Ultrahigh-speed permanent magnet synchronous motor resonance suppression method considering digital delay control

Abstract

The invention discloses an ultra-high-speed permanent magnet synchronous motor resonance suppression method considering digital delay control. The method specifically comprises the following steps: step 1, establishing a d-q axis mathematical model of an ultra-high-speed permanent magnet synchronous motor with an LC filter; step 2, designing a motor current feedback gain through the mathematical model of the ultra-high-speed permanent magnet synchronous motor with the LC filter obtained in the step 1; and step 3, connecting a lead phase compensator in series on the basis of the motor current feedback gain obtained in the step 2. The problem of phase lag of the control effect of active damping caused by digital delay is solved, and the stability of a motor system is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of high-speed permanent magnet synchronous motor control, and relates to an ultra-high-speed permanent magnet synchronous motor resonance suppression method considering digital delay control. Background Art

[0002] High-speed permanent magnet synchronous motors have the advantages of high power density, high efficiency, compact structure and good dynamic characteristics. They have important research prospects and wide application value in the fields of military, aerospace, industry, medical, and civil applications. Due to the high current frequency and small inductance of high-speed permanent magnet synchronous motors, there are obvious switching frequency harmonic components in the stator current, which leads to increased motor losses and reduced efficiency. To solve this problem, an LC output filter is added to the traditional drive topology to eliminate the harmonic components of the motor current. However, the LC filter and the motor stator inductance form a third-order LCL filter structure, which not only increases the order of the system model, but also its inherent resonance peak will affect the stability of the system operation. Therefore, it is particularly important to explore the resonance suppression strategy of the high-speed permanent magnet synchronous motor drive system with LC filter.

[0003] Active damping technology based on motor current feedback does not require additional sensors, and can directly use the existing current sensors in the motor control system to achieve the effect of suppressing resonance. However, due to the influence of digital control delay, the feedback gain is no longer equivalent to a pure resistor, but a frequency-dependent virtual impedance. When the resonant frequency of the system appears in the negative damping characteristic frequency range, the system will become a non-minimum phase system, which cannot effectively suppress resonance and may even cause system instability. Summary of the invention

[0004] The purpose of the present invention is to provide a method for suppressing resonance of an ultra-high-speed permanent magnet synchronous motor taking into account digital delay control, thereby solving the problem that digital delay causes phase lag in the control effect of active damping.

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

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

[0007] Step 2, designing the motor current feedback gain by using the mathematical model of the ultra-high-speed permanent magnet synchronous motor with LC filter obtained in step 1;

[0008] Step 3, a leading phase compensator is connected in series based on the motor current feedback gain obtained in step 2.

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

[0010] The specific process of step 1 is:

[0011] The mathematical model of the ultra-high-speed permanent magnet synchronous motor under the dq axis of the synchronous rotating coordinate system is shown in the following formula (1):

[0012]

[0013] Among them, U sd , U sq is the dq axis voltage at the motor end, I sd ,I sq is the dq axis current at the motor end, 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;

[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]

[0017] Among them, U hd , U hq is the dq axis voltage at the input of the LC filter, I hd ,I hq is the dq axis current at the input end of the LC filter, L h is the filter inductance, C h is the filter capacitor.

[0018] The specific process of step 2 is:

[0019] Based on the mathematical model of HSPMSM and LC filter in the synchronous rotating coordinate system obtained in step 1, a d-axis current loop motor current feedback active damping control system is established in the s-domain, and the s-domain motor current I sd (s) multiplied by the motor current feedback gain G s (s) and fed back to the s-domain LC filter input voltage U hd (s), the system transfer function G of the s-domain d-axis current loop motor current feedback active damping control is obtained LC (s), as shown in the following formula (4):

[0020]

[0021] Among them, G s (s) represents the motor current feedback gain, G d (s) represents digital control delay;

[0022] The forward path generates 1.5T s Digital delay, T s is the sampling period, and the delay function is expressed as shown in the following formula (5):

[0023]

[0024] Define the motor current feedback gain G s (s) = K s s 2 , the system transfer function G of the s-domain d-axis current loop motor current feedback active damping control is obtained LC (s), as shown in the following formula (6):

[0025]

[0026] Among them, K s is the motor current feedback coefficient.

[0027] The specific process of step 3 is:

[0028] Due to the existence of digital control delay, the motor current feedback loop is equivalent to a virtual impedance Z in parallel with the capacitor. eq , the expression is shown in the following formula (7):

[0029]

[0030] Substitute s=jω into formula (7) and calculate the delay term e in formula (7): 1.5sTs Using the Euler formula to expand and simplify, equation (7) is equivalent to the virtual resistance R eq Virtual InductorX eq The virtual impedance Z formed by parallel connection eq As shown in the following formula (8):

[0031]

[0032] Where ω=2πf s , f s is the sampling frequency, R eq (ω) and X eq The expression of (ω) is shown in the following formula (9):

[0033]

[0034] In step 3, the virtual impedance Z eq The resistive component R eq (ω) in 0~f s / 6 frequency band shows positive damping characteristics, at f s / 6~f sIt exhibits negative damping characteristics in the / 4 frequency band.

[0035] In step 3, the phase advance compensation link G p (s) can be greater than the resonant frequency f s / 6 frequency range, the transfer function of this link in the s domain is shown in the following formula (10):

[0036]

[0037] Among them, K d , a, b are the compensation parameters of this link, satisfying K d >0, a>0, b>0.

[0038] In step 3, parameter a is used to determine the maximum phase angle compensation Ψ m , as shown in the following formula (11):

[0039]

[0040] Parameter b is used to determine the maximum compensation amount Ψ m The corresponding frequency point f m , as shown in the following formula (12):

[0041]

[0042] This compensation link can achieve a phase advance of 0 to 45°. The parameter a and the frequency point f can be calculated by equation (11). m Corresponding to f s / 6, the parameter b can be determined by equation (12), and the leading phase compensator can be designed accordingly.

[0043] In step 3, the equivalent impedance after adding the phase advance compensation link is as shown in the following formula (13):

[0044]

[0045] Substitute s=jω into formula (13), and change the delay term e in formula (13) to 1.5sTs The Euler formula is used to expand and simplify as shown in the following formula (14):

[0046]

[0047] Among them, the virtual resistance R eq1 (ω) and virtual inductance X eq1 The expression of (ω) is shown in the following formula (15):

[0048]

[0049] in:

[0050]

[0051] The beneficial effect of the present invention is that, compared with the conventional capacitor current feedback and inductor current feedback methods, the motor 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, an advanced phase compensator is connected in series in the motor current feedback gain loop to make the virtual resistance boundary frequency reach f s / 4, significantly improving the effective damping area of ​​the motor current feedback active damping strategy, solving the problem of phase lag caused by digital delay in the control effect of active damping, and improving the stability of the motor system. This method can compensate for control delay, improve the effective damping area of ​​active damping control, and improve the stability of the motor system. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a block diagram of a vector control system used in the ultra-high-speed permanent magnet synchronous motor resonance suppression method considering digital delay control of the present invention;

[0053] Figure 2 It is a system block diagram of the motor current feedback active damping control in the ultra-high-speed permanent magnet synchronous motor resonance suppression method considering digital delay control of the present invention;

[0054] Figure 3 It is a Bode diagram of the transfer function of the s-domain d-axis current loop motor current feedback active damping control system in the ultra-high-speed permanent magnet synchronous motor resonance suppression method considering digital delay control of the present invention;

[0055] Figure 4 It is a system block diagram after the motor feedback coefficient is equivalent to virtual impedance in the ultra-high-speed permanent magnet synchronous motor resonance suppression method considering digital delay control of the present invention;

[0056] Figure 5 It is the virtual resistance R without adding the phase advance compensator in the ultra-high-speed permanent magnet synchronous motor resonance suppression method considering digital delay control of the present invention. eq (ω) and virtual reactance X eq (ω) characteristic diagram;

[0057] Figure 6 It is the virtual resistance R of the phase advance compensator added in the ultra-high-speed permanent magnet synchronous motor resonance suppression method considering digital delay control of the present invention. eq1 (ω) and virtual reactance X eq1 (ω) characteristic diagram. DETAILED DESCRIPTION

[0058] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0059] Example 1

[0060] The present invention considers a method for suppressing resonance of an ultra-high-speed permanent magnet synchronous motor using digital delay control, wherein the vector control system block diagram used is as follows: Figure 1 As shown in the figure, the system consists of three PI regulators to form 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 the 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 d-axis voltage is output through the current loop PI controller. 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 the αβ / dq transformation, given the mechanical angular velocity and mechanical angular velocity ω m The q-axis excitation current is output through the speed loop PI controller Excitation current With the feedback current i q The q-axis voltage is output through the current loop PI controller. After dq / αβ transformation, the two-phase voltage u in the two-phase stationary coordinate system is obtained α 、u β , change i α and i β Multiply by the feedback gain G s (s) and leading phase compensation G p (s) get u α-LC and u β-LC , will u α 、u β with u α-LC and u β-LCSubtract, and then control the three-phase inverter (VSI) through space vector pulse width modulation (SVPWM), connect an LC filter in series between the VSI and the ultra-high-speed permanent magnet synchronous motor, and finally the ultra-high-speed permanent magnet synchronous motor is driven by the three-phase inverter.

[0061] Example 2

[0062] The present invention considers the resonance suppression method of an ultra-high-speed permanent magnet synchronous motor with digital delay control, which is specifically implemented according to the following steps:

[0063] Step 1, establishing a dq axis mathematical model of an ultra-high-speed permanent magnet synchronous motor with an LC filter;

[0064] Step 2, designing the motor current feedback gain by using the mathematical model of the ultra-high-speed permanent magnet synchronous motor with LC filter obtained in step 1;

[0065] Step 3, connecting a leading phase compensator in series based on the motor current feedback gain obtained in step 2;

[0066] Example 3

[0067] The specific process of step 1 is:

[0068] The mathematical model of the ultra-high-speed permanent magnet synchronous motor in the synchronous rotating coordinate system is shown in the following formula (1):

[0069]

[0070] Among them, U sd , U sq is the dq axis voltage at the motor end, I sd ,I sq is the dq axis current at the motor end, 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.

[0071] The mathematical model of the LC filter in the synchronous rotating coordinate system is shown in the following formulas (2) and (3):

[0072]

[0073] Among them: U hd , U hq is the dq axis voltage at the input of the LC filter, I hd ,I hq is the dq axis current at the input end of the LC filter, L h is the filter inductance, C h is the filter capacitor.

[0074] Example 4

[0075] The specific process of step 2 is:

[0076] When HSPMSM is running at high speed, the equivalent impedance of the winding resistance is smaller than that of the winding inductance, so it can be ignored. In the steady state, the dq-axis back electromotive force of HSPMSM usually does not change much and can be regarded as an interference term. Therefore, the LC filter will form an LCL filter circuit together with the motor inductance.

[0077] The reason for the system resonance is a pair of conjugate poles on the imaginary axis after adding the LC filter. Therefore, the PI controller and PWM links in the current loop are ignored, and only the LCL filter system is analyzed. Due to the dq axis symmetry, only the d axis is analyzed.

[0078] The mathematical model of HSPMSM and LC filter in the synchronous rotating coordinate system obtained in step 1 is used to establish the system block diagram of d-axis current loop motor current feedback active damping control in s domain as shown in the figure. Figure 2 As shown, the s-domain motor current I sd (s) multiplied by the motor current feedback gain G s (s) and fed back to the s-domain LC filter input voltage U hd (s), the system transfer function G of the s-domain d-axis current loop motor current feedback active damping control is obtained LC (s) can be expressed as shown in the following formula (4):

[0079]

[0080] Where: G s (s) represents the motor current feedback gain, G d (s) represents digital control delay.

[0081] 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):

[0082]

[0083] If we refer to the traditional active damping solution, the motor current feedback gain is designed as a proportional coefficient, i.e. G s (s) = K, and the resonance suppression effect cannot be achieved at this time. By analyzing the system transfer function G LC It can be seen from the denominator of (s) 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, the motor current feedback gain G is defined s (s) = K s s 2, the system transfer function G of the s-domain d-axis current loop motor current feedback active damping control is obtained LC (s) can be expressed as shown in the following formula (6):

[0084]

[0085] Where: K s is the motor current feedback coefficient.

[0086] Plot the system transfer function G of the s-domain d-axis current loop motor current feedback active damping control LC (s) Figure 3 As shown, it can be seen that with the increase of K s In the process of increasing from 0.1 to 1.2, the amplitude at the resonant frequency gradually decreases, so the invention takes K s =1.2, so G s (s)=1.2s 2 .

[0087] Example 5

[0088] The specific process of step 3 is:

[0089] Due to the existence of digital control delay, the motor current feedback loop is equivalent to a virtual impedance connected in parallel with the capacitor, whose size is Z eq The system block diagram after equivalent to virtual impedance is as follows Figure 4 As shown, the expression is as shown in the following formula (7):

[0090]

[0091] Substitute s=jω into formula (7) and calculate the delay term e in formula (7): 1.5sTs By expanding and simplifying the Euler formula, equation (7) can be equivalent to the virtual resistance R eq Virtual InductorX eq The virtual impedance Z formed by parallel connection eq As shown in the following formula (8):

[0092]

[0093] Where ω=2πf s , f s is the sampling frequency, R eq (ω) and X eq The expression of (ω) is shown in the following formula (9):

[0094]

[0095] According to formula (9), we can get R eq (ω) and Xeq (ω) Frequency-dependent characteristics such as Figure 5 As shown. Virtual impedance Z eq The resistive component R eq (ω) in (0~f s / 6) frequency band shows positive damping characteristics, and in (f s / 6~f s / 4) shows negative damping characteristics in the frequency band. Negative damping characteristics will turn the system into a non-minimum phase system, causing system instability.

[0096] Phase advance compensation link G p (s) can be greater than the resonant frequency f s / 6 frequency range, a certain phase compensation function is provided. The transfer function expression of this link in the s domain is shown in the following formula (10):

[0097]

[0098] Among them, K d , a, b are the compensation parameters of this link, satisfying K d >0,a>0,b>0, parameter K d Used to adjust the impact of this link on the system amplitude response, K d The change of K does not affect the phase compensation function of this link, but it will change the amplitude response of the feedback branch. In order to maintain the low-frequency gain of the original system branch, it is recommended to d Take 1.

[0099] Parameter a is used to determine the maximum phase angle compensation Ψ m , as shown in the following formula (11):

[0100]

[0101] Parameter b is used to determine the maximum compensation amount Ψ m The corresponding frequency point f m , as shown in the following formula (12):

[0102]

[0103] This compensation link can achieve a phase advance of 0 to 45°, so the maximum phase angle compensation value Ψ m Taking 45°, the parameter a and the frequency point f can be calculated by formula (11). m Corresponding to f s / 6, the parameter b can be determined by equation (12), and the leading phase compensator can be designed accordingly.

[0104] The equivalent impedance after adding the phase advance compensation link is shown in the following formula (13):

[0105]

[0106] Similarly, substitute s=jω into formula (13) and change the delay term e in formula (13) to 1.5sTs The Euler formula is used to expand and simplify as shown in the following formula (14):

[0107]

[0108] Among them, the virtual resistance R eq1 (ω) and virtual inductance X eq1 The expression of (ω) is shown in the following formula (15):

[0109]

[0110] in

[0111]

[0112] According to formula (15), we can get R eq1 (ω) and X eq1 (ω) Frequency-dependent characteristics such as Figure 6 As shown. Virtual impedance Z eq1 The resistive component R eq1 (ω) in (0~f s / 4) The frequency band shows positive damping characteristics, making the boundary frequency reach f s / 4, which significantly improves the effective damping area of ​​the motor current feedback active damping strategy.

[0113] Example 6

[0114] The parameters of the LC filter and the phase lead compensator are set according to Table 1 below, and the methods proposed in Examples 2 to 5 are simulated.

[0115] Table 1 Parameters of LC filter and phase lead compensator

[0116] parameter Numeric <![CDATA[Motor current feedback coefficient K s > 1.2 <![CDATA[Filter capacitor C h > <![CDATA[3×10 -5 F]]> <![CDATA[Filter inductor L h > <![CDATA[2×10 -3 mH]]> <![CDATA[Sampling frequency f s > 20kHz Phase lead compensator parameter a 5.83 Phase lead compensator parameter b <![CDATA[2×10 -5 ]]> <![CDATA[Phase lead compensator parameter K d > 1

[0117] Figure 5 is the virtual resistor R without phase lead compensator eq (ω) and virtual reactance X eq (ω) characteristic diagram; Figure 6 It is the virtual resistor R of the phase advance compensator. eq1 (ω) and virtual reactance X eq1 (ω) characteristic diagram. Figure 5 and Figure 6 The parameters of the LC filter and phase lead compensator used in the simulation are shown in Table 1; Figure 5 and Figure 6The resistive component R eq (ω) and R eq1 (ω) It can be found that Figure 5 The resistive component R eq (ω) in (0~f s / 6) The frequency band shows positive damping characteristics, and the boundary frequency is f s / 6, and Figure 6 The resistive component R eq1 (ω) in (0~f s / 4) The frequency band shows positive damping characteristics, making the boundary frequency reach f s / 4, which significantly improves the effective damping area of ​​the motor current feedback active damping strategy.

Claims

1. A method for suppressing resonance of an ultra-high-speed permanent magnet synchronous motor considering digital delay control, characterized in that: The specific steps include: Step 1, establishing a dq axis mathematical model of an ultra-high-speed permanent magnet synchronous motor with an LC filter; Step 2, designing the motor current feedback gain by using the mathematical model of the ultra-high-speed permanent magnet synchronous motor with LC filter obtained in step 1; Step 3, a leading phase compensator is connected in series based on the motor current feedback gain obtained in step 2.

2. The method for suppressing resonance of an ultra-high-speed permanent magnet synchronous motor considering digital delay control according to claim 1 is characterized in that: The specific process of step 1 is as follows: The mathematical model of the ultra-high-speed permanent magnet synchronous motor under the dq axis of the synchronous rotating coordinate system is shown in the following formula (1): Among them, U sd , U sq is the dq axis voltage at the motor end, I sd ,I sq is the dq axis current at the motor end, 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): Among them, U hd , U hq is the dq axis voltage at the input of the LC filter, I hd ,I hq is the dq axis current at the input end of the LC filter, L h is the filter inductance, C h is the filter capacitor.

3. The method for suppressing resonance of an ultra-high-speed permanent magnet synchronous motor considering digital delay control according to claim 2 is characterized in that: The specific process of step 2 is: Based on the mathematical model of HSPMSM and LC filter in the synchronous rotating coordinate system obtained in step 1, a d-axis current loop motor current feedback active damping control system is established in the s-domain, and the s-domain motor current I sd (s) multiplied by the motor current feedback gain G s (s) and fed back to the s-domain LC filter input voltage U hd (s), the system transfer function G of the s-domain d-axis current loop motor current feedback active damping control is obtained LC (s), as shown in the following formula (4): Among them, G s (s) represents the motor current feedback gain, G d (s) represents digital control delay; The forward path generates 1.5T s Digital delay, T s is the sampling period, and the delay function is expressed as shown in the following formula (5): Define the motor current feedback gain G s (s) = K s s 2 , the system transfer function G of the s-domain d-axis current loop motor current feedback active damping control is obtained LC (s), as shown in the following formula (6): Where: K s is the motor current feedback coefficient.

4. The method for suppressing resonance of an ultra-high-speed permanent magnet synchronous motor considering digital delay control according to claim 3 is characterized in that: The specific process of step 3 is as follows: Due to the existence of digital control delay, the motor current feedback loop is equivalent to a virtual impedance Z in parallel with the capacitor. eq , the expression is shown in the following formula (7): Substitute s=jω into formula (7) and calculate the delay term e in formula (7): 1.5sTs Using the Euler formula to expand and simplify, equation (7) is equivalent to the virtual resistance R eq Virtual InductorX eq The virtual impedance Z formed by parallel connection eq As shown in the following formula (8): Where ω=2πf s , f s is the sampling frequency, R eq (ω) and X eq The expression of (ω) is shown in the following formula (9):

5. The method for suppressing resonance of an ultra-high-speed permanent magnet synchronous motor considering digital delay control according to claim 4 is characterized in that: In step 3, the virtual impedance Z eq The resistive component R eq (ω) in 0~f s / 6 frequency band shows positive damping characteristics, at f s / 6~f s / 4 frequency band shows negative damping characteristics.

6. The method for suppressing resonance of an ultra-high-speed permanent magnet synchronous motor considering digital delay control according to claim 5 is characterized in that: In step 3, the phase advance compensation link G p (s) can be greater than the resonant frequency f s / 6 frequency range, the transfer function of this link in the s domain is shown in the following formula (10): Among them, K d , a, b are the compensation parameters of this link, satisfying K d >0, a>0, b>0.

7. The method for suppressing resonance of an ultra-high-speed permanent magnet synchronous motor taking into account digital delay control according to claim 6 is characterized in that: In step 3, parameter a is used to determine the maximum phase angle compensation value Ψ m , as shown in the following formula (11): Parameter b is used to determine the maximum compensation amount Ψ m The corresponding frequency point f m , as shown in the following formula (12): This compensation link can achieve a phase advance of 0 to 45°. The parameter a and the frequency point f can be calculated by equation (11). m Corresponding to f s / 6, the parameter b can be determined by equation (12), and the leading phase compensator can be designed accordingly.

8. The method for suppressing resonance of an ultra-high-speed permanent magnet synchronous motor considering digital delay control according to claim 7 is characterized in that: In step 3, the equivalent impedance after adding the phase advance compensation link is as shown in the following formula (13): Substitute s=jω into formula (13), and change the delay term e in formula (13) to 1.5sTs The Euler formula is used to expand and simplify as shown in the following formula (14): Among them, the virtual resistance R eq1 (ω) and virtual inductance X eq1 The expression of (ω) is shown in the following formula (15): in:

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