Resonance suppression method for super-high-speed permanent magnet synchronous motor considering digital delay control

Abstract

The present invention discloses a method for suppressing resonance in an ultra-high-speed permanent magnet synchronous motor using digital delay control. The method comprises 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 the motor current feedback gain based on the mathematical model of the ultra-high-speed permanent magnet synchronous motor with an LC filter obtained in Step 1; and Step 3: connecting a series lead phase compensator based on the motor current feedback gain obtained in Step 2. This method solves the problem of phase lag in the control effect of active damping caused by digital delay, thereby improving the stability of the motor system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of high-speed permanent magnet synchronous motor control, and relates to a resonance suppression method for a super-high-speed permanent magnet synchronous motor considering digital delay control. BACKGROUND

[0002] The high-speed permanent magnet synchronous motor has the advantages of high power density, high efficiency, compact structure and good dynamic characteristics, and has important research prospects and wide application value in the fields of military, aerospace, industry, medical treatment and civil use. Due to the high current frequency and small inductance of the high-speed permanent magnet synchronous motor, there are obvious switching frequency harmonic components in the stator current, which increases the motor loss and reduces the efficiency. In order to solve this problem, an LC type output filter is added in the traditional driving 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 affects 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 driving system with an LC filter.

[0003] The active damping technology based on motor current feedback can directly utilize the original current sensor in the motor control system without additional sensors 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 resistance, but a virtual impedance related to frequency. When the resonance frequency of the system is in the frequency range of negative damping characteristics, the system becomes a non-minimum phase system, which cannot effectively suppress resonance, and even leads to system instability. SUMMARY

[0004] The purpose of the application is to provide a resonance suppression method for a super-high-speed permanent magnet synchronous motor considering digital delay control, which solves the problem of phase lag of the control effect of active damping caused by digital delay.

[0005] The technical solution adopted by the application is a resonance suppression method for a super-high-speed permanent magnet synchronous motor considering digital delay control, which specifically includes the following steps:

[0006] Step 1: establishing a d-q axis mathematical model of a super-high-speed permanent magnet synchronous motor with an LC filter;

[0007] Step 2: designing motor current feedback gain through the mathematical model of the super-high-speed permanent magnet synchronous motor with an LC filter obtained in step 1;

[0008] Step 3: connecting a phase lead compensator in series on the basis of the motor current feedback gain obtained in step 2.

[0009] The application also has the following characteristics:

[0010] The specific process of step 1 is as follows:

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

[0012]

[0013] Wherein, U sd , U sq are the d-q axis voltages at the motor end, I sd , I sq are the d-q axis currents 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 linkage.

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

[0015]

[0016]

[0017] Wherein, U hd , U hq are the d-q axis voltages at the input end of the LC filter, I hd , I hq are the d-q axis currents at the input end of the LC filter, L h is the filter inductance, C h is the filter capacitance.

[0018] The specific process of step 2 is as follows:

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

[0020]

[0021] Wherein, G s (s) represents the motor current feedback gain, G d (s) represents the digital control delay.

[0022] Forward path generates 1.5T s , T s is the sampling period, the delay function is expressed as shown in the following equation (5):

[0023]

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

[0025]

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

[0027] The specific process of step 3 is:

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

[0029]

[0030] Substitute s=jω into equation (7), and the delay element term e 1.5sTs in equation (7) is expanded and simplified by using Euler formula, and equation (7) is equivalent to a virtual resistance R eq , a virtual inductance X eq and a virtual impedance Z eq in parallel, as shown in the following equation (8):

[0031]

[0032] Wherein, ω=2πf s , f s is the sampling frequency, the expressions of R eq (ω) and X eq (ω) are shown in the following equation (9):

[0033]

[0034] In step 3, the resistive component R eq (ω) in the virtual impedance Z eq shows positive damping characteristics in the frequency band of 0~f s / 6, and shows negative damping characteristics in the frequency band of f s / 6~f sThe phase compensation element G

[0035] In step 3, the phase lead compensation element G p (s) can provide phase compensation in the frequency range of f s / 6, and the transfer function of the element in s domain is shown in equation (10) as follows:

[0036]

[0037] Wherein, K d , a, b are compensation parameters of the element, and K d >0, a>0, b>0.

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

[0039]

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

[0041]

[0042] The compensation element can realize 0-45° phase lead, and the parameter a can be calculated from equation (11), and the frequency point f m corresponding to f s / 6 can be determined from equation (12), so as to design the phase lead compensator.

[0043] In step 3, the equivalent impedance after compensation by adding the phase lead compensation element is shown in equation (13) as follows:

[0044]

[0045] Substitute s=jω into equation (13), and expand and simplify the time delay element term e 1.5sTs in equation (13) by using Euler formula, as shown in equation (14) as follows:

[0046]

[0047] Wherein, the expression of virtual resistance R eq1 (ω) and virtual inductance X eq1 (ω) is shown in equation (15) as follows:

[0048]

[0049] Wherein:

[0050]

[0051] The beneficial effect of the present application is that, compared with the traditional capacitor current feedback and inductance current feedback method, the motor current feedback method adopted by the present application can not measure the capacitor branch current and the inductance branch current, thereby reducing the cost of the control system. Meanwhile, a phase lead compensator is connected in series in the motor current feedback gain loop, so that the virtual resistance demarcation frequency reaches f s / 4, which significantly improves the effective damping area of the motor current feedback active damping strategy, solves the problem of phase lag of the control effect of the active damping caused by the digital delay, and improves the stability of the motor system. The method can compensate for the control delay, improve the effective damping area of the active damping control, and improve the stability of the motor system. BRIEF DESCRIPTION OF DRAWINGS

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

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

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

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

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

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

[0058] The present application will be described in detail below in combination with the drawings and specific embodiments.

[0059] Example 1

[0060] The present application considers a digital delay control method for suppressing resonance of a super-high-speed permanent magnet synchronous motor, wherein the vector control system block diagram used is as shown in the figure Figure 1 The system is formed by three PI regulators, forming a double-loop control of speed loop and current loop. The stator currents i a , i b , i c of the super-high-speed permanent magnet synchronous motor in three-phase stationary coordinate system are detected by the current Hall sensor a , i b , i c Through abc / αβ transformation, the current values i α , i β in two-phase stationary coordinate system are converted α , i β Through αβ / dq transformation, the current values i d , i q in two-phase synchronous rotating coordinate system are converted d The given excitation current i is subtracted from the feedback current i m , and the d-axis voltage u is output through the current loop PI controller m The mechanical angle θ m and the mechanical angular velocity ω p of the super-high-speed permanent magnet synchronous motor are detected by the encoder e The mechanical angle θ e is multiplied by the number of pole pairs n m to convert to the electrical angle θ q , and the electrical angle θ α is input to the αβ / dq transformation, and the given mechanical angular velocity ω is subtracted from the mechanical angular velocity ω β , and the q-axis excitation current i is output through the speed loop PI controller α The excitation current i is subtracted from the feedback current i β , and the q-axis voltage u is output through the current loop PI controller s Two-phase voltages u p , u α-LC in two-phase stationary coordinate system are obtained through dq / αβ transformation β-LC , u α are multiplied by the feedback gain G β (s) and the lead phase compensation G α-LC (s) respectively to obtain u β-LCSubtract, and then through the space vector pulse width modulation (SVPWM) modulation control three-phase inverter (VSI), in VSI and super high speed permanent magnet synchronous motor intermediate series LC filter, finally by three-phase inverter drive super high speed permanent magnet synchronous motor work.

[0061] Embodiment 2

[0062] The present application considers the digital delay control super high speed permanent magnet synchronous motor resonance suppression method, specifically according to the following steps implementation:

[0063] Step 1, the d-q axis mathematical model of the LC filter type super high speed permanent magnet synchronous motor is established;

[0064] Step 2, the motor current feedback gain is designed through the mathematical model of the LC filter type super high speed permanent magnet synchronous motor obtained in step 1;

[0065] Step 3, the lead phase compensator is connected in series on the basis of the motor current feedback gain obtained in step 2;

[0066] Embodiment 3

[0067] The specific process of step 1 is:

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

[0069]

[0070] Wherein, U sd , U sq is the d-q axis voltage at the motor end, I sd , I sq is the d-q 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 linkage.

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

[0072]

[0073] Wherein: U hd , U hq is the d-q axis voltage at the input end of the LC filter, I hd , I hq is the d-q axis current at the input end of the LC filter, L h is the filter inductance, C h is the filter capacitance.

[0074] Example 4

[0075] The specific process of Step 2 is:

[0076] The equivalent impedance of the winding resistance of HSPMSM is smaller than the winding inductance in high-speed operation state, which can be ignored. The d-q axis back EMF usually changes little in steady state, which can be treated as a disturbance term. Therefore, the LC filter will form an LCL filter circuit with the motor inductance.

[0077] The reason for system resonance is a pair of conjugate poles on the imaginary axis after adding the LC filter. Therefore, the PI controller and PWM element in the current loop are ignored, and only the LCL filter system is analyzed. Since the d-q axis is symmetrical, only the d-axis is analyzed.

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

[0079]

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

[0081] The forward path produces a digital delay of 1.5T s , and T s is the sampling period. The delay function is represented as shown in the following formula (5):

[0082]

[0083] If the traditional active damping scheme is used, the motor current feedback gain is designed as a proportional coefficient, i.e. G s (s) = K, which cannot achieve the effect of suppressing resonance. By analyzing the denominator of the system transfer function G LC (s), it can be seen that to reconfigure the pole position to the left half of the imaginary axis, a second-order term needs to be added. Therefore, the motor current feedback gain G s (s) = K s s 2, the system transfer function G LC (s) of the motor current feedback active damping control of the d-axis current loop in s domain can be obtained

[0084]

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

[0086] The Bode diagram of the system transfer function G LC (s) of the motor current feedback active damping control of the d-axis current loop in s domain is shown in Figure 3 As can be seen, the amplitude at the resonance frequency gradually decreases as K s increases from 0.1 to 1.2, so the present application takes K s =1.2, so G s (s) = 1.2s 2 .

[0087] Example 5

[0088] The specific process of step 3 is as follows:

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

[0090]

[0091] Substitute s = jω into formula (7), and expand and simplify the time delay term e 1.5sTs in formula (7) by using Euler formula, so that formula (7) can be finally equivalent to a virtual resistance R eq , a virtual inductance X eq and a virtual impedance Z eq in parallel, as shown in the following formula (8):

[0092]

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

[0094]

[0095] According to formula (9), R eq (ω) and Xeq (ω) with frequency as shown in Fig. 1. The virtual impedance Z Figure 5 eq The resistive component R eq (ω) in the virtual impedance Z s (ω) is positive damping in the frequency range of (0~f s / 6) and negative damping in the frequency range of (f s / 6~f / 4). The negative damping characteristic will make the system become a non-minimum phase system, causing the system to be unstable.

[0096] The phase lead compensation element G p (s) can provide a certain phase compensation function in the frequency range where the resonance frequency is greater than f s / 6. The transfer function expression of the element in the s domain is shown in the following formula (10):

[0097]

[0098] wherein K d , a, b are compensation parameters of the element, satisfying K d >0, a>0, b>0. The parameter K d is used to adjust the influence of the element on the amplitude response of the system. The change of the value of K d does not affect the phase compensation function of the element, but will change the amplitude response of the feedback branch. In order to maintain the low frequency gain on the original system branch, it is recommended that K d =1.

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

[0100]

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

[0102]

[0103] The compensation element can realize a phase lead of 0~45°, so the maximum phase angle compensation Ψ m is 45°. The parameter a can be calculated from formula (11), and the frequency point f m corresponds to f s / 6. The parameter b can be determined from formula (12), so the lead phase compensator can be designed.

[0104] The size of the equivalent impedance after compensation by adding the phase lead compensation element is shown in the following formula (13):

[0105]

[0106] Similarly, substitute s=jω into formula (13), and change the delay link term e in formula (13) to 1.5sTs Euler's formula is used to expand and simplify the 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), 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, significantly improving 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 Value Motor current feedback coefficient K s ]] 1.2 Filter capacitor C h ]]> 3 x 10 -5 F]] Filter inductance L h ]]> 2 x 10 -3 mH Sampling frequency f s ]]> 20 kHz Phase lead compensator parameter a 5.83 Phase lead compensator parameter b 2 x 10 -5 ]] Phase lead compensator parameter K d ]]> 1

[0117] Figure 5 is the virtual resistance R without phase lead compensator eq (ω) and virtual reactance X eq (ω) characteristic diagram; Figure 6 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 in eq (ω) and R eq1 (ω) can be found, Figure 5 the resistive component R in eq (ω) shows positive damping characteristics in the frequency band of (0~f s / 6), and the critical frequency is f s / 6, while Figure 6 the resistive component R in eq1 (ω) shows positive damping characteristics in the frequency band of (0~f s / 4), and the critical frequency is 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 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; Step 2, designing the motor current feedback gain using the mathematical model of the ultra-high-speed permanent magnet synchronous motor with LC filter obtained in step 1; The specific process of step 2 is: The mathematical model of HSPMSM and LC filter in the synchronous rotating coordinate system obtained in step 1 is s Established in the domain d Axis current loop motor current feedback active damping control system, s Domain motor current I sd (s) multiplied by the motor current feedback gain G s (s) and feedback to s Domain LC filter input voltage U hd (s) on, get s domain d System transfer function of shaft current loop motor current feedback active damping control G LC (s), as shown in the following formula (1): （1） in, G s (s) represents the motor current feedback gain, G d (s) represents digital control delay; L s is the motor stator inductance; L h is the filter inductance, C h is the filter capacitor; The forward path generates 1.5 T s Digital delay, T s is the sampling period, and the delay function is expressed as shown in the following formula (2): （2） Define the motor current feedback gain G s (s)= K s s 2 ,get s domain d System transfer function of shaft current loop motor current feedback active damping control G LC (s), as shown in the following formula (3): （3） in: K s is the motor current feedback coefficient; Step 3: Connecting a leading phase compensator in series based on the motor current feedback gain obtained in step 2; the specific process of step 3 is: due to the existence of digital control delay, the motor current feedback loop is equivalent to a virtual impedance in parallel with the capacitor. Z eq , the expression is shown in the following formula (4): （4） Will s = jω Substitute into formula (4) and calculate the delay link term in formula (4) e 1.5sTs Using Euler's formula to expand and simplify, Equation (4) is equivalent to a virtual resistor R eq Virtual Inductor X eq Virtual impedance formed by parallel connection Z eq As shown in the following formula (5): （5） in, ω =2π f s , f s is the sampling frequency, R eq ( ω )and X eq ( ω ) is expressed as follows: （6）； In step 3, the phase advance compensation link G p (s) can be used at a resonant frequency greater than f s / 6 frequency range to provide phase compensation, s The transfer function expression of this link in the domain is shown in the following formula (7): （7） in, K d 、 a 、 b These are the compensation parameters of this link, satisfying K d >0, a >0, b >0.

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: Synchronous rotating coordinate system d - q The mathematical model of the down-axis ultra-high-speed permanent magnet synchronous motor is shown in the following formula (8): （8） in, U sd 、 U sq For the motor end d - q Shaft voltage, I sd 、 I sq 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 (9) and (10): （9） （10） in, U hd 、 U hq LC filter input d - q Shaft voltage, I hd 、 I hq LC filter input d - q Shaft current, 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 1, characterized in that: In step 3, the virtual impedance Z eq The resistive component in R eq ( ω ) in 0~ f s / 6 frequency band shows positive damping characteristics, f s / 6~ f s It exhibits negative damping characteristics in the / 4 frequency band.

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: In step 3, the parameters a Used to determine the maximum phase angle compensation Ψ m , as shown in the following formula (11): （11） parameter b To determine the maximum compensation Ψ m The corresponding frequency point f m , as shown in the following formula (12): （12） This compensation link can achieve a phase advance of 0~45°. The parameter can be calculated from formula (11): a , frequency point f m correspond f s / 6, the parameter can be determined by formula (12) b , from which the leading phase compensator can be designed.

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 equivalent impedance after adding the phase advance compensation link is shown in the following formula (13): （13） Will s = jω Substitute into formula (13) and calculate the delay link term in formula (13) e 1.5sTs Euler's formula is used to expand and simplify the formula (14): （14） Among them, the virtual resistance R eq1 ( ω ) and virtual inductance X eq1 ( ω ) is expressed as follows: （15） in: （16） in, a 、 b Both are phase advance compensation links G p (s) compensation parameters.

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