Method for suppressing two-fold electrical frequency torque pulsation of permanent magnet synchronous motor under coexistence of multiple factors

Abstract

The application discloses a method for suppressing two times electric frequency torque ripple of a permanent magnet synchronous motor under multiple factors coexistence, and belongs to the technical field of motor control. k q d k= 1, 2, 3…; according to the calculation result, pulse information is reconstructed, the command current of the motor is corrected, and torque ripple suppression is realized; and whether the suppressed torque ripple meets preset stop conditions is judged. d q In the algorithm implementation process, the motor body parameters of the controlled motor do not need to be known in advance, a redundant control loop or an online tuning controller parameter does not need to be established, and only the motor control system feedback information is used to complete the torque ripple, so that the two times electric frequency torque ripple can be adaptively suppressed under the coexistence of multiple factors such as stator resistance asymmetry and current sampling proportion error, and the method has good engineering significance and practical value.​​​​

Description

Technical Field

[0001] This invention belongs to the field of motor control technology. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are key actuators in industrial automation equipment, widely used in CNC machine tools, industrial robots, aerospace, and general-purpose servo systems. However, due to various non-ideal factors in motor manufacturing and current sampling, the motor's output torque exhibits periodic fluctuations. Existing research indicates that stator resistance asymmetry and current sampling ratio errors are the main reasons for the periodic pulsations in the d-axis and q-axis current feedback at twice the electrical frequency. Since the q-axis current is directly proportional to the motor's output torque, the motor torque also experiences torque pulsations, further leading to speed fluctuations at the same frequency, thus affecting the operational performance of the PMSM control system.

[0003] In existing technologies, relatively mature suppression strategies exist for double-frequency torque ripple caused by a single problem ("stator resistance asymmetry" or "current sampling ratio error"). However, due to different torque ripple suppression mechanisms, existing strategies targeting a single influencing factor cannot effectively suppress double-frequency torque ripple when multiple influencing factors coexist (such as stator resistance asymmetry and current sampling ratio error). However, in practical engineering, stator resistance asymmetry and current sampling ratio error can easily occur simultaneously. Therefore, developing targeted double-frequency torque ripple suppression strategies for multiple coexisting influencing factors has significant theoretical and practical value. Summary of the Invention

[0004] The purpose of this invention is to propose a method for suppressing double-frequency torque ripple in permanent magnet synchronous motors under the coexistence of multiple factors, such as stator resistance asymmetry and current sampling ratio error.

[0005] The steps of this invention are: S01. Calculate the corresponding amplitude and initial phase angle at twice the frequency of the k-th q-axis command current and the d-axis sampled current, k = 1, 2, 3...; S02. Based on the calculation results, the motor drive system makes corresponding corrections to the command currents of the d and q axes to achieve double frequency torque pulsation suppression. S03, Determine the suppressed torque pulsation S031, the i-th q-axis command current of the motor control system Obtain speed commands and speed feedback; determine the speed tracking error for the i-th time according to equation (1): Δspeed(i)=speed_ref(i)-speed_fed(i) (1) Where Δspeed(i) is the speed tracking error of the i-th time, speed_ref(i) is the speed command of the i-th time, speed_fed(i) is the speed feedback of the i-th time, and i is an integer greater than or equal to zero; S032, q-axis command current of the discretized motor control system: in, Let k be the q-axis command current for the i-th time. ps k is the speed loop proportional coefficient. is The integral coefficient of the velocity loop; S033, the i-th d-axis sampling current of the motor control system: The sampling currents of phase a and phase b can be obtained using a current sensor, and then the sampling current of phase c can be determined according to equation (3): i cm =-(i am +i bm (3) Among them, i cm Represents the sampling current of phase c, i am Represents the sampling current of phase a, i bm This represents the sampling current of phase b; The i-th d-axis sampling current of the motor control system: Among them, i dm (i) represents the current sampled along the d-axis for the i-th time, θ e This is the electrical angle feedback value, where π is the mathematical constant pi. Electrical angle feedback value θ e : θ e =2πf base t (5) Among them, f base t is the fundamental frequency of the electrical frequency; Determine the fundamental frequency f of the electrical frequency base : f base =speed_ref*p0 / 60 (6) Where p0 represents the number of pole pairs of the motor; S04. Methods for suppressing speed pulsation due to stator resistance asymmetry S041. Determine whether the system has entered a stable state; S042. The motor control system calculates the corresponding amplitude and initial phase angle at twice the electrical frequency of the k-th q-axis command current and the d-axis sampled current, k = 1, 2, 3...; S043. The motor control system makes corresponding corrections to the command currents of the d and q axes based on the calculation results to achieve double frequency torque pulsation suppression. S044. The motor control system determines whether the suppressed torque pulsation meets the preset stopping conditions. S05. Determine whether the system has entered a stable state, including: If the motor speed of the motor control system remains constant within a preset time, the motor control system is considered to have entered a stable state; or, if the q-axis command current of the motor control system remains constant within a preset time, the motor control system is considered to have entered a stable state. S06. Calculate the amplitude at twice the electrical frequency in the k-th q-axis command current or d-axis sampled current of the motor control system according to formula (7): Where x can be q * Or dm, I xk This represents the amplitude at twice the electrical frequency in the k-th q-axis command current or d-axis sampled current. This represents the real part amplitude of the k-th q-axis command current or d-axis sampling current at twice the electrical frequency. The imaginary part of the k-th q-axis command current or d-axis sampled current at twice the electrical frequency; S07. Calculate the real part of the current of the k-th q-axis command according to equation (8): Where N is the total number of sampling points, Let m be the q-axis command current for the i-th time, and f be the frequency of sampling. s , electrical frequency f base Quantities related to the total number of sampling points N, i∈N; S08. Calculate the imaginary part of the q-axis command current for the kth time according to formula (9): Where N is the total number of sampling points, Let m be the q-axis command current for the i-th time, and f be the frequency of sampling. s , electrical frequency f base Quantities related to the total number of sampling points N, i∈N; S09. Calculate the amplitude of the real part of the d-axis sampling current for the kth time according to equation (10): Where N is the total number of sampling points, i d (i) represents the d-axis sampling current of the i-th time, and m is the sampling frequency f. s , electrical frequency f base Quantities related to the total number of sampling points N, i∈N; S10. Calculate the amplitude of the imaginary part of the d-axis sampling current for the kth time according to formula (11): Where N is the total number of sampling points, i d (i) represents the d-axis sampling current of the i-th time, and p is the current relative to the sampling frequency f. s , electrical frequency f base Integers related to the total number of sampling points N, i∈N; S11. Calculate the total number of sampling points N according to formula (12): N = pf s / 2f base (12) Among them, f s The sampling frequency; S12. Calculate the initial phase angle corresponding to twice the electrical frequency in the k-th q-axis command current or d-axis sampled current of the motor control system according to formula (13): Where x can be q * Or dm, representing the q-axis command current or the d-axis sampling current; S13, according to The calculation results determine the initial phase angle corresponding to twice the electrical frequency, including: When equation (8) and equation (10) are in When the calculation result is less than 0, in equation (13) It should be modified by equation (14): Where x can be q * Or dm, where π is the mathematical constant pi; S14. Calculate the pulsation information of twice the electrical frequency in the k-th q-axis command current or d-axis sampled current of the motor control system according to formula (15): in, This represents the frequency 2f in the q-axis command current after the k-th DFT calculation. base The current pulsation component. After the DFT calculation, the frequency of the sampled current along the d-axis is 2f. base The current pulsation component, ω e Let t be the electric angular velocity of the motor, and t be the running time. For reconstruction frequency of 2f base The pulsating phase angle of the q-axis command current or the d-axis sampling current; S15. Calculate the reconstructed phase angle according to the DFT signal reconstruction principle, including: Guarantee the instantaneous removal of pulsating phase angle during reconstruction The remaining phase angles are 0 rad, that is It should be defined by equation (16): Where x can be q * or dm, θ e_start The instantaneous electrical angle value at the start time for DFT calculation, and the time taken to accumulate data Δt; S16. Correct the command currents of the q-axis and d-axis according to equation (17) to complete the suppression of double frequency torque ripple under the coexistence of multiple influencing factors: in, Represents the q-axis and d-axis command currents after the k-th speed pulsation suppression, where x is either q or d; S17. Under stator resistance asymmetry, the voltage equation of the permanent magnet synchronous motor in the three-phase stationary coordinate system is expressed by equation (18): Among them, u x (x = a, b, c) represents the three-phase voltages a, b, and c, ΔR x (x=a,b,c) represents the asymmetrical components of the three-phase stator resistances a, b, and c, and ΔR a ≠ΔR b ≠ΔR c i x (x = a, b, c) represents the actual three-phase currents a, b, and c, p represents the differential operator, and ψ x (x = a, b, c) Three-phase winding flux linkage; S18. Ignoring the effects of magnetic flux and inductance, transforming equation (18) to a rotating coordinate system with d and q axes, we have: in, Let represent the transformation matrix from the three-phase stationary coordinate system a, b, c to the two-phase rotating coordinate system d, q, and its expression is given by equation (20). The transformation matrix representing the transformation from the two-phase rotating coordinate system d and q to the three-phase stationary coordinate system a, b, and c is expressed as equation (21): The resistance transformation process in equation (21) is denoted as equation (22): Let R x =R s +ΔR x (x = a, b, c), R in equation (22) dd R dq Rqd With R qq The expression is: Substituting equation (22) into equation (21), the expressions for the d-axis and q-axis currents under stator resistance asymmetry are: Where, θ e The expression is as shown in equation (25), k6~k 12 The expression is as shown in equation (26): θ e =2πf base t (25) S19. When there is a proportional error in the current sampling circuit, the phase sampling current is a sinusoidal signal. Let the sampling currents of phases a and b be as follows: Among them, I A I B k represents the peak value of the sampling current of phases a and b. a k b k represents the sampling ratio coefficient for phases a and b. When a current sampling ratio error occurs, k a ≠k b , that is I A ≠I B ; According to equation (27), the actual current expressions for phases a and b are: According to Kirchhoff's current law, the c-phase current sampling i cm Compared with the actual current i in phase c c for: Combining equations (27) and (29), the result of the controller sampling phase current after Clark and Park transformation is as follows: Combining equations (28) and (29), the actual phase current after Clark and Park transformations is obtained as follows: The effects of current sampling ratio error on d-axis and q-axis currents are as follows: The expressions for k1 to k5 are as follows:

[0006] This invention does not require prior knowledge of the parameters of the controlled motor, nor does it require the establishment of redundant control loops or online tuning controller parameters. It can complete torque pulsation based solely on feedback information from the motor control system. It can achieve adaptive suppression of double-frequency torque pulsation under multiple influencing factors such as stator resistance asymmetry and current sampling ratio error, and has good engineering significance and practical value. Attached Figure Description

[0007] Figure 1(a) is a control block diagram of a method for suppressing double-frequency torque ripple under the coexistence of multiple influencing factors provided in an embodiment of this disclosure; Figure 1(b) is an equivalent circuit diagram of a three-phase winding of a permanent magnet synchronous motor under stator resistance asymmetry provided in an embodiment of this disclosure; Figure 2 This is a flowchart of a method for suppressing double-frequency torque pulsation under the coexistence of multiple influencing factors, provided by an embodiment of this disclosure; Figure 3 This is a flowchart of another method for suppressing double-frequency torque ripple under the coexistence of multiple influencing factors, provided in an embodiment of this disclosure; Figure 4(a) is a schematic diagram of the path from speed closed loop to current closed loop in a motor control system under multiple influencing factors without using the algorithm proposed in this embodiment, provided by an embodiment of this disclosure. Figure 4(b) is a schematic diagram of the path from speed closed loop to current closed loop in a motor control system under multiple influencing factors after adopting the algorithm proposed in this embodiment of the present disclosure. Figure 5 This is a simulation data diagram of the speed feedback before and after using only the torque ripple suppression method for stator resistance asymmetry under the condition that stator resistance asymmetry and current sampling ratio error coexist, with the motor speed at 600 r / min and load at 2 N·m. Figure 6 This is a simulation data diagram of the speed feedback before and after using only the torque ripple suppression method for the current sampling ratio error when the motor operates at a speed of 600 r / min and a load of 2 N·m under the condition of coexistence of stator resistance asymmetry and current sampling ratio error. Figure 7 This is a simulation data diagram of the speed feedback before and after the method proposed in this embodiment is used to suppress double frequency torque ripple under the condition that stator resistance asymmetry and current sampling ratio error coexist, with the motor speed at 600 r / min and load at 2 N·m. Figure 8(a) shows the FFT analysis results of the speed feedback of a motor at a speed of 600 r / min and a load of 2 N·m under the condition of coexistence of stator resistance asymmetry and current sampling ratio error, without using the method proposed in this embodiment to suppress the torque ripple of twice the electric frequency. Figure 8(b) shows the FFT analysis results of the speed feedback when the motor is operating at 600 r / min and under a load of 2 N·m under the condition of coexisting stator resistance asymmetry and current sampling ratio error, using the method proposed in this embodiment to suppress double frequency torque ripple. Figure 9 This is a simulation data diagram of the output waveforms of the speed loop before and after the method proposed in this embodiment for suppressing double frequency torque ripple under the condition that stator resistance asymmetry and current sampling ratio error coexist, with the motor speed at 600 r / min and load at 2 N·m. Figure 10 This is a simulation data diagram of the actual q-axis current waveform before and after the method proposed in this embodiment is used to suppress the torque ripple of twice the electric frequency under the condition that stator resistance asymmetry and current sampling ratio error coexist, with the motor speed at 600 r / min and load at 2 N·m. Figure 11(a) shows the FFT analysis results of the real q-axis current waveform when the motor operates at a speed of 600 r / min and under a load of 2 N·m, without using the method proposed in this embodiment to suppress the torque ripple at twice the electric frequency, under the condition that stator resistance asymmetry and current sampling ratio error coexist. Figure 11(b) shows the FFT analysis results of the real q-axis current waveform when the motor operates at a speed of 600 r / min and a load of 2 N·m under the condition of stator resistance asymmetry and current sampling ratio error coexisting, using the method proposed in this embodiment to suppress the torque ripple of twice the electric frequency. Figure 12 This is a schematic diagram of a device for suppressing torque pulsation at twice the electrical frequency of a permanent magnet synchronous motor under the coexistence of multiple influencing factors, provided in an embodiment of this disclosure. Detailed Implementation

[0008] This invention provides a method for suppressing speed pulsation caused by stator resistance asymmetry, comprising: Calculate the corresponding amplitude and initial phase angle of the k-th q-axis command current and the d-axis current feedback at twice the electrical frequency in the motor control system, k = 1, 2, 3...

[0009] Based on the calculation results, the command currents of the d and q axes are corrected to complete the suppression of double frequency torque ripple when stator resistance asymmetry and current sampling ratio error occur simultaneously. Determine whether the suppressed torque pulsation meets the preset stopping condition.

[0010] Methods for suppressing double-frequency torque ripple under multiple influencing factors include: The processor and the memory storing program instructions are configured to, when running the program instructions, execute the above-described method for suppressing double-frequency torque ripple in a permanent magnet synchronous motor under conditions of coexisting stator resistance asymmetry and current sampling ratio error.

[0011] The motor control system includes: a method, as described above, for suppressing double-frequency torque pulsation caused by the coexistence of stator resistance asymmetry and current sampling ratio error.

[0012] The method for suppressing torque ripple caused by the coexistence of stator resistance asymmetry and current sampling ratio error provided in this disclosure can achieve the following technical effects: By calculating the corresponding amplitude and initial phase angle at twice the electrical frequency in the q-axis command current and d-axis current feedback of the running motor, the periodic components of the q-axis command current and d-axis current feedback at this frequency are reconstructed. Based on the reconstruction results, the d-axis and q-axis command currents are corrected, thus achieving torque ripple suppression under the coexistence of stator resistance asymmetry and current sampling ratio error. In the algorithm implementation, it is not necessary to know the controlled motor's moment of inertia and viscosity coefficient in advance. Instead, the reconstruction information extraction and torque ripple suppression effect judgment are completed based on the given and feedback information from the motor control system. This effectively reduces the algorithm complexity of the torque ripple suppression strategy for motor control systems under multiple coexisting causes and improves the algorithm's adaptability.

[0013] To gain a more detailed understanding of the features and technical content of the embodiments of this disclosure, the implementation of the embodiments of this disclosure will be described in detail below with reference to the accompanying drawings: AC servo systems have many non-ideal factors. Among them, the stator resistance asymmetry caused by high-resistance connection or motor manufacturing inconsistency deviation, and the double frequency torque pulsation caused by current sampling ratio error will seriously affect the control performance of permanent magnet synchronous motors. Numerous scholars have conducted extensive research on the above problems and proposed specific solutions. Regarding torque ripple caused by stator resistance asymmetry, the journal *IEEE Transactions on Industrial Electronics*, in its published paper "Torque Ripple Minimization Using Online Estimation of the Stator Resistances With Consideration of Magnetic Saturation," employs an online parameter identification method to extract the resistance asymmetry component and feed forward the voltage component requiring compensation, thereby suppressing the double-frequency torque ripple caused by resistance asymmetry. Similarly, the journal *IEEE Transactions on Industry Applications*, in its published paper "Improved Sensorless Control Method and Asymmetric Phase Resistances Determination for Permanent Magnet Synchronous Machines," uses a symmetric component method to extract and eliminate the negative-sequence components of the d-axis and q-axis currents caused by stator resistance asymmetry, thus suppressing the double-frequency torque ripple caused by resistance asymmetry. To address torque ripple caused by current sampling ratio error, the IEEE Transactions on Industry Applications, in its published paper "Compensation of Current Measurement Error for Current-Controlled PMSM Drives," proposes a current sampling error elimination method based on a motor parameter model. This method suppresses double-frequency torque ripple caused by current sampling ratio error by theoretically deriving from real current feedback and current sampling information with sampling errors. However, existing methods only address a single problem: suppressing double-frequency torque ripple caused by stator resistance asymmetry or current sampling ratio error. Few studies address double-frequency torque ripple suppression strategies under multiple influencing factors (stator resistance asymmetry or current sampling ratio error). This is because the torque ripple suppression mechanisms corresponding to the two different influencing factors are not the same. Under resistance asymmetry, the three-phase voltage command amplitudes after torque ripple suppression are unequal, while under current sampling ratio error, the three-phase voltage command amplitudes after torque ripple suppression are equal.Therefore, when a torque pulsation occurs at twice the electrical frequency, if multiple influencing factors coexist, it is impossible to suppress the torque pulsation using existing technologies targeting a single influencing factor.

[0014] Considering that stator resistance asymmetry and current sampling ratio error caused by the consistency of motor body manufacturing and high resistance connection can occur simultaneously in actual engineering, it is necessary to study the double frequency torque ripple suppression strategy under the coexistence of multiple influencing factors.

[0015] Referring to Figure 1(a), this disclosure provides a control block diagram for a method to suppress double-frequency torque ripple under the coexistence of stator resistance asymmetry and current sampling ratio error. In this embodiment, the permanent magnet synchronous motor (PMSM) has a q-axis command current i*q and a d-axis command current i*d. p0 represents the number of pole pairs of the motor, k a k b i represents the sampling ratio coefficient of phases a and b. a i b i represents the actual current in phases a and b. am i bm This represents the sampled currents of phases a and b. Based on the sampled phase current values ​​and the electrical angle feedback θ... e Determine the d-axis sampling current i dm With q-axis sampling current i qm The current loop PI controller outputs voltage commands u*d and u*q. After determining the speed and achieving steady-state operation under load, a Discrete Fourier Transform (DFT) is performed on the q-axis command current and d-axis current feedback information to obtain the corresponding amplitude and initial phase angle at twice the electrical frequency in the q-axis command current and d-axis sampled current, thus reconstructing the pulsation information. Based on the reconstruction results, the d- and q-axis command currents are corrected to suppress twice-frequency torque pulsation caused by stator resistance asymmetry and current sampling ratio error in the permanent magnet synchronous motor.

[0016] Referring to Figure 1(b), this embodiment of the present disclosure provides an equivalent circuit diagram of a three-phase winding under asymmetrical stator resistance of a motor. In this embodiment, ΔR a ΔR b ΔR c This represents the unbalanced components of the stator resistance in phases a, b, and c, and ΔR a ≠ΔR b ≠ΔR c R s For the ideal parameters of the three-phase stator resistance; L a Lb L c Represents the self-inductance of a three-phase winding; ψ a ψ b ψ c This represents the flux linkage of phases a, b, and c.

[0017] Combination Figure 2 As shown, this disclosure provides a method for suppressing speed pulsation under stator resistance asymmetry, comprising: S01, calculate the corresponding amplitude and initial phase angle at twice the frequency of the k-th q-axis command current and the d-axis sampled current, k = 1, 2, 3...

[0018] In this technical solution, the q-axis command current of the motor drive system is obtained from the speed loop output. By performing DFT calculations on it, the corresponding amplitude and initial phase angle of the pulsating component at twice the electrical frequency in the q-axis command current are obtained. The d-axis current feedback is obtained by sampling the phase current and performing Clark and Park transforms. By performing DFT calculations on it, the corresponding amplitude and initial phase angle of the pulsating component at twice the electrical frequency in the d-axis sampled current are obtained.

[0019] S02, the motor drive system corrects the command current of the d and q axes according to the calculation results to achieve double frequency torque pulsation suppression.

[0020] In this technical solution, the calculated amplitude and initial phase angle information can reconstruct the pulsating component of twice the electrical frequency in the q-axis command current and d-axis current feedback. Due to the influence of closed-loop control, the amplitude of this pulsating component may vary with the motor speed and load conditions. Therefore, online speed pulsation suppression is required to optimize the motor control performance.

[0021] S03, determine whether the suppressed torque pulsation meets the preset stopping condition.

[0022] Optionally, the calculation of the corresponding amplitude and initial phase angle at twice the electrical frequency in the k-th q-axis command current and the d-axis sampled current of the motor control system includes: Calculate the i-th q-axis command current of the motor control system; based on the i-th q-axis command current, calculate the corresponding amplitude and initial phase angle at twice the electrical frequency in the k-th q-axis command current of the motor control system.

[0023] Optionally, the calculation of the i-th q-axis command current of the motor control system includes: Obtain speed commands and speed feedback; determine the speed tracking error for the i-th time according to equation (1): Δspeed(i)=speed_ref(i)-speed_fed(i) (1) Where Δspeed(i) is the speed tracking error of the i-th time, speed_ref(i) is the speed command of the i-th time, speed_fed(i) is the speed feedback of the i-th time, and i is an integer greater than or equal to zero.

[0024] Optionally, the q-axis command current of the discretized motor control system is calculated according to equation (2): in, Let k be the q-axis command current for the i-th time. ps k is the speed loop proportional coefficient. is For the velocity loop integral coefficient. Optionally, the calculation of the i-th d-axis sampling current of the motor control system includes:

[0025] Obtain the sampled currents of the three phases a, b, and c; based on the sampled currents of the three phases a, b, and c, calculate the i-th d-axis sampled current of the motor control system.

[0026] In practical applications, the sampling current of phase a and phase b can be obtained through a current sensor, and then the sampling current of phase c can be determined according to equation (3): i cm =-(i am +i bm (3) Among them, i cm Represents the sampling current of phase c, i am Represents the sampling current of phase a, i bm This represents the sampling current of phase b.

[0027] Optionally, the i-th d-axis sampling current of the motor control system is calculated according to equation (4): Among them, i dm (i) represents the current sampled along the d-axis for the i-th time, θ e The value is the electrical angle feedback value, and π is the mathematical constant pi, which has a value of 3.1415926.

[0028] Optionally, the electrical angle feedback value can be calculated according to equation (5): θ e =2πf base t (5) Among them, f base t is the fundamental frequency of the electrical circuit, and t is the running time.

[0029] Alternatively, the fundamental frequency can be determined according to equation (6): f base =speed_ref*p0 / 60 (6) Where p0 represents the number of pole pairs of the motor.

[0030] In some alternative implementations, combined with Figure 3 As shown, this disclosure provides another method for suppressing speed pulsation under stator resistance asymmetry, including: S11, the motor control system determines whether the system has entered a stable state.

[0031] S12, the motor control system calculates the corresponding amplitude and initial phase angle at twice the frequency of the k-th q-axis command current and the d-axis sampled current, k = 1, 2, 3...

[0032] S13, the motor control system makes corresponding corrections to the command currents of the d and q axes based on the calculation results, thereby achieving double frequency torque pulsation suppression.

[0033] S14, the motor control system determines whether the suppressed torque pulsation meets the preset stopping conditions.

[0034] Optionally, determining whether the system has entered a stable state includes: If the motor speed of the motor control system remains constant within a preset time, the motor control system is considered to have entered a stable state; or, If the q-axis command current of the motor control system remains unchanged within a preset time, the motor control system is considered to have entered a stable state.

[0035] In practical applications, the current speed of the motor in the motor control system is an obtainable value, and the q-axis command current of the motor control system is determined by the above equations (1) and (2).

[0036] Optionally, the amplitude at twice the electrical frequency in the k-th q-axis command current or d-axis sampled current of the motor control system is calculated according to equation (7): Where x can be q * Or dm, I xk This represents the amplitude at twice the electrical frequency in the k-th q-axis command current or d-axis sampled current. This represents the real part amplitude of the k-th q-axis command current or d-axis sampling current at twice the electrical frequency. It is the imaginary amplitude of the k-th q-axis command current or d-axis sampling current at twice the electrical frequency.

[0037] Optionally, the real part of the q-axis command current for the kth time is calculated according to equation (8): Where N is the total number of sampling points, Let m be the q-axis command current for the i-th time, and f be the frequency of sampling. s, electrical frequency f base A quantity related to the total number of sampling points N, where i∈N.

[0038] Optionally, the imaginary part of the q-axis command current for the kth time is calculated according to equation (9): Where N is the total number of sampling points, Let m be the q-axis command current for the i-th time, and f be the frequency of sampling. s , electrical frequency f base A quantity related to the total number of sampling points N, where i∈N.

[0039] Optionally, the magnitude of the real part of the d-axis sampling current for the kth time is calculated according to equation (10): Where N is the total number of sampling points, i d (i) represents the d-axis sampling current of the i-th time, and m is the sampling frequency f. s , electrical frequency f base A quantity related to the total number of sampling points N, where i∈N.

[0040] Optionally, the amplitude of the imaginary part of the d-axis sampling current for the kth time is calculated according to equation (11): Where N is the total number of sampling points, i d (i) represents the d-axis sampling current of the i-th time, and p is the current relative to the sampling frequency f. s , electrical frequency f base An integer related to the total number of sampling points N, where i∈N.

[0041] Optionally, the total number of sampling points N can be calculated according to equation (12): N = pf s / 2f base (12) Among them, f s The sampling frequency.

[0042] In practical applications, the preset period p should theoretically take as many values ​​as possible to ensure more accurate calculations of the amplitudes of the real and imaginary parts. However, in actual operating conditions, abrupt changes caused by load or other objective factors need to be considered. Therefore, in this technical solution, the value of the preset period p is taken as a positive integer less than 5.

[0043] Optionally, the initial phase angle corresponding to twice the electrical frequency in the k-th q-axis command current or d-axis sampled current of the motor control system is calculated according to equation (13): Where x can be q *Or dm, representing the q-axis command current or the d-axis sampling current.

[0044] Optionally, according to (x can be q) * The initial phase angle corresponding to twice the electrical frequency is determined based on the calculation results (or dm), including: Determine the initial phase angle for DFT reconstruction; considering the range of the arctan function is... When equation (8) and equation (10) are in (x can be q) * When the calculation result of (or dm) is less than 0, in equation (13) It should be modified by equation (14): Where x can be q * Or dm, where π is the mathematical constant of a circle, and its value is 3.1415926.

[0045] Optionally, the pulsation information of twice the electrical frequency in the k-th q-axis command current or d-axis sampled current of the motor control system is calculated according to equation (15): in, This represents the frequency 2f in the q-axis command current after the k-th DFT calculation. base The current pulsation component. After the DFT calculation, the frequency of the sampled current along the d-axis is 2f. base The current pulsation component, ω e Let t be the electric angular velocity of the motor, and t be the running time. (x can be q) * (or dm) is used for reconstructing a frequency of 2f base The pulsating phase angle of the q-axis command current or the d-axis sampling current.

[0046] Optionally, based on the DFT signal reconstruction principle, the reconstructed phase angle is calculated, including: Guarantee the instantaneous removal of pulsating phase angle during reconstruction (x can be q) * The remaining phase angles outside of dm are 0 rad, i.e. It should be defined by equation (16): Where x can be q * or dm, θ e_start The instantaneous electrical angle value at the start of the DFT calculation is Δt, which is the time taken to accumulate the data.

[0047] Optionally, the command currents for the d and q axes are corrected to suppress double-frequency torque ripple under multiple influencing factors (stator resistance asymmetry and current sampling ratio error), including: Based on the amplitude and phase angle at twice the frequency of the k-th q-axis command current and the d-axis sampled current, the q-axis command current and the d-axis command current are corrected accordingly; based on the amplitude of the current feedback harmonics after correction, it is determined whether the required correction value of the command current needs to be recalculated.

[0048] Optionally, the command currents for the q-axis and d-axis are corrected according to equation (17) to achieve double-frequency torque ripple suppression under multiple influencing factors (stator resistance asymmetry and current sampling ratio error): in, (x can be q or d) represents the command current of the q and d axes after the kth speed pulsation suppression.

[0049] In practical applications, it should be understood that the suppression of the double frequency torque pulsation is continuous when the preset stopping conditions are not met. During this process, the command currents of the q and d axes are repeatedly corrected using Equation (17).

[0050] In this technical solution, under the condition of stator resistance asymmetry, the voltage equation of the permanent magnet synchronous motor in the three-phase stationary coordinate system can be expressed by equation (18): Among them, u x (x = a, b, c) represents the three-phase voltages a, b, and c, ΔR x (x=a,b,c) represents the asymmetrical components of the three-phase stator resistances a, b, and c, and ΔR a ≠ΔR b ≠ΔR c i x (x = a, b, c) represents the actual three-phase currents a, b, and c, p represents the differential operator, and ψ x (x=a,b,c) Three-phase winding flux linkage.

[0051] In this derivation, since we only discuss the effect of resistance asymmetry on current harmonics, the effects of magnetic flux and inductance are ignored in the following analysis. Transforming equation (18) to the d- and q-axis rotating coordinate system, we have: in, Let represent the transformation matrix from the three-phase stationary coordinate system a, b, c to the two-phase rotating coordinate system d, q, and its expression is given by equation (20). The transformation matrix representing the transformation from the two-phase rotating coordinate system d and q to the three-phase stationary coordinate system a, b, and c is expressed as equation (21): Furthermore, equation (19) can be rewritten as equation (21):

[0052] Furthermore, the resistance transformation process in equation (21) is denoted as equation (22):

[0053] Let R x =R s +ΔR x (x = a, b, c), R in equation (22) dd R dq R qd With R qq The expression is:

[0054] Considering the case of three-phase stator electronic asymmetry, substituting equation (22) into equation (21), we can obtain the expressions for the d-axis and q-axis currents under stator resistance asymmetry as follows: Where, θ e The expression is as shown in equation (25), k6~k 12 The expression is as shown in equation (26): θ e =2πf base t (25)

[0055] Therefore, it can be seen that stator resistance asymmetry will cause the actual currents along the d and q axes to have a frequency twice the electrical frequency (2f). base The periodic pulsation of the q-axis current will cause the torque to pulsate at the same frequency, which in turn will cause the speed feedback to pulsate at the same frequency.

[0056] Furthermore, when there is a proportional error in the current sampling circuit, the phase sampling current is a sinusoidal signal. Let the sampling currents of phases a and b be as follows: Among them, I A I B k represents the peak value of the sampling current of phases a and b. a k b k represents the sampling ratio coefficient for phases a and b. When a current sampling ratio error occurs, k a ≠k b , that is I A ≠IB .

[0057] According to equation (27), the actual current expressions for phases a and b are:

[0058] Considering that the three-phase windings in the permanent magnet synchronous motor are connected in a star configuration, according to Kirchhoff's current law, the c-phase current sampling i can be obtained. cm Compared with the actual current i in phase c c for:

[0059] Combining equations (27) and (29), the result of the controller sampling phase current after Clark and Park transformation is as follows:

[0060] Combining equations (28) and (29), the actual phase current after Clark and Park transformations is obtained as follows:

[0061] Therefore, the effect of the current sampling ratio error on the d-axis and q-axis currents can be obtained as follows: The expressions for k1 to k5 are as follows:

[0062] Therefore, it can be seen that the current sampling ratio error will cause the actual current on the d and q axes to appear at a frequency twice the electrical frequency (2f). base The periodic pulsation of the q-axis current will cause the torque to pulsate at the same frequency, which in turn will cause the speed feedback to pulsate at the same frequency.

[0063] Based on the above analysis, stator resistance asymmetry and current sampling ratio error will simultaneously cause the actual currents d and q to appear at a frequency of 2f. base The periodic pulsations, therefore, when the actual motor control system exhibits a frequency of 2f... base When there is torque pulsation, it is difficult to determine the specific source of the pulsation, which also brings practical difficulties to the double frequency torque pulsation suppression strategy in industrial applications.

[0064] Figure 4(a) shows the speed loop to current loop controller path when the two influencing factors, stator resistance asymmetry and current sampling ratio error, coexist or exist alone, without the method of this embodiment. When the motor is running at a certain speed in a steady-state under load, since the speed command is a constant and the frequency is 2f... baseThe rotational speed fluctuation will cause the q-axis command current to fluctuate at the same frequency. Under the conditions of rotational speed and load steady state, the expressions for the q-axis command current and d-axis sampling current under the condition of asymmetrical sub-resistance are as shown in equation (34): Where A represents the DC component of the q-axis command current, and B represents the frequency of 2f in the q-axis command current. base The amplitude of the AC component, where C represents the frequency of the d-axis sampling current as 2f. base Periodic pulsation amplitude, The frequency of the q-axis command current is 2f. base The phase angle of the periodic pulsations, The frequency in the d-axis current feedback is 2f. base The phase angle of periodic pulsations.

[0065] Furthermore, Figure 4(b) shows the path diagram of the speed loop to current loop controller after applying the method of this embodiment when the two influencing factors of stator resistance asymmetry and current sampling ratio error coexist or exist alone. As can be seen from Figure 4(b), for the q-axis, after superimposing the disturbance to i*q, in order to maintain the current speed and load steady state unchanged, the speed loop output becomes a constant A, that is, at this time the speed loop input and output are both constant. Affected by the speed closed-loop control, the periodic pulsation contained in the speed feedback is also suppressed. Therefore, the double frequency torque pulsation caused by different kinds of influencing factors can also be suppressed. For the d-axis current control loop, since a surface-mounted permanent magnet synchronous motor is used, it is not affected by the speed closed loop. The periodic pulsation component is directly subtracted from the command, which is equivalent to using the current loop controller to weaken the harmonics at a fixed frequency to suppress the frequency 2f in the d-axis current feedback. base The periodic pulsation.

[0066] In some embodiments, the method for suppressing torque ripple at twice the electrical frequency of a permanent magnet synchronous motor under multiple influencing factors (stator resistance asymmetry and current sampling ratio error) provided in this disclosure is verified. Table 1 shows some parameter information of the permanent magnet synchronous motor used in the experiment: Table 1

[0067] Figure 5The figure shows the speed feedback simulation waveforms before and after applying only the torque ripple suppression method targeting stator resistance asymmetry, when the motor operates at 600 r / min and is under a 2 N·m load, under the coexistence of multiple influencing factors such as stator resistance asymmetry and current sampling ratio error. It can be seen that due to the presence of current sampling ratio error, periodic ripples still exist in the speed feedback after eliminating the influence of stator resistance asymmetry.

[0068] like Figure 6 The figure shows the simulated speed feedback waveforms before and after applying only a torque ripple suppression method targeting the current sampling ratio error, when the motor operates at 600 r / min and is under a 2 N·m load, under the coexistence of multiple influencing factors such as stator resistance asymmetry and current sampling ratio error. It can be seen that due to the presence of the current sampling ratio error, periodic ripples still exist in the speed feedback after eliminating the influence of stator resistance asymmetry.

[0069] like Figure 7 The figure shows the speed feedback simulation waveforms before and after using the method proposed in this embodiment to suppress double-frequency torque ripple under the coexistence of multiple influencing factors, namely stator resistance asymmetry and current sampling ratio error, when the motor is running at 600 r / min and under a load of 2 N·m. It can be seen that, compared with using only a single method for double-frequency torque ripple suppression, the method proposed in this embodiment can effectively suppress double-frequency torque ripple under the coexistence of multiple influencing factors (stator resistance asymmetry and current sampling ratio error).

[0070] Figure 8(a) shows the results of a Fast Fourier Transform (FFT) analysis of the speed feedback before torque ripple suppression, under the condition that multiple influencing factors such as stator resistance asymmetry and current sampling ratio error coexist, when the motor is running at 600 r / min and under a load of 2 N·m. Since the experimental motor is a 4-pole motor, the fundamental frequency f is... base The frequency is 40Hz. It can be seen that when multiple influencing factors coexist, there is a periodic pulsation in the speed feedback with a frequency of twice the electrical fundamental frequency (80Hz), and the pulsation amplitude at this frequency is 6.69r / min.

[0071] Figure 8(b) shows the results of Fast Fourier Transform (FFT) analysis of the speed feedback after torque ripple suppression using the method described in this embodiment, under the coexistence of multiple influencing factors such as stator resistance asymmetry and current sampling ratio error, when the motor operates at 600 r / min and is under a load of 2 N·m. It can be seen that the ripple amplitude at twice the fundamental frequency (80 Hz) is 0.7139 r / min, which is 10.67% of the ripple amplitude before compensation.

[0072] like Figure 9The figure shows simulation data of the speed loop output waveforms before and after double-frequency torque ripple suppression using the method proposed in this embodiment, under the coexistence of multiple influencing factors such as stator resistance asymmetry and current sampling ratio error, when the motor operates at 600 r / min and is loaded with 2 N·m. It can be seen that after adopting the method proposed in this embodiment, the harmonic components of the speed loop output are effectively suppressed.

[0073] In practical applications, such as Figure 10 As shown, the actual q-axis current feedback waveforms before and after double frequency torque ripple suppression are obtained when the motor is running at 600 r / min and under a load of 2 N·m, under the coexistence of multiple influencing factors such as stator resistance asymmetry and current sampling ratio error. This is achieved using the method proposed in this embodiment.

[0074] Figure 11(a) shows the results of a Fast Fourier Transform (FFT) analysis of the actual q-axis current feedback before torque ripple suppression, under the condition that multiple influencing factors such as stator resistance asymmetry and current sampling ratio error coexist, with the motor operating at 600 r / min and a load of 2 N·m. At this time, the fundamental frequency f... base The frequency is 40Hz. It can be seen that when multiple influencing factors coexist, there is a periodic pulsation in the real q-axis current feedback with a frequency of twice the electrical fundamental frequency (80Hz), and the pulsation amplitude at this frequency is 0.1363A.

[0075] Figure 11(b) shows the results of Fast Fourier Transform (FFT) analysis of the actual q-axis current feedback after torque ripple suppression using the method described in this embodiment, under the coexistence of multiple influencing factors such as stator resistance asymmetry and current sampling ratio error, when the motor operates at 600 r / min and is under a load of 2 N·m. It can be seen that the ripple amplitude at twice the fundamental frequency (80 Hz) is 0.01353 A, which is 9.93% of the ripple amplitude before compensation.

[0076] Combination Figure 12 As shown, this disclosure provides an apparatus for suppressing speed pulsation under stator resistance asymmetry in a permanent magnet synchronous motor, including a processor 100 and a memory 101. Optionally, the apparatus may further include a communication interface 102 and a bus 103. The processor 100, communication interface 102, and memory 101 can communicate with each other via the bus 103. The communication interface 102 can be used for information transmission. The processor 100 can call logic instructions in the memory 101 to execute the method for suppressing speed pulsation under stator resistance asymmetry in a permanent magnet synchronous motor as described in the above embodiment.

[0077] Furthermore, the logic instructions in the aforementioned memory 101 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium.

[0078] The memory 101, as a computer-readable storage medium, can be used to store software programs and computer-executable programs, such as program instructions / modules corresponding to the methods in the embodiments of this disclosure. The processor 100 executes functional applications and data processing by running the program instructions / modules stored in the memory 101, that is, it implements the method for suppressing speed pulsation under stator resistance asymmetry of permanent magnet synchronous motors in the above embodiments.

[0079] The memory 101 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created based on the use of the terminal device. Furthermore, the memory 101 may include high-speed random access memory and may also include non-volatile memory.

[0080] This disclosure provides a motor control system including the above-described device for suppressing twice-frequency torque pulsation.

[0081] The technical solutions of this disclosure can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes one or more instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in this disclosure. The aforementioned storage medium can be a non-transitory storage medium, including: a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, and other media capable of storing program code; it can also be a transient storage medium.

Claims

1. A method for suppressing torque ripple at twice the electrical frequency in a permanent magnet synchronous motor under multiple coexisting factors, characterized in that: Includes the following steps: S1. Determine whether the system has entered a stable state, including: If the motor speed of the motor control system remains constant within a preset time, the motor control system is considered to have entered a stable state; or, if the motor speed of the motor control system remains constant within a preset time, the motor control system is considered to have entered a stable state. If the shaft command current remains constant, the motor control system is considered to have entered a stable state. S2, Calculate the first Second-rate Shaft command current and The amplitude and initial phase angle at twice the electrical frequency in the shaft sampling current. ; S3, The motor control system, based on the calculation results, , The shaft command current is corrected accordingly to achieve double frequency torque ripple suppression; S4. Determine whether the preset stopping condition is met. If the preset stopping condition is not met, repeatedly use equation (17) to check the conditions. , The axis command current is corrected; Among the factors are stator resistance asymmetry and proportional error in the current sampling circuit. Step S2 includes: S21, Obtain the first Second-rate Shaft command current and the first Second-rate Shaft sampling current; Determine the first according to formula (1) Sub-velocity tracking error: （1） in, For the first Secondary speed tracking error, For the first Secondary speed command For the first Secondary speed feedback Integers greater than or equal to zero; Discretized motor control system Shaft command current: （2） in, For the first Second-rate Shaft command current, This is the speed loop proportional coefficient. The integral coefficient of the velocity loop; This can be obtained through a current sensor. Phase sampling current and The sampling current of the phase is then determined according to equation (3). Phase sampling current: （3） in, represent Phase sampling current, represent Phase sampling current, represent Phase sampling current; The first motor control system Second-rate Shaft sampling current: （4） in, For the first Second-rate Shaft sampling current, This is the electrical angle feedback value. Pi; Electrical angle feedback value : （5） in, The fundamental frequency of the electrical circuit. Runtime; Determine the fundamental frequency of the electrical frequency : （6） in, Represents the number of pole pairs of the motor; S22, Calculate the first Second-rate Shaft command current and The amplitude and initial phase angle at twice the electrical frequency in the shaft sampling current; The calculation of the motor control system according to formula (7) is as follows: Second-rate Shaft command current or The amplitude corresponding to twice the electrical frequency in the shaft sampling current: （7） in, Can be or , Representing the Second-rate Shaft command current or The amplitude corresponding to twice the electrical frequency in the shaft sampling current. For the first Second-rate Shaft command current or The real part amplitude of the shaft sampling current at twice the electrical frequency. For the first Second-rate Shaft command current or The imaginary part amplitude of the shaft sampling current at twice the electrical frequency; Calculate the first according to formula (8) Second-rate The real part of the shaft command current: （8） in, This represents the total number of sampling points. For the first Second-rate Shaft command current, To match the sampling frequency , radio frequency Total number of sampling points The relevant quantity; Calculate the first according to formula (9) Second-rate The imaginary part of the shaft command current: （9） in, This represents the total number of sampling points. For the first Second-rate Shaft command current, To match the sampling frequency , radio frequency Total number of sampling points The relevant quantity; Calculate the first according to formula (10) Second-rate The magnitude of the real part of the shaft sampling current: （10） in, This represents the total number of sampling points. For the first Second-rate Shaft sampling current, To match the sampling frequency , radio frequency Total number of sampling points The relevant quantity; Calculate the first according to formula (11) Second-rate The amplitude of the imaginary part of the shaft sampling current: （11） in, This represents the total number of sampling points. For the first Second-rate Shaft sampling current, To match the sampling frequency , radio frequency Total number of sampling points The relevant quantity; Calculate the total number of sampling points according to formula (12). : （12） in, The sampling frequency; Calculate the first step of the motor control system according to formula (13). Second-rate Shaft command current or The initial phase angle corresponding to twice the electrical frequency in the shaft sampling current is: （13） in, for or ; When equation (8) and equation (10) are in When the calculation result is less than 0, in equation (13) It should be modified by equation (14): （14） in, for or , Pi; Calculate the first step of the motor control system according to formula (15). Second-rate Shaft command current or The pulsation information at twice the electrical frequency in the shaft sampling current: （15） in, Representing the After the next DFT calculation The frequency of the shaft command current is The current pulsation component. Representing the After the next DFT calculation The frequency of the shaft sampling current is The current pulsation component. The electric angular velocity of the motor. For runtime, For use in reconstructing frequency of Shaft command current or The pulsating phase angle of the shaft sampling current; Based on the DFT signal reconstruction principle, the reconstructed phase angle is calculated, including: Guarantee the instantaneous removal of pulsating phase angle during reconstruction The remaining phase angles are 0 rad, that is It should be defined by equation (16): （16） in, Can be or , To calculate the instantaneous electrical angle value at the start time of the DFT, The time taken to accumulate data; Step S3 includes: According to formula (17) shaft and The shaft command current is corrected to suppress double-frequency torque ripple under multiple influencing factors: （17） in, , Representing the first After suppressing the sub-speed pulsation , Shaft command current, , Before and after the correction Shaft command current, Shaft command current.

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