Servo feeding system frequency characteristic identification method based on composite excitation signal

Abstract

A servo feeding system of a numerical control machine tool generally has certain flexibility, so that a servo system generates mechanical resonance. In order to accurately identify frequency characteristics of a system, a system frequency characteristic identification method based on an excitation signal and a signal processing algorithm based on fast Fourier transform are used for further identifying mechanical resonance of the system, and a system frequency characteristic identification method based on a composite excitation signal is designed for a burr phenomenon in an identification result. A constant value signal is superposed on a frequency sweep excitation signal, the creeping phenomenon caused by nonlinear friction force is overcome, the identification precision is improved, therefore, the burr phenomenon in an identification result can be remarkably reduced, the identification of the harmonic amplitude value is more accurate, and the method has rich application prospects and practical significance.

Description

Technical Field

[0001] The invention relates to an identification method, in particular to a frequency characteristic identification method of a servo feed system based on a composite excitation signal, which can be used for identifying the frequency domain characteristics and resonance characteristics of a servo system. 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] Domestic and foreign scholars have proposed many methods for the identification of system frequency characteristics and mechanical resonance. Jiantao Li et al. established a flexible dynamics model based on the Lagrange equation and obtained the frequency characteristics of the system according to the harmonic response. However, the frequency components contained in the signal used were relatively few, and the frequency characteristics of some frequency bands could not be accurately identified. Zhang Qi et al. used the tapping method to obtain the vibration information of the robot arm joint, and then fitted the vibration curve of the robot arm joint torque by the least squares method to obtain the least squares solution of the flexible joint parameters. However, the torque fluctuations generated by the tapping method are easily confused with the noise signal, thus affecting the accuracy of parameter identification. Wu Chun et al. applied a sinusoidal sweep frequency signal to the given position of the current loop to identify the resonant frequency of the servo system offline to obtain the frequency characteristics of the system, but there were large burrs in the identification results; Li Yingli et al. applied a sweep frequency excitation signal to the output torque of the robot joint motor, collected the motor position signal, and then obtained the torque-position frequency response of the flexible joint motor by fast Fourier transform. Summary of the invention

[0004] The purpose of the present invention is to solve the problems that the signals obtained by the vibration frequency identification methods widely exist in the current mechanical systems contain few frequency components and low precision. A frequency characteristic identification method based on a composite excitation signal is provided, that is, a constant value signal is superimposed on the swept frequency excitation signal to reduce the influence of nonlinear friction on the identification result and improve the identification accuracy. Therefore, the burr phenomenon in the identification result can be significantly reduced, and the identification of the resonance amplitude is more accurate.

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

[0006] The frequency characteristic identification method of the servo feed system based on the composite excitation signal is as follows: Figure 1 As shown, the excitation signal is formed by superimposing the scanning signal and the constant value signal. The signal is input into the servo feed system. After the system outputs, the input and output signals are collected. These signals are processed by fast Fourier transform and finally used to identify the frequency domain characteristics of the system.

[0007] Furthermore, the method for identifying the frequency domain characteristics of the system by subjecting the excitation signal and the system output signal to fast Fourier transform is as follows:

[0008] The servo feed system is equivalent to a dual-inertia system, that is, a system consisting of motor inertia, load inertia and flexible transmission links, such as Figure 2 As shown, the dual inertia model of the system is established:

[0009]

[0010] In the formula, J m is the motor equivalent moment of inertia, J l is the equivalent moment of inertia of the load, T m is the motor torque, T w is the transmission system torque, T l is the load torque, K is the transmission system stiffness coefficient, C w is the transmission system damping coefficient, θ m is the motor rotation angle, θ l is the load angle, ω m is the motor speed, ω l is the load speed.

[0011] Furthermore, according to the above equations, a simulink simulation model of the dual inertia system can be established, such as Figure 3 shown.

[0012] Furthermore, the method for identifying the excitation signal is specifically as follows:

[0013] The main feature of the input signal required for system identification is that it can contain all frequency components within the required frequency range. Commonly used excitation signals include pseudo-random binary signals (PRBS) and swept frequency signals.

[0014] The pseudo-random sequence is a sequence generated by a shift register. For the sequence x1x2…x n-1 x n …, the relationship between the elements is as follows:

[0015] x n+1 =a1x n+a2x n-1 +…a n x i (2)

[0016] where a1…a n Take 0 or 1, n is the level of PRBS sequence, i = 1, 2, 3... Its time domain waveform is as follows Figure 4 As shown, the frequency domain characteristics are Figure 5 shown.

[0017] For the frequency sweep signal, assuming that the initial frequency of the frequency sweep is f0, the cutoff frequency is f1, the signal amplitude is A, the frequency sweep time is T, the current time is t, the frequency at the current time is f, and the frequency sweep given signal u(t) is:

[0018] ut=Asin2πft(3)

[0019] in

[0020]

[0021] Substituting formula (4) into formula (3), we get:

[0022]

[0023] From the above formula, it can be clearly concluded that the frequency sweep signal is a sinusoidal function whose frequency changes logarithmically over time. Compared with the linear frequency sweep, the low-frequency signal contained in the logarithmic signal is more dense, and its time domain waveform is as follows: Figure 6 As shown, the frequency domain characteristics are Figure 7 shown.

[0024] Furthermore, based on the signal processing method of fast Fourier transform, Fourier transform is to represent a more complex function curve as a linear combination of sinusoidal functions with different amplitudes and phases. As a method of analyzing signals, Fourier transform can analyze the components of signals. Fast Fourier transform (FFT) is a fast algorithm of Fourier transform and is widely used in signal processing. The acquisition and processing process of the input and output signals of the servo system is as follows: Figure 8 shown.

[0025] Through FFT calculation, we can get the in-phase and quadrature components of the input and output data at the same frequency, which are expressed as follows:

[0026]

[0027] Among them, A i , A0 represents the input and output amplitude, Φ i, Φ0 represents the phase of the input and output signals, R is the real part, and I is the imaginary part. Then, the amplitude ratio and phase difference of the input and output signals at each frequency point are calculated to obtain the amplitude-frequency characteristics and phase-frequency characteristics of the measured object. After performing FFT transformation on the input and output data, the algorithm can be written through formula (7) to calculate the amplitude-frequency characteristics and phase-frequency characteristics of the system and draw the Bode diagram.

[0028]

[0029] To solve the burr problem in the identification results, an identification method based on a composite excitation signal is proposed. A constant value signal is superimposed on the swept frequency excitation signal to reduce the identification error caused by nonlinear friction, especially the influence of nonlinear friction on the amplitude identification results, and improve the identification accuracy.

[0030] The beneficial effects of the present invention compared to the prior art are as follows: the present invention reduces the influence of nonlinear friction on the frequency characteristic identification result, can significantly reduce the burr phenomenon in the identification result, and is more accurate in identifying the resonance amplitude. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 This is the principle flow chart of the present invention

[0032] Figure 2 Schematic diagram of dual inertia system structure

[0033] Figure 3 Dual inertia system simulink model block diagram

[0034] Figure 4 Pseudo-random binary signal time domain waveform

[0035] Figure 5 Pseudo-random binary signal frequency domain characteristics diagram

[0036] Figure 6 Time domain waveform of swept frequency signal

[0037] Figure 7 Frequency domain characteristic diagram of swept frequency signal

[0038] Figure 8 Data collection and processing flow chart

[0039] Fig. 9 Composite excitation signal time domain waveform

[0040] Fig.10 Frequency domain characteristics of composite excitation signal

[0041] Fig.11 Simulation diagram of the effect of friction on identification results

[0042] Fig.12 Comparison of frequency characteristics identification results of servo feed system DETAILED DESCRIPTION

[0043] The specific implementation cases of the present invention will be described in detail below. It should be noted that the present invention can be implemented in various forms and should not be limited by the implementation cases described here. In fact, the implementation cases are provided to enable a more thorough understanding of the present invention and to fully convey the scope of application of the present invention to those skilled in the art.

[0044] Example 1

[0045] The frequency identification method proposed in the present invention is based on the identification method of the composite excitation signal, that is, a constant value signal is superimposed on the swept frequency excitation signal to reduce the adverse effects caused by nonlinear friction and improve the identification accuracy. The time domain waveform of the composite excitation signal is as follows: Fig. 9 As shown, the frequency characteristics are Fig.10 shown.

[0046] It can be seen from the time domain waveform and frequency domain characteristics of the composite excitation signal that after superimposing the constant value signal, the amplitude gain at each frequency point in the frequency domain remains basically unchanged, and it can be used as an excitation signal to identify the frequency characteristics of the system.

[0047] The identification results of the feed system containing friction using the sweep frequency signal and the composite excitation signal are shown in the figure below. Fig.12 shown.

[0048] Fig.11 It can be seen from the simulation results that after adding the friction model, the burrs in the frequency response curve of the swept frequency signal identification are greatly increased, especially in the medium and high frequency bands, which further illustrates that nonlinear friction is the main factor leading to inaccurate identification results.

[0049] Figure 1 The processing process and principle of the above method are demonstrated. Through this method, the identification error caused by nonlinear friction can be reduced.

[0050] According to the above method, the program of the composite excitation signal is written on PMAC. During the operation, the corresponding input and output signals are collected by the PMACplot Pro function module to obtain the input and output data. Then, the frequency characteristics of the system are identified according to the input and output data, and the identification results of the swept frequency signal are compared with the identification results based on the composite signal. Fig.12 As shown in the figure, it can be seen from the composite signal curve that the influence of nonlinear friction on the identification result is reduced due to the superposition of the constant value signal, thereby greatly reducing the burr phenomenon in the swept frequency signal identification result and making the amplitude identification result more accurate.

Claims

1. A method for identifying the frequency characteristics of a servo feed system based on a composite excitation signal, characterized in that: By superimposing a constant value signal on the swept frequency excitation signal, the creeping phenomenon caused by nonlinear friction can be overcome and the recognition accuracy can be improved. The principle is: The excitation signal is formed by superimposing the scanning signal and the constant value signal. The signal is input into the servo feed system. After the system outputs, the input and output signals are collected. These signals are processed by fast Fourier transform and finally used to identify the frequency domain characteristics of the system. Furthermore, the method for identifying the frequency domain characteristics of the system by subjecting the excitation signal and the system output signal to fast Fourier transform is as follows: The servo feed system is equivalent to a dual-inertia system, that is, a system composed of motor inertia, load inertia and flexible transmission links, and a dual-inertia model of the system is established: In the formula, J m is the motor equivalent moment of inertia, J l is the equivalent moment of inertia of the load, T m is the motor torque, T w is the transmission system torque, T l is the load torque, K is the transmission system stiffness coefficient, C w is the transmission system damping coefficient, θ m is the motor rotation angle, θ l is the load angle, ω m is the motor speed, ω l is the load speed. According to the above equations, the Simulink simulation model of the dual-inertia system can be established. The method for identifying the excitation signal is specifically as follows: The main feature of the input signal required for system identification is that it can contain all frequency components within the required frequency range. Commonly used excitation signals include pseudo-random binary signals (PRBS) and swept frequency signals. The pseudo-random sequence is a sequence generated by a shift register. For the sequence x1x2…x n-1 x n …, the relationship between the elements is as follows: x n+1 =a1x n +a2x n-1 +…a n x i (2) where a1…a n Takes 0 or 1, n is the level of the PRBS sequence, i = 1, 2, 3…. For the frequency sweep signal, assuming that the initial frequency of the frequency sweep is f0, the cutoff frequency is f1, the signal amplitude is A, the frequency sweep time is T, the current time is t, the frequency at the current time is f, and the frequency sweep given signal u(t) is: u(t)=Asin(2πft) (3) in Substituting formula (14) into formula (13), we get: It can be clearly seen from the above formula that the frequency sweep signal is a sinusoidal function whose frequency changes logarithmically over time. Compared with the linear frequency sweep, the low-frequency signals contained in the logarithm are more dense. Furthermore, based on the signal processing method of fast Fourier transform, the Fourier transform is to represent a more complex function curve as a linear combination of sinusoidal functions of different amplitudes and phases. As a method of analyzing signals, the Fourier transform can analyze the components of the signal. Fast Fourier transform (FFT) is a fast algorithm of Fourier transform and is widely used in signal processing. Through FFT calculation, we can get the in-phase and quadrature components of the input and output data at the same frequency, which are expressed as follows: in, A i , A0 represents the input and output amplitude, Φ i , Φ0 represents the phase of the input and output signals, R is the real part, and I is the imaginary part. Then, the amplitude ratio and phase difference of the input and output signals at each frequency point are calculated to obtain the amplitude-frequency characteristics and phase-frequency characteristics of the measured object. After performing FFT transformation on the input and output data, the algorithm can be written through formula (7) to calculate the amplitude-frequency characteristics and phase-frequency characteristics of the system and draw the Bode diagram. To solve the burr problem in the identification results, a constant value signal is superimposed on the swept frequency excitation signal to overcome the creeping phenomenon caused by nonlinear friction and improve the identification accuracy.

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