Three-parameter notch filter parameter self-tuning method based on frequency characteristics

Abstract

In the research on precision control of a servo system of a numerical control machine tool, the most common method for eliminating mechanical resonance of the system is to add a notch filter, and the invention provides a notch filter parameter self-tuning strategy aiming at the problems that the manual tuning efficiency of the notch filter parameter is low and the tuning result is greatly influenced by experience of engineers. After the frequency characteristics of the system are obtained, parameters of multiple groups of notch filters can be quickly obtained through a self-tuning algorithm. And finally, testing the notch filter parameter self-tuning algorithm by using the simulation model with three resonances, comparing the frequency characteristic curves of the system before and after notch, and setting the parameters obtained by the notch filter self-tuning algorithm into the system, so that the mechanical resonance of the system can be effectively inhibited.

Description

Technical Field

[0001] The invention belongs to the technical field of control accuracy of numerical control servo systems, and in particular relates to a parameter self-tuning method for a three-parameter notch filter. Background Art

[0002] Servo control systems are widely used in industrial production, such as CNC machine tools, automated production lines, and industrial robots. Most transmission systems are composed of transmission components such as couplings, lead screws, transmission shafts, gears, and belts. Since the connection between these components is not completely rigid, they show a certain degree of flexibility during the transmission process, which introduces mechanical resonance into the system. The existence of mechanical resonance will cause the control performance of the CNC machine tool servo system to deteriorate, causing inaccurate positioning of the system, damage to the mechanical structure of the system, and shorten the life of components. In severe cases, it will cause shaft breakage, posing a great threat to mechanical equipment and personnel. Therefore, the accurate identification of the frequency characteristics of the mechanical transmission system is of great significance for determining and suppressing mechanical resonance and improving the motion control performance of the feed system.

[0003] The most common method to eliminate mechanical resonance of the system is to add a notch filter. The main function of the notch filter is to attenuate the convex amplitude of the resonant frequency band in the amplitude-frequency characteristic of the servo system and improve the amplitude margin of the system. In engineering practice, after identifying the frequency characteristics of the system, engineers usually observe in which frequency band the system produces mechanical resonance by human eyes, determine the resonant frequency of the system, and then adjust the parameters of the notch filter through formulas and experience to suppress the resonance of the system. This method of determining the resonant frequency band and notch filter parameters through human eyes and experience has major defects. The notch filter parameters finally adjusted by this method are greatly affected by human factors, and the adjustment process is cumbersome and the adjustment efficiency is low. Summary of the invention

[0004] The purpose of the present invention is to provide a notch filter parameter self-tuning method, which automatically calculates the three parameters of the notch filter through a program algorithm according to the system frequency characteristic identification result. Figure 1 As shown, the resonance amplitude at the mechanical resonance of the system is offset, thereby suppressing the mechanical resonance of the system.

[0005] The three-parameter notch filter transfer function is as follows:

[0006]

[0007] In the formula, f 0 ——The notch center frequency of the notch filter, in Hz;

[0008] p——notch depth coefficient, which indicates the depth of the amplitude depression of the amplitude-frequency characteristic of the notch filter at the center frequency;

[0009] k is the notch width coefficient, which indicates the width when the amplitude of the amplitude-frequency characteristic drops by 3dB with the notch center frequency as the center, and its unit is Hz.

[0010] To achieve the above object, the present invention is implemented through the following technical solutions:

[0011] The method for self-tuning the parameters of a notch filter based on frequency characteristics is characterized in that after obtaining the frequency characteristics of the system, the notch center frequency f is obtained by a resonant frequency search method based on a sliding window algorithm. 0 ; Combined with the depth coefficient calculation formula, the self-tuning of the notch depth coefficient p is realized; finally, the algorithm is used to determine the intersection of the threshold line and the resonant frequency segment to realize the self-tuning of the notch width coefficient k. The specific parameter tuning process includes: Step 1: After obtaining the data of the system's logarithmic amplitude-frequency characteristic curve through experiments, the resonant frequency of the system is obtained through a resonant frequency search method based on a sliding window algorithm; Step 2: Use a self-tuning algorithm to loop to find the maximum points and their amplitude gains in the system's logarithmic amplitude-frequency characteristic data, and determine the threshold point corresponding to each resonant point, and calculate the depth coefficient through the algorithm to realize the self-tuning of the notch depth coefficient. Step 3: Based on the previous self-tuning algorithm, after obtaining multiple resonant frequencies of the system, an algorithm is written to determine the intersection of the system's logarithmic amplitude-frequency characteristic curve on the left and right sides of the resonant frequency with the threshold line H' th The intersection point is then found, and an algorithm is written based on the calculation formula of the width coefficient to complete the self-tuning of the notch width coefficient.

[0012] Compared with the prior art, the present invention has the following beneficial effects:

[0013] 1) The notch effect of the notch filter is better: The three parameters in the transfer function of the three-parameter notch filter correspond to the three characteristics of the notch filter, and each characteristic can be adjusted by its corresponding parameter.

[0014] 2) The tuning process is simple and efficient: Based on the system frequency characteristic identification results, the three parameters of the notch filter are automatically calculated through the program algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is the technical roadmap for the self-tuning of the notch filter parameters of the present invention.

[0016] Figure 2 Schematic diagram of the resonant frequency search method based on the sliding window algorithm of the present invention

[0017] Figure 3 The logarithmic amplitude-frequency characteristic curve of the feeding system in the embodiment of the present invention is

[0018] Figure 4 The result of searching for the resonance frequency in the present invention is shown in FIG.

[0019] Figure 5 This is the result of the depth coefficient self-tuning in the example of the present invention.

[0020] Figure 6 The width coefficient self-tuning result diagram in the example of the present invention

[0021] Figure 7 The frequency response curve of the system before and after adding the notch filter in the example of the present invention DETAILED DESCRIPTION

[0022] The technical solution of the present invention will be clearly and completely described below in conjunction with specific examples. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments.

[0023] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the specific embodiments required to be used in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the specific embodiments described below are some implementation methods of the present invention. For ordinary technicians in this field, other specific embodiments can be obtained based on these specific embodiments without paying creative work.

[0024] The components of the embodiments of the present invention generally described and shown in the specific embodiments herein can be arranged and designed in countless different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the specific embodiments is not intended to limit the scope of the claimed invention, but is merely representative of selected embodiments of the present invention.

[0025] The control process of the embodiment of the present invention is as follows Figure 1 As shown, in order to suppress the mechanical resonance of the servo feed system of the CNC machine tool, it is necessary to add a notch filter to the servo. Since the signal in the actual CNC system is based on the adopted discrete sequence, it is necessary to discretize the transfer function of the notch filter (the discretization method is the bilinear transformation method, which only considers that the method can ensure the stability of the system after discretization, and does not play a decisive role in the present invention, so the calculation process is not described in detail).

[0026] The transfer function of the notch filter is discretized using the bilinear transformation method, and the simultaneous equations are obtained:

[0027]

[0028] Solving equation (2), that is, substituting s into the transfer function G(s), we can obtain:

[0029]

[0030] Among them, u(n) is the input of the notch filter, and y(n) is the output of the notch filter.

[0031] make

[0032] Formula (3) can be simplified as follows through formula (4):

[0033]

[0034] Transformed into the form of difference equation:

[0035] y(k)=-a 0 y(k-2)-a 1 y(k-1)+b 0 u(k-2)+b 1 u(k-1)+b 2 u(k#(6)

[0036] According to the discretized differential equation of the notch filter, the notch filter algorithm is written in the PMAC open CNC system, and then the frequency characteristics of the system after adding the notch filter are tested. According to the experimental identification of the system frequency characteristics and mechanical resonance results, the parameters of the notch filter are determined through the notch filter parameter self-tuning algorithm. The logarithmic amplitude-frequency characteristic curve of the feed system is as follows: Figure 3 As shown in the figure, the resonant frequency search result (notch center frequency self-tuning result) is as follows Figure 4 As shown, the notch depth coefficient self-tuning results are as follows Figure 5 As shown, the notch width coefficient self-tuning result is as follows Figure 6 shown.

[0037] The resonant frequency search algorithm based on the sliding window algorithm can effectively search for each resonant frequency of a system with multiple resonant frequency points. The self-tuning result of the notch center frequency is basically consistent with the actual resonant frequency of the system, and the self-tuning algorithm gives the self-tuning results of the notch depth coefficient and width coefficient according to the system logarithmic amplitude-frequency characteristic data, and organizes the self-tuning results of the notch filter parameters into a table, as shown in Table 1.

[0038] Table 1 Notch filter parameters

[0039]

[0040] In order to verify the effectiveness of the notch depth coefficient and width coefficient self-tuning algorithm, this paper sets the results obtained by the self-tuning algorithm to the three notch filters of the system. By comparing the frequency response curves of the system before and after the notch, the effect of the notch filter parameter self-tuning results on the suppression of system resonance is checked. The frequency response curves of the system before and after the notch are shown in Figure 2. Figure 7 shown.

Claims

1. Three-parameter notch filter parameter self-tuning based on frequency characteristics, characterized by: After obtaining the frequency characteristics of the system, the maximum value of the system amplitude-frequency characteristic curve is first searched through the resonant frequency search method based on the sliding window algorithm to determine the resonant frequency and amplitude gain, thereby obtaining the notch center frequency f0; then a threshold line H' is determined according to the system's logarithmic amplitude-frequency characteristic curve th ; Then determine the threshold point H at the resonant frequency point according to the threshold line th At the same time, combined with the depth coefficient calculation formula, the self-tuning of the notch depth coefficient p is realized; finally, the intersection of the threshold line and the resonant frequency band is determined by the algorithm to realize the self-tuning of the notch width coefficient k.

2. The setting method according to claim 1, characterized in that: First, the resonant frequency of the system is obtained by the resonant frequency search method based on the sliding window algorithm. This algorithm is part of the self-tuning algorithm. Its principle is shown in Figure 2. The principle is: Determine a sliding window with a width of 2a+1. Let the serial number of the middle data in the sliding window be i, then the serial number of the leftmost data is ia, and the serial number of the rightmost data is i+a. By comparing the size of the middle data with multiple data points on the left and right sides, determine whether the middle data is a maximum value, and thus determine whether the point is a resonance point. The sliding window starts from the leftmost end of the data and gradually moves to the right, and searches for the resonant frequency point of the system through iterative operations.

3. The self-tuning method according to claim 1, characterized in that: The resonant frequency point of the system is searched through iterative calculation, and then the notch center frequency and depth coefficient are automatically adjusted. The specific calculation process of the notch center frequency and depth coefficient self-tuning algorithm in the method is: Step 1: Initialize a series of variables to store values ​​such as center frequency, resonance amplitude gain, threshold point, etc. Step 2: Find the maximum value point and its amplitude gain in the system logarithmic amplitude-frequency characteristic data through a loop, and determine the threshold point corresponding to each resonance point, and store it in the initialized variable; Step 3: Calculate the depth coefficient through an algorithm to achieve self-tuning of the notch depth coefficient.

4. The setting method according to claim 1, characterized in that: The specific calculation process of the notch width coefficient self-tuning algorithm in the method is: Step 1: After reaching multiple resonant frequencies of the system, write an algorithm to determine the logarithmic amplitude-frequency characteristic curve of the system on both sides of the resonant frequency and the threshold line H' th The intersection of . Step 2: Then write an algorithm based on the calculation formula of the width coefficient to complete the self-tuning of the notch width coefficient.

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