A robust sensorless predictive current control method for permanent magnet synchronous motors

Abstract

The present invention discloses a robustly enhanced sensorless permanent magnet synchronous motor predictive current control method. The method comprises: designing an adaptive super-helical sliding mode disturbance observer based on the predictive current equation of the permanent magnet synchronous motor; establishing a predictive voltage equation and an online parameter identifier; obtaining a predicted voltage based on the motor operating parameters, the sliding mode disturbance observer, and the predictive voltage equation, obtaining an identification parameter error based on the online parameter identifier, and jointly participating in vector closed-loop control to achieve predictive current control. The present invention solves the limitation that predictive current control only achieves robust enhancement of the current loop and achieves online identification of multiple parameters of the motor. The robustness of the sensorless observer is further enhanced through feedback of the identification parameters. The method has a better vibration suppression effect, can achieve accurate observation of lumped disturbances under a large range of parameter mismatches, further weakens current harmonics and improves the accuracy of parameter identification, thereby improving the stability and robustness of the motor vector closed-loop control.

Description

Technical Field

[0001] The present invention relates to a motor predictive current control method, and relates to the technical field of sensorless permanent magnet synchronous motor predictive control and parameter identification, and in particular to a robust enhanced sensorless permanent magnet synchronous motor predictive current control method. Background Art

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in electric vehicles, wind turbines, and industrial drive systems. Their high efficiency and stability make them an ideal replacement for traditional motors. High dynamic response and robust control algorithms are key requirements for sensorless control of PMSMs. High dynamic response determines the motor's ability to quickly adjust speed and torque, enabling it to adapt to rapidly changing operating conditions and load requirements. Robust control algorithms ensure control stability under various disturbances and uncertainties, ensuring efficient and stable operation of the motor in diverse environments and operating conditions.

[0003] The current loop, as the innermost loop of a permanent magnet synchronous motor (PMSM) control system, largely determines the dynamic response capability and steady-state error level of the PMSM's output electromagnetic torque. Model Predictive Control (MPC), due to its simple design process and fast dynamic response for handling multiple control variables and multiple system constraints, has gradually replaced the traditional proportional integral controller (PI) as the advanced control strategy for the current loop. Factors such as temperature rise, demagnetization, and magnetic saturation during operation of a PMSM cause a certain degree of drift in the resistance, inductance, and flux linkage parameters. To decouple the parameter dependence of MPC and improve the robustness of the current loop, methods such as the extended state disturbance observer (ESDO) and the sliding mode disturbance observer (SMO) have been proposed and applied. However, traditional SMOs are limited by bandwidth, while low-order SMOs inevitably suffer from chattering due to fixed gains. In particular, designing a complex reaching law for SMOs can lead to difficulties in parameter tuning and exacerbate chattering. It is worth noting that traditional predictive control strategies are mostly applied to sensor-based control systems. For sensorless permanent magnet synchronous motor FOC (Field-Oriented Control) control, parameter mismatch of the sensorless observer can lead to oscillation of the observer's electrical angle and electrical angular velocity, and even algorithm divergence. Summary of the Invention

[0004] To address the problems in the background art, the present invention provides a robust sensorless permanent magnet synchronous motor predictive current control method. When motor parameters are mismatched, the sensorless observer will have errors in estimating the electrical angle and electrical angular velocity, leading to divergence of the FOC algorithm. The present invention designs a sliding mode disturbance observer combined with a chattering suppression algorithm. This, combined with current loop predictive control and parameter identification, can improve the robustness of the current loop and sensorless observer while maintaining the high dynamic response capability of the current loop. This method enables sensorless permanent magnet synchronous motor FOC control to have the advantages of high dynamic response and strong robustness, thus possessing significant research value and application potential.

[0005] The technical solution adopted in the present invention is:

[0006] The robust enhanced sensorless permanent magnet synchronous motor predictive current control method of the present invention comprises:

[0007] S1: Establish a predictive current equation for a sensorless permanent magnet synchronous motor and design an adaptive super-helical sliding mode disturbance observer based on the predictive current equation; design an adaptive super-helical sliding mode disturbance observer to achieve online observation of the lumped disturbance.

[0008] S2: Establish a predictive voltage equation based on zero-beat current control and an online parameter identifier using the recursive least squares method with a forgetting factor. The predictive voltage equation realizes online compensation of disturbances while considering the one-beat delay problem of the actual digital system. The online parameter identifier realizes online identification of multiple motor parameters such as resistance, inductance, and flux linkage errors.

[0009] S3: The d-axis and q-axis stator currents and stator voltages and rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the current moment are input into the adaptive super-helical sliding mode disturbance observer for processing. After processing, the adaptive super-helical sliding mode disturbance observer outputs the d-axis and q-axis stator currents and estimated values ​​of the lumped disturbance at the next moment. The d-axis and q-axis stator currents and estimated values ​​of the lumped disturbance at the next moment, the d-axis and q-axis reference currents and rotor electrical angular velocity at the current moment are input into the predicted voltage equation based on zero-beat current control for processing. After processing, the predicted voltage equation of zero-beat current control outputs the d-axis and q-axis stator voltages at the next moment to perform vector control FOC closed-loop control of the sensorless permanent magnet synchronous motor.

[0010] S4: The current d-axis and q-axis stator currents and voltages of the sensorless permanent magnet synchronous motor, the rotor electrical angular velocity, and the estimated d-axis and q-axis lumped disturbances output by the adaptive super-helical sliding mode disturbance observer are input into a recursive least squares online parameter identifier with a forgetting factor for processing. After processing, the recursive least squares online parameter identifier with a forgetting factor outputs a parameter error vector to the sensorless observer in the vector control (FOC) closed-loop control, ultimately achieving predictive current control of the sensorless permanent magnet synchronous motor. The identified parameter error is fed back online to the sensorless observer to achieve observer robustness enhancement.

[0011] In step S1, the predicted current equation of the permanent magnet synchronous motor is as follows:

[0012]

[0013] in, and are the predicted stator currents of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k+1th sampling moment; T s is the sampling interval, i.e. the execution period of vector control FOC closed-loop control; R s and L s are the stator rated phase resistance and stator rated phase inductance of the sensorless permanent magnet synchronous motor respectively; i d (k) and i q (k) are the stator currents of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; ω e (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment; u d (k) and u q (k) are the stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; f d (k) and f q (k) are the lumped disturbances of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; ψ f is the permanent magnet flux linkage of the sensorless permanent magnet synchronous motor.

[0014] The prerequisite for establishing the ideal voltage equation of a sensorless permanent magnet synchronous motor in a rotating coordinate system is to ignore factors such as the cross-saturation effect of the motor inductance and the deviation of the motor's rated parameters. To characterize the voltage deviation caused by motor parameter mismatch, the ideal voltage equation is reconstructed into an actual voltage equation as follows:

[0015]

[0016] Among them, u d 、u q 、i d and iq are the stator voltage and stator current of d-axis and q-axis respectively; f d and f q are the lumped disturbances of the d-axis and q-axis caused by the deviation of the actual parameters of the motor from the rated parameters; L d and L q are the stator inductances of the d-axis and q-axis respectively. Taking the surface-mounted permanent magnet synchronous motor as an example, the d-axis and q-axis inductances are equal and unified as the stator rated phase inductance L s ; After further discretization through the forward Euler method, the actual voltage equation under discrete conditions can be obtained, that is, the predicted current equation.

[0017] In step S1, the adaptive super-helical sliding mode disturbance observer is specifically as follows:

[0018]

[0019]

[0020]

[0021]

[0022] in, and are the estimated values ​​of the stator current of the sensorless permanent magnet synchronous motor on the d-axis and q-axis at the k+1th sampling time, respectively. and are the estimated values ​​of the lumped disturbances of the sensorless permanent magnet synchronous motor on the d-axis and q-axis at the k+1th sampling moment; T s is the sampling interval; R s and L s are the stator rated phase resistance and stator rated phase inductance of the sensorless permanent magnet synchronous motor respectively; and are the estimated values ​​of the stator current of the sensorless permanent magnet synchronous motor along the d-axis and q-axis at the k-th sampling moment; ω e (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment; u d (k) and u q (k) are the stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; and are the estimated values ​​of the lumped disturbances of the sensorless permanent magnet synchronous motor on the d-axis and q-axis at the k-th sampling moment; U dSTA and U qSTAare the sliding mode functions based on the adaptive superhelical algorithm for the d-axis and q-axis of the sensorless permanent magnet synchronous motor respectively; δ is the disturbance term gain, δ>0; λ1 and λ2 are the first and second positive gains; s d and s q are the sliding surfaces formed by the d-axis and q-axis current errors, respectively, and the input error s d 、s q Adaptation is achieved through the hyperbolic tangent function inside the sliding mode function to suppress the sliding mode chattering problem; tanh() is a hyperbolic tangent function with adjustable boundary layer. The traditional superhelical algorithm itself is a second-order sliding mode algorithm and has a certain chattering suppression effect, but its built-in sign function is a step switching function, which cannot achieve adaptation to the input error under fixed gain. When the error decreases, it will be affected by the fixed gain and cause sliding mode chattering; τ is the time variable; i d (k) and i q (k) are the d-axis and q-axis stator currents of the sensorless permanent magnet synchronous motor at the k-th sampling moment; x is the input of the hyperbolic tangent function tanh(), and m is the positive gain of the hyperbolic tangent function tanh(). When the input error is within the gain constraint range, the hyperbolic tangent function can achieve error adaptation and further improve the jitter problem caused by fixed gain.

[0023] In step S2, the predicted voltage equation based on deadbeat current control is as follows:

[0024]

[0025] Among them, u d (k+1) and u q (k+1) are the predicted stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k+1th sampling moment, respectively, to compensate for the one-beat delay of the actual digital system; R s and L s are the stator rated phase resistance and stator rated phase inductance of the sensorless permanent magnet synchronous motor respectively; T s is the sampling interval; and are the reference currents of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment, based on i d =0 controlled d-axis reference current is always zero, that is, The q-axis reference current is provided by the speed loop output, and the speed loop execution frequency is approximately 1 / 20 to 1 / 10 of the current loop execution frequency. It is worth noting that the mechanical frequency of the permanent magnet synchronous motor is much smaller than the electrical frequency, so the electrical angular velocity in adjacent cycles can be considered equal; and are the estimated values ​​of the stator current of the sensorless permanent magnet synchronous motor on the d-axis and q-axis at the k+1th sampling moment; ωe (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment; and are the estimated values ​​of the lumped disturbances of the sensorless permanent magnet synchronous motor on the d-axis and q-axis at the k+1th sampling moment, The disturbance observer is used to observe and compensate online; ψ f is the permanent magnet flux linkage of the sensorless permanent magnet synchronous motor.

[0026] The command voltage u calculated at the kth sampling moment of the actual digital control system d (k) and u q (k) is actually applied to the inverter module at the k+1th moment, and the inverter module takes about half of the sampling period to apply the voltage to the permanent magnet synchronous motor winding. A one-step advance prediction voltage equation is further established based on the predicted current equation.

[0027] In step S2, the recursive least squares online parameter identifier with forgetting factor is specifically as follows:

[0028]

[0029] Φ(k)=[ΔR s ,ΔL s ,Δψ f ] T

[0030]

[0031] Among them, Φ(k) and Φ(k-1) are the parameter error vectors to be identified of the sensorless permanent magnet synchronous motor at the kth and k-1th sampling moments, respectively, ΔR s , ΔL s and Δψ f are the resistance error, inductance error, and flux linkage error of the sensorless permanent magnet synchronous motor respectively; P(k) and P(k-1) are the covariance matrices at the k-th and k-1-th sampling moments respectively, and the order is the number of objects to be identified; y(k) is the disturbance input of the online parameter identifier at the k-th sampling moment, including the estimated value of the lumped disturbance of the d-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment and the estimated value of the lumped disturbance on the q axis is the measurement input of the online parameter identifier at the kth sampling moment; κ is the forgetting factor of the least squares parameter identification method.

[0032] Measurement input The details are as follows:

[0033]

[0034] The recursive least squares parameter identification equation with forgetting factor is designed based on the lumped disturbance formula to realize the online identification of motor multi-parameters including resistance, inductance and flux linkage errors.

[0035] In the step S4, the recursive least squares method with a forgetting factor is used to process the online parameter identifier and output the parameter error vector to the sensorless observer in the vector control FOC closed-loop control. The motor parameter error is corrected for the stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor in the synchronous rotating coordinate system, or the motor parameter error is corrected for the stator voltages of the α-axis and β-axis of the sensorless permanent magnet synchronous motor in the stationary coordinate system. After the motor parameter error is corrected, the sensorless observer outputs the electrical angular velocity and electrical angle to realize FOC control of the sensorless permanent magnet synchronous motor.

[0036] The identification parameter error is fed back online to the sensorless observer to achieve robust enhancement of the observer. Generally, the sensorless observer based on back electromotive force or permanent magnet flux signal is established under the voltage equation of the permanent magnet synchronous motor stationary coordinate system or the voltage equation of the synchronous rotating coordinate system, that is, the identification parameter error is fed back and updated to the voltage equation of the sensorless observer to achieve robust enhancement.

[0037] The stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor in the synchronous rotating coordinate system after the motor parameter error correction are specifically as follows:

[0038]

[0039] Among them, u d ′(k) and u q ′(k) are the stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the kth sampling moment after the motor parameter error correction; R s and L s are the stator rated phase resistance and stator rated phase inductance of the sensorless permanent magnet synchronous motor respectively; ΔR s , ΔL s and Δψ f are the resistance error, inductance error and flux linkage error of the sensorless permanent magnet synchronous motor respectively; i d (k) and i q (k) are the stator currents of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; ω e (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment; ψ f is the permanent magnet flux linkage of the sensorless permanent magnet synchronous motor.

[0040] The stator voltages of the α-axis and β-axis of the sensorless permanent magnet synchronous motor in the stationary coordinate system after the motor parameter error correction are specifically as follows:

[0041]

[0042] Among them, u α ′(k) and u′ β (k) are the stator voltages of the α-axis and β-axis of the sensorless permanent magnet synchronous motor at the kth sampling moment after the motor parameter error correction; R s and L s are the stator rated phase resistance and stator rated phase inductance of the sensorless permanent magnet synchronous motor respectively; ΔR s , ΔL s and Δψ f are the resistance error, inductance error and flux linkage error of the sensorless permanent magnet synchronous motor respectively; i α (k) and i β (k) are the stator currents of the α-axis and β-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; ω e (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment; ψ f is the permanent magnet flux linkage of the sensorless permanent magnet synchronous motor; θ e (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment.

[0043] The electronic device of the present invention comprises: a memory and a processor coupled to each other, wherein the memory stores program data, and the processor calls the program data to execute the method described above.

[0044] The computer-readable storage medium of the present invention stores program data thereon, and when the program data is executed by a processor, the method described above is implemented.

[0045] The method of the present invention can achieve input error adaptation for the sliding mode disturbance observer and effectively suppress the chattering phenomenon inherent in traditional sliding mode, enabling accurate observation of lumped disturbances and suppression of total harmonic distortion of phase currents. Furthermore, a recursive least squares parameter identification algorithm with a forgetting factor based on the lumped disturbance equation can achieve multi-parameter online identification of motor resistance, inductance, and flux linkage error parameters. The identified parameter errors are fed back to the sensorless observer equation to achieve robust enhancement of the sensorless observer.

[0046] The beneficial effects of the present invention are:

[0047] This invention addresses the limitation of most current predictive current control strategies, which only achieve robustness enhancement of the current loop, and enables online identification of multiple motor parameters. The robustness of the sensorless observer is further enhanced through feedback of the identified parameters. This invention expands the application of traditional predictive current control algorithms in sensorless permanent magnet synchronous motor FOC control. By using a hyperbolic tangent function-based superhelical algorithm to adapt input errors and effectively suppress the inherent chattering of the sliding mode, the invention enables precise online observation and compensation of disturbances while suppressing harmonic distortion of phase currents. The adaptive superhelical sliding mode disturbance observer possesses the advantages of the strong robustness of the sliding mode algorithm and has better chattering suppression than traditional low-order sliding mode observers. It can achieve precise observation of lumped disturbances under a wide range of parameter mismatches, further weaken current harmonics, and improve parameter identification accuracy, thereby enhancing the overall stability and robustness of the sensorless permanent magnet synchronous motor FOC algorithm. A recursive least squares method with a forgetting factor is used to online identify motor parameter errors and feedback updates to the sensorless observer to achieve robustness enhancement of the sensorless permanent magnet synchronous motor control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Schematic diagram of applying the robust enhanced sensorless permanent magnet synchronous motor predictive current control method of the present invention to participate in vector FOC control;

[0049] Figure 2 is a graph showing the mechanical speed, q-axis current, and phase current of the conventional super-spiral sliding mode and the adaptive super-spiral sliding mode disturbance observer of the present invention before and after the motor parameter mismatch in an embodiment of the present invention, wherein: Figure 2 (a) is the mechanical speed, q-axis current and phase current curve of the traditional super-helical sliding mode disturbance observation. Figure 2 (b) is a graph showing the mechanical speed, q-axis current and phase current of the adaptive super-helical sliding mode disturbance observer of the present invention;

[0050] Figure 3 The total harmonic distortion (THD) of the phase current corresponding to the non-sliding mode disturbance observer, the traditional super-spiral sliding mode disturbance observer, and the adaptive super-spiral sliding mode disturbance observer after the motor parameter mismatch at different speeds in the embodiment of the present invention is analyzed and statistically analyzed;

[0051] Figure 4 is a graph showing the resistance identification results of the least squares method parameter identification using the lumped perturbation equation in the embodiment of the present invention compared with the traditional voltage equation;

[0052] Figure 5 is a graph showing the results of least squares parameter identification using the lumped perturbation equation in the embodiment of the present invention compared with the traditional voltage equation;

[0053] Figure 6 It is a curve diagram of flux linkage identification results of least squares parameter identification performed by applying the lumped perturbation equation in an embodiment of the present invention compared with the traditional application of the voltage equation. DETAILED DESCRIPTION

[0054] The following will clearly and completely describe the technical solutions of the present invention in conjunction with the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0055] like Figure 1 As shown, the hardware sampling circuit of the permanent magnet synchronous motor controller performs current sampling according to the FOC algorithm execution frequency and converts the sampled value into the two-phase current i at the current kth moment of the controller algorithm. a (k), i b (k). The phase current is converted into the stationary coordinate system current i via Clark transformation and Park transformation. α (k), i β (k) and the synchronous rotating coordinate system current i d (k), i q (k). The synchronous rotating coordinate system current i at the current kth moment d (k), i q (k), command voltage u d (k),u q (k) and the sensorless observer (taking the saturation function sliding mode observer SMO (Sliding Mode Observer) as an example) to estimate the electrical angular velocity ω e (k) serves as the input of the adaptive super-helical sliding mode disturbance observer, performs one-step-ahead current prediction and disturbance estimation, and outputs the predicted current at the k+1th moment and perturbation observations The predicted current and disturbance observation are input into the deadbeat predicted current control module to perform one-step ahead voltage prediction and output the command voltage u at the k+1th moment. d (k+1) and u q (k+1). At the same time, the permanent magnet synchronous motor i d =0 control, d-axis reference current Always 0. Reference speed and sensorless observer feedback speed ω e (k) constitutes the error and is input into the speed loop PI controller. The output of the PI controller is the q-axis reference current The synchronous rotating coordinate system reference current is input into the deadbeat prediction current control module and serves as the expected current at the k+2th moment. In addition, the disturbance observation quantity at the kth moment, the synchronous rotating coordinate system current, and the sensorless observer estimated electrical angular velocity are used as inputs to the recursive least squares method online parameter identification module with forgetting factor to identify the resistance error ΔR online. s , inductance error ΔL s and flux linkage error Δψ f The identification error is fed back to the sensorless observer module to correct the observer parameter mismatch. The observer outputs the electrical angular velocity as feedback for the speed loop, the adaptive super-helical sliding mode disturbance observer, the recursive least squares method with forgetting factor online parameter identification module, etc. The output electrical angle is used for Park and Anti-Park transformation. The command voltage u at the k+1th moment d (k+1) and u q (k+1) is converted into the command voltage u in the stationary coordinate system through Anti-Park transformation α (k+1) and u β (k+1), the command voltage in the stationary coordinate system is not only fed back to the sensorless observer module but also serves as the input of the space vector pulse width modulation (SVPWM) module. The modulation wave is used for switching the two-level inverter and realizing the FOC closed-loop control of the sensorless permanent magnet synchronous motor.

[0056] The specific embodiments of the present invention are as follows:

[0057] First, the premise for establishing the ideal voltage equation of the permanent magnet synchronous motor in the rotating coordinate system is to ignore factors such as the cross-saturation effect of the motor inductance and the deviation of the motor rated parameters. However, factors such as temperature rise, demagnetization and magnetic saturation effects during the actual operation of the permanent magnet synchronous motor cause the motor resistance, inductance and flux parameters to drift to varying degrees. The mismatch of the resistance and flux parameters leads to a steady-state error in the current in the synchronous coordinate system, while the mismatch of the inductance parameters leads to oscillation of the current in the synchronous coordinate system. In order to characterize the voltage deviation caused by the motor parameter mismatch, the concept of equivalent voltage disturbance caused by parameter mismatch is introduced, and the ideal voltage equation is reconstructed into an actual voltage equation, as follows:

[0058]

[0059] Among them, u d 、u q 、i d and i q are the stator voltage and stator current of d-axis and q-axis respectively; f d and f q are the lumped disturbances of the d-axis and q-axis caused by the deviation of the actual parameters of the motor from the rated parameters; L d and Lq are the stator inductances of the d-axis and q-axis respectively. Taking the surface-mounted permanent magnet synchronous motor as an example, the d-axis and q-axis inductances are equal and unified as the stator rated phase inductance L s .

[0060] After further discretization by the forward Euler method, the actual voltage equation under discrete conditions, that is, the predicted current equation, can be obtained as follows:

[0061]

[0062] in, and are the predicted stator currents of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k+1th sampling moment; T s is the sampling interval, i.e. the execution period of vector control FOC closed-loop control; R s and L s are the stator rated phase resistance and stator rated phase inductance of the sensorless permanent magnet synchronous motor respectively; i d (k) and i q (k) are the stator currents of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; ω e (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment; u d (k) and u q (k) are the stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; f d (k) and f q (k) are the lumped disturbances of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; ψ f is the permanent magnet flux of the sensorless permanent magnet synchronous motor. In this embodiment, T s =0.00005, that is, the FOC execution frequency is 20kHz.

[0063] Then, an adaptive super-helical sliding mode disturbance observer is designed based on the predicted current equation; the adaptive super-helical sliding mode disturbance observer is designed to achieve online observation of the lumped disturbance. The adaptive super-helical sliding mode disturbance observer is as follows:

[0064]

[0065]

[0066]

[0067]

[0068] in, and are the estimated values ​​of the stator current of the sensorless permanent magnet synchronous motor on the d-axis and q-axis at the k+1th sampling time, respectively. and are the estimated values ​​of the lumped disturbances of the sensorless permanent magnet synchronous motor on the d-axis and q-axis at the k+1th sampling moment; T s is the sampling interval; R s and L s are the stator rated phase resistance and stator rated phase inductance of the sensorless permanent magnet synchronous motor respectively; and are the estimated values ​​of the stator current of the sensorless permanent magnet synchronous motor along the d-axis and q-axis at the k-th sampling moment; ω e (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment; u d (k) and u q (k) are the stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; and are the estimated values ​​of the lumped disturbances of the sensorless permanent magnet synchronous motor on the d-axis and q-axis at the k-th sampling moment; U dSTA and U qSTA are the sliding mode functions based on the adaptive superhelical algorithm for the d-axis and q-axis of the sensorless permanent magnet synchronous motor respectively; δ is the disturbance term gain, δ>0; λ1 and λ2 are the first and second positive gains; s d and s q are the sliding surfaces formed by the d-axis and q-axis current errors, respectively, and the input error s d 、s q Adaptation is achieved through the hyperbolic tangent function inside the sliding mode function to suppress the sliding mode chattering problem; tanh() is a hyperbolic tangent function with adjustable boundary layer. The traditional superhelical algorithm itself is a second-order sliding mode algorithm and has a certain chattering suppression effect, but its built-in sign function is a step switching function, which cannot achieve adaptation to the input error under fixed gain. When the error decreases, it will be affected by the fixed gain and cause sliding mode chattering; τ is the time variable; i d (k) and i q (k) are the d-axis and q-axis stator currents of the sensorless permanent magnet synchronous motor at the k-th sampling moment; x is the input of the hyperbolic tangent function tanh( ), and m is the positive gain of the hyperbolic tangent function tanh( ). When the input error is within the gain constraint range, the hyperbolic tangent function can achieve error adaptation and further improve the chattering problem caused by fixed gain.

[0069] Adaptive super-helical sliding mode disturbance observation can effectively reduce the chattering problem inherent in traditional low-order sliding mode and achieve accurate observation of predicted current and disturbance. In this embodiment, δ1000, λ1=900, λ2=150, and m=5 are taken.

[0070] The command voltage u calculated at the kth sampling moment in the actual digital control system d (k),u q (k) is not actually applied to the inverter module until the k+1th moment, and the inverter module takes about half of the sampling period to apply this voltage to the permanent magnet synchronous motor winding. Therefore, by predicting the current one step ahead and compensating for the disturbance observation, a predicted voltage equation based on deadbeat current control is further established based on the predicted current equation, as follows:

[0071]

[0072] Among them, u d (k+1) and u q (k+1) are the predicted stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k+1th sampling moment, respectively, to compensate for the one-beat delay of the actual digital system; R s and L s are the stator rated phase resistance and stator rated phase inductance of the sensorless permanent magnet synchronous motor respectively; T s is the sampling interval; and are the reference currents of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment, based on i d =0 controlled d-axis reference current is always zero, that is, The q-axis reference current is provided by the speed loop output, and the speed loop execution frequency is approximately 1 / 20 to 1 / 10 of the current loop execution frequency. It is worth noting that the mechanical frequency of the permanent magnet synchronous motor is much smaller than the electrical frequency, so the electrical angular velocity in adjacent cycles can be considered equal; and are the estimated values ​​of the stator current of the sensorless permanent magnet synchronous motor on the d-axis and q-axis at the k+1th sampling moment; ω e (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment; and are the estimated values ​​of the lumped disturbances of the sensorless permanent magnet synchronous motor on the d-axis and q-axis at the k+1th sampling moment, The disturbance observer is used to observe and compensate online; ψ f is the permanent magnet flux linkage of the sensorless permanent magnet synchronous motor.

[0073] The predicted voltage equation realizes online compensation of disturbances by considering the one-beat delay problem of actual digital systems.

[0074] Then, a recursive least squares online parameter identifier with a forgetting factor is established; the online parameter identifier realizes the online identification of multiple motor parameters including resistance, inductance, and flux linkage errors. The recursive least squares online parameter identifier with a forgetting factor is as follows:

[0075]

[0076] Φ(k)=[ΔR s ,ΔL s ,Δψ f ] T

[0077]

[0078] Among them, Φ(k) and Φ(k-1) are the parameter error vectors to be identified of the sensorless permanent magnet synchronous motor at the kth and k-1th sampling moments, respectively, ΔR s , ΔL s and Δψ f are the resistance error, inductance error, and flux linkage error of the sensorless permanent magnet synchronous motor respectively; P(k) and P(k-1) are the covariance matrices at the k-th and k-1-th sampling moments respectively, and the order is the number of objects to be identified; y(k) is the disturbance input of the online parameter identifier at the k-th sampling moment, including the estimated value of the lumped disturbance of the d-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment and the estimated value of the lumped disturbance on the q axis is the measured input to the online parameter identifier at the kth sampling moment; κ is the forgetting factor of the least squares parameter identification method. The value of the forgetting factor should take into account the convergence speed and identification stability of the recursive least squares parameter identification algorithm. In this embodiment, k = 1e3 and κ = 0.99995.

[0079] Measurement input The details are as follows:

[0080]

[0081] The recursive least squares parameter identification equation with forgetting factor is designed based on the lumped disturbance formula to realize the online identification of motor multi-parameters including resistance, inductance and flux linkage errors.

[0082] The d-axis and q-axis stator currents and stator voltages and rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the current moment are input into the adaptive super-helical sliding mode disturbance observer for processing. After processing, the adaptive super-helical sliding mode disturbance observer outputs the d-axis and q-axis stator currents and estimated values ​​of the lumped disturbance at the next moment. The d-axis and q-axis stator currents and estimated values ​​of the lumped disturbance at the next moment, the d-axis and q-axis reference currents and rotor electrical angular velocity at the current moment are input into the predicted voltage equation based on zero-beat current control for processing. After processing, the predicted voltage equation of zero-beat current control outputs the d-axis and q-axis stator voltages at the next moment, thereby performing vector control FOC closed-loop control of the sensorless permanent magnet synchronous motor.

[0083] The current d-axis and q-axis stator currents and voltages, rotor electrical angular velocity, and estimated d-axis and q-axis lumped disturbances of the sensorless permanent magnet synchronous motor (PMSM) are fed into an online parameter identifier using a recursive least squares method with a forgetting factor. This method then outputs a parameter error vector to the sensorless observer in the vector control (FOC) closed-loop control system, ultimately achieving predictive current control of the PMSM. The identified parameter error is fed back online to the sensorless observer to enhance observer robustness.

[0084] After processing by the recursive least squares method online parameter identifier with a forgetting factor, the parameter error vector is output to the sensorless observer in the vector control FOC closed-loop control, and the motor parameter error correction is performed on the stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor in the synchronous rotating coordinate system, or the motor parameter error correction is performed on the stator voltages of the α-axis and β-axis of the sensorless permanent magnet synchronous motor in the stationary coordinate system. After the motor parameter error correction, the sensorless observer outputs the electrical angular velocity and electrical angle to realize the FOC control of the sensorless permanent magnet synchronous motor.

[0085] Finally, the identification parameter error is fed back online to the sensorless observer to achieve robust enhancement of the observer. Generally, sensorless observers based on back electromotive force or permanent magnet flux linkage signals are established under the voltage equation of the permanent magnet synchronous motor in the stationary coordinate system or the synchronous rotating coordinate system. That is, the identification parameter error is fed back and updated to the sensorless observer voltage equation to achieve robust enhancement. In this embodiment, the sensorless observer is a sliding mode observer based on a saturation function. The observer is established on the voltage equation of the stationary coordinate system. The stator voltages of the α-axis and β-axis of the sensorless permanent magnet synchronous motor in the stationary coordinate system after the motor parameter error correction are as follows:

[0086]

[0087] Among them, u α ′(k) and u β′(k) are the stator voltages of the α-axis and β-axis of the sensorless permanent magnet synchronous motor at the kth sampling moment after the motor parameter error correction; R s and L s are the stator rated phase resistance and stator rated phase inductance of the sensorless permanent magnet synchronous motor respectively; ΔR s , ΔL s and Δψ f are the resistance error, inductance error and flux linkage error of the sensorless permanent magnet synchronous motor respectively; i α (k) and i β (k) are the stator currents of the α-axis and β-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; ω e (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment; ψ f is the permanent magnet flux linkage of the sensorless permanent magnet synchronous motor; θ e (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment.

[0088] The stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor in the synchronous rotating coordinate system after the motor parameter error correction are as follows:

[0089]

[0090] Among them, u d ′(k) and u q ′(k) are the stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the kth sampling moment after the motor parameter error correction; R s and L s are the stator rated phase resistance and stator rated phase inductance of the sensorless permanent magnet synchronous motor respectively; ΔR s , ΔL s and Δψ f are the resistance error, inductance error and flux linkage error of the sensorless permanent magnet synchronous motor respectively; i d (k) and i q (k) are the stator currents of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; ω e (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment; ψ f is the permanent magnet flux linkage of the sensorless permanent magnet synchronous motor.

[0091] The identification parameter error is fed back online to the sensorless observer to achieve robust enhancement of the observer. Generally, the sensorless observer based on back electromotive force or permanent magnet flux signal is established under the voltage equation of the permanent magnet synchronous motor stationary coordinate system or the voltage equation of the synchronous rotating coordinate system, that is, the identification parameter error is fed back and updated to the voltage equation of the sensorless observer to achieve robust enhancement.

[0092] The sliding mode observer formula after parameter error feedback update is as follows:

[0093]

[0094] in, represents the estimated value of the variable x; σ is the gain of the saturation function sliding mode; sat( ) is the traditional saturation function; They are the estimated back-electromotive force components of the α-axis and β-axis in the stationary coordinate system, respectively. The back-electromotive force components output the electrical angular velocity and electrical angle through the phase-locked loop, and the output is fed back to the disturbance observer, parameter identification module and coordinate transformation module to realize the closed-loop FOC control of the sensorless permanent magnet synchronous motor.

[0095] The method in this embodiment expands the application of traditional predictive current control algorithms in sensorless permanent magnet synchronous motor field-oriented control (FOC) control. A hyperbolic tangent function-based superhelical algorithm achieves adaptive input error and effectively suppresses inherent chattering in sliding mode control. This allows for precise online observation and compensation of disturbances while also suppressing harmonic distortion in phase currents. A recursive least squares method with a forgetting factor based on the lumped disturbance equation is used to identify motor parameter errors online and feed them back to the sensorless observer for robustness enhancement of the sensorless permanent magnet synchronous motor control system.

[0096] like Figure 2 (a) and Figure 2 As shown in (b), the mechanical speed, q-axis current, and phase current curves of the traditional super-helical sliding mode and adaptive super-helical sliding mode algorithms before and after parameter mismatch at 1200 r / m and 50% rated load are shown. The main parameters of the three-phase permanent magnet synchronous motor and control method in this embodiment are: phase resistance 0.5Ω, phase inductance 1mH, permanent magnet flux 0.012Wb, rated speed 3000rpm, maximum speed 3500rpm, carrier frequency 20kHz (carrier period 50us). To simulate the actual effect of motor parameter mismatch, the main parameters in the control algorithm are changed to: phase resistance 1.0Ω, phase inductance 2mH, permanent magnet flux 0.006Wb after 0.1s. When the motor parameters are mismatched, due to the online observation and compensation of the disturbance observer, the speed of both the traditional super-helical sliding mode disturbance observation and the adaptive super-helical sliding mode disturbance observation has obvious steady-state errors, while the phase current still maintains a smooth sine-like curve. Notably, the adaptive superhelical algorithm achieves smaller q-axis current ripple. Since q-axis current represents torque, this demonstrates that the adaptive algorithm can effectively reduce torque ripple, enabling high-performance torque control. Furthermore, the improvement in q-axis current directly impacts the precise observation of the disturbance and further improves the accuracy of parameter identification using the recursive least squares method with a forgetting factor.

[0097] like Figure 3 The data shown in the figure shows the phase current THD analysis statistics for the motor under 50% rated load and different speed conditions, corresponding to the no-disturbance observer, the traditional super-helical sliding mode disturbance observer, and the adaptive super-helical sliding mode disturbance observer after motor parameter mismatch. The minimum phase current THD is 25.86% without the disturbance observer, while the maximum phase current THD with the super-helical sliding mode disturbance observer does not exceed 3.02%. In comparison, the adaptive super-helical sliding mode disturbance observer has lower THD than the traditional super-helical sliding mode disturbance observer at all speeds, achieving better harmonic suppression and facilitating accurate disturbance observation and parameter identification.

[0098] like Figure 4 The figure shows the resistance identification results curve using the lumped perturbation equation of the present invention compared to the traditional least squares parameter identification using the voltage equation. The resistance error identification result of the recursive least squares method with a forgetting factor based on the lumped perturbation equation is 0.5209Ω, and the corrected resistance identification result is 0.4791Ω. Compared with the traditional recursive least squares resistance identification result of 0.3714Ω based on the voltage equation with a forgetting factor, the identification error is reduced from 0.1286Ω to 0.0209Ω, achieving a significant improvement in identification accuracy.

[0099] like Figure 5 The figure shows the inductance identification results curve using the lumped perturbation equation of the present invention compared to the traditional least squares parameter identification using the voltage equation. The inductance error identification result of the recursive least squares method with a forgetting factor based on the lumped perturbation equation is 0.7232mH, and the corrected inductance identification result is 1.2768mH. Compared with the traditional recursive least squares inductance identification result of 1.264mH based on the voltage equation with a forgetting factor, the identification accuracy is similar.

[0100] like Figure 6 The figure shows the flux linkage identification results curve using the lumped perturbation equation of the present invention compared to the traditional least squares parameter identification using the voltage equation. The recursive least squares method with a forgetting factor based on the lumped perturbation equation has a flux linkage error of -0.005676Wb, while the corrected flux linkage identification result is 0.011676Wb. Compared with the traditional recursive least squares method with a forgetting factor based on the voltage equation, which has a flux linkage error of 0.01256Wb, the identification error is reduced from 0.00056Wb to 0.000327Wb, slightly improving the identification accuracy.

[0101] By adopting the above technical solutions, the sliding mode disturbance observer achieves input error adaptation and effectively suppresses the inherent chattering phenomenon of traditional sliding mode systems, enabling accurate observation of lumped disturbances and suppression of total harmonic distortion of phase currents. Furthermore, a recursive least squares parameter identification algorithm with a forgetting factor based on the lumped disturbance equation enables online multi-parameter identification of motor resistance, inductance, and flux linkage errors. The identification accuracy is improved compared to the traditional recursive least squares method with a forgetting factor based on the voltage equation. The identified parameter errors are fed back to the sensorless observer equation to achieve robust enhancement of the sensorless observer.

[0102] The above description is only a preferred embodiment of the present invention and does not limit the implementation mode and protection scope of the present invention. For those skilled in the art, it should be aware that all solutions obtained by equivalent substitutions and obvious changes made using the description and illustrations of the present invention should be included in the protection scope of the present invention.

Claims

1. A robust enhanced sensorless permanent magnet synchronous motor predictive current control method, characterized in that: include: S1: Establish the predictive current equation of the sensorless permanent magnet synchronous motor and design an adaptive super-helical sliding mode disturbance observer based on the predictive current equation; S2: Establish a predictive voltage equation based on deadbeat current control and an online parameter identifier using the recursive least squares method with a forgetting factor; S3: inputting the d-axis and q-axis stator currents and stator voltages and rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the current moment into the adaptive super-helical sliding mode disturbance observer for processing, and after processing, the adaptive super-helical sliding mode disturbance observer outputs the d-axis and q-axis stator currents and estimated values ​​of the lumped disturbance at the next moment, and inputting the d-axis and q-axis stator currents and estimated values ​​of the lumped disturbance at the next moment, the d-axis and q-axis reference currents and rotor electrical angular velocity at the current moment into the predicted voltage equation based on deadbeat current control for processing, and after processing, the predicted voltage equation of deadbeat current control outputs the d-axis and q-axis stator voltages at the next moment, thereby performing vector control FOC closed-loop control of the sensorless permanent magnet synchronous motor; S4: The d-axis and q-axis stator currents and stator voltages, rotor electrical angular velocity, and estimated values ​​of the d-axis and q-axis lumped disturbances output by the adaptive super-helical sliding mode disturbance observer of the sensorless permanent magnet synchronous motor at the current moment are input into a recursive least squares online parameter identifier with a forgetting factor for processing. After processing, the recursive least squares online parameter identifier with a forgetting factor outputs a parameter error vector to the sensorless observer in the vector control FOC closed-loop control, thereby ultimately realizing predictive current control of the sensorless permanent magnet synchronous motor. In step S1, the predicted current equation of the permanent magnet synchronous motor is as follows: in, and are the predicted stator currents of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k+1th sampling moment; T s is the sampling interval, i.e. the execution period of vector control FOC closed-loop control; R s and L s are the stator rated phase resistance and stator rated phase inductance of the sensorless permanent magnet synchronous motor respectively; i d (k) and i q (k) are the stator currents of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; ω e (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment; u d (k) and u q (k) are the stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; f d (k) and f q (k) are the lumped disturbances of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; ψ f is the permanent magnet flux linkage of the sensorless permanent magnet synchronous motor; In step S1, the adaptive super-helical sliding mode disturbance observer is specifically as follows: in, and are the estimated values ​​of the stator current of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k+1th sampling moment; and are the estimated values ​​of the lumped disturbances of the sensorless permanent magnet synchronous motor on the d-axis and q-axis at the k+1th sampling moment; T s is the sampling interval; R s and L s are the stator rated phase resistance and stator rated phase inductance of the sensorless permanent magnet synchronous motor respectively; and are the estimated values ​​of the stator current of the sensorless permanent magnet synchronous motor along the d-axis and q-axis at the k-th sampling moment; ω e (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment; u d (k) and u q (k) are the stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; and are the estimated values ​​of the lumped disturbances of the sensorless permanent magnet synchronous motor on the d-axis and q-axis at the k-th sampling moment; U dSTA and U qSTA are the sliding mode functions of the d-axis and q-axis of the sensorless permanent magnet synchronous motor respectively; δ is the disturbance term gain, δ>0; λ1 and λ2 are the first and second positive gains; s d and s q are the sliding surfaces formed by the d-axis and q-axis current errors respectively; tanh() is the hyperbolic tangent function; τ is the time variable; i d (k) and i q (k) are the d-axis and q-axis stator currents of the sensorless permanent magnet synchronous motor at the k-th sampling moment; In step S2, the predicted voltage equation based on deadbeat current control is as follows: Among them, u d (k+1) and u q (k+1) are the predicted stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k+1th sampling moment; R s and L s are the stator rated phase resistance and stator rated phase inductance of the sensorless permanent magnet synchronous motor respectively; T s is the sampling interval; and are the reference currents of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment respectively; and are the estimated values ​​of the stator current of the sensorless permanent magnet synchronous motor on the d-axis and q-axis at the k+1th sampling moment; ω e (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment; and are the estimated values ​​of the lumped disturbances of the sensorless permanent magnet synchronous motor on the d-axis and q-axis at the k+1th sampling moment; ψ f is the permanent magnet flux linkage of the sensorless permanent magnet synchronous motor; In step S2, the recursive least squares online parameter identifier with forgetting factor is specifically as follows: Φ(k)=[ΔR s ,ΔL s ,Dp f ] T Among them, Φ(k) and Φ(k-1) are the parameter error vectors to be identified of the sensorless permanent magnet synchronous motor at the kth and k-1th sampling moments, respectively, ΔR s , ΔL s and Δψ f are the resistance error, inductance error, and flux linkage error of the sensorless permanent magnet synchronous motor respectively; P(k) and P(k-1) are the covariance matrices at the k-th and k-1-th sampling moments respectively, and the order is the number of objects to be identified; y(k) is the disturbance input of the online parameter identifier at the k-th sampling moment, including the estimated value of the lumped disturbance of the d-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment and the estimated value of the lumped disturbance on the q axis is the measurement input of the online parameter identifier at the kth sampling moment; κ is the forgetting factor of the least squares parameter identification method; In step S4, after processing by the recursive least squares method with a forgetting factor online parameter identifier, the parameter error vector is output to the sensorless observer in the vector control FOC closed-loop control, and the motor parameter error correction is performed on the stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor in the synchronous rotating coordinate system, or the motor parameter error correction is performed on the stator voltages of the α-axis and β-axis of the sensorless permanent magnet synchronous motor in the stationary coordinate system; The stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor in the synchronous rotating coordinate system after the motor parameter error correction are specifically as follows: Among them, u d ′(k) and u q ′(k) are the stator voltages of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the kth sampling moment after the motor parameter error correction; R s and L s are the stator rated phase resistance and stator rated phase inductance of the sensorless permanent magnet synchronous motor respectively; ΔR s , ΔL s and Δψ f are the resistance error, inductance error and flux linkage error of the sensorless permanent magnet synchronous motor respectively; i d (k) and i q (k) are the stator currents of the d-axis and q-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; ω e (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment; ψ f is the permanent magnet flux linkage of the sensorless permanent magnet synchronous motor; The stator voltages of the α-axis and β-axis of the sensorless permanent magnet synchronous motor in the stationary coordinate system after the motor parameter error correction are specifically as follows: Among them, u α ′(k) and u β ′(k) are the stator voltages of the α-axis and β-axis of the sensorless permanent magnet synchronous motor at the kth sampling moment after the motor parameter error correction; R s and L s are the stator rated phase resistance and stator rated phase inductance of the sensorless permanent magnet synchronous motor respectively; ΔR s , ΔL s and Δψ f are the resistance error, inductance error and flux linkage error of the sensorless permanent magnet synchronous motor respectively; i α (k) and i β (k) are the stator currents of the α-axis and β-axis of the sensorless permanent magnet synchronous motor at the k-th sampling moment; ω e (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment; ψ f is the permanent magnet flux linkage of the sensorless permanent magnet synchronous motor; θ e (k) is the rotor electrical angular velocity of the sensorless permanent magnet synchronous motor at the kth sampling moment.

2. An electronic device, characterized in that: include: A memory and a processor coupled to each other, wherein the memory stores program data, and the processor calls the program data to execute the method according to claim 1.

3. A computer-readable storage medium having program data stored thereon, characterized in that: When the program data is executed by a processor, the method according to claim 1 is implemented.

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