Resonance suppression method for ultra-high-speed permanent magnet synchronous motor with LC filter

Abstract

The present invention discloses a resonance suppression method for an ultra-high-speed permanent magnet synchronous motor with an LC filter, which specifically includes the following steps: step 1, establishing a d-q axis mathematical model of the ultra-high-speed permanent magnet synchronous motor with an LC filter; step 2, designing a motor winding current feedback gain based on the mathematical model of the ultra-high-speed permanent magnet synchronous motor established in step 1, and obtaining a system transfer function of an equivalent capacitor current feedback active damping loop based on the feedback gain; step 3, designing an equivalent capacitor current feedback coefficient in the winding current feedback gain in step 2, and calculating the motor winding current feedback gain G based on the feedback coefficient. s The method of the present invention can suppress LCL resonance without introducing additional power loss.

Description

Technical Field

[0001] The invention belongs to the technical field of high-speed permanent magnet synchronous motor control and relates to a resonance suppression method for an ultra-high-speed permanent magnet synchronous motor with an LC filter. Background Art

[0002] Ultra-high-speed permanent magnet synchronous motors (UPMS) offer high speed, compact size, and high power density. Their rotors are directly connected to high-speed loads, reducing system complexity and redundancy while improving system integration and reliability. These motors hold significant research potential and broad application value in military, aerospace, industrial, medical, and civilian applications. High-speed UPMS have low stator inductance and large stator current harmonics. Excessive current harmonics can lead to torque ripple, severe heat generation, and reduced efficiency. To suppress stator current harmonics and improve the performance of UPMS, LC filters are typically added between the inverter and motor. While LC filters can suppress stator current harmonics, they can also cause LCL resonance.

[0003] Currently, traditional methods add resistors to the system to suppress resonance, but this leads to additional power loss. Therefore, it is crucial to develop a resonance suppression technology for ultra-high-speed permanent magnet synchronous motors with LC filters that does not increase additional power loss. Summary of the Invention

[0004] The object of the present invention is to provide a method for suppressing resonance of an ultra-high-speed permanent magnet synchronous motor with an LC filter, which can suppress LCL resonance without introducing additional power loss.

[0005] The technical solution adopted by the present invention is a method for suppressing resonance of an ultra-high-speed permanent magnet synchronous motor with an LC filter, which specifically includes the following steps:

[0006] Step 1: Establish a dq-axis mathematical model of an ultra-high-speed permanent magnet synchronous motor with an LC filter;

[0007] Step 2: Designing the motor winding current feedback gain using the mathematical model of the ultra-high-speed permanent magnet synchronous motor established in step 1, and obtaining the system transfer function of the equivalent capacitive current feedback active damping loop based on the feedback gain;

[0008] Step 3: Design the equivalent capacitor current feedback coefficient in the winding current feedback gain in step 2, and calculate the motor winding current feedback gain G according to the feedback coefficient. s The value of (s).

[0009] The present invention is also characterized in that:

[0010] The specific process of step 1 is:

[0011] The mathematical model of the permanent magnet synchronous motor in the synchronous rotating coordinate system is shown in the following formula (1):

[0012]

[0013] Among them: U d 、U q They are the dq axis voltage at the motor end, I d , I q is the dq axis current at the motor end, R s is the motor stator resistance, L s is the stator inductance of the motor; ω e is the rotor angular velocity, Ψ f is the permanent magnet flux;

[0014] The mathematical model of the LC filter in the synchronous rotating coordinate system is shown in the following formulas (2) and (3):

[0015]

[0016] Among them, U fd 、U fq are the dq axis voltage at the input of the LC filter, I fd , I fq is the dq axis current at the input of the LC filter, L f is the filter inductance, C f is the filter capacitor.

[0017] The specific process of step 2 is:

[0018] Since the permanent magnet synchronous motor is symmetrical along the dq axis, only the q axis is analyzed. The mathematical model of the PMSM and LC filter in the synchronous rotating coordinate system obtained in step 1 is used to obtain the system transfer function G of the s-domain q-axis current loop equivalent capacitor current feedback active damping loop. LCL-R (s), as shown in the following formula (4):

[0019]

[0020] Among them: G d (s) represents digital delay, G s (s) represents the motor winding current feedback gain, I q (s) represents the s-domain q-axis motor current, U fq (s) represents the q-axis voltage at the input of the s-domain LC filter;

[0021] The forward path generates 1.5T s Digital delay, T s is the sampling period, and the delay function is expressed as the following formula (5):

[0022]

[0023] Define the motor winding current feedback gain G s (s) = K r C f L f s 2 , the system transfer function G of the equivalent capacitor current feedback active damping loop of the s-domain q-axis current loop is obtained LCL-R (s) is expressed as the following formula (6):

[0024]

[0025] Among them: K r is the equivalent capacitor current feedback coefficient.

[0026] The specific process of step 3 is:

[0027] The filter inductor voltage U l(s) To the motor current I q(s) The transfer function is expressed as G1(s), the filter inductor voltage U l(s) To the filter capacitor voltage U c(s) The transfer function is expressed as G2(s), the filter inductor voltage U l(s) Current to filter capacitor I c(s) The transfer function is expressed as G3(s), and the s-domain model of the equivalent capacitor current feedback active damping control system is established. The filter inductor voltage U l(s) To the motor current I q(s) The s-domain transfer function is shown in the following formula (7):

[0028]

[0029] Among them, ω r is the resonant angular frequency, which is expressed as follows:

[0030]

[0031] Among them, f r is the resonant frequency;

[0032] Filter inductor voltage U l(s) To the filter capacitor voltage U c(s) The s-domain transfer function is shown in the following formula (9):

[0033]

[0034] Filter inductor voltage U l(s) Current to filter capacitor I c(s) The s-domain transfer function is shown in the following formula (10):

[0035]

[0036] The zero-order hold discretization method is used to discretize G 1(s) , G 2(s) and G 3(s) Discretize, G 1(s) , G 2(s) and G 3(s) The discrete domain expression G 1(z) , G 2(z) and G 3(z) As shown in the following formulas (11), (12), and (13):

[0037]

[0038] Digitally controlled delay is expressed in the discrete domain using Z -1 According to G 1(z) , G 2(z) and G 3(z) The open-loop transfer function of the discrete domain system with equivalent capacitor current feedback active damping control is shown in the following formula (14):

[0039]

[0040] Extract T in formula (14) op(z) The denominator of is shown in the following formula (15):

[0041] Den(z)=sinω r T s +(L f -K r cosω r T s )z+(K r -2L f cosω r T s )z 2 +L f z 3 (15)

[0042] Determine the open-loop transfer function T according to the Jully criterion op(z) The stability condition is shown in the following formula (16):

[0043]

[0044] Due to the existence of digital control delay, the equivalent capacitor current feedback loop coefficient K r Equivalent to a virtual impedance Z in parallel with the capacitor eq , virtual impedance Z eq The expression is shown in the following formula (17):

[0045]

[0046] The virtual impedance Z eq Expressed in complex form, it is shown in the following formula (18):

[0047] Z eq (ω)=R eq (ω)+jX eq (ω) (18)

[0048] Where ω = 2πf s , f s is the sampling frequency, R eq and X eq As shown in the following formulas (19) and (20):

[0049] R eq (ω)=K s cos(1.5ωT s ) (19)

[0050] X eq (ω)=K s sin(1.5ωT s ) (20)

[0051] in, When 0 <f r <f s / 6 o'clock, R eq >0; when f s / 6 <f r <f s / 4, R eq <0;

[0052] In addition, K r The system output impedance should have sufficient phase margin (P M ), the phase margin range is [30°, 60°], so it must also satisfy the following formula (21):

[0053] 30°≤P M ≤60° (21)

[0054] According to the stability condition of Juli criterion, the equivalent capacitance current feedback coefficient K r It is expressed as the following formula (22):

[0055]

[0056] So the motor winding current feedback gain G s (s) is expressed as the following formula (23):

[0057]

[0058] In step 3, select Among them, 0 <f r <f s / 6.

[0059] The beneficial effect of the present invention is that, compared with the traditional method of adding resistors to the system to suppress resonance, the equivalent capacitor current feedback method adopted by the present invention can avoid the additional power loss caused by the resistor. Compared with the traditional capacitor current feedback and inductor current feedback methods, the equivalent capacitor current feedback method adopted by the present invention does not need to measure the capacitor branch current and the inductor branch current, thereby reducing the cost of the control system. At the same time, the designed feedback gain G s (s) satisfies the Juli stability criterion. When the resonant frequency is less than 1 / 6 of the sampling frequency, the stability range of the system expands with the increase of the feedback coefficient. The system can remain stable before the root locus of the system moves to the right and crosses the imaginary axis. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 This is a block diagram of a vector control system used in the resonance suppression method of an ultra-high-speed permanent magnet synchronous motor with an LC filter according to the present invention;

[0061] Figure 2 This is a system block diagram of the motor winding current feedback active damping control in the resonance suppression method of the ultra-high-speed permanent magnet synchronous motor with LC filter of the present invention;

[0062] Figure 3 This is a system block diagram of the active damping control using equivalent capacitor current feedback in the resonance suppression method of the ultra-high-speed permanent magnet synchronous motor with an LC filter according to the present invention;

[0063] Figure 4 This is a block diagram of an S-domain model system for active damping control using equivalent capacitor current feedback in a resonance suppression method for an ultra-high-speed permanent magnet synchronous motor with an LC filter according to the present invention;

[0064] Figure 5 This is a block diagram of a z-domain model system for active damping control using equivalent capacitor current feedback in a resonance suppression method for an ultra-high-speed permanent magnet synchronous motor with an LC filter according to the present invention;

[0065] Figure 6 This is a system block diagram after the feedback coefficient is equivalent to the virtual impedance in the resonance suppression method of the ultra-high-speed permanent magnet synchronous motor with LC filter of the present invention;

[0066] Figure 7 is a Bode diagram of an open-loop transfer function of a q-axis current control loop when the resonance suppression method of the ultra-high-speed permanent magnet synchronous motor with an LC filter of the present invention is not adopted;

[0067] Figure 8It is a Bode diagram of the open-loop transfer function of the q-axis current control loop using the resonance suppression method of the ultra-high-speed permanent magnet synchronous motor with an LC filter of the present invention. DETAILED DESCRIPTION

[0068] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0069] Example 1

[0070] The resonance suppression method of the ultra-high-speed permanent magnet synchronous motor with LC filter of the present invention, wherein the vector control system block diagram adopted is as follows Figure 1 As shown in the figure, the system consists of three PI regulators, forming a dual-loop control of speed loop and current loop. The stator current i of the ultra-high-speed permanent magnet synchronous motor in the three-phase stationary coordinate system is detected by the current Hall sensor. a 、i b 、i c ; Detected three-phase stator current i a 、i b 、i c Through abc / αβ transformation, the current value i is converted to the two-phase stationary coordinate system α 、i β ;i α 、i β Through αβ / dq transformation, the current value i is converted to the two-phase synchronous rotating coordinate system d 、i q ; Given excitation current With the feedback current i d The PI controller outputs the d-axis voltage through the current loop. Detecting the mechanical angle θ of the ultra-high-speed permanent magnet synchronous motor using an encoder m and mechanical angular velocity ω m , mechanical angle θ m Multiply by the number of pole pairs n p Convert to electrical angle θ e , and the electrical angle θ e Input to αβ / dq transformation, given mechanical angular velocity and mechanical angular velocity ω m The PI controller of the speed loop outputs the q-axis excitation current. Excitation current With the feedback current i q The PI controller outputs the q-axis voltage through the current loop. After dq / αβ transformation, the two-phase voltage u in the two-phase stationary coordinate system is obtained α 、u β , change i α 、i β Multiply by the feedback gain G s(s) Get the active damping control output u α-LC and u β-LC , will u α 、u β with u α-LC and u β-LC The phases are subtracted, and then the three-phase inverter (VSI) is controlled by space vector pulse width modulation (SVPWM). An LC filter is connected in series between the VSI and the ultra-high-speed permanent magnet synchronous motor. Finally, the ultra-high-speed permanent magnet synchronous motor is driven by the three-phase inverter.

[0071] Example 2

[0072] The resonance suppression method of the ultra-high-speed permanent magnet synchronous motor with an LC filter of the present invention is specifically implemented according to the following steps:

[0073] Step 1: Establish the dq axis mathematical model of the ultra-high-speed permanent magnet synchronous motor with LC filter, specifically:

[0074] The mathematical model of the permanent magnet synchronous motor (PMSM) in the synchronous rotating coordinate system is shown in the following formula (1):

[0075]

[0076] Among them: U d 、U q is the dq axis voltage at the motor end, I d , I q is the dq axis current at the motor end, R s is the motor stator resistance, L s is the stator inductance of the motor; ω e is the rotor angular velocity, Ψ f is the permanent magnet flux.

[0077] The mathematical model of the LC filter in the synchronous rotating coordinate system is shown in the following formulas (2) and (3):

[0078]

[0079] Among them: U fd 、U fq is the dq axis voltage at the input of the LC filter, I fd , I fq is the dq axis current at the input of the LC filter, L f is the filter inductance, C f is the filter capacitor.

[0080] Step 2: Design the motor winding current feedback gain using the mathematical model of the ultra-high-speed permanent magnet synchronous motor in step 1 to obtain the system transfer function of the equivalent capacitor current feedback active damping loop, specifically:

[0081] Since PMSM can be equivalent to a circuit consisting of back electromotive force, winding inductance, and winding resistance in series, the back electromotive force of the ultra-high-speed permanent magnet synchronous motor under the dq axis usually does not change much under the steady-state condition, so it can be regarded as an interference term. The stator resistance R s Compared with the motor stator inductance L s The equivalent impedance is small and can be ignored, so the LC filter and the motor winding inductance together form an LCL filter circuit.

[0082] The cause of system resonance is a pair of conjugate poles on the imaginary axis after the LC filter is added. Therefore, the PI controller and PWM steps in the current loop are ignored, and only the LCL filter system is analyzed. Since the permanent magnet synchronous motor is symmetrical along the d-q axis, only the q axis is analyzed.

[0083] The mathematical model of PMSM and LC filter in the synchronous rotating coordinate system obtained in step 1 is used to establish the system block diagram of the s-domain q-axis current loop equivalent capacitor current feedback active damping loop as shown in the following figure: Figure 2 As shown, I l (s) represents the s-domain filter inductor current, and the s-domain motor current I q (s) multiplied by the motor winding current feedback gain G s (s) and fed back to the s-domain LC filter input voltage U fq (s), and the system transfer function G of the equivalent capacitor current feedback active damping loop of the s-domain q-axis current loop is obtained. LCL-R (s) can be expressed as shown in the following formula (4):

[0084]

[0085] Among them: G d (s) indicates digital delay.

[0086] The forward path generates 1.5T s Digital delay, T s is the sampling period. The delay function is expressed as shown in the following formula (5):

[0087]

[0088] If we refer to the traditional active damping solution, the feedback gain is designed as a proportional coefficient, that is, G s (s) = K, and the effect of suppressing resonance cannot be achieved at this time. By analyzing the system transfer function G LCL-R From the denominator of (s), we can see that if we want to reconfigure the pole position to the left half of the imaginary axis, we need to add a second-order term. Therefore, we define the winding current feedback gain G s (s) = Kr C f L f s 2 , the system transfer function G of the equivalent capacitor current feedback active damping loop of the s-domain q-axis current loop is obtained LCL-R (s) can be expressed as shown in the following formula (6):

[0089]

[0090] Among them: K r is the equivalent capacitor current feedback coefficient.

[0091] Step 3: Design the equivalent capacitor current feedback coefficient in the winding current feedback gain in step 2 to obtain the motor winding current feedback gain G s The value of (s) is:

[0092] The motor winding current feedback gain G s (s) is equivalent to the capacitance current feedback loop coefficient K r The active damping suppression of motor winding current feedback is further simplified to the equivalent capacitor current feedback active damping control strategy. The system control block diagram is as follows: Figure 3 As shown, K r is the equivalent capacitor current feedback coefficient.

[0093] The direct discretization process suffers from zero-pole mismatch or frequency deviation, which leads to inconsistency between the expected control performance and the actual control performance. Therefore, analysis based on the z-domain discrete model can more accurately simulate the actual situation.

[0094] First, Figure 3 The transfer function is decomposed, and the filter inductor voltage U l(s) To the motor current I q(s) The transfer function is expressed as G1(s), the filter inductor voltage U l(s) To the filter capacitor voltage U c(s) The transfer function is expressed as G2(s), the filter inductor voltage U l(s) Current to filter capacitor I c(s) The transfer function is expressed as G3(s). The s-domain model of the equivalent capacitor current feedback active damping control system is obtained as Figure 4 shown.

[0095] Filter inductor voltage U l(s) To the motor current I q(s) The s-domain transfer function is shown in the following formula (7):

[0096]

[0097] where ω ris the resonant angular frequency, which is expressed as follows:

[0098]

[0099] where f r is the resonant frequency.

[0100] Filter inductor voltage U l(s) To the filter capacitor voltage U c(s) The s-domain transfer function is shown in the following formula (9):

[0101]

[0102] Filter inductor voltage U l(s) Current to filter capacitor I c(s) The s-domain transfer function is shown in the following formula (10):

[0103]

[0104] The zero-order hold discretization method is used to discretize G 1(s) , G 2(s) and G 3(s) Discretize, G 1(s) , G 2(s) and G 3(s) The discrete domain expression G 1(z) , G 2(z) and G 3(z) As shown in the following formulas (11), (12), and (13):

[0105]

[0106] Digitally controlled delay is expressed in the discrete domain using Z -1 According to G 1(z) , G 2(z) and G 3(z) The z-domain model of the equivalent capacitor current feedback active damping control system can be obtained as follows: Figure 5 As shown, the open-loop transfer function of the discrete domain system with active damping control based on equivalent capacitor current feedback is shown in the following formula (14):

[0107]

[0108] Extract T in formula (14) op(z) The denominator of is shown in the following formula (15):

[0109] Den(z)=sinω r T s +(L f -K r cosω r Ts )z+(K r -2L f cosω r T s )z 2 +L f z 3 (15)

[0110] According to Jurry's criterion, the open-loop transfer function T op(z) The stability condition is (16)

[0111]

[0112] Due to the existence of digital control delay, the equivalent capacitor current feedback loop coefficient K r It is equivalent to a virtual impedance in parallel with the capacitor, whose size is Z eq The system block diagram after equivalent virtual impedance is as follows Figure 6 As shown, the virtual impedance expression is as shown in the following formula (17):

[0113]

[0114] To study Z eq The impact on system stability can be expressed in complex form:

[0115] Z eq (ω)=R eq (ω)+jX eq (ω) (18)

[0116] Where: ω=2πf s , f s is the sampling frequency, R eq and X eq As shown in the following formulas (19) and (20):

[0117] R eq (ω)=K s cos(1.5ωT s ) (19)

[0118] X eq (ω)=K s sin(1.5ωT s ) (20)

[0119] in According to R eq and X eq The frequency characteristics show that when 0 <f r <f s / 6 o'clock, R eq >0; when fs / 6 <f r <f s / 4, R eq <0, the negative real part will make the system become a non-minimum phase system, which may cause system instability, so the resonant frequency f must be guaranteed. r Less than f s / 6.

[0120] In addition, K r The system output impedance should have sufficient phase margin (P M ), the phase margin value range is generally [30°, 60°]. Therefore, the following formula (21) must also be satisfied:

[0121] 30°≤P M ≤60° (21)

[0122] According to the stability condition of Juli criterion, the designed equivalent capacitance current feedback coefficient K r It is expressed as the following formula (22):

[0123]

[0124] So the motor winding current feedback gain G s (s) is expressed as shown in the following formula (23):

[0125]

[0126] Recommended choice

[0127] Example 3

[0128] The parameters of the LC filter are set according to Table 1 below, and the method proposed in Example 2 is simulated.

[0129] Table 1 LC filter parameters

[0130] parameter Numerical <![CDATA[Filter capacitor C f > <![CDATA[3×10 -5 F]]> <![CDATA[Filter inductor L f > <![CDATA[2×10 -3 mH]]> <![CDATA[Winding inductance L s > 0.1mH

[0131] Figure 7 is a Bode diagram of the open-loop transfer function of the q-axis current control loop without adopting the method of the present invention; Figure 8 It is a Bode diagram of the open-loop transfer function of the q-axis current control loop using the method of the present invention. Figure 7 and Figure 8 The parameters of the LC filter used in the simulation are shown in Table 1; Figure 7 The mid-resonance peak a point and Figure 8It can be found at point b of the middle resonance peak that the amplitude of point b is significantly lower than that of point a. The amplitude is determined by the resonance. The larger the resonance, the higher the amplitude. By comparison, it can be seen that the method of the present invention can significantly suppress the LCL resonance. At the same time, since the method of the present invention does not require the introduction of additional resistors, it will not increase power consumption.

Claims

1. A resonance suppression method for an ultra-high-speed permanent magnet synchronous motor with an LC filter, characterized by: The specific steps include: Step 1: Build an ultra-high-speed permanent magnet synchronous motor with an LC filter. d - q Axis mathematical model; The specific process of step 1 is: The mathematical model of the permanent magnet synchronous motor in the synchronous rotating coordinate system is shown in the following formula (1): （1） in: U d 、 U q Motor end d - q Shaft voltage, I d 、 I q For the motor end d - q Shaft current, R s is the motor stator resistance, L s is the motor stator inductance; ω e is the rotor angular velocity, Ψ f is the permanent magnet flux; The mathematical model of the LC filter in the synchronous rotating coordinate system is shown in the following formulas (2) and (3): （2） （3） in, U fd 、 U fq They are the LC filter input terminals d - q Shaft voltage, I fd 、 I fq LC filter input d - q Shaft current, L f is the filter inductance, C f is the filter capacitor; Step 2: Design the motor winding current feedback gain using the mathematical model of the ultra-high-speed permanent magnet synchronous motor established in step 1, and obtain the system transfer function of the equivalent capacitive current feedback active damping loop based on the feedback gain; the specific process of step 2 is as follows: Since permanent magnet synchronous motor d - q Axis symmetry, only q The mathematical model of PMSM and LC filter in the synchronous rotating coordinate system obtained in step 1 is obtained. s domain q System transfer function of the shaft current loop equivalent capacitive current feedback active damping loop G LCL-R (s), as shown in the following formula (4): （4） in: G d (s) represents digital delay, G s (s) represents the motor winding current feedback gain, I q (s) indicates the s domain q Shaft motor current, U fq (s) indicates s Domain LC filter input q Shaft voltage; The forward path generates 1.5 T s Digital delay, T s is the sampling period, and the delay function is expressed as the following formula (5): （5） Define the motor winding current feedback gain ,get s domain q System transfer function of the shaft current loop equivalent capacitive current feedback active damping loop G LCL-R (s) is expressed as the following formula (6): （6） in: K r is the equivalent capacitor current feedback coefficient; Step 3: Design the equivalent capacitor current feedback coefficient in the winding current feedback gain in step 2, and calculate the motor winding current feedback gain based on the feedback coefficient. G s the value of (s); The specific process of step 3 is: The filter inductor voltage U l(s) To motor current I q(s) The transfer function is expressed as G 1(s), filter inductor voltage U l(s) To filter capacitor voltage U c(s) The transfer function is expressed as G 2(s), filter inductor voltage U l(s) Current to filter capacitor I c(s) The transfer function is expressed as G 3(s), establish the equivalent capacitance current feedback active damping control system s Domain model, filter inductor voltage U l(s) To motor current I q(s) of s The domain transfer function is shown in the following formula (7): （7） in, ω r is the resonant angular frequency, which is expressed as follows: （8） in, f r is the resonant frequency; Filter inductor voltage U l(s) To filter capacitor voltage U c(s) of s The domain transfer function is shown in the following formula (9): （9） Filter inductor voltage U l(s) Current to filter capacitor I c(s) of s The domain transfer function is shown in the following formula (10): (10) The zero-order hold discretization method is used to G 1(s) 、 G 2(s) and G 3(s) To discretize, G 1(s) 、 G 2(s) and G 3(s) The discrete domain expression of G 1(z) 、 G 2(z) and G 3(z) As shown in the following formulas (11), (12), and (13): （11） （12） （13） Digitally controlled delay is used in the discrete domain Z -1 Said that according to G 1(z) 、 G 2(z) and G 3(z) The open-loop transfer function of the discrete domain system with equivalent capacitor current feedback active damping control is shown in the following formula (14): （14） Extract formula (14) T op(z) The denominator of is shown in the following formula (15): （15） Determine the open-loop transfer function based on the Jully criterion T op(z) The stability condition is shown in the following formula (16): (16) Due to the existence of digital control delay, the equivalent capacitor current feedback loop coefficient K r Equivalent to a virtual impedance in parallel with the capacitor Z eq , virtual impedance Z eq The expression is shown in the following formula (17): （17） The virtual impedance Z eq Expressed in complex form, it is shown in the following formula (18): （18） in, , is the sampling frequency, R eq and X eq As shown in the following formulas (19) and (20): （19） （20） in, , when 0< f r < f s / 6 o'clock, R eq >0; when f s / 6< f r < f s / 4 o'clock, R eq <0; also, K r The system output impedance should have sufficient phase margin in the resonant frequency band P M The phase margin range is , so the following formula (21) must be satisfied: （21） According to the stability condition of Juli criterion, the equivalent capacitance current feedback coefficient K r It is expressed as the following formula (22): （22） So the motor winding current feedback gain G s (s) is expressed as the following formula (23): （23）。 2. The resonance suppression method of an ultra-high-speed permanent magnet synchronous motor with an LC filter according to claim 1, characterized in that: In step 3, select , where 0< f r < f s / 6.

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