 Hz frequency components. At the same time, the contents of the above tracking results are plotted on Figure 7 middle.

[0087] Table 2

[0088]

[0089] According to the results shown in Table 2, compared with the original ultra-precision lathe control system (i.e., the existing controller in the table), adding a feedforward controller can effectively reduce the tracking error of the servo Z axis 1. Comparing the improvement effect of ZPETC (Zero Phase Error Tracking Controller) and FIR filter (i.e., the feedforward controller in the present invention) on the tracking accuracy of the servo Z axis 1, when the reference signal only contains a 40 Hz frequency component, using the FIR filter as the feedforward controller can reduce the peak error (e PV ) and mean square error (e RMS) is reduced by about 72%, and when the reference signal is mixed with 30, 35, and 40 Hz frequency components, using the FIR filter as a feedforward controller can reduce the peak error (e PV ) and mean square error (e RMS ) The error is reduced by about 80%. According to the trajectory tracking results shown in Table 2 and Figure 7 The tracking error comparison shows that compared with the ZPETC controller based on the fixed-order model, the feedforward controller formed by the FIR filter to approximate the inverse model of the servo axis can obtain better feedforward compensation effect.

[0090] The following example is used to illustrate the difference in machining accuracy between the tool trajectory corrected by the feedforward controller of the present invention and the original reference tool trajectory. Specifically, a reference tool trajectory is generated according to the target free-form surface shape parameters and process parameters, and is input into a feedforward controller composed of an FIR controller and a low-pass filter to obtain a filtered corrected tool trajectory. The reference tool trajectory and the filtered corrected tool trajectory are used for machining respectively, and the machining results are compared;

[0091] The expression of the target free-form surface is:

[0092] ;

[0093] Among them, A represents the amplitude of the target free-form surface, which is 3 μm, and λ represents the wavelength of the target free-form surface, which is 0.6 mm. The ultra-precision turning process parameters during the machining process are shown in Table 3:

[0094] Table 3

[0095]

[0096] like Figure 8 As shown in the figure, by comparing the tracking of the reference tool trajectory and the filtered corrected tool trajectory executed by the machine tool, it can be found that when the reference tool trajectory is executed, the actual trajectory will have an obvious overshoot relative to the ideal trajectory at the turning point, resulting in a large fluctuation in the tracking error. In the filtered corrected tool trajectory, the feedforward controller designed based on the frequency response data is used to suppress the amplitude to varying degrees, which significantly improves the tracking accuracy, significantly reduces the peak value (PV value) and mean square error value of the tracking error, and effectively improves the following performance of the servo axis within the expected frequency band.

[0097] like Fig. 9As shown in the figure, the three-dimensional surface morphology and two-dimensional cross-sectional profile of the target free-form surface machined by the reference tool trajectory and the filtered corrected tool trajectory are measured by white light interferometry. The PV values ​​of the cross-sectional profile errors along AA, BB, CC and DD are reduced from 1246, 917, 1309 and 978 nm to 369, 162, 376 and 130 nm, respectively, and the RMS values ​​are reduced from 539, 259, 542 and 271 nm to 22, 82, 24 and 54 nm, respectively. The results show that the ultra-precision turning feedforward control method based on frequency response data can effectively improve the machining accuracy of optical free-form surfaces.

[0098] like Fig.10 As shown in the figure, the roughness results of the target free-form surface machined by the reference tool trajectory and the filtered corrected tool trajectory were measured using a white light interferometer. It shows that the arithmetic mean height values ​​(Sa values) of the two surfaces are both around 4 nm, and the root mean square values ​​(Sq values) are both around 5 nm. The results show that the ultra-precision turning feedforward control method based on frequency response data has no negative impact on the roughness of the machined surface.

[0099] As another possible embodiment of the present invention, Fig.11 As shown, a method for obtaining an inverse model of an ultra-precision turning axis based on frequency is also provided, and the method comprises the following steps:

[0100] S400: The intersection of the sensitive processing frequency interval of the servo axis to be optimized and the high energy proportion frequency interval of the processing trajectory corresponding to the servo axis to be optimized is used as the first frequency interval of the inverse model. The sensitive processing frequency interval is the frequency interval corresponding to the tracking accuracy of the servo axis to be optimized being less than the preset accuracy threshold. The high energy proportion frequency interval is the frequency interval corresponding to the energy of the preset proportion threshold in the processing trajectory.

[0101] Before obtaining the first frequency interval of the inverse model, it is also necessary to obtain the sensitive processing frequency interval of the servo axis to be optimized and the high energy proportion frequency interval of the processing trajectory corresponding to the servo axis to be optimized.

[0102] Specifically, the sensitive processing frequency range of the servo axis to be optimized is obtained according to the following steps:

[0103] S401: Acquire a first sensitive frequency interval whose phase response is greater than a preset phase threshold according to the frequency response data of the servo axis to be optimized.

[0104] S402: Acquire a second sensitive frequency interval having an amplitude-frequency response greater than a preset amplitude-frequency threshold according to the frequency response data of the servo axis to be optimized.

[0105] S403: Taking the union of the first sensitive frequency interval and the second sensitive frequency interval as the sensitive processing frequency interval of the servo axis to be optimized.

[0106] like Figure 5 As shown in (a), the Bode diagram corresponding to the frequency response data of the servo Z axis 1 includes curves of two characteristics, namely, the amplitude-frequency response and the phase response. When obtaining the first sensitive frequency interval, the frequency interval corresponding to the part of the phase response diagram where the phase is greater than the preset phase threshold (such as -5deg, the negative sign indicates the direction) can be determined as the first sensitive frequency interval, such as [50Hz, 100Hz]. When obtaining the second sensitive frequency interval, the frequency interval corresponding to the part of the amplitude-frequency response diagram where the amplitude is greater than the preset amplitude-frequency threshold (such as 1dB) can be determined as the second sensitive frequency interval, such as [25Hz, 100Hz]. The corresponding sensitive processing frequency interval after the intersection is obtained is [25Hz, 100Hz], thereby determining the frequency interval with poor tracking error of the servo axis to be optimized.

[0107] Specifically, the high energy proportion frequency interval corresponding to the machining trajectory of the servo axis to be optimized is obtained according to the following steps:

[0108] S404: Obtain a single-sided frequency spectrum diagram corresponding to the processing trajectory of the servo axis to be optimized.

[0109] S405: According to the unilateral frequency spectrum, a frequency interval corresponding to 95% of the energy of the processing trajectory is used as a high energy proportion frequency interval.

[0110] like Figure 4 As shown in Figure 1, the single-sided spectrum of the machining trajectory is obtained by Fourier transform, which reflects the energy distribution of the signal at different frequencies. Therefore, the frequency interval where the main energy is concentrated in the tool trajectory can be obtained based on the single-sided spectrum diagram, such as Figure 4 As shown, the corresponding high energy frequency interval is [0 Hz, 40 Hz]. This high energy frequency interval represents the interval of the main frequency in the processing trajectory signal. Therefore, the first frequency interval obtained is [25 Hz, 40 Hz].

[0111] In this embodiment, the sensitive processing frequency interval of the servo axis to be optimized specifically refers to the frequency interval with poor tracking accuracy of the servo axis, and the high energy proportion frequency interval of the processing trajectory mainly refers to the frequency interval of the main energy distribution of the servo axis in the corresponding processing trajectory. By combining these two factors, it is possible to more accurately determine the frequency interval where the servo axis to be optimized needs to pay more attention to accuracy in actual work. Then, when the inverse model is constructed, a more demanding fitting process is performed on the frequency interval to more specifically improve the accuracy of the servo axis to be optimized when processing the corresponding product.

[0112] S500: Downsampling the frequency response data sequence corresponding to the servo axis to be optimized according to the first frequency interval to obtain a first fitting frequency response data sequence corresponding to the servo axis to be optimized. The data density corresponding to the first frequency interval in the first fitting frequency response data sequence is greater than the data density corresponding to the non-first frequency interval.

[0113] S500, including:

[0114] S501: Use the linear frequency sweep signal as a reference signal to drive the servo axis to be optimized to move along a given trajectory to obtain a frequency response data sequence corresponding to the servo axis to be optimized. The frequency range of the linear frequency sweep signal is the same as the expected frequency band range.

[0115] S502: Perform downsampling processing using a first sampling frequency in a frequency interval corresponding to the first frequency interval in the frequency response data sequence.

[0116] S503: Downsampling is performed using a second sampling frequency in the frequency interval that does not correspond to the first frequency interval in the frequency response data sequence. The first sampling frequency is greater than the second sampling frequency.

[0117] S600: Based on the frequency response data in the first fitting frequency response data sequence, frequency response information of the servo axis to be optimized is obtained by discrete Fourier transform .

[0118] Specifically, Follow the steps below to obtain:

[0119] S601: uniformly downsample the frequency response data sequence corresponding to the servo axis to be optimized to obtain a second fitting frequency response data sequence corresponding to the servo axis to be optimized.

[0120] S602: Based on the frequency response data in the second fitting frequency response data sequence, frequency response information of the servo axis to be optimized is obtained by discrete Fourier transform .

[0121] S700: According to , generate the inverse model of the servo axis to be optimized.

[0122] Specifically, S700 includes:

[0123] S701: According to the order of the preset FIR filter, obtain the frequency response information of the FIR filter obtained by discrete Fourier transform .

[0124] S702: According to and , which generates the optimal cost function of the FIR filter coefficients .

[0125] in, for In the filter corresponding coefficient Q = (h 0 ,h 1 ,h 2 ,…,h Nf ), . N f is the order of the FIR filter. Nf For FIR filter N f The coefficient of the order. d Indicates the highest frequency component in the desired frequency band. The desired frequency band ranges from 0Hz to the frequency where the gain drops to +3dB or -3dB. m is the discrete positive frequency component in the frequency domain after discrete Fourier transform, T s Represents the sampling time. j is the definition of an imaginary number, j 2 =-1.

[0126] As another possible embodiment of the present invention, after the first frequency interval of the inverse model is obtained, the remaining steps in the above-mentioned frequency-based inverse model acquisition method for an ultra-precision turning axis are replaced by:

[0127] A500: Generate an optimized function for the coefficients of the FIR filter according to the first frequency interval .

[0128] in, for In the filter corresponding coefficient Q = (h 0 ,h 1 ,h 2 ,…,h Nf ), . is the frequency response information of the servo axis to be optimized obtained by discrete Fourier transform. is the frequency response information of the FIR filter obtained by discrete Fourier transform. f is the order of the FIR filter. A is the first frequency interval, a1 and a2 are weight coefficients, a1>a2. Nf For FIR filter N f The coefficient of the order. d Indicates the highest frequency component in the desired frequency band. The desired frequency band ranges from 0Hz to the frequency where the gain drops to +3dB or -3dB. m is a series of discrete positive frequency components in the frequency domain after discrete Fourier transform, T s represents the sampling time, j is the definition of an imaginary number, j 2 =-1.

[0129] A600: Optimize and solve g(Q) in the feasible region F corresponding to Q. The corresponding Q is used as the coefficient information of the FIR filter, and the target filter is generated. is the minimum value of g(Q) in the feasible domain F corresponding to Q.

[0130] A700: Use the target filter to construct an initial inverse model of the servo axis to be optimized in the desired frequency band.

[0131] After obtaining the frequency interval (first frequency interval) that needs to be optimized, when solving the inverse model later, the following two methods can be used to improve the inverse model fitting accuracy in this interval. The first method is to increase the sampling density of the data in the first frequency interval when obtaining the fitting frequency response data sequence to ensure the fitting accuracy of the inverse model in the first frequency interval. This is shown in steps S500 to S700. The second method is to introduce the weight K to adjust the importance of different frequency ranges when constructing the optimization function to be evaluated to ensure the fitting accuracy of the inverse model in the first frequency interval. This is shown in steps A500 to A700.

[0132] In addition, although the steps of the method in the present disclosure are described in a specific order in the drawings, this does not require or imply that the steps must be performed in this specific order, or that all the steps shown must be performed to achieve the desired results. Additionally or alternatively, some steps may be omitted, multiple steps may be combined into one step, and / or one step may be decomposed into multiple steps, etc.

[0133] Through the description of the above implementation, it is easy for those skilled in the art to understand that the example implementation described here can be implemented by software, or by combining software with necessary hardware. Therefore, the technical solution according to the implementation of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, and includes several instructions to enable a computing device (which can be a personal computer, a server, a mobile terminal, or a network device, etc.) to execute the method according to the implementation of the present disclosure.

[0134] In an exemplary embodiment of the present disclosure, an electronic device capable of implementing the above method is also provided.

[0135] It will be appreciated by those skilled in the art that various aspects of the present invention may be implemented as a system, method or program product. Therefore, various aspects of the present invention may be specifically implemented in the following forms, namely: a complete hardware implementation, a complete software implementation (including firmware, microcode, etc.), or a combination of hardware and software, which may be collectively referred to herein as a "circuit", "module" or "system".

[0136] The electronic device according to this embodiment of the present invention is only an example and should not bring any limitation to the functions and scope of use of the embodiments of the present invention.

[0137] The electronic device is presented in the form of a general-purpose computing device. The components of the electronic device may include, but are not limited to: the at least one processor mentioned above, the at least one storage device mentioned above, and a bus connecting different system components (including storage devices and processors).

[0138] The storage stores program codes, which can be executed by the processor, so that the processor executes the steps according to various exemplary embodiments of the present invention described in the above “Exemplary Method” section of this specification.

[0139] The memory may include readable media in the form of volatile memory, such as random access memory (RAM) and / or cache memory, and may further include read only memory (ROM).

[0140] The storage may also include a program / utility having a set (at least one) of program modules, such program modules including but not limited to: an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment.

[0141] The bus may represent one or more of several types of bus structures including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, a processor, or a local bus using any of a variety of bus architectures.

[0142] The electronic device may also communicate with one or more external devices (e.g., keyboards, pointing devices, Bluetooth devices, etc.), may communicate with one or more devices that enable a user to interact with the electronic device, and / or may communicate with any device that enables the electronic device to communicate with one or more other computing devices (e.g., routers, modems, etc.). This communication may be performed through an input / output (I / O) interface. In addition, the electronic device may also communicate with one or more networks (e.g., local area networks (LANs), wide area networks (WANs), and / or public networks, such as the Internet) through a network adapter. The network adapter communicates with other modules of the electronic device through a bus. It should be understood that, although not shown in the figure, other hardware and / or software modules may be used in conjunction with the electronic device, including but not limited to: microcode, device drivers, redundant processors, external disk drive arrays, RAID systems, tape drives, and data backup storage systems, etc.

[0143] Through the description of the above implementation, it is easy for those skilled in the art to understand that the example implementation described here can be implemented by software, or by software combined with necessary hardware. Therefore, the technical solution according to the implementation of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, and includes a number of instructions to enable a computing device (which can be a personal computer, a server, a terminal device, or a network device, etc.) to execute the method according to the implementation of the present disclosure.

[0144] In an exemplary embodiment of the present disclosure, a computer-readable storage medium is also provided, on which a program product capable of implementing the above method of the present specification is stored. In some possible implementations, various aspects of the present invention may also be implemented in the form of a program product, which includes a program code, and when the program product is run on a terminal device, the program code is used to enable the terminal device to execute the steps according to various exemplary embodiments of the present invention described in the above "Exemplary Method" section of the present specification.

[0145] The program product may adopt any combination of one or more readable media. The readable medium may be a readable signal medium or a readable storage medium. The readable storage medium may be, for example, but not limited to, a system, device or component of electricity, magnetism, light, electromagnetic, infrared, or semiconductor, or any combination thereof. More specific examples (non-exhaustive list) of readable storage media include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof.

[0146] Computer readable signal media may include data signals propagated in baseband or as part of a carrier wave, in which readable program code is carried. Such propagated data signals may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. Readable signal media may also be any readable medium other than a readable storage medium, which may send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0147] The program code embodied on the readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wired, optical cable, RF, etc., or any suitable combination of the foregoing.

[0148] Program code for performing the operations of the present invention may be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, etc., and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user computing device, partially on the user device, as a separate software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device may be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computing device (e.g., through the Internet using an Internet service provider).

[0149] In addition, the above-mentioned figures are only schematic illustrations of the processes included in the method according to an exemplary embodiment of the present invention, and are not intended to be limiting. It is easy to understand that the processes shown in the above-mentioned figures do not indicate or limit the time sequence of these processes. In addition, it is also easy to understand that these processes can be performed synchronously or asynchronously, for example, in multiple modules.

[0150] It should be noted that, although several modules or units of the device for action execution are mentioned in the above detailed description, this division is not mandatory. In fact, according to the embodiments of the present disclosure, the features and functions of two or more modules or units described above can be embodied in one module or unit. On the contrary, the features and functions of one module or unit described above can be further divided into multiple modules or units to be embodied.

[0151] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. An ultra-precision turning feedforward control method based on frequency response data, characterized in that: The method comprises the following steps: According to the frequency response data of the servo axis to be optimized in the machine tool, the expected frequency band range and cutoff frequency of the servo axis to be optimized are obtained; the expected frequency band range is 0 Hz to the frequency when the gain drops to +3 dB or -3 dB; A feedforward controller composed of a FIR filter and a low-pass filter connected in series is used to establish an inverse model of the servo axis to be optimized in the desired frequency band according to the frequency response data of the servo axis to be optimized in the machine tool; the FIR filter is used to fit the inverse model of the servo axis to be optimized in the desired frequency band, and the low-pass filter is used to filter out the inverse model data greater than the cutoff frequency in the inverse model fitted by the FIR filter; the cutoff frequency is the maximum frequency value in the desired frequency band; The initial machining trajectory corresponding to the servo axis to be optimized is input into the inverse model to generate the optimized machining trajectory corresponding to the servo axis to be optimized.

2. The method according to claim 1, characterized in that: The order of the FIR filter is selected in the range of [15, 25].

3. The method according to claim 2, characterized in that The order of the FIR filter is 20.

4. The method according to claim 1, characterized in that A feedforward controller composed of a FIR filter and a low-pass filter connected in series is used to establish an inverse model of the servo axis to be optimized in the desired frequency band according to the frequency response data of the servo axis to be optimized in the machine tool, including: Based on the collected frequency response data of the servo axis to be optimized in the machine tool, the frequency response information of the servo axis to be optimized is obtained by discrete Fourier transform. ; According to the order of the preset FIR filter, the frequency response information of the FIR filter obtained by discrete Fourier transform ; according to and , which generates the optimal cost function of the FIR filter coefficients ; in, for In the filter corresponding coefficient Q=(h0,h1,h2,…,h Nf ), ; N f is the order of the FIR filter; h Nf For the FIR filter N f The coefficient of the order; f d Indicates the highest frequency component within the desired frequency band; f m is a series of discrete frequency components in the frequency domain after discrete Fourier transform, T s represents the sampling time, j is the definition of an imaginary number, j 2 =-1; Optimize and solve g(Q) in the feasible domain F corresponding to Q. The corresponding Q is used as the coefficient information of the FIR filter, and the target filter is generated; where, is the minimum value of g(Q) in the feasible domain F corresponding to Q; An initial inverse model of the servo axis to be optimized within the desired frequency band is constructed using the target filter.

5. The method according to claim 4, characterized in that After constructing an initial inverse model of the servo axis to be optimized within the desired frequency band, the method further includes: A low-pass filter is used to filter out the inverse model data having a frequency greater than a cutoff frequency in the initial inverse model, so as to generate an inverse model of the servo axis to be optimized within the desired frequency band.

6. The method according to claim 4, characterized in that Optimize and solve g(Q) in the feasible domain F corresponding to Q, including: Use a heuristic algorithm to optimize and solve g(Q) in the feasible domain F corresponding to Q.

7. The method according to claim 6, characterized in that Optimize and solve g(Q) in the feasible domain F corresponding to Q, including: Based on the differential evolution algorithm, g(Q) is optimized and solved in the feasible domain F corresponding to Q.

8. The method according to claim 1, characterized in that: The cut-off frequency is 100Hz.

9. A non-transitory computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, an ultra-precision turning feedforward control method based on frequency response data as described in any one of claims 1 to 8 is implemented.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the ultra-precision turning feedforward control method based on frequency response data as described in any one of claims 1 to 8 is implemented.

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