Permanent magnet synchronous motor single current detection sampling delay error suppression method, suppression evaluation method and current control system

Abstract

This invention relates to a method for suppressing sampling delay error in single-current detection of permanent magnet synchronous motors (PMSMs), an evaluation method for suppression, and a current control system. It falls under the technical field of single-current detection in PMSMs. To address the problem that existing technologies cannot effectively suppress sampling delay error in single-current detection of PMSMs, this invention analyzes and confirms the existence of periodic disturbances related to the stator electrical frequency in the sampling delay error. Based on this, a sampling delay error suppression strategy that does not require calculation of the current change rate is proposed. Addressing the resonance phenomenon caused by the coupling between the filtering performance and the observer bandwidth in traditional quasi-resonant extended state observers, the periodic disturbance attenuation transfer function is redesigned, resulting in an improved resonant extended state observer. Based on this improved resonant extended state observer, single-current detection sampling delay error suppression is achieved, and current control is realized.

Description

Technical Field

[0001] This invention belongs to the field of single current detection technology for permanent magnet synchronous motors, specifically relating to a method for suppressing sampling delay error in single current detection of permanent magnet synchronous motors, a suppression evaluation method, and a current control system. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) possess advantages such as fast dynamic response, high power density, and high efficiency, and have been widely used in robotics, electric vehicles, and aerospace. A common approach is to use two or three current sensors at the three-phase output to achieve closed-loop current control, with a current sensor installed at the DC bus for protection. However, current sensors can fail during operation due to environmental corrosion and other factors, leading to a decrease in current sampling accuracy and affecting motor control performance. Reconstructing the three-phase current using a DC bus current sensor for motor current control, known as single-DC-link current sensor control or phase current reconstruction (PCR), can reduce system cost and size and can serve as a fault-tolerant solution for two-phase current sensors. This approach has received extensive research and is already being applied in the home appliance industry.

[0003] However, single-bus current sensor control suffers from situations where the effective voltage vector's duration is insufficient to accurately measure the bus current. This leads to a current reconstruction dead zone at sector boundaries and in low-modulation regions, resulting in severe distortion of the reconstructed current. Modifying the pulse width modulation (PWM) waveform is a common strategy. Kim and Jahns proposed the measurement vector insertion method (MVIM), which inserts a measurement vector to sample the bus current at the end of each space vector PWM (SVPWM) cycle. Gu et al.'s switching-state phase shift (SSPS) method can extend the effective voltage vector's duration by shifting the PWM waveform without changing the duty cycle. In "Independent phasecurrent reconstruction strategy for IPMSM sensorless control without using null switching states," the zero vector is replaced by the effective voltage vector, reducing the reconstruction dead zone but increasing switching losses and total harmonic distortion (THD). Robust current observers have been proposed to suppress the current reconstruction dead zone and improve the current loop bandwidth; however, they still require modification of the PWM. Multiple-branch current sampling eliminates reconfiguration dead zones in sector boundaries and low-modulation regions by moving the bus current sensor to the current branch. However, this method requires changes to the inverter topology and is not suitable for intelligent power modules (IPMs).

[0004] Since single-bus current sensor control samples the bus current and reconstructs the phase current using two effective voltage vectors within a PWM cycle, a sampling delay error arises between the reconstructed current and the ideal phase current sampled at the zero vector. This sampling delay error reduces current accuracy and increases current harmonics. Because the electrical time constant of the motor is much smaller than the mechanical time constant, the current change within a PWM cycle can be considered linear. Based on this, Ha predicts the current value at the end of the cycle by calculating the three-phase current change rate. In "Improved three-phase current reconstruction for induction motor drives with DC-link shunt," after optimizing the bus current sampling points, the current change rate in the two-phase stationary coordinate system is calculated, and the sampling delay error is compensated. However, these methods require multiple integrations, which can easily lead to error accumulation. To address the problem of sampling delay error affecting high-frequency voltage signal injection into sensorless control, Im and Kim proposed a rotating coordinate linear observer for current compensation. However, in the low-modulation region, it cannot provide accurate feedback current information to the observer, and the observation performance deteriorates sharply. Wang et al. calculated the current change rate using a sliding mode observer and proposed a traceback-prediction current correction method (TPCC) to compensate for sampling delay errors, but the calculation is quite complex. Building on this, Zhu et al. approximate the linearization of the motor model to reduce the computational load, but the compensation effect decreases with increasing speed. In "Expanding limit of minimum sampling time using auxiliary vectors for PMSMdrives with single DC-link current sensor," the zero vector is replaced with an effective voltage vector, ensuring that the bus current is sampled at the PWM midpoint, thus theoretically eliminating sampling delay errors. However, this method causes fluctuations in the bus current due to the lack of a zero vector. Variable vector model predictive control moves the bus current sampling point to the end of the switching state, directly eliminating sampling delay errors. Since the sampling delay time of multiple-branch current sampling is fixed, compensation for sampling delay errors is simpler; however, these methods are not suitable for single-bus current sensor control.

[0005] While the methods described above can address the sampling delay error to some extent, they all require compensation by calculating the rate of change of current, which is highly dependent on motor parameters. Furthermore, they necessitate obtaining the duration of each voltage vector, but the actual on / off state of the switching devices differs from the given PWM, introducing additional errors. Summary of the Invention

[0006] This invention aims to address the problem that existing technologies cannot effectively suppress the sampling delay error of single current detection in permanent magnet synchronous motors.

[0007] A method for suppressing sampling delay error in single current detection of a permanent magnet synchronous motor includes:

[0008] Based on the parameter perturbation and dq-axis cross-coupling disturbance of the permanent magnet synchronous motor (PMSM), the concentrated disturbance is determined to be the d-axis concentrated disturbance. d and q-axis concentrated perturbation d q Furthermore, an improved resonant extended state observer (IRESO) is used to suppress the sampling delay error of single current detection in a permanent magnet synchronous motor; the IRESO is as follows:

[0009]

[0010] in, It is the Laplace operator, i q It is the stator current along the q-axis. It is the q-axis prediction of stator current. It is a q-axis inductor. It is the q-axis given voltage. , These are all IRESO bandwidth parameters; ζ 3rd and ζ 9th These are the resonant gains of the 3rd and 9th order improved resonant controllers, respectively; ω b3rd and ω b9th These are the bandwidths of the 3rd and 9th resonant controllers, respectively; ω n3rd and ω n9th These are the resonant frequencies of the 3rd and 9th resonant controllers, respectively. This is the estimated value of the concentrated disturbance along the q-axis. , For resonant controller, This represents the current estimation error.

[0011] Furthermore, the concentrated disturbance along the d-axis d d for q-axis concentrated disturbance d q for ; where: i d i q These are the stator currents along the d and q axes, respectively; R so ψfo For nominal stator resistance and permanent magnet flux linkage; ω e Indicates electric angular velocity; k d and k q These are the proportional gains of the dq-axis current controllers; L do L qo These are the nominal d-axis inductance and q-axis inductance. , For Δi dq The proportional dq-axis voltage perturbation containing the 3rd and 9th harmonics.

[0012] Furthermore, the improved resonant extended state observer IRESO is determined based on a current controller, the feedback control law of which is: .

[0013] Furthermore, the actual process of the feedback control law of the current controller includes:

[0014] Based on the voltage equation of a permanent magnet synchronous motor (PMSM) with disturbances in the dq axis system, the current dynamic equation of the PMSM is obtained as follows:

[0015] (19)

[0016] Concentrate the cross-coupling of the dq axes to d d d q Then, the decoupling of the dq axis is achieved, and the feedback control law of the current controller is designed.

[0017] Furthermore, the voltage equation of the permanent magnet synchronous motor (PMSM) in the dq axis system is as follows:

[0018]

[0019] In the formula: p is the differential operator; u d u q and i d i q These are the stator voltage and current along the dq axis, respectively; R so ψ fo For nominal stator resistance and permanent magnet flux linkage; ω e Indicates electric angular velocity; k d and k q These are the proportional gains of the dq-axis current controllers; L do L qo These are the nominal d-axis inductance and q-axis inductance. , For Δi dq The dq-axis voltage disturbances are proportional and also contain the 3rd and 9th harmonics.

[0020] Preferably, ζ 3rd Take 0.01, ζ 9th Take 0.018.

[0021] A method for suppressing and evaluating the sampling delay error of a single current detection in a permanent magnet synchronous motor includes:

[0022] according to The Bode plot of the periodic disturbance decay transfer function is obtained, based on Obtain the Bode plot of the disturbance attenuation transfer function, according to Bode plots of the estimated lumped disturbance transfer functions are obtained. The effectiveness of a method for suppressing sampling delay error of single current detection in permanent magnet synchronous motors is evaluated based on the periodic disturbance attenuation transfer function, the disturbance attenuation transfer function, and the Bode plots of the estimated lumped disturbance transfer functions.

[0023] A current control system for a permanent magnet synchronous motor with single current detection, the system comprising an improved resonant extended state observer (IRESO); the IRESO is as follows:

[0024]

[0025] in, It is the Laplace operator, i q It is the stator current along the q-axis. It is the q-axis prediction of stator current. It is a q-axis inductor. It is the q-axis given voltage. , These are all IRESO bandwidth parameters; ζ 3rd and ζ 9th These are the resonant gains of the 3rd and 9th order improved resonant controllers, respectively; ω b3rd and ω b9th These are the bandwidths of the 3rd and 9th resonant controllers, respectively; ω n3rd and ω n9th These are the resonant frequencies of the 3rd and 9th resonant controllers, respectively. This is the estimated value of the concentrated disturbance along the q-axis. , For resonant controller, This is the current estimation error;

[0026] Will and As input to IRESO, the output of IRESO is and , and The current is fed into the current controller in a feedforward manner to achieve control.

[0027] Furthermore, the feedback control law of the current controller is: .

[0028] Beneficial effects:

[0029] This invention analyzes the periodic disturbance characteristics of sampling delay error and proposes a current control based on a resonant extended state observer to suppress sampling delay error. Furthermore, this invention designs the periodic disturbance transfer function, resulting in an improved resonant extended state observer that decouples periodic disturbance attenuation capability from bandwidth and suppresses resonance phenomena. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the PMSM three-phase two-level drive topology and the defined positive current direction.

[0031] Figure 2 This is a schematic diagram of the current reconstruction blind zone in the DC bus sampling method.

[0032] Figure 3 The diagram shows the analysis of the PWM waveform and sampling delay error under the pulse width shifting method (sector I).

[0033] Figure 4 For modulation ratio, φ e Relationship with three-phase current error (sector I).

[0034] Figure 5 For the three-phase reconfiguration current error and φ e Approximate relationship diagram.

[0035] Figure 6 This is a block diagram of the single bus current sensor control system proposed in this invention.

[0036] Figure 7 Bode plot for predicting the transfer function of lumped disturbances.

[0037] Figure 8 This is the Bode plot of the disturbance attenuation transfer function.

[0038] Figure 9 This represents the amplitude-frequency characteristic of the periodic perturbation attenuation transfer function.

[0039] Figure 10 This is a system block diagram of IRESO.

[0040] Figure 11 This is a physical image of the experimental platform.

[0041] Figure 12 The figure shows the experimental results of three-phase reconfiguration current error and Fourier analysis.

[0042] Figure 13 This is a comparison chart of experimental results for the dq-axis current error under rated operating conditions.

[0043] Figure 14 This is a comparison chart of the 3rd and 9th harmonic content of the dq axis current error under rated operating conditions for four methods.

[0044] Figure 15 This is a comparison chart of the phase current experimental results under rated operating conditions.

[0045] Figure 16 The Fourier analysis results are for the phase a current under rated operating conditions.

[0046] Figure 17 This is a comparison graph of the experimental results of four methods when PMSM is suddenly accelerated.

[0047] Figure 18 This is a comparison graph of the experimental results of the four methods when the load torque suddenly increases.

[0048] Figure 19 For rated operating conditions, L dqo Comparison of experimental results of dq-axis current error under varying conditions. Detailed Implementation

[0049] The difference between the sampling points of the reconstructed phase current and the ideal phase current leads to an inherent sampling delay error, reducing current accuracy. Furthermore, in single-bus current sensor control, the method of suppressing sampling delay error by calculating the online current change rate is not only computationally intensive but also dependent on the accuracy of parameters and voltage vector action time. This invention proposes a method for suppressing sampling delay error in a single current sensor for permanent magnet synchronous motors and a current control system, with the following main contributions:

[0050] (1) The periodic disturbance characteristics of the sampling delay error are analyzed, and a current control based on the resonant expansion state observer is proposed to suppress the sampling delay error.

[0051] (2) The periodic disturbance transfer function is redesigned and an improved resonant expansion state observer is proposed. Its periodic disturbance attenuation capability is decoupled from its bandwidth and the resonance phenomenon is suppressed.

[0052] The following describes in detail the method for suppressing sampling delay error of single current detection in permanent magnet synchronous motors, the suppression evaluation method, and the current control system, with specific implementation methods. The method for suppressing sampling delay error of single current detection in permanent magnet synchronous motors is a method based on an improved resonant expansion state observer. The suppression evaluation method is actually formulas (29), (32), and (33). Based on the form of (29), (32), and (33), the suppression effect can be evaluated. The current control system is actually a current control system based on IRESO.

[0053] Before proceeding with a detailed explanation, the basic principle of single bus current sensor control will first be explained:

[0054] exist Figure 1 In the three-phase two-level voltage source inverter topology shown, there is a specific relationship between the bus current and the three-phase current under eight voltage vectors:

[0055] (1)

[0056] Among them, S x (x=a,b,c) represents the switching states of two switches in one bridge arm, S x =1 indicates that the upper tube of phase x is on while the lower tube is off, S x =0 indicates the opposite; i dc Indicates bus current; i abc This represents the three-phase currents a, b, and c.

[0057] In SVPWM, each switching cycle contains two distinct effective voltage vectors, from which the corresponding two-phase currents can be reconstructed. Assuming the three-phase system is balanced, i.e., the zero-sequence current is zero, the third-phase current can be determined according to i... a +i b +i c =0 is obtained. However, in reality, the switching on and off of the switching devices and the current sampling are not instantaneous; the effective voltage vector needs to act for at least the minimum current sampling time T. min This is to ensure reliable sampling of the bus current. Conversely, if the bus current sensor samples incorrect current, it will cause phase current reconstruction failure. The area where phase current reconstruction fails is called the current reconstruction dead zone, located in the low-modulation region and sector boundary region of the space vector hexagon, such as... Figure 2 As shown. At any modulation ratio, the voltage vector will switch sectors, which inevitably leads to a blind zone in the sector boundary region during current reconstruction. This invention mainly targets the blind zone in this region.

[0058] When there is a sector boundary blind zone in the current reconstruction, the effective voltage vector is moved for a time less than T. min The PWM phase is used to eliminate the current reconstruction dead zone and ensure accurate sampling of the bus current, such as Figure 3 The S shown above c In the figure, t a and t c These represent the sampling times for reconstructing the currents in phases a and c, respectively. and This represents the reconfiguration current of phase a and phase c.

[0059] from Figure 3 It can be seen that after PWM phase shifting, the currents i in phase a and phase c... aSSPS and icSSPS Compared to average current and The fluctuations are all higher than before the PWM phase shift, i.e., the currents i in phase a and phase c under SVPWM. aSV and i cSV The fluctuation should be large. The sampling current at the PWM midpoint, i.e., when the carrier wave is 0, after PWM phase shift. and Not with average current and Since they are equal, the ideal phase current sampling point under SSPS is the starting point of the PWM period. Therefore, with and As the actual a-phase and c-phase currents.

[0060] There is an error Δi between the actual three-phase current and the three-phase reconfigured current. abc ,satisfy:

[0061] (2)

[0062] In the formula, Δi a , Δi b , Δi c The error is the reconfiguration current of the three phases abc. , and These are the actual currents of phases a, b, and c, respectively. , and These are the reconfiguration currents for phases a, b, and c, respectively.

[0063] Assuming the PMSM is in three-phase balance at this point, according to Kirchhoff's current law, we have... and ,for Figure 3 Given the situation in sector I, we can obtain:

[0064] (3)

[0065] In the formula, and These are the sampling delay errors for phase a and phase c, respectively.

[0066] The sampling delay errors of phases a and c can be derived from the three-phase current slopes and the three-phase duty cycles under various voltage vectors:

[0067] (4)

[0068] Where p represents the differential operator; T s Sampling time; and These represent the rate of change of phase a current under voltage vectors of 000 and 100, respectively; and These represent the duty cycles of phase a under voltage vectors of 000 and 100, respectively. , , and These represent the rate of change of phase c current under voltage vectors of 000, 100, 110, and 111, respectively. , , and These represent the c-phase duty cycles under voltage vectors of 000, 100, 110, and 111, respectively.

[0069] Based on the Thevenin equivalent circuit, the three-phase current change rate under eight voltage vectors can be obtained as shown in Table 1. U dc The bus voltage is represented by L, the phase inductance of the motor is represented by k. a k b k c k is an intermediate variable used to calculate the rate of change of the three-phase currents abc. a =-2d a +d b +d c k b =-2d b +d a +d c k c =-2d c +d a +d b d a d b d c The three-phase duty cycle is 0 to 1. Based on Table 1, the relationship between sampling delay error and three-phase duty cycle is shown in (5). Due to factors such as inverter dead zone, switch turn-on and turn-off delay, the actual voltage vector action time deviates from the ideal time, and the accuracy of sampling delay error compensation directly through (5) will also be affected.

[0070] (5)

[0071] In the formula, U dc L represents the bus voltage, and T represents the motor phase inductance. min For the minimum current sampling time, k a k b k c k is an intermediate variable used to calculate the rate of change of the three-phase currents abc, and k a =-2d a +d b +d c kb =-2d b +d a +d c k c =-2d c +d a +d b d a d b d c The three-phase duty cycle is 0 to 1.

[0072] Table 1 Relationship between three-phase current change rate and voltage vector

[0073]

[0074] According to the principle of SVPWM, the three-phase duty cycle satisfies the following relationship:

[0075] (6)

[0076] Among them, T 1st and T 2nd These represent the durations of the first and second voltage vectors, respectively; T0 and T7 both represent the duration of the zero vector; M is the modulation index, and U... m φ represents the amplitude of the phase voltage. e The angle between the voltage space vector and the a-phase axis is given.

[0077] Combining (5) and (6), we can further deduce that the sampling delay error for sector I is:

[0078] (7)

[0079] Take the base value of current i base =U dc T s / (3L), according to (7), Figure 4 Figures (a) and (b) show the M and φ values ​​under sector I, respectively. e and , Relationship, Figure 4 For modulation ratio, φ e The relationship between the error and the three-phase current error is shown in the diagram (sector I), where (a) represents the sampling delay error of phase a; (b) represents the sampling delay error of phase c; and (c) represents the reconstructed current error of phase b. It can be seen that... and With M, φ e It's a non-linear relationship, difficult to compensate for directly. According to... ,from Figure 4 It can be seen from (c) The amplitude is basically greater than and The error is large for the non-reconfigured phase current of the current sector, and the same applies to other sectors. Therefore, it can be assumed that the error of the non-reconfigured phase current of the current sector is larger than that of the other two reconfigured phase currents.

[0080] To simplify the analysis, assume that the reconstructed two-phase current error is k0 in any sector, and the non-reconstructed phase current error is 2k0. In this case, Δi abc With φ e Relationship such as Figure 5 As shown, Figure 5 The three-phase reconfiguration current error and φ e In the approximate relationship, (a) represents phase a, (b) represents phase b, and (c) represents phase c. According to... Figure 5 The Fourier series of the three-phase reconfiguration current error can be further obtained as follows:

[0081] (8)

[0082] The coefficients of each Fourier series are shown below:

[0083]

[0084] Expanding equation (8), we get:

[0085] (9)

[0086] (10)

[0087] (11)

[0088] After Clarke transformation, the reconstruction current error on the αβ axis of the two-phase stationary coordinate system can be obtained:

[0089] (12)

[0090] (13)

[0091] With the a(α) phase axis as the zero position, φ e With rotor electrical angle θ e The relationship is: φ e =θ e +β+φ, where β is the torque angle and φ is the power factor angle. Let θ0=β+φ, and perform a Park transform on the reconstructed current error along the αβ axis to obtain:

[0092] (14)

[0093] (15)

[0094] In summary, when higher-order terms are ignored, the sampling delay error introduces 2nd, 4th, 8th, and 10th harmonics into the αβ-axis feedback current, and 3rd and 9th harmonics into the dq-axis feedback current.

[0095] This implementation proposes a current control strategy based on an improved resonant extended state observer:

[0096] As the preceding analysis shows, the sampling delay error of single-bus current sensor control introduces the 3rd and 9th harmonics into the dq-axis feedback current, affecting the given voltage of the dq-axis. , (Reference value) becomes:

[0097] (16)

[0098] In the formula: , Given the dq-axis current; k d and k q These are the proportional gains of the dq-axis current controllers; L do L qo These are the nominal d-axis inductance and q-axis inductance. , For Δi dq The dq-axis voltage disturbances are proportional and also contain the 3rd and 9th harmonics.

[0099] At this point, the voltage equation of PMSM in the dq axis system is:

[0100] (17)

[0101] In the formula: p is the differential operator; u d u q and i d i q These are the stator voltage and current along the dq axis, respectively; R so ψ fo For nominal stator resistance and permanent magnet flux linkage; ω e It represents electric angular velocity.

[0102] Considering the parameter perturbations of the PMSM and the dq-axis cross-coupling disturbances, the concentrated disturbance is defined as the d-axis concentrated disturbance d. d and q-axis concentrated perturbation d q :

[0103] (18)

[0104] Among them, the concentrated disturbance along the d-axis d d Defined as resistance variation, q-axis cross-coupling, and d-axis sampling delay error. Commonly caused disturbances; q-axis concentrated disturbance d q Defined as resistance change, d-axis cross-coupling, back EMF, and q-axis sampling delay error. The disturbances caused by the joint efforts. This indicates a definition.

[0105] Furthermore, a sampling delay error suppression method is proposed that does not require online calculation of the current change rate and voltage vector action time. Its block diagram is shown below. Figure 6 As shown, concentrated disturbances are predicted using a resonant extended state observer (RESO). , This cancels out the effects of the 3rd and 9th harmonics and parameter perturbations, thereby suppressing sampling delay errors while ensuring robustness.

[0106] From (17) and (18), the current dynamic equation of PMSM can be obtained as follows:

[0107] (19)

[0108] From the above equation, it can be seen that the cross-coupling of the dq axes is concentrated on d. d d q After that, the decoupling of the dq axis was achieved. Therefore, this invention takes the q axis as an example for analysis, and the same applies to the d axis.

[0109] The feedback control law is constructed as follows:

[0110] (20)

[0111] Specifically, the predicted lumped disturbance, including sampling delay error, is introduced into the current controller via feedforward to offset the effect of the sampling delay error. It is approximately assumed that... and Converges to d q From (19) and (20), we can obtain:

[0112] (twenty one)

[0113] Due to resistance R so , magnetic flux ψ fo q-axis inductance L qo Isoparametric perturbations and dq-axis cross-coupling are aperiodic disturbances, which can be suppressed by constructing a linear extended state observer (LESO):

[0114] (twenty two)

[0115] Where β1=2ωo ,β2= ω o This refers to the bandwidth of the ESO.

[0116] (22) Combining with (19), the estimated transfer function of the lumped disturbance can be derived. :

[0117] (twenty three)

[0118] make The disturbance attenuation transfer function can be obtained. :

[0119] (twenty four)

[0120] Take k q =200π, LESO bandwidth ω o ω is 1-2 times the bandwidth of the current loop. o =300π, Bode plots of the LESO-predicted lumped disturbance transfer function and disturbance decay transfer function are shown below. Figure 7 and Figure 8 As shown. Figure 7 To predict the Bode plot of the lumped disturbance transfer function, take ω o =300π, k r3rd =k r9th =4400π,ω b3rd =ω b9th =15π,ζ 3rd =0.01, ζ 9th =0.018, ω n3rd =600π,ω n9th =1800π Figure 7 In the diagram, (a) represents the amplitude frequency response, and (b) represents the phase frequency response. Figure 8 Let ω be the Bode plot of the disturbance attenuation transfer function. o =300π, k r3rd =k r9th =4400π,ω b3rd =ω b9th =15π,ζ 3rd =0.01, ζ 9th =0.018, ω n3rd =600π,ω n9th =1800π Figure 8In the diagram, (a) represents the amplitude-frequency response, and (b) represents the phase-frequency response. It can be seen that LESO can effectively suppress low-frequency disturbances caused by PMSM parameter perturbations, but its ability to suppress periodic disturbances is relatively poor.

[0121] To suppress the third and ninth periodic disturbances, a resonant controller R can be introduced into the disturbance loop of LESO shown in (22). 3rd (s) and R 9th (s), thus obtaining the quasi-resonant ESO (quasi-resonant textended state observer, QRESO):

[0122] (25)

[0123] Where, k r3rd and k r9th ω b3rd and ω b9th ω n3rd and ω n9th These are the resonant gain, bandwidth, and resonant frequency of the 3rd and 9th order resonant controllers, respectively. The predicted lumped disturbance transfer function can then be obtained:

[0124] (26)

[0125] make The disturbance attenuation transfer function can be obtained. and the periodic disturbance attenuation transfer function :

[0126] (27)

[0127] in, It includes β1 and β2, which are related to the observer's bandwidth ω. o The Bode plot of the coupling, QRESO periodic perturbation decay transfer function is as follows: Figure 9 As shown, Figure 9 Let k be the amplitude-frequency characteristic of the periodic perturbation decay transfer function. r3rd =k r9th =4400π,ω b3rd =ω b9th =15π,ζ 3rd =0.01, ζ 9th =0.018, ω n3rd =600π,ω n9th =1800π Figure 9 (a) represents taking ω o =300π, (b) indicates taking ωo =30π. The graph shows that coupling effects cause resonance, and as the bandwidth decreases, s = -ω. o Gradually becoming The dominant pole of the system exhibits a more pronounced coupling effect, leading to a stronger resonance phenomenon, which in turn affects the system's stability. Decreasing k... r Although it can suppress resonance, its ability to suppress periodic disturbances will also decrease.

[0128] In order to make the periodic perturbation suppression capability of RESO unaffected by ω o To mitigate the impact of this, the present invention proposes to introduce an improved resonant controller Q into the perturbation loop of the LESO shown in (22) for IRESO. 3rd (s) and Q 9th (s), as shown below:

[0129] (28)

[0130] make IRESO can be obtained and :

[0131] (29)

[0132] (30)

[0133] Design an improved resonant controller Q 3rd (s) and Q 9th (s) is:

[0134] (31)

[0135] Where, ζ 3rd and ζ 9th These represent the resonant gains of the 3rd and 9th order improved resonant controllers, respectively. The derivation is as follows: for:

[0136] (32)

[0137] in, The absence of β1 and β2 decouples the periodic perturbation suppression capability from the observer bandwidth.

[0138] Figure 9 This further verifies that the amplitude-frequency characteristics of the IRESO are not affected by the observer bandwidth, and that the resonance phenomenon is eliminated.

[0139] Similarly, the IRESO's predicted lumped perturbation transfer function can be derived:

[0140] (33)

[0141] Based on (21) and (29), the current control closed-loop transfer function based on IRESO proposed in this invention is:

[0142]

[0143] In summary, the IRESO proposed in this invention is as follows:

[0144] (34)

[0145] Figure 6 The control system is an improvement upon the one described in "Smooth and robust current control of PMSMs with decoupling-type extended state observers," where the control strategy is used to suppress current harmonics in permanent magnet synchronous motors. This invention will... Figure 6 The RESO in this paper is an improvement on QRESO, namely IRESO, which is used to suppress sampling delay error. IRESO uses... and As input, with and For output, and The current is fed forward into the current controller to cancel out the 3rd and 9th harmonics caused by the sampling delay error, thereby achieving the effect of suppressing the sampling delay error without having to calculate the current change rate online.

[0146] The predicted lumped disturbance transfer functions and disturbance attenuation transfer functions of QRESO and IRESO are as follows: Figure 7 and Figure 8 As shown. From Figure 7 As can be seen from Figure 8, both QRESO and IRESO can predict periodic disturbances, but QRESO exhibits a resonant frequency shift, which reduces its predictive performance. The IRESO proposed in this invention does not have a frequency shift and achieves 0 dB at the resonant frequency, meaning it predicts periodic disturbances without error. Figure 8 shows that both QRESO and IRESO can suppress periodic disturbances, but QRESO still exhibits undesirable resonant spikes and a phase shift at the resonant frequency. The disturbance attenuation function of IRESO still does not exhibit resonance and has a stronger periodic disturbance attenuation capability than QRESO.

[0147] Figure 10 The diagram of the IRESO structure proposed in this invention is shown, from which the improved resonant controller Q can be seen. 3rd (s) and Q 9th(s) can be directly implemented using an integrator, and its structure and discretization are simple.

[0148] Example: To verify the single bus current sensor control strategy based on IRESO proposed in this invention, a system was built as follows: Figure 11 The experimental platform shown in Table 2 has identical parameters for both the test PMSM and the load PMSM. Various algorithms were implemented using a Texas Instruments 32-bit digital signal processor (DSP) TMS320F28377D. A Hall-effect linear current sensor ACS758 with a bandwidth of 120kHz was selected as the current sensor. An Infineon IGBT module FS50R12W1T7 was used as the driving unit for the test PMSM. Experimental waveforms were acquired by an oscilloscope using the DSP's internal three-channel 12-bit digital-to-analog converter (DAC). The dead time of the driving unit was set to 1.5μs, and the minimum current sampling time T was... min Set to 5μs. Set the SSPS switching frequency to 10kHz.

[0149] Table 2 Parameters for testing PMSM and motor drive system

[0150]

[0151] The motor speed is set to 1000 r / min, the load torque is 2.39 N∙m, and the three-phase reconfiguration current error and sector are as follows: Figure 12 As shown in the figure, the magnitude of the current error in phase a is largest in sectors II and V, in phase b in sectors I and IV, and in phase c in sectors III and VI. Although the magnitude of the current error is greater than that in phase a due to electromagnetic noise and current sensor errors, the magnitude of the current error varies with these factors. Figure 5 The theoretical waveforms differ, but they are generally consistent. Furthermore, from... Figure 12 The Fourier analysis of the reconstructed current of phase a in (d) shows that the harmonic content of the 2nd, 4th, 8th and 10th harmonics is relatively large, which is consistent with the analysis of this invention.

[0152] To verify the advantages of the method proposed in this paper, it is compared with the SSPS method, the TPCC method, and a method using the same control law but employing QRESO. Similarly, k is taken... d =k q =200π,ω o =300π, k r3rd =k r9th =4400π,ζ 3rd =0.01, ζ 9th =0.018, ω of QRESO and IRESO b3rdand ω b9th Both are equal to 15π, and the dq axis parameters are the same.

[0153] Figure 13 The experimental results of dq-axis current error under four methods are presented at 1000 r / min and 2.39 N·m. (a) represents the SSPS method, (b) represents the TPCC method, (c) represents the QRESO method, and (d) represents the IRESO method proposed in this invention. Δi in the figure... dq_SSPS , Δi dq_TPCC , Δi dq_QRESO and Δi dq_IRESO These represent the errors between the actual dq-axis current and the dq-axis reconstructed current obtained from SSPS, TPCC, QRESO, and the IRESO proposed in this invention, respectively, and their 3rd and 9th harmonic contents are compared to, for example... Figure 14 As shown, TPCC can compensate for some sampling delay errors by calculating the current change rate. However, since the calculation of the current change rate and voltage vector action time is prone to introducing errors, the compensation effect is limited, resulting in the dq-axis current after TPCC compensation still containing a large number of 3rd and 9th harmonics. Current control based on QRESO or IRESO directly suppresses the 3rd and 9th harmonics in the dq-axis current loop, achieving higher current accuracy than SSPS and TPCC. Furthermore, this invention proposes that IRESO has a stronger periodic disturbance suppression capability compared to QRESO, improving the d-axis and q-axis current accuracy by 16.1% and 15.6%, respectively.

[0154] The three-phase reconstruction current and phase current errors of the four methods are as follows: Figure 15 As shown, (a) represents the SSPS method, (b) represents the TPCC method, (c) represents the QRESO method, and (d) represents the IRESO method proposed in this invention. In the figure, i... abc_SSPS i abc_TPCC i abc_QRESO and i abc_IRESO The three-phase reconfiguration currents Δi are obtained from SSPS, TPCC, QRESO, and the IRESO proposed in this invention, respectively. a_SSPS , Δi a_TPCC , Δi a_QRESO and Δi a_IRESO It is the error between the actual current of phase a and the reconstructed current of phase a. Figure 16Fourier analysis results of phase a current under four methods are presented. SSPS has a peak-to-peak current error as high as 3.39 A. After TPCC, the peak-to-peak error decreases to 2.03 A, and the THD of phase a current decreases by 5.8%, but the 2nd and 4th harmonic content remains relatively high. Suppressing the 3rd and 9th harmonics on the dq axis is equivalent to suppressing the 2nd, 4th, and 8th harmonics on the abc axis. Compared to SSPS and TPCC, QRESO and the proposed IRESO have lower peak-to-peak current error and THD. IRESO has lower 2nd and 4th harmonic content in phase current than QRESO, and among the four methods, it has the highest current accuracy and the lowest THD.

[0155] Figure 17 The experiment demonstrated a load torque of 2.39 N·m and a PMSM speed ranging from 0 to 1000 r / min. It can be seen that at the moment of PMSM startup, all four methods exhibit a spike in reconfiguration current, but the IRESO method shows the smallest current overshoot. Figure 17 As shown in the red dashed box, the QRESO exhibits a significant current surge, causing a sudden drop in PMSM speed, indicating that the QRESO's resonance phenomenon affects system stability. Experimental results for a sudden increase in load torque from 0 to rated torque are shown below. Figure 18 As shown, (a) represents the SSPS method, (b) represents the TPCC method, (c) represents the QRESO method, and (d) represents the IRESO method proposed in this invention. The QRESO in the figure also exhibits a large peak-to-peak current error of 5.81A, while the IRESO proposed in this invention consistently maintains lower q-axis current fluctuations and current errors. The two experiments above verify that the current control based on IRESO proposed in this invention has superior transient performance.

[0156] To verify the robustness of the proposed method, the dq-axis inductance was reduced by 50%. Experimental results for both the TPCC and IRESO methods were obtained at 1000 r / min and 2.39 N∙m. Figure 19 As shown, Figure 19 For rated operating conditions, L dqo Comparison of experimental results of dq-axis current error under varying conditions, where (a) corresponds to 50% L do The TPCC method is used. (b) Corresponding to 50%L qo The TPCC method is used. (c) Corresponds to 50%L do The proposed IRESO was used. (d) 50% L qo The proposed IRESO method was adopted. (Comparison) Figure 12 ,from Figure 19 It can be seen that because TPCC compensates for sampling delay errors based on the PMSM model, it is affected by parameters, especially L.d The impact is relatively large. Because the integral term of the IRESO disturbance loop can compensate for parameter changes, it is basically unaffected by L. dq It is more robust to changes than TPCC.

[0157] Table 3 lists the execution time of each algorithm in TMS320F28377D. It can be seen that TPCC involves online calculation of current change rate, which requires a long execution time. Although the execution time of IRESO proposed in this invention is slightly longer than that of QRESO, it reduces the execution time by 64.6% compared to TPCC and only requires less computing resources.

[0158] Table 3 Execution time of each algorithm

[0159]

[0160] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for suppressing sampling delay error in single current detection of a permanent magnet synchronous motor, characterized in that, include: Based on the parameter perturbation and dq-axis cross-coupling disturbance of the permanent magnet synchronous motor (PMSM), the concentrated disturbance is determined to be the d-axis concentrated disturbance. d and q-axis concentrated perturbation d q Furthermore, an improved resonant extended state observer (IRESO) is used to suppress the sampling delay error of single current detection in a permanent magnet synchronous motor; the IRESO is as follows: in, It is the Laplace operator, i q It is the stator current along the q-axis. It is the q-axis prediction of stator current. It is a q-axis inductor. It is the q-axis given voltage. , These are all IRESO bandwidth parameters; ζ 3rd and ζ 9th These are the resonant gains of the 3rd and 9th order improved resonant controllers, respectively; ω b3rd and ω b9th These are the bandwidths of the 3rd and 9th resonant controllers, respectively; ω n3rd and ω n9th These are the resonant frequencies of the 3rd and 9th resonant controllers, respectively. This is the estimated value of the concentrated disturbance along the q-axis. , For resonant controller, This represents the current estimation error.

2. The method for suppressing sampling delay error of single current detection in a permanent magnet synchronous motor according to claim 1, characterized in that, d-axis concentrated disturbance d d for q-axis concentrated disturbance d q for ; where: i d i q These are the stator currents along the d and q axes, respectively; R so ψ fo For nominal stator resistance and permanent magnet flux linkage; ω e Indicates electric angular velocity; k d and k q These are the proportional gains of the dq-axis current controllers; L do L qo For d-axis inductance and q-axis inductance; , For Δi dq The proportional dq-axis voltage perturbation containing the 3rd and 9th harmonics.

3. The method for suppressing sampling delay error of single current detection in a permanent magnet synchronous motor according to claim 2, characterized in that, The improved resonant extended state observer (IRESO) is determined based on a current controller, the feedback control law of which is: ; Given the q-axis current; k q This is the proportional gain of the q-axis current controller.

4. The method for suppressing sampling delay error of single current detection in a permanent magnet synchronous motor according to claim 3, characterized in that, The actual process of the feedback control law of the current controller includes: Based on the voltage equation of a permanent magnet synchronous motor (PMSM) with disturbances in the dq axis system, the current dynamic equation of the PMSM is obtained as follows: （19） p is a differential operator; the cross-coupling of the dq axes is concentrated in d. d d q Then, the decoupling of the dq axis is achieved, and the feedback control law of the current controller is designed.

5. The method for suppressing sampling delay error of single current detection in a permanent magnet synchronous motor according to claim 4, characterized in that, The voltage equation of the permanent magnet synchronous motor (PMSM) in the dq axis system is as follows: In the formula: p is the differential operator; u d u q and i d i q These are the stator voltage and current along the dq axis, respectively; R so ψ fo For nominal stator resistance and permanent magnet flux linkage; ω e Indicates electric angular velocity; k d and k q These are the proportional gains of the dq-axis current controllers; L do L qo For d-axis inductance and q-axis inductance; , For Δi dq The dq-axis voltage disturbances are proportional and also contain the 3rd and 9th harmonics.

6. The method for suppressing sampling delay error of single current detection in a permanent magnet synchronous motor according to claim 3, characterized in that, g 3rd Take 0.01, g 9th Take 0.

018.

7. A method for suppressing and evaluating the sampling delay error of a single current detection in a permanent magnet synchronous motor, characterized in that, include: according to The Bode plot of the periodic disturbance decay transfer function is obtained, based on Obtain the Bode plot of the disturbance attenuation transfer function, k q The proportional gain of the q-axis current controller; according to The Bode plot of the estimated lumped disturbance transfer function is obtained, and the effectiveness of the single current detection sampling delay error suppression method for permanent magnet synchronous motor described in claim 1 or 2 is evaluated based on the periodic disturbance attenuation transfer function, the disturbance attenuation transfer function and the Bode plot of the estimated lumped disturbance transfer function.

8. A current control system for a permanent magnet synchronous motor with single current detection, characterized in that, The system includes an improved resonance extension state observer (IRESO); the IRESO is as follows: in, It is the Laplace operator, i q It is the stator current along the q-axis. It is the q-axis prediction of stator current. It is a q-axis inductor. It is the q-axis given voltage. , These are all IRESO bandwidth parameters; ζ 3rd and ζ 9th These are the resonant gains of the 3rd and 9th order improved resonant controllers, respectively; ω b3rd and ω b9th These are the bandwidths of the 3rd and 9th resonant controllers, respectively; ω n3rd and ω n9th These are the resonant frequencies of the 3rd and 9th resonant controllers, respectively. This is the estimated value of the concentrated disturbance along the q-axis. , For resonant controller, This is the current estimation error; Will and As input to IRESO, the output of IRESO is and , and The current is fed into the current controller in a feedforward manner to achieve control.

9. A current control system for single current detection of a permanent magnet synchronous motor according to claim 8, characterized in that, The feedback control law of the current controller is: .

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