Low-speed sensorless control method for permanent magnet synchronous motor

Abstract

The invention discloses a low-speed sensorless control method for a permanent magnet synchronous motor, and relates to the field of motors, the low-speed sensorless control method for the permanent magnet synchronous motor comprises the following steps: establishing a mapping model between an injection frequency and a position observation error, and selecting an optimal injection frequency according to the mapping model, injecting a voltage signal under the optimal injection frequency into a static shaft system of the motor; a cross decoupling complex coefficient filter is used, response current generated by excitation of voltage signals under the optimal injection frequency is extracted from a static shafting, and compared with the prior art, the method has the advantages that a unified mapping model between the injection frequency and the position observation error is established, and the optimal injection frequency selection criterion is defined; the problem of phase deviation introduced in the separation process of the fundamental current and the response current in a traditional filtering method is avoided; noise caused by signal injection is reduced, and position observation errors introduced by stator resistance and mutual inductance are effectively reduced.

Description

Technical Field

[0001] This invention relates to the field of electric motors, specifically a sensorless control method for low-speed permanent magnet synchronous motors. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) have become core power units in transportation equipment due to their high power density and high efficiency. The control algorithms for PMSMs also need further improvement to better adapt to the evolving needs of transportation equipment. Accurate position information is crucial for achieving high-performance vector control, typically obtained using mechanical position sensors such as photoelectric encoders and rotary transformers. However, mechanical position sensors are prone to failure in harsh environments such as high temperature, high humidity, and vibration. Sensorless control technology, which acquires position through algorithms, can replace mechanical position sensors, further improving the reliability of PMSM drive systems in harsh environments.

[0003] High-frequency signal injection methods calculate rotor position by injecting high-frequency voltage or current into the motor and utilizing the impedance difference caused by the salient pole effect or saturation effect of the motor. Depending on the form of the injected signal and the shaft system, high-frequency signal injection methods can be divided into high-frequency rotating sinusoidal injection, high-frequency pulsed sinusoidal injection, and high-frequency pulsed square wave injection. However, high-frequency signal injection methods inevitably generate high-frequency noise and reduce voltage utilization, limiting their application scenarios. Existing noise reduction methods include increasing the injection frequency, reducing the injection amplitude, pseudo-random signal injection, and low-frequency signal injection. However, increasing the injection frequency requires setting the injection frequency above 20kHz, significantly increasing switching losses; reducing the injection amplitude reduces the signal-to-noise ratio of the position tracking error signal, affecting position observation performance; while pseudo-random injection can reduce noise to some extent, its effect is limited because the injection frequency is relatively high and still within the range of human hearing sensitivity. On the other hand, low-frequency signal injection methods can reduce noise, but traditional bandpass and high-pass filters can cause phase shifts in the extracted response current, introducing position observation errors; simultaneously, stator resistance, mutual inductance, and other factors introduce inherent position observation errors into the observed position. Large position observation errors can affect the control performance of sensorless systems and even cause instability in the control system.

[0004] In summary, while existing high-frequency signal injection methods reduce noise, they generally face the problem of difficulty in synergistically optimizing observation accuracy, noise suppression, and system efficiency (different noise reduction methods have problems such as increased switching losses, decreased signal-to-noise ratio leading to deteriorated observation performance, limited noise suppression effect, and inherent observation errors introduced by filter phase shift and motor parameters), and need to be improved. Summary of the Invention

[0005] The purpose of this invention is to provide a low-speed sensorless control method for permanent magnet synchronous motors to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A sensorless control method for low-speed permanent magnet synchronous motors includes the following steps: Establish a mapping model between injection frequency and position observation error, select the optimal injection frequency based on the mapping model, and inject a voltage signal at the optimal injection frequency into the stationary shaft system of the motor. Using a cross-decoupling complex coefficient filter, the response current generated by the voltage signal excitation at the optimal injection frequency is extracted from the stationary axis system. The phase and amplitude of the extracted response current are reconstructed to obtain the reconstructed current observation value. The fundamental frequency response current signal of the reconstructed current observation is extracted from the reconstructed current observation using a cross-decoupling phase-locked loop; and an equivalent rotor position tracking error signal is constructed using the fundamental frequency response current signal. The observed position and speed of the rotor are obtained based on the equivalent rotor position tracking error signal (processed by a proportional-integral converter). The observed position and speed of the rotor are used as feedback signals for closed-loop vector control, thereby realizing sensorless control of the permanent magnet synchronous motor (low noise, high precision).

[0007] In one embodiment, the present invention provides a low-speed sensorless control method for a permanent magnet synchronous motor. In the steps of establishing a mapping model between the injection frequency and the position observation error, selecting the optimal injection frequency based on the mapping model, and injecting a voltage signal at the optimal injection frequency into the stationary shaft system of the motor, the mapping model between the injection frequency and the position observation error is as follows: (1); In the formula For rotor position observation error, This is the actual position signal of the rotor. For rotor position observation signal, ; φ represents the expected maximum rotor position observation error. n φ is the phase of the negative sequence current component in the response current of the stationary shaft system. p The phase of the positive sequence current component in the response current of the stationary shaft system; φ n and φ p The calculation method is as follows: (2); In the formula, L dh For the d-axis self-inductance of the dq-axis system, L qh For the q-axis self-inductance of the dq-axis system, Ldqh The mutual inductance is caused by the cross-coupling effect of the dq axis system, and L0 is the average inductance. For differential inductance, L0 = (L dh +L qh ) / 2, L1=(L dh -L qh ) / 2; R s ω is the stator resistance; i The frequency of the low-frequency sinusoidal voltage signal is denoted as ; atan2(y, x) represents the arctangent function in the four quadrants, and the return value is the angle (in radians) between the point (x, y) and the positive x-axis, with the angle range within (-π, π].

[0008] In one embodiment, the present invention provides a low-speed sensorless control method for a permanent magnet synchronous motor. In the steps of establishing a mapping model between the injection frequency and the position observation error, selecting the optimal injection frequency based on the mapping model, and injecting a voltage signal at the optimal injection frequency into the stationary shaft system of the motor, the voltage signal injected into the stationary shaft system of the motor at the optimal injection frequency is a sinusoidal voltage signal. (3); In the formula, u αi For the low-frequency sinusoidal voltage signal along the α-axis of the stationary axis, u βi For the stationary axis β-axis low-frequency sinusoidal voltage signal, U i t represents the amplitude of a low-frequency sinusoidal voltage signal in a stationary axis system; t represents time.

[0009] In one embodiment, the present invention provides a low-speed sensorless control method for a permanent magnet synchronous motor. In the step of extracting the response current generated by the voltage signal excitation at the optimal injection frequency from the stationary shaft system using a cross-decoupling complex coefficient filter, and reconstructing the phase and amplitude of the extracted response current to obtain the reconstructed current observation value, the cross-decoupling complex coefficient filter is: (4); In the formula, i αβ For the sampled stationary shaft current, i αβf i is the fundamental frequency current component of the stationary axis current. αβi1 i is the negative-sequence component of the response current of the stationary shaft system. αβi2 ω represents the positive-sequence component of the response current of the stationary shaft system. e ω is the electrical angular frequency of the motor; k is the filter gain of the cross-decoupling complex coefficient filter; s is the Laplace operator; j is the twitch factor.

[0010] In one embodiment, the present invention provides a low-speed sensorless control method for a permanent magnet synchronous motor. In the step of extracting the response current generated by the voltage signal excitation at the optimal injection frequency from the stationary shaft system using a cross-decoupling complex coefficient filter, and reconstructing the phase and amplitude of the extracted response current to obtain the reconstructed current observation value, the extracted response current is: (5); In the formula, i αi Let i be the α-axis response current of the stationary axis system. βi I is the β-axis response current of the stationary axis system. n I represents the magnitude of the negative sequence current component in the response current of the stationary shaft system. p This represents the amplitude of the positive sequence current component in the response current of the stationary shaft system.

[0011] In one embodiment, the present invention provides a low-speed sensorless control method for a permanent magnet synchronous motor. In the step of extracting the response current generated by the voltage signal excitation at the optimal injection frequency from the stationary shaft system using a cross-decoupling complex coefficient filter, and reconstructing the phase and amplitude of the extracted response current to obtain the reconstructed current observation value, the calculation method for the reconstructed current observation value is as follows: (6); In the formula, For the reconstructed α-axis current observations, For the reconstructed β-axis current observations; φ d To account for phase errors caused by system delays, including pulse width modulation update delays and hardware delays.

[0012] In one embodiment, the present invention provides a low-speed sensorless control method for a permanent magnet synchronous motor. In the step of extracting the fundamental frequency response current signal from the reconstructed current observations using a cross-decoupling phase-locked loop (PLL), and constructing an equivalent rotor position tracking error signal using the fundamental frequency response current signal, the cross-decoupling PLL is: (7); In the formula, For the reconstructed current observations, For the fundamental frequency component in the reconstructed current observations, For the negative sequence component in the reconstructed current observations, k1 represents the positive sequence component in the reconstructed current observation; k1 is the filter gain value of the cross-decoupling phase-locked loop.

[0013] In one embodiment, the present invention provides a low-speed sensorless control method for a permanent magnet synchronous motor. In the step of extracting the fundamental frequency response current signal from the reconstructed current observations using a cross-decoupling phase-locked loop, and constructing an equivalent rotor position tracking error signal using the fundamental frequency response current signal, the fundamental frequency response current signal is: (8); In the formula, For the fundamental frequency current along the α axis in the reconstructed current observations, The fundamental frequency current of the β-axis in the reconstructed current observations.

[0014] In one embodiment, the present invention provides a low-speed sensorless control method for a permanent magnet synchronous motor. In the step of extracting the fundamental frequency response current signal from the reconstructed current observations using a cross-decoupling phase-locked loop, and constructing an equivalent rotor position tracking error signal using the fundamental frequency response current signal, the equivalent rotor position tracking error signal is: (9); In the formula, ε is the constructed equivalent rotor position tracking error signal.

[0015] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention establishes a unified mapping model between injection frequency and position observation error, and clarifies the selection criteria for the optimal injection frequency; it designs a cross-decoupled complex coefficient filter to extract the stationary shaft response current, avoiding the phase shift problem introduced by traditional filtering methods in the separation of fundamental frequency current and response current; by reconstructing the positive and negative sequence components in the stationary shaft response current, and using a cross-decoupled phase-locked loop to extract the fundamental frequency component from the reconstructed current observation value, the rotor position and speed are finally obtained using the fundamental frequency response current signal from the reconstructed current observation value; this invention not only reduces the noise caused by the injection signal, but also effectively reduces the position observation error introduced by stator resistance and mutual inductance. Attached Figure Description

[0016] Figure 1 This is an overall control block diagram of a low-speed sensorless control method for permanent magnet synchronous motors.

[0017] Figure 2 The block diagram of the cross-decoupling complex coefficient filter for extracting the response current is shown.

[0018] Figure 3 A schematic diagram of a cross-decoupled phase-locked loop (PLL) for using reconstructed current observations to achieve position and speed observations.

[0019] Figure 4The waveform diagram shows an experiment with a permanent magnet synchronous motor operating at 100 r / min under rated load without employing a sensorless control method for low speed.

[0020] Figure 5 This is an experimental waveform diagram of a sensorless control method for a low-speed permanent magnet synchronous motor when the motor is running at 100 r / min and under rated load.

[0021] Figure 6 This is an experimental result diagram comparing acoustic noise under different injection strategies. Detailed Implementation

[0022] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0023] Please see Figure 1 , Figure 2 and Figure 3 A sensorless control method for low-speed permanent magnet synchronous motors includes the following steps: Establish a mapping model between injection frequency and position observation error, select the optimal injection frequency based on the mapping model, and inject a voltage signal at the optimal injection frequency into the stationary shaft system of the motor. Using a cross-decoupling complex coefficient filter, the response current generated by the voltage signal excitation at the optimal injection frequency is extracted from the stationary axis system. The phase and amplitude of the extracted response current are reconstructed to obtain the reconstructed current observation value. The fundamental frequency response current signal of the reconstructed current observation is extracted from the reconstructed current observation using a cross-decoupling phase-locked loop; and an equivalent rotor position tracking error signal is constructed using the fundamental frequency response current signal. The observed position and speed of the rotor are obtained based on the equivalent rotor position tracking error signal (processed by a proportional-integral converter). The observed position and speed of the rotor are used as feedback signals for closed-loop vector control, thereby realizing sensorless control of the permanent magnet synchronous motor (low noise, high precision).

[0024] In this embodiment, please refer to Figure 1 ω in the figure eref The given value for the rotational speed, i represents the observed rotational speed; dref For the given value of the d-axis current of the rotating shaft system, i qref For the given value of the q-axis current of the rotating shaft system, i d For the d-axis stator current of the rotating shaft system, iq For the q-axis stator current of the rotating shaft system, i αf For the fundamental frequency current component of the α-axis of the stationary axis, i βf For the fundamental frequency current component of the β-axis in the stationary axis system, i α For the sampled α-axis current of the stationary axis, i β For the sampled stationary β-axis current, i a Let i be the stator current of phase A. c For the C-phase stator current, U dc The bus voltage, u α For the α-axis stator voltage of the stationary axis system, u β For the β-axis stator voltage of the stationary axis system, u d For the d-axis stator voltage of the rotating shaft system, u q For the q-axis stator voltage of the rotating shaft system, t d Representing dead time, SVPWM stands for Space Vector Pulse Width Modulation; A sensorless control method for low-speed permanent magnet synchronous motors. Figure 1 The main components include dual-loop vector control, response current extraction, and a cross-decoupled phase-locked loop (PLL). The response current extraction module uses a cross-decoupled complex coefficient filter to extract the response current of the stationary shaft system, which is then fed into the cross-decoupled PLL. Finally, the position and rotational speed are observed for vector control. The mapping model between the injected frequency and the position observation error is as follows: (1); In the formula For rotor position observation error, This is the actual position signal of the rotor. For rotor position observation signal, ; φ represents the expected maximum rotor position observation error. n φ is the phase of the negative sequence current component in the response current of the stationary shaft system. p The phase of the positive sequence current component in the response current of the stationary shaft system; φ n and φ p The calculation method is as follows: (2); In the formula, L dh For the d-axis self-inductance of the dq-axis system, L qh For the q-axis self-inductance of the dq-axis system, L dqh The mutual inductance is caused by the cross-coupling effect of the dq axis system, and L0 is the average inductance. For differential inductance, L0 = (L dh +L qh ) / 2, L1=(L dh -L qh ) / 2; Rs ω is the stator resistance; i The frequency of the low-frequency sinusoidal voltage signal is denoted as ; atan2(y, x) represents the arctangent function in the four quadrants, and the return value is the angle (in radians) between the point (x, y) and the positive x-axis, which is usually within (-π, π].

[0025] The voltage signal injected into the stationary shaft system of the motor at the optimal injection frequency is a (low-frequency) sinusoidal voltage signal: (3); In the formula, u αi For the low-frequency sinusoidal voltage signal along the α-axis of the stationary axis, u βi For the stationary axis β-axis low-frequency sinusoidal voltage signal, U i t represents the amplitude of a low-frequency sinusoidal voltage signal in a stationary axis system; t represents time.

[0026] Furthermore, combined with Figure 1 The stator current under the three-phase stationary shaft system of the permanent magnet synchronous motor is obtained by Clark transformation to obtain the stationary shaft current signal. The current signal is then used to obtain the stationary shaft response current through a response current extraction module. The specific structure of the response current extraction module is as follows. Figure 2 As described in the figure, i αi1 For the negative sequence component of the α-axis response current of the stationary axis system, i βi1 For the negative sequence component of the β-axis response current of the stationary axis system, i αi2 i represents the positive-sequence component of the α-axis response current in a stationary system. βi2 The positive sequence component of the β-axis response current in the stationary axis system; In this embodiment, please refer to Figure 2 A sensorless control method for low-speed permanent magnet synchronous motors, wherein the method utilizes a cross-decoupling complex coefficient filter to extract the response current generated by the voltage signal excitation at the optimal injection frequency from the stationary shaft system, and reconstructs the phase and amplitude of the extracted response current to obtain the reconstructed current observation value, wherein the cross-decoupling complex coefficient filter is: (4); In the formula, i αβ For the sampled stationary shaft current, i αβf i is the fundamental frequency current component of the stationary axis current. αβi1 i is the negative-sequence component of the response current of the stationary shaft system. αβi2 ω represents the positive-sequence component of the response current of the stationary shaft system. e ω is the electrical angular frequency of the motor; k is the filter gain of the cross-decoupling complex coefficient filter; s is the Laplace operator; j is the twitch factor.

[0027] The extracted response current is: (5); In the formula, i αi Let i be the α-axis response current of the stationary axis system. βi I is the β-axis response current of the stationary axis system. n I represents the magnitude of the negative sequence current component in the response current of the stationary shaft system. p This represents the amplitude of the positive sequence current component in the response current of the stationary shaft system.

[0028] The method for calculating the reconstructed current observations is as follows: (6); In the formula, For the reconstructed α-axis current observations, For the reconstructed β-axis current observations; φ d To account for phase errors caused by system delays, including pulse width modulation update delays and hardware delays.

[0029] In this embodiment, please refer to Figure 3 In the figure, k p_PLL For proportional gain, k i_PLL For integral gain; a sensorless control method for low-speed permanent magnet synchronous motors, wherein the method involves extracting the fundamental frequency response current signal from the reconstructed current observations using a cross-decoupling phase-locked loop (PLL); and constructing an equivalent rotor position tracking error signal using the fundamental frequency response current signal. The cross-decoupling PLL is: (7); In the formula, For the reconstructed current observations, For the fundamental frequency component in the reconstructed current observations, For the negative sequence component in the reconstructed current observations, k1 represents the positive sequence component in the reconstructed current observation; k1 is the filter gain value of the cross-decoupling phase-locked loop.

[0030] The fundamental frequency response current signal is: (8); In the formula, For the fundamental frequency current along the α axis in the reconstructed current observations, The fundamental frequency current of the β-axis in the reconstructed current observations.

[0031] The equivalent rotor position tracking error signal is: (9); In the formula, ε is the constructed equivalent rotor position tracking error signal.

[0032] Finally, the constructed equivalent rotor position tracking error signal is used to obtain the observed position and observed speed of the rotor through a proportional-integral converter, and the observed position and observed speed of the rotor are used as feedback signals for closed-loop vector control to realize low-noise injection sensorless operation of permanent magnet synchronous motor. To further verify the beneficial effects of the present invention, experimental verification was conducted: The experiment was conducted on a permanent magnet synchronous motor (PMSM) tractor test platform. A 2.2kW PMSM was coaxially connected to an induction motor, with the induction motor providing the load torque. The main parameters of the PMSM used were: rated voltage 380V, rated current 4.4A, rated torque 14N∙m, rated speed 1500r / min, d-axis inductance 22mH, q-axis inductance 52mH, number of pole pairs 3, rotor flux linkage 0.46Wb, and stator resistance 1.86Ω. The injected sinusoidal signal frequency was 80Hz, and the injected sinusoidal voltage amplitude was 9V.

[0033] Figure 4 and Figure 5 The figure shows the experimental waveform when the motor is running at 100 r / min and under rated load. Figure 4 This is the result when the motor is operating under position sensor control. Figure 5 The results show the motor operating without position sensor control. Due to the influence of resistance and filter phase shift, the position observation error reaches 42.1° without the method of this invention, making it difficult to achieve sensorless operation. After adopting the method of this invention, the position observation error is reduced to about 2.7°. The experimental results show that the method of this invention can effectively reduce the impact of factors such as filter phase shift and resistance on the position observation accuracy at low injection frequencies.

[0034] Figure 6 To compare the acoustic noise results of different injection strategies, a commercially available BSWA 308 sound level meter was used for sound pressure level testing. The experimental results show that the sound level of the method described in this invention is significantly lower than that of the fixed-frequency injection and the half-cycle switching random high-frequency sinusoidal injection methods, and the acoustic noise is close to that of no-signal injection. Compared with the fixed-frequency injection method, the method described in this invention reduces noise by approximately 12.9 dBA and 6.0 dBA at 100% rated load, respectively, compared to injections at 750 Hz and 500 Hz. Compared with the half-cycle switching random high-frequency sinusoidal injection method, the proposed method reduces noise by 3.8 dBA at 100% rated load, compared to injections at 500 / 300 Hz.

[0035] It should be understood that although the steps in the flowcharts of the various embodiments of the present invention are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the various embodiments may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.

[0036] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0037] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

[0038] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0039] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A low-speed position sensorless control method for permanent magnet synchronous motor, characterized in that, The low-speed position sensorless control method of the permanent magnet synchronous motor comprises the following steps: A mapping model between the injection frequency and the position observation error is established, an optimal injection frequency is selected according to the mapping model, and a voltage signal under the optimal injection frequency is injected into the stationary shaft system of the motor; A cross-decoupling complex coefficient filter is used to extract a response current generated by the voltage signal under the optimal injection frequency from the stationary shaft system, the extracted response current is reconstructed in phase and amplitude, and a reconstructed current observation value is obtained; A cross-decoupling phase-locked loop is used to extract a base frequency response current signal from the reconstructed current observation value, and the base frequency response current signal is used to construct an equivalent rotor position tracking error signal; The observation position and the observation speed of the rotor are obtained based on the equivalent rotor position tracking error signal, and the observation position and the observation speed of the rotor are used as feedback signals for closed-loop vector control, so that the permanent magnet synchronous motor is controlled without a position sensor.

2. The low-speed position sensorless control method of permanent magnet synchronous motor according to claim 1, characterized in that, In the step of establishing a mapping model between the injection frequency and the position observation error, selecting an optimal injection frequency according to the mapping model, and injecting a voltage signal under the optimal injection frequency into the stationary shaft system of the motor, the mapping model between the injection frequency and the position observation error is: （1）； wherein is the rotor position observation error, is the rotor actual position signal, is the rotor position observation signal, ; is the expected maximum rotor position observation error; φ n is the phase of the negative sequence current component in the stationary axis system response current, φ p is the phase of the positive sequence current component in the stationary axis system response current; φ n and φ p The calculation method is: （2）； where Ld dh is the d-axis self-inductance of the dq-axis system, Lq qh is the q-axis self-inductance of the dq-axis system, Lm dqh is the mutual inductance caused by the cross-coupling effect of the dq-axis system, L0 is the average inductance, is the difference inductance, L0 = (L dh + L qh ) / 2, L1 = (L dh - L qh ) / 2; R s is the stator resistance; ω i is the frequency of the low-frequency sinusoidal voltage signal; atan2(y, x) represents the four-quadrant inverse tangent function, which returns the angle between the point (x, y) and the positive x-axis, with the angle range being (-π, π].

3. The low-speed position sensorless control method of a permanent magnet synchronous motor according to claim 1 or 2, characterized by, In the step of establishing a mapping model between the injection frequency and the position observation error, selecting an optimal injection frequency according to the mapping model, and injecting a voltage signal under the optimal injection frequency into the stationary shaft system of the motor, the voltage signal under the optimal injection frequency injected into the stationary shaft system of the motor is a sinusoidal voltage signal: （3）； where u αi is the low frequency sinusoidal voltage signal of the stationary α-axis, u βi is the low frequency sinusoidal voltage signal of the stationary β-axis, U i is the low frequency sinusoidal voltage signal amplitude of the stationary axis system; t is time.

4. The low-speed position sensorless control method of permanent magnet synchronous motor according to claim 1, characterized in that, In the step of using a cross-decoupling complex coefficient filter to extract a response current generated by the voltage signal under the optimal injection frequency from the stationary shaft system, reconstructing the extracted response current in phase and amplitude, and obtaining a reconstructed current observation value, the cross-decoupling complex coefficient filter is: （4）； where i αβ is the sampled stationary axis system current, i αβf is the fundamental frequency current component of the stationary axis system current, i αβi1 is the negative sequence component of the stationary axis system response current, i αβi2 is the positive sequence component of the stationary axis system response current; ω e is the electrical angular frequency of the motor operation; k is the filter gain value of the cross-decoupling complex coefficient filter; s is the Laplace operator; j is the rotation factor.

5. The low-speed position sensorless control method of permanent magnet synchronous motor according to claim 4, characterized in that, In the step of using a cross-decoupling complex coefficient filter to extract a response current generated by the voltage signal under the optimal injection frequency from the stationary shaft system, reconstructing the extracted response current in phase and amplitude, and obtaining a reconstructed current observation value, the extracted response current is: （5）； where i αi is the alpha axis response current of the static shaft system, i βi is the beta axis response current of the static shaft system; I n is the negative sequence current component amplitude in the static shaft system response current, I p is the positive sequence current component amplitude in the static shaft system response current.

6. The low-speed position sensorless control method of a permanent magnet synchronous motor according to any one of claims 1, 4, and 5, characterized by, In the step of using a cross-decoupling complex coefficient filter to extract a response current generated by the voltage signal under the optimal injection frequency from the stationary shaft system, reconstructing the extracted response current in phase and amplitude, and obtaining a reconstructed current observation value, the calculation method of the reconstructed current observation value is: （6）； wherein is a reconstructed alpha-axis current observation value, is a reconstructed beta-axis current observation value; φ d is a phase error caused by system delay including pulse width modulation update delay and hardware delay.

7. The low-speed position sensorless control method of permanent magnet synchronous motor according to claim 1, characterized in that, In the step of using a cross-decoupling phase-locked loop to extract a base frequency response current signal from the reconstructed current observation value, and using the base frequency response current signal to construct an equivalent rotor position tracking error signal, the cross-decoupling phase-locked loop is: （7）； wherein is the reconstructed current observation value, is the fundamental frequency component in the reconstructed current observation value, is the negative sequence component in the reconstructed current observation value, is the positive sequence component in the reconstructed current observation value; and k1 is the filter gain value of the cross-decoupled phase-locked loop.

8. The low-speed position sensorless control method of a permanent magnet synchronous motor according to claim 7, characterized by, In the step of using a cross-decoupling phase-locked loop to extract a base frequency response current signal from the reconstructed current observation value, and using the base frequency response current signal to construct an equivalent rotor position tracking error signal, the base frequency response current signal is: （8）； In the formula, is the α-axis fundamental frequency current in the reconstructed current observation value, is the β-axis fundamental frequency current in the reconstructed current observation value.

9. The low-speed position sensorless control method of a permanent magnet synchronous motor according to any one of claims 1, 7, 8, characterized by, In the step of using a cross-decoupling phase-locked loop to extract a base frequency response current signal from the reconstructed current observation value, and using the base frequency response current signal to construct an equivalent rotor position tracking error signal, the equivalent rotor position tracking error signal is: （9）； In the formula, ε is the constructed equivalent rotor position tracking error signal.

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