A method of reconstructing error compensation single current sensor positionless control

Abstract

The application discloses a kind of reconfiguration error compensation single current sensor positionless control methods, it is related to permanent magnet synchronous motor positionless control field.The method includes: generating inverter driving signal using symmetric double side modulation strategy, sampling and reconfiguration are obtained to the complex phase current containing fundamental frequency current and high frequency current response for direct current bus current, reconfiguration error is divided into sampling interval error and period alignment error, the mapping relationship between current reconfiguration error and the sector where reference voltage vector is located is established under synchronous rotating coordinate system, current reconfiguration error is calculated by average current and error interval length, and the fundamental frequency current component in reconfiguration current is compensated;Second-order generalized integrator is used to extract high frequency current response from compensated reconfiguration current, after obtaining rotor position error signal according to the high frequency current response, rotor position estimation value is obtained through phase-locked loop, and positionless sensor closed-loop control is realized.The application can reduce the phase current reconfiguration error caused by single current sensor sampling, inhibit the distortion of reconfiguration current caused by the coupling of high frequency component and fundamental frequency component, improve rotor position estimation accuracy, and reduce control system cost.

Description

Technical Field

[0001] This invention relates to the field of sensorless control of permanent magnet synchronous motors, and in particular to a single current sensor-based sensor-based positionless control method with reconfiguration error compensation. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) offer advantages such as simple structure, high power density, and high efficiency. Sensorless control eliminates the cost associated with installing position sensors. While the fundamental wave model method can meet the system's control requirements at medium to high speeds, the motor's back EMF is small and the signal-to-noise ratio is low at zero and low speeds. Therefore, at low speeds, high-frequency signals are injected to estimate the rotor position. The introduction of single-current sensor technology further reduces system costs and avoids errors caused by different gain variations when using multiple current sensors. Traditional current reconfiguration schemes suffer from reconfiguration blind zones due to the need to consider inverter dead time and switching device turn-on and turn-off times. Failure to address these blind zones can lead to increased current reconfiguration errors or even reconfiguration failure. Therefore, to improve system control performance, effective solutions are needed to address these issues. Summary of the Invention

[0003] The purpose of this invention is to address the problems existing in the prior art by providing a single current sensor-based position control method with reconfiguration error compensation, which can reduce the error of the fundamental frequency component of the reconfigured current and thus improve the estimation accuracy of the rotor position.

[0004] The technical solution proposed in this invention is as follows:

[0005] A single-current-sensor-less position control method with reconstruction error compensation is disclosed. This method employs a symmetrical bilateral modulation strategy to generate an inverter drive signal, samples and reconstructs the DC bus current to obtain a composite phase current containing a fundamental frequency current component and a high-frequency current response component. The phase current reconstruction error is divided into sampling interval error and period alignment error. A mapping relationship between the current reconstruction error and the sector where the reference voltage vector is located is established in a synchronous rotating coordinate system. The current reconstruction error is calculated based on the average d-axis current, average q-axis current, and error interval duration within the two error intervals, and the fundamental frequency current component in the reconstructed current is compensated. Alternating polarity high-frequency square wave voltages are injected during adjacent switching cycles. A second-order generalized integrator extracts the high-frequency current response from the compensated reconstructed current. The rotor position error signal is obtained based on the high-frequency current response, and the rotor position estimate is obtained through a phase-locked loop, achieving sensorless closed-loop control.

[0006] The reconstruction error compensation method for a single current sensor without position control includes the following steps:

[0007] Step 1: Generate inverter drive signal using a symmetrical bilateral modulation strategy, and insert complementary effective voltage vector in the middle of the pulse width modulation period when the duration of the effective voltage vector is less than the minimum sampling time;

[0008] Step 2: Based on the symmetrical bilateral modulation waveform, the DC bus current is sampled in the second half of the switching cycle to reconstruct a composite phase current containing the fundamental frequency current component and the high-frequency current response component, and the reconstruction error is divided into sampling interval error and period alignment error.

[0009] Step 3: Establish the mapping relationship between reconstruction error and sector change. Under the synchronous rotating coordinate system, calculate the current reconstruction error based on the average d-axis and q-axis currents and the duration of the error interval in each error interval, and compensate for the fundamental frequency current component in the reconstruction current.

[0010] Step 4: Use a second-order generalized integrator to extract the high-frequency current response from the compensated reconstructed current, obtain the rotor position error signal based on the high-frequency current response, and obtain the rotor position estimate through a phase-locked loop to achieve sensorless closed-loop control.

[0011] Further analysis reveals the minimum sampling time T required for accurate sampling of the DC bus current. min The expression is:

[0012]

[0013] In the formula T d T represents the dead time of the inverter's switching devices. set T represents the duration of the transient process during the switching of the transistor state. con T is the analog-to-digital conversion time. min This represents the minimum sampling time required to sample the DC bus current.

[0014] When the duration T of the effective voltage vector a Less than the minimum sampling time T min At that time, an effective voltage vector that complements the insufficient duration vector is inserted into the middle of the pulse width modulated wave. The duration T of the inserted vector is... b for:

[0015]

[0016] In the formula T a T represents the effective vector duration that is insufficient in duration. b The duration of the inserted valid vector;

[0017] Based on the generated symmetrical pulse width modulation waveform, the first sampling time t1 and the second sampling time t2 are selected at the falling edge of the switching state of the second largest and largest duty cycles, respectively, and the end time of the current switching cycle is recorded as t. end ;

[0018] The reconstruction error is decomposed into the sampling interval error during t1 to t2 and the error during t2 to t... end The periodic alignment error consists of two parts, with a sampling interval error interval duration of T. gap1 The duration of the periodic alignment error interval is T. gap2 ;

[0019] When the reference voltage vector is located in the low modulation ratio dead zone, the sampling interval error interval duration T gap1 Take the minimum sampling time T min When the reference voltage vector is located in the sector boundary dead zone, the sampling interval error interval duration T gap1 Determined based on the effective voltage vector with insufficient action time, its expression is:

[0020]

[0021] In the formula, V1 to V6 represent the six effective voltage vectors; T x The duration of the effective voltage vector that first acts within the sector where the reference voltage vector is located;

[0022] Periodic alignment error interval duration T gap2 The value is fixed at the zero vector action time, and is independent of the sector where the reference vector is located;

[0023] Establish the voltage equations for the permanent magnet synchronous motor in the synchronous rotating coordinate system:

[0024]

[0025] In the formula u d and u q Represents the d-axis and q-axis voltage components, i d and i q Represents the d-axis and q-axis current components, ω e R is the electric angular velocity. s L is the stator resistance. d and L q ψ represents the inductance values ​​along the d-axis and q-axis. f For permanent magnet flux linkage;

[0026] Establish the mapping relationship between the d-axis and q-axis current reconstruction errors and the sector where the reference voltage vector is located. The total d-axis and q-axis current reconstruction errors are expressed as:

[0027]

[0028] In the formula, Δi d1 and Δi q1 These represent the d-axis current error and q-axis current error within the sampling interval error range, respectively; Δi d2 and Δi q2 These represent the d-axis current error and q-axis current error within the periodic alignment error interval, respectively; Δi d and Δi q T represents the total d-axis current reconstruction error and the total q-axis current reconstruction error obtained after sector mapping, respectively; p (θ e ) indicates that the rotor position angle is θ e The Park transformation matrix at time T; ip (θ e ) represents the corresponding inverse Park transformation matrix; T c T represents the Clarke transformation matrix; ic H represents the inverse Clarke transformation matrix; N This represents the phase current selection matrix when the reference voltage vector is located in the Nth sector, where N∈{1,2,3,4,5,6};

[0029] The first sector selection matrix H1 can be represented as:

[0030]

[0031] Within a very short error interval, the average current is used to approximate the rate of change of current. The reconstruction error is obtained based on the voltage vector effect and the duration of the error interval. Within the sampling interval error interval, the effective voltage vector is considered. The expressions for the d-axis and q-axis current reconstruction errors within the sampling interval error interval are as follows:

[0032]

[0033] In the formula, u d1 and u q1 These represent the d-axis voltage component and q-axis voltage component of the effective voltage vector within the sampling interval error interval, respectively; i avd1 and i avq1 These represent the average values ​​of the d-axis current and q-axis current within the sampling interval error range, respectively.

[0034] Within the period alignment error interval, the voltage vector acts as zero, and both the d-axis and q-axis components of the inverter output voltage are zero. The d-axis and q-axis current errors within the period alignment error interval can be expressed as:

[0035]

[0036] In the formula, i avd2 and i avq2 These represent the average values ​​of the d-axis current and q-axis current within the periodic alignment error interval, respectively.

[0037] The compensated d-axis and q-axis currents are expressed as follows:

[0038]

[0039] In the formula i dtotal and i qtotal For the compensated d-axis and q-axis currents, i dcon and i qcon Reconstruct the current for the d-axis and q-axis;

[0040] When square wave voltages with different polarities are injected in adjacent switching cycles, the high-frequency current response components of the reconstructed current obtained by superimposing the high-frequency square wave voltage with the symmetrical bilateral modulation strategy satisfy the following:

[0041]

[0042] In the formula i dqh (k-1) and i dqh (k) represents the high-frequency current response values ​​of the reconstructed current at time k-1 and time k, respectively;

[0043] The transfer function of the second-order generalized integrator is:

[0044]

[0045] In the formula, s represents the Laplace operator; ω0 represents the center angular frequency of the second-order generalized integrator; and k represents the damping coefficient of the second-order generalized integrator.

[0046] When a high-frequency square wave voltage is injected, the voltage equation of the motor simplifies to:

[0047]

[0048] In the formula u dh and u qh For the d-axis and q-axis voltages at high frequencies, i dh and i qh For the d-axis and q-axis currents at high frequencies, L dh and L qh d represents the d-axis and q-axis inductance at high frequencies; p represents the differential operator, and p = d / dt;

[0049] Inject a high-frequency voltage along the selected estimated d-axis, as follows:

[0050]

[0051] In the formula u d̂h and u q̂h This represents the estimated d-axis and q-axis injection voltages, V inj Indicates the injected voltage amplitude; k represents the switching cycle number;

[0052] The expression for the rotor position error is obtained as follows:

[0053]

[0054] In the formula, Δθ e This represents the estimated rotor position error between the synchronous rotating coordinate system and the actual synchronous rotating coordinate system; i q̂h This represents the estimated q-axis high-frequency current response in a synchronously rotating coordinate system;

[0055] By inputting the rotor position error into the phase-locked loop, the rotor position estimate and the electrical angular velocity estimate can be obtained. The rotor position estimate is then fed back to the coordinate transformation stage and the base frequency current control stage to achieve sensorless closed-loop control of the permanent magnet synchronous motor.

[0056] Beneficial Effects: Due to the adoption of the above technical solution, this invention is applicable to a single-current sensor positionless control method with reconstruction error compensation. It employs a symmetrical modulation method, and through the reasonable setting of sampling points and the application of a current reconstruction error compensation scheme, it can reduce the error of the reconstructed current, improve the control performance of the fundamental frequency current loop, and thus reduce the position estimation error. A second-order generalized integrator is used for frequency selection and decoupling of the high-frequency current response, reducing the distortion of the reconstructed current caused by the mixing of high-frequency response components with the fundamental frequency component. Furthermore, since only one current sensor is used, the system cost is significantly reduced. Therefore, this technical solution is suitable for low-cost positionless control methods. Attached Figure Description

[0057] Figure 1 This is a control block diagram of the single current sensor positionless control method for reconstructing error compensation in this invention;

[0058] Figure 2 This is a schematic diagram of the symmetrical pulse width modulation waveform and the sampling time in the first sector in this invention;

[0059] Figure 3 A schematic diagram for inserting a vector when the effective vector duration of the first sector is insufficient;

[0060] Figure 4This is a structural diagram of a second-order generalized integrator;

[0061] Figure 5 This is a schematic diagram showing the relationship between the coordinate axes during square wave injection in this invention; Detailed Implementation

[0062] The permanent magnet synchronous motor to which this invention is applicable will be further described below with reference to the accompanying drawings:

[0063] The minimum sampling time T required to accurately sample the DC bus current min The expression is:

[0064]

[0065] In the formula T d T represents the dead time of the inverter's switching devices. set T represents the duration of the transient process during the switching of the transistor state. con T is the analog-to-digital conversion time. min This represents the minimum sampling time required to sample the DC bus current.

[0066] When the duration T of the effective voltage vector a Less than the minimum sampling time T min At that time, an effective voltage vector that complements the insufficient duration vector is inserted into the middle of the pulse width modulated wave. The duration T of the inserted vector is... b for:

[0067]

[0068] In the formula T a T represents the effective vector duration that is insufficient in duration. b The duration of the inserted valid vector;

[0069] Figure 1 The diagram shows a control block diagram for a single current sensor positionless control method with reconstruction error compensation. During normal operation, the three-phase current is sampled by a single current sensor within one switching cycle. Then, a current compensation scheme is formulated based on the sampling point position to compensate the fundamental frequency current. After the high-frequency signal is decoupled by a second-order generalized integrator, the high-frequency signal is input into the phase-locked loop to extract the position information.

[0070] Based on the generated symmetrical pulse width modulation waveform, the first sampling time t1 and the second sampling time t2 are selected at the falling edge of the switching state of the second largest and largest duty cycles, respectively, and the end time of the current switching cycle is recorded as t. end ;

[0071] The reconstruction error is decomposed into the sampling interval error during t1 to t2 and the error during t2 to t... end The periodic alignment error consists of two parts, with a sampling interval error interval duration of T. gap1 The duration of the periodic alignment error interval is T. gap2 ;

[0072] Figure 2 The symmetrical pulse width modulation wave generated by the symmetrical bilateral modulation strategy extends the effective vector's duration while maintaining the symmetry of the pulse width modulation waveform and not changing the duty cycle of each phase.

[0073] When the reference voltage vector is located in the low modulation ratio dead zone, the sampling interval error interval duration T gap1 Take the minimum sampling time T min When the reference voltage vector is located in the sector boundary dead zone, the sampling interval error interval duration T gap1 Determined based on the effective voltage vector with insufficient action time, its expression is:

[0074]

[0075] In the formula, V1 to V6 represent the six effective voltage vectors; T x The duration of the effective voltage vector that first acts within the sector where the reference voltage vector is located;

[0076] Periodic alignment error interval duration T gap2 The value is fixed at the zero vector action time, and is independent of the sector where the reference vector is located;

[0077] Figure 3 This refers to the processing performed when the reference vector for the first sector is located at the sector boundary. The two valid vectors are V1 and V2, respectively. When the reference vector V... ref Approaching vector V1 means that half the duration of vector V2 at this point may be less than T. min At this point, the effectiveness of sampling cannot be guaranteed. To extend the duration of the V2 vector, a portion of the zero vector V7 in the middle of the pulse width modulation wave is replaced with the complementary vector V5 of the V2 vector. Simultaneously, the corresponding A-phase and B-phase pulse width modulation waveforms are extended to both sides. This satisfies the minimum sampling time T required when V2 is active within half a switching cycle. min This meets the requirements while ensuring that the average voltage vector remains unchanged.

[0078] Establish the voltage equations for the permanent magnet synchronous motor in the synchronous rotating coordinate system:

[0079]

[0080] In the formula ud and u q Represents the d-axis and q-axis voltage components, i d and i q Represents the d-axis and q-axis current components, ω e R is the electric angular velocity. s L is the stator resistance. d and L q ψ represents the inductance values ​​along the d-axis and q-axis. f For permanent magnet flux linkage;

[0081] Establish the mapping relationship between the d-axis and q-axis current errors and the sector where the reference voltage vector is located. The total d-axis and q-axis current reconstruction error is expressed as:

[0082]

[0083] In the formula, Δi d1 and Δi q1 These represent the d-axis current error and q-axis current error within the sampling interval error range, respectively; Δi d2 and Δi q2 These represent the d-axis current error and q-axis current error within the periodic alignment error interval, respectively; Δi d and Δi q T represents the total d-axis current reconstruction error and the total q-axis current reconstruction error obtained after sector mapping, respectively; p (θ e ) indicates that the rotor position angle is θ e The Park transformation matrix at time T; ip (θ e ) represents the corresponding inverse Park transformation matrix; T c T represents the Clarke transformation matrix; ic H represents the inverse Clarke transformation matrix; N This represents the phase current selection matrix when the reference voltage vector is located in the Nth sector, where N∈{1,2,3,4,5,6};

[0084]

[0085] Within a very short error interval, the average current is used to approximate the rate of change of current. The reconstruction error is obtained based on the voltage vector effect and the duration of the error interval. Within the sampling interval error interval, the effective voltage vector is considered. The expressions for the d-axis and q-axis current reconstruction errors within the sampling interval error interval are as follows:

[0086]

[0087] In the formula, ud1 and u q1 These represent the d-axis voltage component and q-axis voltage component of the effective voltage vector within the sampling interval error interval, respectively; i avd1 and i avq1 These represent the average values ​​of the d-axis current and q-axis current within the sampling interval error range, respectively.

[0088] Within the period alignment error interval, the voltage vector acts as zero, and both the d-axis and q-axis components of the inverter output voltage are zero. The d-axis and q-axis current errors within the period alignment error interval can be expressed as:

[0089]

[0090] In the formula, i avd2 and i avq2 These represent the average values ​​of the d-axis current and q-axis current within the periodic alignment error interval, respectively.

[0091] The compensated d-axis and q-axis currents are expressed as follows:

[0092]

[0093] In the formula i dtotal and i qtotal For the compensated d-axis and q-axis currents, i dcon and i qcon Reconstruct the current for the d-axis and q-axis;

[0094] When square wave voltages with different polarities are injected in adjacent switching cycles, the high-frequency current response components of the reconstructed current obtained by superimposing the high-frequency square wave voltage with the symmetrical bilateral modulation strategy satisfy the following:

[0095]

[0096] In the formula i dqh (k-1) and i dqh (k) represents the high-frequency current response values ​​of the reconstructed current at time k-1 and time k, respectively;

[0097] The transfer function of the second-order generalized integrator is:

[0098]

[0099] In the formula, s represents the Laplace operator; ω0 represents the center angular frequency of the second-order generalized integrator; and k represents the damping coefficient of the second-order generalized integrator.

[0100] Figure 4The diagram shows the structure of a second-order generalized integrator, which can extract the target frequency component by utilizing the narrowband bandpass characteristic. In other words, it can directly extract the high-frequency current response with the same frequency as the injection frequency, and extract the position estimation angle from it.

[0101] When a high-frequency square wave voltage is injected, the voltage equation of the motor simplifies to:

[0102]

[0103] In the formula u dh and u qh For the d-axis and q-axis voltages at high frequencies, i dh and i qh For the d-axis and q-axis currents at high frequencies, L dh and L qh d represents the d-axis and q-axis inductance at high frequencies; p represents the differential operator, and p = d / dt;

[0104] Inject a high-frequency voltage along the selected estimated d-axis, as follows:

[0105]

[0106] In the formula u d̂h and u q̂h This represents the estimated d-axis and q-axis injection voltages, V inj Indicates the injected voltage amplitude; k represents the switching cycle number;

[0107] The expression for the rotor position error is obtained as follows:

[0108]

[0109] In the formula, Δθ e This represents the estimated rotor position error between the synchronous rotating coordinate system and the actual synchronous rotating coordinate system; i q̂h This represents the estimated high-frequency q-axis current response in a synchronously rotating coordinate system;

[0110] Figure 5 This diagram illustrates the relationship between the coordinate axes used in high-frequency square wave injection. High-frequency voltage is injected onto the estimated d-axis, and the motor model is transformed to derive the rotor position error expression.

[0111] The rotor position error is input into the phase-locked loop to obtain the rotor position estimate and the electrical angular velocity estimate. The rotor position estimate is then fed back to the coordinate transformation stage and the base frequency current control stage to achieve sensorless closed-loop control of the permanent magnet synchronous motor.

[0112] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, shall fall within the scope of protection of the technical solution of the present invention.

Claims

1. A method for position-free control of a single current sensor with reconstruction error compensation, characterized in that, A symmetrical bilateral modulation strategy is used to generate the inverter drive signal. The DC bus current is sampled and reconstructed to obtain a composite phase current containing a fundamental frequency current component and a high-frequency current response component. The phase current reconstruction error is divided into sampling interval error and period alignment error. A mapping relationship between the current reconstruction error and the sector where the reference voltage vector is located is established in a synchronous rotating coordinate system. The current reconstruction error is calculated based on the average d-axis current, average q-axis current and error interval duration in the two error intervals, and the fundamental frequency current component in the reconstructed current is compensated. High-frequency square wave voltages with alternating polarity are injected in adjacent switching cycles. A second-order generalized integrator is used to extract the high-frequency current response from the compensated reconstructed current. The rotor position error signal is obtained based on the high-frequency current response, and the rotor position estimate is obtained through a phase-locked loop to achieve sensorless closed-loop control. The reconstruction error compensation method for a single current sensor without position control includes the following steps: Step 1: Generate inverter drive signal using a symmetrical bilateral modulation strategy, and insert complementary effective voltage vector in the middle of the pulse width modulation period when the duration of the effective voltage vector is less than the minimum sampling time; Step 2: Based on the symmetrical bilateral modulation waveform, the DC bus current is sampled in the second half of the switching cycle to reconstruct a composite phase current containing the fundamental frequency current component and the high-frequency current response component, and the reconstruction error is divided into sampling interval error and period alignment error. Step 3: Establish the mapping relationship between reconstruction error and sector change. Under the synchronous rotating coordinate system, calculate the current reconstruction error based on the average d-axis and q-axis currents and the duration of the error interval in each error interval, and compensate for the fundamental frequency current component in the reconstruction current. Step 4: Use a second-order generalized integrator to extract the high-frequency current response from the compensated reconstructed current, obtain the rotor position error signal based on the high-frequency current response, and obtain the rotor position estimate through a phase-locked loop to achieve sensorless closed-loop control. The specific steps in step 1 are as follows: The minimum sampling time T required to accurately sample the DC bus current min The expression is: In the formula T d T represents the dead time of the inverter's switching devices. set T represents the duration of the transient process during the switching of the transistor state. con T is the analog-to-digital conversion time. min This represents the minimum sampling time required to sample the DC bus current. When the duration T of the effective voltage vector a Less than the minimum sampling time T min At that time, an effective voltage vector that complements the insufficient effective voltage vector is inserted into the middle of the pulse width modulated wave. The duration T of the inserted vector is... b for: In the formula, T a For the duration of the effective voltage vector that is insufficient in duration, T b The duration of the inserted complementary effective voltage vector; The specific steps in step 2 are as follows: Based on the symmetrical pulse width modulation waveform generated in step 1, the first sampling time t1 and the second sampling time t2 are selected at the falling edge of the switching state of the second largest and largest duty cycles, respectively, and the end time of the current switching cycle is recorded as t. end ; The reconstruction error is divided into the sampling interval error during the period from t1 to t2 and the error during the period from t2 to t... end The periodic alignment error consists of two parts, with a sampling interval error interval duration of T. gap1 The duration of the periodic alignment error interval is T. gap2 ; When the reference voltage vector is located in the low modulation ratio dead zone, the sampling interval error interval duration T gap1 Take the minimum sampling time T min When the reference voltage vector is located in the sector boundary dead zone, the sampling interval error interval duration T gap1 Determined based on the effective voltage vector with insufficient action time, its expression is: In the formula, V1 to V6 represent the six effective voltage vectors; T x The duration of the effective voltage vector that first acts within the sector where the reference voltage vector is located; Periodic alignment error interval duration T gap2 The value is fixed at the zero vector action time, and is independent of the sector where the reference vector is located; The specific steps in step 3 are as follows: Establish the voltage equations for the permanent magnet synchronous motor in the synchronous rotating coordinate system: In the formula, u d and u q These represent the d-axis and q-axis voltage components, respectively; i d and i q These represent the d-axis and q-axis current components, respectively; ω e R is the electric angular velocity; s For stator resistance; L d and L q These represent the inductance values ​​along the d-axis and q-axis, respectively; ψ f For permanent magnet flux linkage; Establish the mapping relationship between the d-axis and q-axis current reconstruction errors and the sector where the reference voltage vector is located. The total d-axis and q-axis current reconstruction errors are expressed as: In the formula, Δi d1 and Δi q1 These represent the d-axis current error and q-axis current error within the sampling interval error range, respectively; Δi d2 and Δi q2 These represent the d-axis current error and q-axis current error within the periodic alignment error interval, respectively; Δi d and Δi q T represents the total d-axis current reconstruction error and the total q-axis current reconstruction error obtained after sector mapping, respectively; p (θ e ) indicates that the rotor position angle is θ e The Park transformation matrix at time T; ip (θ e ) represents the corresponding inverse Park transformation matrix; T c T represents the Clarke transformation matrix; ic H represents the inverse Clarke transformation matrix; N This represents the phase current selection matrix when the reference voltage vector is located in the Nth sector, where N∈{1,2,3,4,5,6}; When the reference voltage vector is located in the first sector, the phase current selection matrix H1 is expressed as: Within a very short error interval, the average current is used to approximate the rate of change of current. The reconstruction error is obtained based on the average current along the d-axis and q-axis and the duration of the error interval. Within the sampling interval error interval, the effective voltage vector acts. The expressions for the d-axis and q-axis current reconstruction errors within the sampling interval error interval are as follows: In the formula, u d1 and u q1 These represent the d-axis voltage component and q-axis voltage component of the effective voltage vector within the sampling interval error interval, respectively; i avd1 and i avq1 These represent the average values ​​of the d-axis current and q-axis current within the sampling interval error range, respectively. Within the period alignment error interval, the voltage vector acts as zero, and both the d-axis and q-axis components of the inverter output voltage are zero. The d-axis and q-axis current errors within the period alignment error interval can be expressed as: In the formula, i avd2 and i avq2 These represent the average values ​​of the d-axis current and q-axis current within the periodic alignment error interval, respectively. The compensated d-axis and q-axis currents are expressed as follows: In the formula, i dtotal and i qtotal Let i represent the compensated d-axis current and q-axis current, respectively. dcon and i qcon These represent the reconstructed d-axis current and the reconstructed q-axis current before compensation, respectively. The specific steps in step 4 are as follows: When square wave voltages with different polarities are injected in adjacent switching cycles, the high-frequency current response components of the reconstructed current obtained by superimposing the high-frequency square wave voltage with the symmetrical bilateral modulation strategy satisfy the following: In the formula, i dqh (k-1) and i dqh (k) represent the high-frequency current response components in the reconstructed current during the (k-1)th and kth switching cycles, respectively; The transfer function of the second-order generalized integrator is: In the formula, s represents the Laplace operator; ω0 represents the center angular frequency of the second-order generalized integrator; and k represents the damping coefficient of the second-order generalized integrator. When a high-frequency square wave voltage is injected, the voltage equation of the motor simplifies to: In the formula, u dh and u qh These represent the d-axis and q-axis voltages at high frequencies, respectively; i dh and i qh L represents the d-axis and q-axis currents at high frequencies, respectively. dh and L qh d and q represent the inductance at high frequencies, respectively; p represents the differential operator, and p = d / dt; Injecting a high-frequency voltage along the selected estimated d-axis can be expressed as: In the formula, u d̂h and u q̂h V represents the estimated d-axis and q-axis injection voltages, respectively. inj Indicates the injected voltage amplitude; k represents the switching cycle number; The expression for the rotor position error is obtained as follows: In the formula, Δθ e This represents the estimated rotor position error between the synchronous rotating coordinate system and the actual synchronous rotating coordinate system; i q̂h This represents the estimated q-axis high-frequency current response in a synchronously rotating coordinate system; By inputting the rotor position error into the phase-locked loop, the rotor position estimate and the electrical angular velocity estimate can be obtained. The rotor position estimate is then fed back to the coordinate transformation stage and the base frequency current control stage to achieve sensorless closed-loop control of the permanent magnet synchronous motor.

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