Permanent magnet synchronous motor torque ripple suppression method based on feedforward compensation

Abstract

The invention relates to the technical field of torque ripple suppression, in particular to a permanent magnet synchronous motor torque ripple suppression method based on feedforward compensation. The method comprises the following steps: S1, establishing a mathematical model of the permanent magnet synchronous motor; s2, analyzing factors causing torque pulsation through electromagnetic parameters and mechanical parameters based on the mathematical model of the permanent magnet synchronous motor; s3, according to an analysis result, designing a fluctuation model based on discrete Fourier transform; s4, generating a compensation signal based on Fourier series expansion by using the designed fluctuation model; and S5, combining the generated compensation signal with an existing control system in a superposition mode, and adding the superposed compensation signal into a control instruction of the permanent magnet synchronous motor to smooth torque output. Through the design and application of the feedforward compensation signal, the method can effectively counteract the periodic torque ripple caused by the cogging effect, the magnetic field nonuniformity, the inverter switching frequency and other factors.

Description

Technical Field

[0001] The present invention relates to the technical field of torque pulsation suppression, and in particular to a method for suppressing torque pulsation of a permanent magnet synchronous motor based on feedforward compensation. Background Art

[0002] During the operation of a permanent magnet synchronous motor (PMSM), torque pulsation often occurs due to the influence of various factors. Torque pulsation can cause the motor to run unsteadily, generate vibration and noise, and seriously affect the performance of the motor and the user experience; the cogging effect is an important factor causing torque pulsation. When the relative position between the stator and the rotor of the motor changes, the magnetic imbalance caused by the change in magnetic permeability will cause periodic torque fluctuations; the manufacturing error of the permanent magnet, the nonlinearity of the magnetic material, and the asymmetry of the internal structure of the motor will all lead to the non-uniformity of the magnetic field, which will in turn cause torque fluctuations; the PWM (pulse width modulation) modulation frequency of the inverter will also generate harmonics, which will be transmitted to the motor, causing torque fluctuations. The inverter switching frequency and the harmonics it generates also have a significant impact on the motor torque; traditional control methods (such as PID control) are often limited in effect when dealing with torque pulsation problems, because these methods usually perform feedback control on existing fluctuations, and it is difficult to compensate in advance or completely eliminate fluctuations. In summary, a method for suppressing torque pulsation of a permanent magnet synchronous motor based on feedforward compensation is provided. Summary of the invention

[0003] The object of the present invention is to provide a method for suppressing torque pulsation of a permanent magnet synchronous motor based on feedforward compensation, so as to solve the problems of unstable operation caused by torque pulsation and limitations of existing control methods proposed in the above background technology.

[0004] To achieve the above object, the present invention provides a method for suppressing torque pulsation of a permanent magnet synchronous motor based on feedforward compensation, comprising the following steps: S1. Establish a mathematical model of permanent magnet synchronous motor; S2. Based on the mathematical model of permanent magnet synchronous motor, the factors causing torque pulsation are analyzed through electromagnetic parameters and mechanical parameters; S3. According to the analysis results, a wave model is designed based on discrete Fourier transform; S4, using the designed wave model to generate a compensation signal based on Fourier series expansion; S5. Combining the generated compensation signal with the existing control system by superposition, and adding the superimposed compensation signal to the control command of the permanent magnet synchronous motor to smooth the torque output.

[0005] As a further improvement of the technical solution, in S1, establishing a mathematical model of the permanent magnet synchronous motor includes the following steps: S1.1. Select a two-phase rotating coordinate system dq, where the d-axis is consistent with the magnetic field direction of the permanent magnet and the q-axis is perpendicular to it; S1.2. In the dq coordinate system, construct the voltage equation, flux equation, torque equation and mechanical motion equation to describe the dynamic characteristics of the permanent magnet synchronous motor during operation; S1.3. Integrate all equations together to form a complete mathematical model of the permanent magnet synchronous motor.

[0006] As a further improvement of the technical solution, in S1.2, the voltage equation, magnetic flux equation, torque equation and mechanical motion equation are specifically: ; ; The magnetic flux equation is: ; ; The torque equation is: ; The mechanical motion equation is: ; in, represents the d-axis voltage; represents the q-axis voltage; Indicates winding resistance; represents the d-axis current; represents the q-axis current; represents the d-axis magnetic flux; represents the q-axis magnetic flux; represents the inductance of the d-axis; represents the inductance of the q-axis; represents the electrical angular velocity; Represents the fixed flux linkage produced by the permanent magnet; represents electromagnetic torque; represents the torque constant; represents the moment of inertia; Represents mechanical angular velocity; Indicates load torque; represents the damping coefficient; Represents a time variable.

[0007] As a further improvement of the technical solution, in S2, the factors causing torque pulsation include: cogging benefit, magnetic field non-uniformity and inverter switching frequency.

[0008] As a further improvement of the technical solution, in S3, designing a fluctuation model according to the analysis result includes the following steps: S3.1, extracting the characteristics of the factors causing the torque pulsation in step S2; S3.2. Establish a fluctuation model to describe the influence of factors causing torque pulsation on torque; S3.3. Based on the fluctuation model, design a compensation signal so that the compensation signal can offset the impact of the fluctuation, and determine the parameters of the compensation signal.

[0009] As a further improvement of the technical solution, in S3.2, a fluctuation model is established to describe the influence of factors causing torque pulsation on torque, including the following steps: S3.21. Use the mathematical model of the permanent magnet synchronous motor to simulate the operating state of the permanent magnet synchronous motor and obtain simulation data of torque fluctuation; S3.22. Perform spectrum analysis on simulation data by discrete Fourier transform, identify the main frequency components of torque fluctuations, and observe the trend of data changes over time; S3.23. Establish a model for the source of tooth-slot efficiency fluctuations and analyze the structure of the stator and rotor of a permanent magnet synchronous motor; establish a model for the uneven magnetic field fluctuations and analyze the magnetic flux density distribution of a permanent magnet; establish a model for the switching frequency fluctuations of an inverter and analyze the PWM modulation frequency of the inverter and the harmonics it generates; S3.24. For periodic fluctuations, use Fourier series expansion to describe the factors that cause torque ripple; S3.25, extracting Fourier coefficients from spectrum analysis; S3.26, constructing a fluctuation model using the parameters of the extracted Fourier coefficients, and verifying the accuracy of the model through simulation, and adjusting the model parameters according to the verification results until the fluctuation model can accurately reflect the actual torque fluctuation; S3.27. Unify the formats of all identified fluctuation source models, including the tooth-slot benefit fluctuation source model, the magnetic field uneven fluctuation model and the inverter switching frequency fluctuation model, and integrate all identified fluctuation source models into a comprehensive torque fluctuation model, and add adaptive parameters, transient compensation signals and interaction coefficients of factors causing torque pulsation to the comprehensive torque fluctuation model.

[0010] As a further improvement of the technical solution, in S3.22, the discrete Fourier transform is: ; in, represents a frequency domain signal; Represents the time domain signal, i.e., the torque fluctuation signal; Indicates the number of sampling points; represents the frequency index; represents an imaginary unit; Represents a time index in a discrete time series.

[0011] As a further improvement of the technical solution, in S3.27, the comprehensive torque fluctuation model is: ; Adding adaptive parameters, transient compensation signals and interaction coefficients of factors causing torque ripple to the comprehensive torque ripple model is: ; in, represents the original integrated torque ripple model; represents a comprehensive torque fluctuation model after adding adaptive parameters, transient compensation signals and interaction coefficients of factors causing torque pulsation; Indicates fundamental torque; Indicates the highest order of fundamental frequency components; represents the amplitude of the 𝑛th order sine wave; represents the time variable; 𝑛 represents the index of the sine wave order; represents the phase of the 𝑛th order sine wave; Indicates the fundamental frequency; Indicates the highest order of the cosine wave frequency components; Indicates The amplitude of the cosine wave of order; The index representing the order of the cosine wave; Indicates The phase of the cosine wave of order; Indicates the highest order of frequency components associated with PWM modulation; represents the amplitude of the 𝑘th order sine wave associated with PWM modulation; 𝑘 represents the index of the order of the sine wave associated with the PWM modulation frequency of the inverter; Indicates the frequency associated with PWM modulation; represents the phase of the 𝑘th order sine wave associated with PWM modulation; Indicates adjustment The gain factor of the sine wave of order; Indicates adjustment The gain factor of the order cosine wave; Indicates adjustment The gain factor of the sine wave related to PWM modulation; Represents the interaction coefficient of factors causing torque ripple; represents the transient compensation signal; Indicates The amplitude of the sine wave of order; represents another parameter related to fluctuations; An index representing the order of the sine wave relative to the fundamental frequency; An index representing the order of another sine wave relative to the fundamental frequency; Denotes the phase of the interaction of the 𝑖th and 𝑗th order fluctuations.

[0012] As a further improvement of the technical solution, in S5, the generated compensation signal is combined with the existing control system by superposition, including the following steps: S5.1. Determine the best insertion point of the compensation signal; S5.2, superimposing the compensation signal with the reference signal of the current loop; S5.3, synthesizing the compensation signal with the original reference signal to generate a new synthesized signal; S5.4. Limit the new synthesized signal to ensure that the new synthesized signal does not exceed the allowable range of the permanent magnet synchronous motor. In the process of limiting the new synthesized signal, a smoothing factor is introduced and filtering is performed; S5.5, transmitting the synthesized signal after the processing of limiting and filtering to the permanent magnet synchronous motor controller as a new control instruction for feedforward compensation.

[0013] As a further improvement of the technical solution, in S5.4, the limiting process of the new synthesized signal is specifically as follows: ; The smoothing factor introduced in the limiting process of the synthesized signal is: ; in, represents the original synthetic signal; Indicates the signal after limiting processing; It represents the amplitude limiting processing signal after the smoothing factor is introduced; Indicates the lower threshold of the signal; Indicates the upper threshold of the signal; Represents the smoothing factor.

[0014] Compared with the prior art, the present invention has the following beneficial effects: 1. In the method for suppressing torque pulsation of permanent magnet synchronous motor based on feedforward compensation, through the design and application of feedforward compensation signal, this method can effectively offset the periodic torque fluctuation caused by factors such as cogging effect, magnetic field inhomogeneity and inverter switching frequency. This not only improves the stability of motor operation and reduces mechanical wear, but also improves the overall performance of the system, making the application of permanent magnet synchronous motor in industrial automation, electric vehicles and other fields more extensive and reliable.

[0015] 2. In the permanent magnet synchronous motor torque pulsation suppression method based on feedforward compensation, the compensation signal is superimposed on the existing control system to achieve real-time compensation of torque fluctuations, thereby improving the dynamic response capability of the system. This method not only simplifies the control strategy and avoids the computational burden brought by complex algorithms, but also ensures that the motor can maintain stable torque output under different working conditions, enhancing the robustness and adaptability of the system. In addition, through reasonable limiting and smoothing processing, it is ensured that the compensation signal will not exceed the working range of the motor, further ensuring the safe and stable operation of the motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 The figure is a flow chart of the overall method of the present invention. DETAILED DESCRIPTION

[0017] 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 ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0018] See also Figure 1 As shown, this embodiment provides a method for suppressing torque pulsation of a permanent magnet synchronous motor based on feedforward compensation, comprising the following steps: S1. Establish a mathematical model of permanent magnet synchronous motor; In this embodiment, establishing a mathematical model of a permanent magnet synchronous motor includes the following steps: S1.1. Select a two-phase rotating coordinate system dq, where the d-axis is consistent with the magnetic field direction of the permanent magnet and the q-axis is perpendicular to it; S1.2. In the dq coordinate system, construct the voltage equation (which describes the relationship between the voltage and current at both ends of the armature winding, providing a basis for voltage control), the flux equation (which describes the relationship between the flux and current, helping to analyze the magnetic field distribution), the torque equation (which describes the electromagnetic torque generated by the motor, which is determined by the q-axis current and flux, providing theoretical support for eliminating torque fluctuations) and the mechanical motion equation (which describes the mechanical motion of the motor rotor, including the influence of speed, load torque and inertia, providing a basis for optimizing dynamic response) to describe the dynamic characteristics of the permanent magnet synchronous motor during operation; Among them, the dynamic characteristics include the electromagnetic field distribution inside the permanent magnet synchronous motor, the changes in current and voltage, the generation of electromagnetic torque, and the mechanical movement of the motor rotor; Furthermore, the voltage equation, flux equation, torque equation and mechanical motion equation are specifically: The voltage equation is: ; ; The magnetic flux equation is: ; ; The torque equation is: ; The mechanical motion equation is: ; in, represents the d-axis voltage; represents the q-axis voltage; Indicates winding resistance; represents the d-axis current; represents the q-axis current; represents the d-axis magnetic flux; represents the q-axis magnetic flux; represents the inductance of the d-axis; represents the inductance of the q-axis; represents the electrical angular velocity; Represents the fixed flux linkage produced by the permanent magnet; represents electromagnetic torque; represents the torque constant; represents the moment of inertia; Represents mechanical angular velocity; Indicates load torque; represents the damping coefficient; represents the time variable; S1.3. Integrate all equations together to form a complete mathematical model of the permanent magnet synchronous motor.

[0019] S2. Based on the mathematical model of permanent magnet synchronous motor, the factors causing torque pulsation are analyzed through electromagnetic parameters and mechanical parameters; Among them, electromagnetic parameters (obtained through flux, current, and voltage sensors) include flux, current, and voltage of permanent magnet synchronous motors; mechanical parameters (obtained through torque sensors, load simulators, vibration analyzers, etc.) include torque, speed, and load torque of permanent magnet synchronous motors; In this embodiment, the factors causing torque pulsation include: cogging effect (if the cogging effect is the main factor causing torque pulsation, determine its periodicity and amplitude, use finite element analysis (FEA) software to simulate the influence of the cogging effect on the magnetic field distribution, so as to derive the specific contribution of the cogging effect to the torque fluctuation), magnetic field inhomogeneity (analyze the inhomogeneity of the magnetic field, especially the magnetic field and harmonic components generated by the permanent magnet, identify the high-order harmonic components in the permanent magnet magnetic field, and analyze how they affect the torque fluctuation) and inverter switching frequency (consider the PWM modulation frequency of the inverter and the harmonics it generates, and evaluate the influence of PWM harmonics on the motor torque, especially those harmonics close to the motor rotation frequency).

[0020] S3. According to the analysis results, a wave model is designed based on discrete Fourier transform; In this embodiment, the discrete Fourier transform can convert the time domain signal into a frequency domain signal, so that various frequency components in the signal can be accurately analyzed, which is very useful for identifying the main frequency components that cause torque pulsation, because different sources of fluctuations (including cogging effect, magnetic field inhomogeneity, inverter switching frequency, etc.) will appear at different frequencies; it is particularly suitable for identifying periodic components in the signal. For permanent magnet synchronous motors, many factors that cause torque pulsation are periodic, such as cogging effect and PWM modulation frequency. These periodic fluctuations can be easily identified by discrete Fourier transform, and their frequency, amplitude and phase can be determined; for periodic torque fluctuations, Fourier series can be used to describe its mathematical model. This expansion form can clearly show the contribution of each harmonic component, so as to facilitate the design of compensation signals; according to the analysis results, the fluctuation model is designed based on discrete Fourier transform, including the following steps: S3.1, extracting the characteristics of the factors causing the torque pulsation in step S2, the characteristics including periodicity, frequency component, amplitude, etc.; S3.2. Establish a fluctuation model to describe the influence of factors causing torque pulsation on torque; Among them, by establishing a fluctuation model, the various factors that cause torque pulsation can be described more accurately. These models can capture the fluctuation characteristics of different sources, such as the slot effect, magnetic field inhomogeneity and the influence of inverter switching frequency, thereby providing a reliable mathematical basis for subsequent compensation design; the fluctuation model usually involves spectrum analysis. Through discrete Fourier transform, the main frequency components of the fluctuation can be identified. This analysis helps to distinguish different types of fluctuation sources and design compensation measures in a targeted manner; based on the fluctuation model, an accurate compensation signal can be designed. For example, for periodic fluctuations, an inverted periodic signal can be designed, and the parameters of the compensation signal (including amplitude, phase, frequency, etc.) can be determined to ensure that the compensation signal can accurately offset the fluctuation; establishing a fluctuation model to describe the influence of factors that cause torque pulsation on torque includes the following steps: S3.21. Use the mathematical model of the permanent magnet synchronous motor to simulate the operating state of the permanent magnet synchronous motor and obtain simulation data of torque fluctuation; S3.22. Perform spectrum analysis on simulation data by discrete Fourier transform, identify the main frequency components of torque fluctuations, and observe the trend of data changes over time; Among them, discrete Fourier transform is a mathematical tool that converts time domain signals into frequency domain signals; the basic idea is to convert a finite length, discrete time domain signal into a series of complex coefficients, which represent the components of the original signal at different frequencies. The discrete Fourier transform is: ; in, represents a frequency domain signal; Represents the time domain signal, i.e., the torque fluctuation signal; Indicates the number of sampling points; represents the frequency index; represents an imaginary unit; Represents the time index in a discrete time series; S3.23. Establish a model for the source of cogging effect fluctuations, analyze the structure of the stator and rotor of the permanent magnet synchronous motor, and identify the influence of the cogging effect on the torque fluctuations; establish a model for magnetic field inhomogeneity fluctuations, analyze the magnetic flux density distribution of the permanent magnet, and identify the influence of magnetic field inhomogeneity on the torque fluctuations; establish an inverter switching frequency fluctuation model, analyze the PWM modulation frequency of the inverter and the harmonics it generates, and identify its influence on the torque fluctuations; S3.24. For periodic fluctuations, use Fourier series expansion to describe the factors that cause torque ripple; Among them, the use of Fourier series can decompose a complex periodic function into a sum of simple sine waves and cosine waves, making complex periodic signals easy to understand and process; S3.25. Extract the Fourier coefficients, i.e. the amplitude and phase of each harmonic, from the spectrum analysis; S3.26, constructing a fluctuation model using the parameters of the extracted Fourier coefficients, and verifying the accuracy of the model through simulation, and adjusting the model parameters according to the verification results until the fluctuation model can accurately reflect the actual torque fluctuation; S3.27. Unify the formats of all identified fluctuation source models, including the cogging benefit fluctuation source model, the magnetic field uneven fluctuation model and the inverter switching frequency fluctuation model, and integrate all identified fluctuation source models into a comprehensive torque fluctuation model, and add adaptive parameters, transient compensation signals and interaction coefficients of factors causing torque pulsation to the comprehensive torque fluctuation model; Furthermore, the comprehensive torque fluctuation model is: ; Adaptive parameters allow the system to adjust the compensation strategy based on real-time feedback, which means that the system can maintain a high compensation effect even when the motor operating conditions change. For example, when the motor characteristics change due to load changes or temperature changes, adaptive parameters can help the system quickly adjust to the new situation. The existence of adaptive parameters allows the system to automatically adjust the strength and phase of the compensation signal according to the actual operating conditions to cope with dynamic changes in the motor operation; by introducing transient compensation signals, the system can better handle sudden or non-periodic disturbances, thereby enhancing the robustness of the system. For example, when the motor starts or encounters a sudden load, the transient compensation signal can respond quickly and reduce instantaneous torque fluctuations. The transient compensation signal can be used to compensate for non-periodic or transient fluctuations that cannot be completely eliminated by fixed periodic compensation signals; the introduction of interaction coefficients enables the model to more carefully reflect the relationship between different fluctuation factors, which helps to design more sophisticated compensation signals. For example, there may be interactions between the cogging effect and the magnetic field inhomogeneity. If these interactions are not taken into account, simple independent compensation may not be accurate enough. The interaction coefficient takes into account the mutual influence between different torque pulsation factors, making the model closer to reality and better able to predict and compensate for actual torque fluctuations. By introducing adaptive parameters, transient compensation signals and interaction coefficients, the actual torque fluctuations can be matched more accurately, thereby improving the effectiveness of the compensation signal. Adding adaptive parameters, transient compensation signals and interaction coefficients that cause torque pulsation factors to the comprehensive torque fluctuation model is: ; in, represents the original integrated torque ripple model; represents a comprehensive torque fluctuation model after adding adaptive parameters, transient compensation signals and interaction coefficients of factors causing torque pulsation; Indicates fundamental torque; Indicates the highest order of fundamental frequency components; represents the amplitude of the 𝑛th order sine wave; represents the time variable; 𝑛 represents the index of the sine wave order; represents the phase of the 𝑛th order sine wave; Indicates the fundamental frequency; Indicates the highest order of the cosine wave frequency components; Indicates The amplitude of the cosine wave of order; The index representing the order of the cosine wave; Indicates The phase of the cosine wave of order; Indicates the highest order of frequency components associated with PWM modulation; represents the amplitude of the 𝑘th order sine wave associated with PWM modulation; 𝑘 represents the index of the order of the sine wave associated with the PWM modulation frequency of the inverter; Indicates the frequency associated with PWM modulation; represents the phase of the 𝑘th order sine wave associated with PWM modulation; Indicates adjustment The gain factor of the sine wave of order; Indicates adjustment The gain factor of the order cosine wave; Indicates adjustment The gain factor of the sine wave related to PWM modulation; Represents the interaction coefficient of factors causing torque ripple; represents the transient compensation signal; Indicates The amplitude of the sine wave of order; represents another parameter related to fluctuations; An index representing the order of the sine wave relative to the fundamental frequency; An index representing the order of another sine wave relative to the fundamental frequency; Denotes the phase of the interaction of the 𝑖th and 𝑗th order fluctuations.

[0021] S3.3. Based on the fluctuation model, design a compensation signal so that the compensation signal can offset or weaken the impact of the fluctuation. For example, for periodic fluctuations, design an inverted periodic signal and determine the parameters of the compensation signal, including amplitude, phase, frequency, etc., to ensure that the compensation signal can accurately offset the fluctuation.

[0022] S4, using the designed fluctuation model to generate a compensation signal based on Fourier series expansion, which can accurately compensate for the factors causing torque fluctuation; In this embodiment, the design principle of the compensation signal is to enable it to offset or weaken the fluctuation component when added to the original torque fluctuation signal in the time domain. Therefore, the compensation signal should have the same frequency component as the original fluctuation signal, but the opposite phase; Compensation signal for: ; in, Used to ensure that the compensation signal is in opposite phase to the original fluctuation signal; S5, combining the generated compensation signal with the existing control system by superposition, and adding the superimposed compensation signal to the control command of the permanent magnet synchronous motor to smooth the torque output; In this embodiment, the generated compensation signal is combined with the existing control system by superposition, including the following steps: S5.1. Determine the best insertion point of the compensation signal. The compensation signal will be added to the reference signal in the current control loop to directly offset the torque fluctuation. If there are multiple control loops in the system, it is necessary to determine at which layer the compensation signal is superimposed to minimize the torque fluctuation. S5.2, superimpose the compensation signal with the reference signal of the current loop. If the compensation signal needs to be superimposed in the speed loop, the compensation signal needs to be converted into a speed signal and then superimposed with the reference signal of the speed loop; S5.3, synthesizing the compensation signal with the original reference signal (adding the compensation signal to the original reference signal of the motor control system) to generate a new synthesized signal; S5.4. Limiting the new synthesized signal to ensure that the new synthesized signal does not exceed the allowable range of the permanent magnet synchronous motor. In the process of limiting the new synthesized signal, a smoothing factor is introduced and filtering is performed to remove high-frequency noise or unnecessary fluctuations. Among them, the limiting processing can prevent the synthetic signal from exceeding the working range of the motor, thereby protecting the motor hardware from damage. If the synthetic signal is too large, it may cause the motor to overload, causing problems such as overheating and excessive current, and even damage the motor. The limiting processing ensures that the signal is always within a safe range to avoid these problems. Through the limiting processing, it can be ensured that the control signal always changes within a controllable range, which helps to maintain the stability of the system. If the signal exceeds the preset range, it may cause the control system to be unstable and affect the normal operation of the motor. The limiting processing can ensure that the system can remain stable under various circumstances. The specific limit processing of the new synthetic signal is as follows: ; The smoothing factor can help avoid sudden changes in the signal at the limit boundary. If the signal jumps directly from one limit value to another, it may cause unstable motor operation and even cause mechanical vibration or noise. Through the smoothing factor, the signal gradually transitions when approaching the limit boundary, reducing the possibility of sudden changes; the smoothing factor can improve the quality of the signal, making it smoother when approaching the limit boundary, which helps to reduce high-frequency noise or unnecessary fluctuations in the signal, thereby improving the smoothness and comfort of motor operation; in motor control, the sharp change of the signal will cause additional stress on the mechanical parts, and the smoothing factor can reduce this stress, thereby extending the service life of the mechanical parts. Smooth transition can reduce the mechanical shock inside the motor and help protect the motor and its related components; the smoothing factor introduced in the process of limiting the synthesized signal is: ; in, represents the original synthetic signal, that is, the compensated signal after synthesis; Indicates the signal after limiting processing; It represents the amplitude limiting processing signal after the smoothing factor is introduced; Indicates the lower threshold, the signal should not be lower than this value; Indicates the upper threshold, the signal should not exceed this value; Represents the smoothing factor, which determines the signal and The smooth transition speed between A value of 0 will make the transition smoother; S5.5, transmitting the synthesized signal after the processing of limiting and filtering to the permanent magnet synchronous motor controller as a new control instruction for feedforward compensation.

[0023] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments, and the above embodiments and descriptions are only preferred examples of the present invention, and are not intended to limit the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. A method for suppressing torque ripple of a permanent magnet synchronous motor based on feedforward compensation, characterized in that: The following steps are involved: S1. Establish a mathematical model of permanent magnet synchronous motor; S2. Based on the mathematical model of permanent magnet synchronous motor, the factors causing torque pulsation are analyzed through electromagnetic parameters and mechanical parameters; S3. According to the analysis results, a wave model is designed based on discrete Fourier transform; S4, using the designed wave model to generate a compensation signal based on Fourier series expansion; S5. Combining the generated compensation signal with the existing control system by superposition, and adding the superimposed compensation signal to the control command of the permanent magnet synchronous motor to smooth the torque output.

2. The method for suppressing torque ripple of a permanent magnet synchronous motor based on feedforward compensation according to claim 1 is characterized in that: In S1, a mathematical model of the permanent magnet synchronous motor is established, including the following steps: S1.

1. Select a two-phase rotating coordinate system dq, where the d-axis is consistent with the magnetic field direction of the permanent magnet and the q-axis is perpendicular to it; S1.

2. In the dq coordinate system, construct the voltage equation, flux equation, torque equation and mechanical motion equation to describe the dynamic characteristics of the permanent magnet synchronous motor during operation; S1.

3. Integrate all equations together to form a complete mathematical model of the permanent magnet synchronous motor.

3. The method for suppressing torque ripple of a permanent magnet synchronous motor based on feedforward compensation according to claim 2 is characterized in that: In S1.2, the voltage equation, magnetic flux equation, torque equation and mechanical motion equation are specifically: The voltage equation is: ； ； The magnetic flux equation is: ； ； The torque equation is: ； The mechanical motion equation is: ； in, represents the d-axis voltage; represents the q-axis voltage; Indicates winding resistance; represents the d-axis current; represents the q-axis current; represents the d-axis magnetic flux; represents the q-axis magnetic flux; represents the inductance of the d-axis; represents the inductance of the q-axis; represents the electrical angular velocity; Represents the fixed flux linkage produced by the permanent magnet; represents electromagnetic torque; represents the torque constant; represents the moment of inertia; Represents mechanical angular velocity; Indicates load torque; represents the damping coefficient; Represents a time variable.

4. The method for suppressing torque ripple of a permanent magnet synchronous motor based on feedforward compensation according to claim 1, characterized in that: In S2, the factors causing the torque pulsation include: cogging effect, magnetic field non-uniformity and inverter switching frequency.

5. The method for suppressing torque ripple of a permanent magnet synchronous motor based on feedforward compensation according to claim 1, characterized in that: In S3, designing a fluctuation model according to the analysis results includes the following steps: S3.1, extracting the characteristics of the factors causing the torque pulsation in step S2; S3.

2. Establish a fluctuation model to describe the influence of factors causing torque pulsation on torque; S3.

3. Based on the fluctuation model, design a compensation signal so that the compensation signal can offset the impact of the fluctuation, and determine the parameters of the compensation signal.

6. The method for suppressing torque ripple of a permanent magnet synchronous motor based on feedforward compensation according to claim 5 is characterized in that: In S3.2, a fluctuation model is established to describe the influence of factors causing torque pulsation on torque, including the following steps: S3.

21. Use a mathematical model of the permanent magnet synchronous motor to simulate the operating state of the permanent magnet synchronous motor and obtain simulation data of torque fluctuation; S3.

22. Perform spectrum analysis on simulation data by discrete Fourier transform, identify the main frequency components of torque fluctuations, and observe the trend of data changes over time; S3.

23. Establish a model for the source of tooth-slot efficiency fluctuations and analyze the structure of the stator and rotor of a permanent magnet synchronous motor; establish a model for the uneven magnetic field fluctuations and analyze the magnetic flux density distribution of a permanent magnet; establish a model for the switching frequency fluctuations of an inverter and analyze the PWM modulation frequency of the inverter and the harmonics it generates; S3.

24. For periodic fluctuations, use Fourier series expansion to describe the factors that cause torque ripple; S3.25, extracting Fourier coefficients from spectrum analysis; S3.26, constructing a fluctuation model using the parameters of the extracted Fourier coefficients, and verifying the accuracy of the model through simulation, and adjusting the model parameters according to the verification results until the fluctuation model can accurately reflect the actual torque fluctuation; S3.

27. Unify the formats of all identified fluctuation source models, including the tooth-slot benefit fluctuation source model, the magnetic field uneven fluctuation model and the inverter switching frequency fluctuation model, and integrate all identified fluctuation source models into a comprehensive torque fluctuation model, and add adaptive parameters, transient compensation signals and interaction coefficients of factors causing torque pulsation to the comprehensive torque fluctuation model.

7. The method for suppressing torque ripple of a permanent magnet synchronous motor based on feedforward compensation according to claim 6 is characterized in that: In S3.22, the discrete Fourier transform is: ； in, represents a frequency domain signal; Represents the time domain signal, i.e., the torque fluctuation signal; Indicates the number of sampling points; represents the frequency index; represents an imaginary unit; Represents a time index in a discrete time series.

8. The method for suppressing torque ripple of a permanent magnet synchronous motor based on feedforward compensation according to claim 6 is characterized in that: In S3.27, the comprehensive torque fluctuation model is: ; Adding adaptive parameters, transient compensation signals and interaction coefficients of factors causing torque ripple to the comprehensive torque ripple model is: ; in, represents the original integrated torque ripple model; represents a comprehensive torque fluctuation model after adding adaptive parameters, transient compensation signals and interaction coefficients of factors causing torque pulsation; Indicates fundamental torque; Indicates the highest order of fundamental frequency components; represents the amplitude of the 𝑛th order sine wave; represents the time variable; 𝑛 represents the index of the sine wave order; represents the phase of the 𝑛th order sine wave; Indicates the fundamental frequency; Indicates the highest order of the cosine wave frequency components; Indicates The amplitude of the cosine wave of order; The index representing the order of the cosine wave; Indicates The phase of the cosine wave of order; Indicates the highest order of frequency components associated with PWM modulation; represents the amplitude of the 𝑘th order sine wave associated with PWM modulation; 𝑘 represents the index of the order of the sine wave associated with the PWM modulation frequency of the inverter; Indicates the frequency associated with PWM modulation; represents the phase of the 𝑘th order sine wave associated with PWM modulation; Indicates adjustment The gain factor of the sine wave of order; Indicates adjustment The gain factor of the order cosine wave; Indicates adjustment The gain factor of the sine wave related to PWM modulation; Represents the interaction coefficient of factors causing torque ripple; represents the transient compensation signal; Indicates The amplitude of the sine wave of order; represents another parameter related to fluctuations; An index representing the order of the sine wave relative to the fundamental frequency; An index representing the order of another sine wave relative to the fundamental frequency; Denotes the phase of the interaction of the 𝑖th and 𝑗th order fluctuations.

9. The method for suppressing torque ripple of a permanent magnet synchronous motor based on feedforward compensation according to claim 1, characterized in that: In S5, the generated compensation signal is combined with the existing control system by superposition, which includes the following steps: S5.

1. Determine the best insertion point of the compensation signal; S5.2, superimposing the compensation signal with the reference signal of the current loop; S5.3, synthesizing the compensation signal with the original reference signal to generate a new synthesized signal; S5.

4. Limit the new synthesized signal to ensure that the new synthesized signal does not exceed the allowable range of the permanent magnet synchronous motor. In the process of limiting the new synthesized signal, a smoothing factor is introduced and filtering is performed; S5.5, transmitting the synthesized signal after the processing of limiting and filtering to the permanent magnet synchronous motor controller as a new control instruction for feedforward compensation.

10. The method for suppressing torque ripple of a permanent magnet synchronous motor based on feedforward compensation according to claim 9, characterized in that: In S5.4, the new synthesized signal is subjected to the limiting process specifically as follows: ； The smoothing factor introduced in the limiting process of the synthesized signal is: ； in, represents the original synthetic signal; Indicates the signal after limiting processing; It represents the amplitude limiting processing signal after the smoothing factor is introduced; Indicates the lower threshold of the signal; Indicates the upper threshold of the signal; Represents the smoothing factor.

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