Harmonic current injection compensation of cogging torque method based on transfer characteristic of control system

Abstract

The application discloses a harmonic current injection compensation cogging torque method based on a control system transmission characteristic, and comprises the following steps: S1, measuring the cogging torque of a permanent magnet synchronous motor; S2, acquiring parameters of the permanent magnet synchronous motor and a vector drive control system thereof; S3, deducing a closed-loop transfer function of q-axis injected harmonic current to motor output electromagnetic torque; and S4, according to the cogging torque required to be compensated obtained from S1 and the transfer function obtained from S3, calculating the amplitude and phase of the q-axis required injected harmonic current. The application does not increase the complexity of the control system, is easy to implement, can effectively compensate the cogging torque, reduces the rotational speed harmonic caused by the cogging torque, and solves the problems of poor effect, failure and even increased inhibition target under some working conditions of the existing harmonic current injection method.

Description

Technical Field

[0001] This invention belongs to the field of permanent magnet motor cogging torque suppression technology, specifically relating to a method for q-axis harmonic current injection to compensate for cogging torque. Background Technology

[0002] Permanent magnet synchronous AC servo systems are widely used in the drive devices of CNC machine tools. However, the inherent cogging torque of permanent magnet motors can cause speed fluctuations and vibrations in the motor drive system, severely affecting the machining quality of parts. For example, in the CNC milling of aero-engine blades and the CNC belt grinding and polishing process, the stability of the spindle and feed axis motor speeds significantly affects the machining quality. Variations in motor speed can cause inconsistent measurements along the same toolpath, leading to problems such as the machined blade dimensions exceeding the design tolerance zone or machining marks appearing on the surface of the polished parts. Therefore, suppressing the cogging torque of permanent magnet motors is of great significance for the development of high-precision CNC machine tools.

[0003] Current methods for suppressing cogging torque mainly fall into two categories: improving motor structural parameters and improving motor control algorithms. However, methods that improve motor structural parameters are only applicable to the motor research and design stage and not to motors that have already been manufactured. Methods for suppressing cogging torque through control algorithms mainly include harmonic current injection and improved control algorithms based on changing the structure of the speed loop and current loop. The harmonic injection method has a clear physical meaning and is easy to implement, so it is widely used, and many domestic companies have already adopted some simple algorithms for engineering applications. Improved control algorithms based on changing the structure of the speed loop and current loop complicate the control system, making parameter adjustment difficult and resulting in poor versatility.

[0004] Xie Yangping, Zhang Xiaoguang, Tu Conghuan, et al. studied the compensation of cogging torque by injecting harmonic current into the q-axis in the Chinese invention patent "Method and device for compensating cogging torque of motor CN111669081A, 2020-09-15". However, this method does not consider the transmission path of the injected harmonic current in the control system and the influence of control parameters on it, as well as the bandwidth limitation of the current loop PI controller. This leads to problems such as poor performance, failure, or even increased suppression target under some working conditions in practical applications. Summary of the Invention

[0005] To address the problems in existing technologies, such as neglecting the transmission path of injected harmonic current in the control system and the influence of control parameters on its transmission process, as well as the bandwidth limitations of the current loop PI controller, which lead to poor performance, failure, or even increased suppression targets in practical applications, this invention aims to propose a harmonic current injection compensation method for cogging torque based on the transmission characteristics of the control system. The closed-loop transfer function of the q-axis injected harmonic current to the motor output electromagnetic torque is derived. Based on the transfer function and the cogging torque to be suppressed, the amplitude and phase of the harmonic current to be injected into the q-axis are calculated.

[0006] This invention can calculate the amplitude and phase of the required injected harmonic current in real time according to different operating conditions and control parameters of the motor, thereby achieving effective compensation for cogging torque, reducing speed harmonics caused by cogging torque. It is simple and easy to implement, does not require changing the motor control algorithm, and does not increase the system complexity. It has good versatility.

[0007] The technical solution of the present invention is as follows:

[0008] The method for harmonic current injection to compensate for cogging torque based on the transmission characteristics of the control system includes the following steps:

[0009] S1. Measure the cogging torque of the permanent magnet synchronous motor;

[0010] S2. Obtain the parameters of the permanent magnet synchronous motor and its vector drive control system;

[0011] S3. Derive the closed-loop transfer function from the q-axis injected harmonic current to the motor output electromagnetic torque, and obtain the electromagnetic torque harmonics generated by the q-axis injected harmonic current based on the closed-loop transfer function.

[0012] S4. Based on the cogging torque required for compensation obtained in S1 and the closed-loop transfer function obtained in S3, calculate the amplitude and phase of the harmonic current required to be injected into the q-axis.

[0013] Furthermore, step S1 includes measuring the order, amplitude, and phase of the cogging torque harmonics of the permanent magnet synchronous motor.

[0014] Furthermore, in step S2, the parameters of the permanent magnet synchronous motor include motor inductance, rotor flux linkage, number of motor pole pairs, moment of inertia, and damping coefficient, and the parameters of the vector drive control system include the current filter cutoff frequency and system delay time parameters.

[0015] Furthermore, step S3 specifically includes,

[0016] S31. Based on the stator voltage equation under the dq axis of the permanent magnet synchronous generator, the stator voltage u is obtained. d u q to stator current i d i q transfer function H u2i (s):

[0017]

[0018] In the formula, s is a complex variable, R is the stator resistance, and L is the stator resistance. s For inductance, w e The electric angular velocity of the motor;

[0019] S32. Based on the electromagnetic torque equation of the permanent magnet synchronous motor, the q-axis current i is obtained. q To electromagnetic torque T e transfer function

[0020]

[0021] In the formula, s is a complex variable, p is the number of pole pairs of the motor, and Ψ f For rotor flux linkage;

[0022] S33. Determine the type of low-pass current filter and determine its transfer function H based on the type. bf (s);

[0023] S34. Equivalently representing SVPWM and the inverter as a delay element, and assuming the total delay time of the control system is τ, the transfer function H of the delay element in the dq axis coordinate system is obtained. delay (s):

[0024]

[0025] In the formula, s is a complex variable, and p is the number of pole pairs of the motor. This is a motor speed command;

[0026] The S35, d, and q-axis current loops use proportional-integral (PI) controllers, with transfer functions as follows:

[0027] H pi_id (s)=k p_id +k i_id / s;

[0028] H pi_iq (s)=k p_iq +k i_iq / s;

[0029] In the formula, s is a complex variable, k p_id k i_id k p_iq k i_iq These are the proportional and integral coefficients of the PI controllers for the d-axis current loop and q-axis current loop, respectively.

[0030] S36, Obtain the q-axis injected harmonic current i qc (s) to the motor output electromagnetic torque T e The closed-loop transfer function of (s) is:

[0031]

[0032] S37. According to the closed-loop transfer function, let T e (s), i qc (s) and Hiqc2Te In (s), s = kwj, which gives the electromagnetic torque T that produces the order kw. e (kwj) Required current harmonics i qc (kwj) is:

[0033]

[0034] In the formula, k is an integer, w is the motor frequency, and j is the imaginary unit.

[0035] Furthermore, in step S33, the current filter is a Butterworth low-pass filter with a transfer function H. bf (s) is:

[0036]

[0037] In the formula, s is a complex variable, ω bf This is the filter cutoff frequency.

[0038] Alternatively, in step S35, the d-axis and q-axis current loops employ a conventional (existing) proportional-integral (PI) controller.

[0039] Furthermore, in step S36, a harmonic current i is injected along the q-axis. qc (s) to the motor output electromagnetic torque T e The closed-loop transfer function H of (s) iqc2Te The process of obtaining (s) is as follows:

[0040] Combining the vector control method and steps S31 to S36, let

[0041]

[0042] In the formula, H ud2id (s) indicates the d-axis voltage command. to d-axis current i d The transfer function, H ud2iq (s) indicates the d-axis voltage command. to q-axis current i q The transfer function, H uq2id (s) indicates the q-axis voltage command. to d-axis current i d The transfer function, H uq2iq (s) indicates the q-axis voltage command. to q-axis current i q The transfer function;

[0043] The q-axis injected harmonic current i can be obtained qc (s) to the motor output electromagnetic torque T e The closed-loop transfer function of (s) is:

[0044]

[0045] Furthermore, step S4 specifically includes:

[0046] S41. Calculate the amplitude of the harmonic current i required to compensate for the cogging torque. qc When compensating for cogging torque, it is necessary to satisfy the electromagnetic torque T generated by the injected harmonic current. e (kwj) and cogging torque T cog (kwj) are equal in magnitude but opposite in phase, therefore:

[0047]

[0048] In the formula T cog (kwj) is to make T cog In (s), s = kwj represents the kw-th order cogging torque, where j is the imaginary unit, |T cog (kwj)|,|H iq2Te (kwj)| represents the magnitude of the kw-th order cogging torque and the time transfer function H with frequency kW, respectively. iqc2Te The amplitude frequency of (kwj);

[0049] S42. Calculate the phase of the required injected harmonic current:

[0050]

[0051] In the formula, ∠T cog (kwj), ∠H iq2Te (kwj) represent the transfer function H when the phase and frequency of the kw-th order cogging torque are respectively kW. iqc2Te The phase frequency of (kwj).

[0052] Compared with the prior art, the present invention has the following characteristics:

[0053] (1) This invention takes into account the influence of the transmission characteristics of the control system and the control parameters on the injected harmonic current. Under various working conditions, it can more accurately and effectively compensate for the cogging torque and reduce the speed harmonics, vibration noise and other issues caused by the cogging torque.

[0054] (2) This invention does not change the original motor control algorithm, does not make the control system structure complex, has good versatility, and is simple and easy to implement.

[0055] (3) The present invention has a small computational load and good real-time performance. In practical applications, the amplitude and phase of the harmonic current to be injected can be calculated in real time.

[0056] (4) This invention introduces a new transfer function for the q-axis injected harmonic current to the output electromagnetic torque of the motor. Attached Figure Description

[0057] Figure 1 This is a flowchart of a method for harmonic current injection to compensate cogging torque based on the transmission characteristics of a control system in an embodiment of the present invention.

[0058] Figure 2 This is a spectrum of the cogging torque amplitude of a permanent magnet synchronous motor measured in an embodiment of the present invention;

[0059] Figure 3 This is a phase spectrum of the cogging rotation of a permanent magnet synchronous motor measured in an embodiment of the present invention;

[0060] Figure 4 This is a parameter diagram of the permanent magnet synchronous motor and control system in an embodiment of the present invention;

[0061] Figure 5 This is a block diagram of the transfer function for q-axis injected harmonic current vector control in an embodiment of the present invention;

[0062] Figure 6 This is a block diagram of the closed-loop transfer function from the q-axis injected harmonic current to the output electromagnetic torque of the motor in an embodiment of the present invention;

[0063] Figure 7 This is a block diagram of the harmonic current injection compensation cogging torque control structure based on the transmission characteristics of the control system in this embodiment of the invention.

[0064] Figure 8 This is a block diagram of the control structure for the traditional harmonic current injection method in an embodiment of the present invention.

[0065] Figure 9 This is a diagram showing the simulation operating condition parameter settings in an embodiment of the present invention;

[0066] Figure 10 This refers to the magnitude of the rotational speed harmonic amplitude caused by the cogging torque obtained by simulation in the embodiments of the present invention, without the injection of harmonic current, using the conventional injection method and the injection method of the present invention;

[0067] Figure 11 This is a diagram of the permanent magnet synchronous motor vector control drive system used in the experiment of this invention embodiment;

[0068] Figure 12 This is a comparison chart of the speed fluctuations under the 1500rpm operating condition obtained in the embodiments of the present invention, with and without the injection of harmonic current, using the traditional injection method and the method of the present invention.

[0069] Figure 13 This is the rotational speed spectrum diagram of the embodiment of the present invention under the condition of 1500 rpm without the injection of harmonic current;

[0070] Figure 14This is a speed spectrum diagram of the conventional injection method under the 1500rpm operating condition in this embodiment of the invention;

[0071] Figure 15 This is a speed spectrum diagram after applying the injection method of the present invention at a working condition of 1500 rpm in an embodiment of the present invention. Detailed Implementation

[0072] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. However, it should not be construed that the scope of the subject matter of the present invention is limited to the following embodiments. All modifications, substitutions and alterations made based on ordinary technical knowledge and conventional means in the art without departing from the above-described technical concept of the present invention are included within the scope of the present invention.

[0073] See Figure 1 This embodiment provides a method for harmonic current injection compensation of cogging torque based on the transmission characteristics of a control system, specifically including the following steps:

[0074] S1: Measure the cogging torque of the permanent magnet synchronous motor;

[0075] In this embodiment, the motor is a surface-mounted permanent magnet synchronous motor. The cogging torque amplitude spectrum and phase spectrum of the motor are measured using existing cogging torque measurement methods, as follows: Figure 2 , Figure 3 As shown, from Figure 2 It can be seen that the 8th order speed harmonic amplitude of the cogging torque of this surface-mounted permanent magnet synchronous motor is the largest, at 38.059 mNm. From Figure 3 It can be seen that the phase of the 8th cogging torque is 81°, that is, the expression for the 8th cogging torque is: T cog =0.038059cos(8θ) r +81°).

[0076] S2: Obtain parameters of the permanent magnet synchronous motor and the vector drive control system parameters of the permanent magnet synchronous motor;

[0077] In this embodiment, the parameters of the permanent magnet synchronous motor include motor inductance, rotor flux linkage, number of motor pole pairs, moment of inertia, and damping coefficient, while the parameters of the vector drive control system include the current filter cutoff frequency and system delay time.

[0078] In this embodiment, the parameters of the motor and its vector drive control system are as follows: Figure 4 As shown.

[0079] Step S3: Derive the closed-loop transfer function from the q-axis injected harmonic current to the motor output electromagnetic torque, and obtain the electromagnetic torque harmonics generated by the q-axis injected harmonic current based on the closed-loop transfer function;

[0080] In this embodiment, S3 includes the following sub-steps:

[0081] S31. Based on the voltage equation under the dq axis of the permanent magnet synchronous generator, the stator voltage u is obtained. d u q to stator current i d i q transfer function H u2i (s):

[0082]

[0083] In the formula, s is a complex variable, R is the stator resistance, and L is the stator resistance. s For inductance, w e The electric angular velocity of the motor;

[0084] S32. Based on the electromagnetic torque equation of the permanent magnet synchronous motor, the q-axis current i is obtained. q To electromagnetic torque T e transfer function

[0085]

[0086] In the formula, s is a complex variable, p is the number of pole pairs of the motor, and Ψ f For rotor flux linkage;

[0087] S33. The low-pass current filter used is a Butterworth low-pass filter, and its transfer function is:

[0088]

[0089] In the formula, s is a complex variable, ω bf This is the filter cutoff frequency;

[0090] It is understood that other low-pass filters may be used in other embodiments, and the corresponding transfer functions may be modified accordingly.

[0091] S34. Equivalently representing SVPWM and the inverter as a delay element, and assuming the total delay time of the control system is τ, the transfer function H of the delay element in the dq axis coordinate system is obtained. delay (s):

[0092]

[0093] In the formula, s is a complex variable, and p is the number of pole pairs of the motor. This is a motor speed command;

[0094] S35, the d-axis current loop, and the q-axis current loop are traditional proportional-integral (PI) controllers, and their transfer functions are as follows:

[0095] H pi_id (s)=kp_id +k i_id / s;

[0096] H pi_iq (s)=k p_iq +k i_iq / s;

[0097] In the formula, s is a complex variable, k p_id k i_id k p_iq k i_iq These are the proportional and integral coefficients of the PI controllers for the d-axis current loop and q-axis current loop, respectively.

[0098] In this embodiment, combining vector control theory and steps S31 to S35, the control transfer function block diagram of vector control is obtained as follows: Figure 5 As shown in the figure. H pi_s (s), H T2wr (s) represent the transfer functions of the speed loop and the mechanical motion equation of the motor, respectively;

[0099] S36, Obtain the q-axis injected harmonic current i qc (s) to the motor output electromagnetic torque T e The closed-loop transfer function of (s);

[0100] In this embodiment, according to Figure 5 The q-axis injected harmonic current i can be obtained. qc (s) to the motor output electromagnetic torque T e The closed-loop transfer function block diagram of (s) is as follows: Figure 6 As shown;

[0101] make

[0102]

[0103] In the formula, H ud2id (s) indicates the d-axis voltage command. to d-axis current i d The transfer function, H ud2iq (s) indicates the d-axis voltage command. to q-axis current i q The transfer function, H uq2id (s) indicates the q-axis voltage command. to d-axis current i d The transfer function, H uq2iq (s) indicates the q-axis voltage command. to q-axis current i q The transfer function;

[0104] The q-axis injected harmonic current i can be obtained qc (s) to the motor output electromagnetic torque Te The closed-loop transfer function of (s) is:

[0105]

[0106] S37. According to the closed-loop transfer function, let T e (s), i qc (s) and H iqc2Te In (s), s = kwj, which gives the electromagnetic torque T that produces the order kw. e (kwj) Required current harmonics i qc (kwj) is:

[0107]

[0108] S4. Based on the cogging torque required for compensation obtained in S1 and the transfer function obtained in S3, calculate the amplitude and phase of the harmonic current required to be injected into the q-axis.

[0109] In this embodiment, the cogging torque has been measured in S1, the motor and control system parameters have been obtained in step S2, and the closed-loop transfer function of the q-axis injected harmonic current to the motor output electromagnetic torque has been obtained in step S36. Thus, the harmonic current that needs to be injected to compensate for the cogging torque can be obtained in step S37.

[0110] S41. Calculate the amplitude of the harmonic current i required to compensate for the cogging torque. qc When compensating for cogging torque, it is necessary to satisfy the electromagnetic torque T generated by the injected harmonic current. e (kwj) and cogging torque T cog (kwj) are equal in magnitude but opposite in phase, therefore:

[0111]

[0112] In the formula T cog (kwj) is to make T cog In (s), s = kwj represents the kw-th order cogging torque, where j is the imaginary unit. |T cog (kwj)|,|H iq2Te (kwj)| represents the magnitude of the kw-th order cogging torque and the time transfer function H with frequency kW, respectively. iqc2Te The amplitude frequency of (kwj);

[0113] S42. Calculate the phase of the required injected harmonic current:

[0114]

[0115] In the formula, ∠T cog (kwj), ∠H iq2Te(kwj) represent the phase and frequency of the kw-th order cogging torque, respectively, and are time transfer functions H with frequency kW. iqc2Te The phase frequency of (kwj).

[0116] In this embodiment, the control block diagram of the harmonic current injection method based on the transmission characteristics of the control system is as follows: Figure 7 As shown in the figure, the harmonic current controller calculates the amplitude and phase of the required injected harmonic current based on the order, amplitude, and phase of the cogging torque harmonic to be suppressed obtained from S1, using S41 and S42.

[0117] In this embodiment, the block diagram of the control structure for the traditional harmonic current injection method is as follows: Figure 8 As shown. The principle of harmonic current injection to compensate for cogging torque is based on the motor electromagnetic torque equation T... e =1.5i q ψ f (where p is the number of pole pairs of the motor, ψ) f (For permanent magnet flux linkage), the magnitude of the compensation current i can be obtained. qc =-T cog (θ r ) / (1.5ψ f ), T cog (θ r ) represents the rotor position angle θ r The magnitude of the cogging torque at that point.

[0118] In this embodiment of the invention, the compensation effect of the harmonic current injection method of the present invention on cogging torque is compared with that of the traditional harmonic current injection method through simulation. The simulation operating parameters are set as follows: Figure 9 As shown, FFT analysis was performed on the speed harmonics under various operating conditions to compare the magnitudes of speed harmonics caused by cogging torque under different methods.

[0119] In this embodiment, compensation is performed for the 8th cogging torque. Traditional methods do not consider the transmission characteristics of the control system. Figure 9 The injected harmonic current for each operating condition is i qc =0.2265sin(8θ) r -9°), the method of this invention will change the injected harmonic current in real time according to the same control parameters, corresponding to Figure 9 The injected harmonic currents for the first to fourth operating conditions are as follows: i qc1 =0.1942sin(8θ) r -5.2675°), i qc2 =0.1993sin(8θ) r -8.7643°), i qc3 =0.2486sin(8θ) r +20.2385°), i qc4=0.2386sin(8θ) r +7.561°).

[0120] In this embodiment, corresponding Figure 9 The comparison diagram of the 8th order speed harmonic amplitude obtained by simulation under various operating conditions—without harmonic current injection, using the traditional harmonic current injection method, and using the harmonic current injection method of this invention—is shown below. Figure 10 As shown. From Figure 10 It is evident that the injection method of this invention can reduce the speed harmonics caused by cogging torque by more than 95% under various operating conditions. In contrast, traditional methods, which do not consider the transmission characteristics of the control system and the influence of control parameters, exhibit poor suppression effects under certain conditions. For example, in the first and second groups of operating conditions, the amplitude of speed harmonics caused by cogging torque can be reduced by approximately 82% and 86%, respectively. However, in the third and fourth groups of operating conditions, the amplitude of speed harmonics after injection is only reduced by approximately 55% and 32%, respectively, indicating a much less effective suppression than the method of this invention.

[0121] In this embodiment, Figure 11 The parameters used in the experiment and Figure 4 A diagram of a consistent permanent magnet synchronous motor vector control drive system.

[0122] In this embodiment, Figure 12 For the corresponding Figure 9 The graph shows a comparison of motor speeds under the following conditions: no harmonic current injection, traditional harmonic current injection method, and the harmonic current injection method of this invention. To better compare the compensation effects of the present invention and the traditional method on cogging torque, the speed curves in the graph have been low-pass filtered to remove high-frequency glitches. The graph shows that without harmonic current injection, the motor rotates one revolution with a speed fluctuation of 8 cycles, indicating a large amplitude of the 8th-order speed harmonic caused by cogging torque. After using the traditional injection method and the injection method of this invention, the 8th-order speed harmonic is significantly reduced, and the speed fluctuation is even smaller with the injection method of this invention, demonstrating the effectiveness of the present invention.

[0123] In this embodiment, Figure 13 , Figure 14 and Figure 15 They are respectively the corresponding Figure 9 The experiment yielded motor speed spectrum diagrams under the following conditions: no harmonic current injection, traditional harmonic current injection method, and the harmonic current injection method of this invention. The diagrams show that injecting harmonic current using the method of this invention reduced the amplitude of the 8th-order speed harmonic caused by cogging torque by 78.8%, while the traditional injection method reduced it by 52.9%. Under other conditions, the method of this invention also significantly outperformed the traditional harmonic current injection method in reducing speed harmonics caused by cogging torque. These results demonstrate that the harmonic current injection method of this invention can more effectively compensate for cogging torque and suppress speed harmonics caused by cogging torque more effectively than the traditional method.

[0124] Contents not described in detail in this specification are prior art known to those skilled in the art. Although illustrative specific embodiments of the invention have been described above to facilitate understanding by those skilled in the art, it should be understood that the invention is not limited to the scope of the specific embodiments. Various modifications are readily apparent to those skilled in the art as long as they fall within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of this invention are protected.

Claims

1. A method for compensating cogging torque by harmonic current injection based on the transmission characteristics of a control system, characterized in that: Includes the following steps: S1. Measure the cogging torque of the permanent magnet synchronous motor; S2. Obtain the parameters of the permanent magnet synchronous motor and its vector drive control system; S3, Derivation q The closed-loop transfer function from shaft-injected harmonic current to the motor output electromagnetic torque is obtained from the closed-loop transfer function. q Electromagnetic torque harmonics generated by shaft-injected harmonic current; S4. Based on the cogging torque required for compensation obtained in S1 and the closed-loop transfer function obtained in S3, calculate the amplitude and phase of the harmonic current required to be injected into the q-axis. Step S3 specifically includes: S31, Based on permanent magnet synchronization dq The stator voltage equation under the shaft is used to obtain the stator voltage. u d , u q to stator current i d , i q transfer function : ； In the formula, s For complex variables, R For stator resistance, L s For inductance, w e The electric angular velocity of the motor; S32. Based on the electromagnetic torque equation of the permanent magnet synchronous motor, we obtain... q shaft current i q To electromagnetic torque T e transfer function : ； In the formula, s is a complex variable. p This represents the number of pole pairs of the motor. Ψ f For rotor flux linkage; S33. Determine the type of low-pass current filter and its transfer function based on the type. ; S34. Equivalently treat SVPWM and the inverter as delay elements, and assume the total delay time of the control system is... τ The delay stage is obtained in dq Transfer function in axial coordinate system : ； In the formula, s is a complex variable. p This represents the number of pole pairs of the motor. This is a motor speed command; S35, d, q The shaft current loop uses a proportional-integral controller, and its transfer functions are as follows: ； ； In the formula, s is a complex variable. k p_id , k i_id , k p_iq , k i_iq They are respectively d Shaft current loop, q The proportional and integral coefficients of the shaft current loop PI controller; S36, obtained q Shaft-injected harmonic current i qc ( s ) to the motor output electromagnetic torque T e ( s The closed-loop transfer function of is: ； S37. According to the closed-loop transfer function, let T e ( s ), i qc ( s )and H iqc2Te ( s In ) s = kwj The result can be obtained kw Electromagnetic torque of order T e ( kwj ) Required current harmonics i qc ( kwj )for: ； In the formula k It is an integer. w For motor speed, j The imaginary unit; In step S33, the current filter is a Butterworth low-pass filter with a transfer function of for: ； In the formula, s For complex variables, This is the filter cutoff frequency; In step S36 q Shaft-injected harmonic current i qc ( s ) to the motor output electromagnetic torque T e ( s Closed-loop transfer function H iqc2Te ( s The process of obtaining ) is as follows: Combining the vector control method and steps S31 to S36, let ； In the formula, H ud2id ( s )express d Shaft voltage command arrive d shaft current i d The transfer function, H ud2iq ( s )express d Shaft voltage command arrive q shaft current i q The transfer function, H uq2id ( s )express q Shaft voltage command arrive d shaft current i d The transfer function, H uq2iq ( s )express q Shaft voltage command arrive q shaft current i q The transfer function; The q-axis injected harmonic current can be obtained. i qc ( s ) to the motor output electromagnetic torque T e ( s The closed-loop transfer function of is: 。 2. The method for harmonic current injection compensation of cogging torque based on the transmission characteristics of a control system according to claim 1, characterized in that: Step S1 includes measuring the order, amplitude, and phase of the cogging torque harmonics of the permanent magnet synchronous motor.

3. The method for harmonic current injection compensation of cogging torque based on the transmission characteristics of the control system according to claim 1, characterized in that: In step S2, the parameters of the permanent magnet synchronous motor include motor inductance, rotor flux linkage, number of motor pole pairs, moment of inertia, and damping coefficient, while the parameters of the vector drive control system include the current filter cutoff frequency and system delay time parameters.

4. The method for harmonic current injection compensation of cogging torque based on the transmission characteristics of the control system according to claim 1, characterized in that: Step S4 specifically includes: S41. Calculate the amplitude of the harmonic current required to compensate for the cogging torque. i qc When compensating for cogging torque, it is necessary to satisfy the electromagnetic torque generated by the injected harmonic current. T e ( kwj ) and cogging torque T cog ( kwj Since they are equal in magnitude but opposite in phase, we have: ； In the formula T cog ( kwj ) for order T cog ( s In ) s = kwj , indicating the first kw Cogging torque, where j For imaginary units, | T cog ( kwj )|,| H iq2Te ( kwj )| respectively represent the first kw The amplitude and frequency of the cogging torque are kw Time transfer function H iqc2Te ( kwj The amplitude frequency of ) S42. Calculate the phase of the required injected harmonic current: ； In the formula ∠ T cog ( kwj ), ∠ H iq2Te ( kwj ) respectively represent the first kw The phase and frequency of the cogging torque are kw Time transfer function H iqc2Te ( kwj The phase frequency of ).

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