A three-phase asymmetric resistance identification method for permanent magnet synchronous motor based on voltage residual error decoupling

Abstract

The application relates to a three-phase asymmetric resistance identification method based on voltage residual decoupling of a permanent magnet synchronous motor, and belongs to the technical field of permanent magnet synchronous motor control and fault diagnosis. The method first establishes a three-phase asymmetric resistance mathematical model of the permanent magnet synchronous motor, defines the difference between actual measured dq voltage and dq voltage based on a three-phase symmetric model as voltage residual, and deduces the analytical mapping relationship between the voltage residual and three-phase asymmetric parameters; then, the voltage residual is estimated in real time based on a Luenberger observer; then, based on a Kalman filter, a random linear discrete state space model taking the three-phase asymmetric parameters as state variables is established by taking the voltage residual as an observation quantity, the three-phase asymmetric parameters are identified on line through a recursive algorithm; finally, the three-phase actual resistance values are calculated according to the identification results. The application realizes high-precision independent decoupling identification of the three-phase asymmetric resistance, has strong anti-interference capability, and is low in identification error.

Description

Technical Field

[0001] This invention belongs to the field of permanent magnet synchronous motor control and fault diagnosis technology, specifically involving a method for identifying the three-phase unbalanced resistance of a permanent magnet synchronous motor based on voltage residual decoupling. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in industrial control and new energy electric drive systems due to their high power density, high efficiency, and excellent control performance. In complex actual working environments, the stator windings of these motors are prone to three-phase resistance asymmetry electrical faults due to factors such as alternating thermal stress, insulation aging, cable damage, or oxidation at connections. This asymmetry is initially highly concealed and difficult to detect. However, with accumulated operating time, the asymmetric fault causes distortion in the stator phase currents, introducing significant periodic pulsating oscillations in the motor's speed and electromagnetic torque. This not only exacerbates localized heating and mechanical vibration but also severely reduces the reliability of the electric drive system.

[0003] Accurate acquisition of motor parameters is a prerequisite for achieving high-performance control and fault diagnosis. Existing technologies have seen extensive research on parameter identification for permanent magnet synchronous motors (PMSMs). For example, Chinese patent CN109728758A discloses a method for identifying the three-phase stator resistance of a PMSM. This method establishes a mathematical model under asymmetrical three-phase resistance and uses a recursive least squares method based on a forgetting factor to estimate the three-phase resistance values. This approach solves the resistance identification problem under asymmetrical operating conditions to some extent. However, this method directly performs parameter regression on the highly nonlinear and strongly coupled voltage equations in the dq rotating coordinate system. Its identification accuracy and convergence speed are easily affected by load current, speed variations, and cross-interference of non-faulty phase parameters, and its stability in noisy environments needs improvement.

[0004] Furthermore, existing technologies have proposed various online multi-parameter identification methods, such as Chinese patents CN110198150A and CN113131817A. These methods typically employ techniques such as high-frequency signal injection, model reference adaptation, or extended Kalman filtering to identify multiple parameters, including inductance, flux linkage, and resistance. However, most of these methods are based on the ideal assumption of perfectly symmetrical three-phase parameters of the motor. When the motor exhibits three-phase resistance asymmetry, traditional symmetrical mathematical models suffer from severe model mismatch, leading to a significant decrease in the identification accuracy of existing methods, and even preventing correct convergence. Additionally, sliding mode observer methods, such as Chinese patent CN115276487A, are primarily used for rotor position and speed estimation, falling under the field of motor control, and do not address the independent identification of stator resistance asymmetry parameters.

[0005] It is evident that existing permanent magnet synchronous motor parameter identification technologies generally suffer from the following problems: First, they rely on the ideal assumption of symmetrical three-phase parameters, which makes it difficult to adapt to the actual operating conditions where the three-phase resistances are asymmetrical; second, for the identification of asymmetrical parameters, there is a lack of effective decoupling methods, which makes them susceptible to the influence of system nonlinearity, strong coupling, and noise interference, resulting in low identification accuracy and poor stability.

[0006] Therefore, there is an urgent need in this field for a method that can perform high-precision, independent decoupling identification of the three-phase asymmetrical resistance parameters of permanent magnet synchronous motors, in order to overcome the shortcomings of existing technologies and provide reliable parameter support for motor fault diagnosis and fault-tolerant control. Summary of the Invention

[0007] This invention addresses the problems of existing permanent magnet synchronous motor parameter identification technologies, which rely on the assumption of three-phase parameter symmetry, are difficult to adapt to three-phase resistance asymmetry, and lack effective decoupling methods for asymmetric parameter identification, are susceptible to system nonlinearity and noise interference leading to low identification accuracy and poor stability. The invention provides a method for identifying three-phase asymmetric resistance of permanent magnet synchronous motors based on voltage residual decoupling.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows: The methods specifically include: S1: Establish a mathematical model for a three-phase resistive asymmetry permanent magnet synchronous motor. Define the difference between the actual measured dq voltage and the dq voltage based on the three-phase symmetrical model as the dq voltage residual Y, and derive the relationship between the dq voltage residual Y and the three-phase asymmetry parameters. The parsing mapping relationship between them: ;in, For d-axis current, For q-axis current, For rotor electrical angle, The rotor's electric angular velocity, This represents the common factor in the resistance disturbance matrix caused by three-phase resistance asymmetry; S2: Based on the Luneburger observer, the system state is reconstructed using the input and output of the permanent magnet synchronous motor, and the dq voltage residual Y is estimated in real time to obtain the observed value of the dq voltage residual. S3: Based on the Kalman filter, establish the three-phase asymmetry parameters... A stochastic linear discrete state-space model with state variables and the observed values ​​of the dq voltage residuals as observation vectors is used to recursively process the three-phase asymmetry parameters. Perform online identification; S4: Based on the identified three-phase asymmetry parameters And the theoretical symmetrical value R of the three-phase resistance, calculate the actual three-phase resistance value of the permanent magnet synchronous motor: .

[0009] Further, in S2, the error feedback gain matrix L of the Luneburger observer is determined by the pole placement method, placing the poles of the observer system in the left half of the complex plane, and ensuring that the distance from the imaginary axis is 3 to 5 times the reciprocal of the electrical time constant of the motor. The recursive algorithm of the Kalman filter follows the closed-loop iterative logic of prediction-correction. The state transition equation adopts a first-order random walk model, that is, assuming that the current state depends only on the superposition of the previous state and the process uncertainty; the process noise vector w k It follows a pattern with a mean of 0 and a covariance of Q. k The observation noise vector v is a Gaussian distribution. k It follows a pattern with a mean of 0 and a covariance of R. k The Gaussian distribution.

[0010] Furthermore, the process noise covariance matrix Q k The resistance parameter is set according to the expected rate of change: for step faults, Q... k Set as a diagonal matrix, with diagonal elements taken as... Order of magnitude; for slowly varying faults, Q k Set as a diagonal matrix, with diagonal elements taken as... Order of magnitude; the observation noise covariance matrix R k The setting is based on the signal-to-noise ratio of the voltage residual signal.

[0011] Furthermore, for extremely low-speed or zero-speed operating conditions, this invention also includes an optimization step of injecting a high-frequency sinusoidal voltage signal with a small amplitude into the d-axis. The frequency of the injected signal is much higher than the fundamental frequency of the motor, used to enhance the fault characteristic components in the voltage residual. In addition, the error feedback gain matrix L is determined using a linear quadratic regulator method. The optimal gain matrix L is obtained by minimizing the performance index that includes state estimation error and control cost.

[0012] Furthermore, the process noise covariance Q k and observation noise covariance R k An adaptive Kalman filter algorithm is used for online estimation and adjustment. The adaptive Kalman filter algorithm is based on the maximum likelihood estimation or covariance matching method.

[0013] Furthermore, the state equation and observation equation are discretized using any one of the following methods: zero-order hold discretization, first-order forward Euler discretization, or bilinear transformation discretization.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: First, by defining the voltage residual and establishing its analytical mapping relationship with the three-phase asymmetric parameters, this invention decouples the asymmetric parameters from the nonlinear coupling of the system, so that parameter identification no longer depends on the ideal assumption of three-phase parameter symmetry, and can accurately adapt to the three-phase resistance asymmetry working condition in actual operation.

[0015] Second, the present invention adopts an architecture of Luneburger observer and Kalman filter in series. The Luneburger observer estimates the voltage residual in real time, and the Kalman filter performs optimal state estimation in random noise environment. The two work together to effectively suppress the interference of load current, speed change and measurement noise, and significantly improve the accuracy and stability of parameter identification.

[0016] Third, the present invention can independently identify the three-phase resistance parameters. In the case of a single-phase fault, the parameters of the non-faulty phase remain near zero. In the case of a multi-phase fault, the parameters of each phase converge independently to their respective set values. The identification error does not exceed 3%, providing reliable parameter support for motor fault diagnosis and fault-tolerant control.

[0017] Fourth, through optimization of pole placement range, low-speed signal injection, LQR observer design, and adaptive filtering, this invention can adapt to different working conditions and application requirements, and has wide applicability and practical value.

[0018] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0019] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a schematic diagram of the equivalent circuit model of a permanent magnet synchronous motor under healthy conditions in an embodiment of the present invention; Figure 2 This is a schematic diagram of the operation process of the Kalman filter in an embodiment of the present invention; Figure 3 The diagram shows the identification results of resistance parameters under single-phase asymmetrical fault in an embodiment of the present invention; where (a) is the waveform diagram of the observed value of the dq axis voltage residual, and (b) is the waveform diagram of the identification results of the three-phase asymmetrical parameters. Figure 4 The diagram shows the identification results of resistance parameters under two-phase asymmetrical fault in an embodiment of the present invention; where (a) is the waveform diagram of the observed value of the dq axis voltage residual, and (b) is the waveform diagram of the identification results of the three-phase asymmetrical parameters. Detailed Implementation

[0020] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0021] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0022] Example 1 This embodiment provides a method for identifying the three-phase unbalanced resistance parameters of a permanent magnet synchronous motor. In this embodiment, the rated parameters of the permanent magnet synchronous motor are: stator resistance symmetrical ideal value R = 0.2Ω, dq-axis inductance Ld = Lq = 0.5mH, and permanent magnet flux linkage... =0.1Wb, with 4 pole pairs. This embodiment simulates insulation degradation in phase A winding, causing its resistance to become 0.8 times the ideal value, i.e., R a =0.16Ω, while phases B and C remain healthy, i.e., R b =R c =0.2Ω.

[0023] The method includes the following steps: S1: Establish a mathematical model of a three-phase resistive asymmetrical permanent magnet synchronous motor.

[0024] In theoretical derivations, it is usually assumed that the motor winding parameters have three-phase symmetry to simplify the mathematical model, and its equivalent circuit model is as follows: Figure 1 As shown. In the three-phase stationary coordinate system abc, the PMSM voltage equation considering three-phase resistance asymmetry is: (1) in, , , It is a three-phase voltage; , , Stator current; For three-phase winding self-inductance; For mutual inductance of three-phase windings; Stator resistance; It is an electrical angle; It is a permanent magnet flux linkage.

[0025] The back electromotive force can be expressed as: (2) in, This is the electric angular velocity of the motor.

[0026] When considering the asymmetry of three-phase resistance, a relative deviation is introduced. (x=a, b, c), representing the relative deviation between the actual motor resistance and the theoretical symmetrical resistance, the three-phase resistance can be expressed as:

[0027] Where R is the theoretical symmetrical value of the three-phase resistance.

[0028] At this point, the mathematical model of PMSM in the abc coordinate system is: (3) Substituting the resistance matrix into the voltage equation, and then performing the Clark and Park transformations, we obtain the voltage equation in the two-phase rotating dq coordinate system as follows: (4) in, and This refers to the dq-axis stator voltage; and This refers to the dq-axis stator current; = = It is the dq axis inductance.

[0029] The four elements of the resistance matrix R are: (5) If the three phases of the PMSM resistor are symmetrical (i.e., R) a =R b =R c =R), then the voltage equation for dq at this time is: (6) in, and dq is the voltage when the resistors are three-phase symmetrical.

[0030] Comparing equations (5) and (6), when the resistors are three-phase symmetrical, the resistance matrix R in the dq voltage equation can be divided into an ideal parameter part and an asymmetric parameter part, written as: (7) Define dq voltage residual This represents the difference between the actual measured dq voltage and the dq voltage based on the three-phase symmetry model: (8) in, (9) (10) Equation (8) reveals the analytical mapping relationship between the voltage residual and the three-phase resistance asymmetry parameters. This is obtained using an observer. Then, using equation (8), we can identify... .

[0031] S2: Voltage residual estimation based on Luneburg observer.

[0032] The Luneburger observer reconstructs the system state variables by analyzing the inputs and outputs of the observed system. When the three phases of the resistor are unbalanced, the state equations of the motor system are reconstructed as follows: (11) Based on the pole placement principle, the error feedback matrix is ​​configured and determined. The value of is such that the state error approaches 0 at a certain speed and with a certain accuracy, thus realizing the estimation of the dq voltage residual.

[0033] In a preferred embodiment of this invention, the error feedback gain matrix L is configured according to the following principle: the poles of the observer system are placed in the left half of the complex plane, and the distance from the imaginary axis is equal to the reciprocal of the electrical time constant of the motor. The speed is 3 to 5 times that of the observer to ensure that the observer has sufficient speed and stability.

[0034] S3: Three-phase asymmetric parameter identification based on Kalman filter.

[0035] Although the voltage residual contains fault information, its value is affected by nonlinear coupling factors such as load current, speed, rotor angle, and motor parameter perturbations. Therefore, a Kalman filter is introduced, utilizing its optimal estimation characteristics under random noise conditions to establish an identification model from the voltage residual to the three-phase asymmetry parameters.

[0036] S3.1: Discretized state-space modeling of the identification system.

[0037] To apply the Discrete Kalman Filter (DKF) algorithm, a stochastic linear discrete state-space model with three-phase asymmetry parameters as its core is first constructed. The three-phase asymmetry parameters are selected as the system state variables to be identified. (12) Considering that after a three-phase asymmetrical resistor fault occurs, the resistance parameters typically remain stable or exhibit a slow, gradual change over a short period, with numerical characteristics displaying a non-periodic step change or gradual variation process, lacking a clear dynamic evolution mechanism, this embodiment employs a first-order random walk model to model it. This assumes that the current state depends only on the superposition of the previous state and process uncertainties. The state transition equation is defined as: (13) Among them, A=I 3×3 w is the unit state transition matrix; k Let Q be the process noise vector, which has a mean of 0 and a covariance of Q. k The Gaussian distribution is used to characterize the uncertainty of fault development.

[0038] In practical applications, the process noise covariance matrix Q k The resistance parameter can be empirically set based on the expected rate of change. For step faults, Q can be... k Set as a diagonal matrix, with diagonal elements taken as... Magnitude; for slowly changing faults, a value can be taken as... Magnitude.

[0039] The voltage residual output from the Luneburger observer is selected as the observation vector: (14) Combining equation (8), the online observation equation is constructed as follows: (15) Among them, v k The observed noise vector follows a pattern with a mean of 0 and a covariance of R. k Gaussian distribution; H k The observation matrix is ​​2×3 dimensional, i.e., the regression matrix Φ in equation (8), whose elements are the system state at the current time (current i). d i q Rotation speed and rotor position Real-time calculation yields: (16) Observation noise covariance matrix R k It is usually set based on the signal-to-noise ratio of the voltage residual signal.

[0040] In the embodiment, take .

[0041] S3.2: Kalman filter recursive algorithm flow.

[0042] Based on the above model, the Kalman filter algorithm is used to iteratively and recursively solve for the three-phase asymmetry parameters. This algorithm follows a closed-loop iterative logic of prediction and correction, as follows: Figure 2 As shown, at each sampling time k, the fault parameters are dynamically approximated by calculating the prior and posterior estimates of the system state. The specific calculation process is as follows: The first step is prior state estimation. Based on the optimal estimate from the previous time step, a stochastic linear discrete state-space model is used to estimate the prior state at time step k. and the prior state estimation error covariance matrix Make a prediction: (17) Then calculate the Kalman gain K. k The calculation formula is as follows: (18) Finally, using the observed voltage residual z k Compared with the predicted residual H k The deviation between the two values ​​is used to correct the prior estimate, thus obtaining the optimal estimate at the current time. And update the error covariance matrix: (19) In the above recursive process, Q c and R c These are the discretized process noise covariance matrix and the observation noise covariance matrix, respectively.

[0043] Therefore, the designed Kalman filter can estimate the three-phase asymmetry parameters in real time based on the voltage residual estimated by the Luneburg observer. and further according to Calculate the actual three-phase resistance values ​​of the PMSM.

[0044] As an extension of this embodiment, when the motor operates at extremely low or zero speeds, the back electromotive force signal is weak, and the signal-to-noise ratio of the voltage residual signal decreases. To address this condition, the following optimization measures can be adopted: inject a high-frequency sinusoidal voltage signal with a small amplitude into the d-axis to enhance the fault characteristic component in the voltage residual. The frequency of this injected signal should be much higher than the motor's fundamental frequency to avoid interfering with the normal operation of the motor.

[0045] To verify the effectiveness of the PMSM three-phase asymmetrical resistance parameter identification method proposed in this embodiment, simulation verification was performed. The motor initially operated stably under a three-phase symmetrical and healthy state. At t=0.3s, a phase A resistance asymmetry fault occurred, and the actual resistance value of phase A became 0.8 times the ideal value, i.e. =0.16Ω, = =0.2Ω.

[0046] Figure 3 (a) reflects the observed values ​​of the dq voltage residuals before and after the asymmetrical fault. As shown in the figure, before 0.3s, the motor is in a healthy state with zero voltage residual; after the three-phase resistance asymmetrical fault occurs, the dq voltage residual rapidly increases and exhibits oscillating fluctuations. This indicates that the proposed method, using a Luneburger observer to estimate the voltage residuals, can accurately and sensitively capture the asymmetrical changes in three-phase parameters.

[0047] Figure 3 (b) Reflects the parameters of three-phase resistance asymmetry The identification results. After the fault occurred, the asymmetry parameters of phase A... The system responds rapidly, quickly converging to the set value of 0.2, corresponding to a resistance that becomes 0.8 times its original value, with an identification error of no more than 3%; while the identification parameters for phases B and C remain near 0. This demonstrates that this application can perform independent and high-precision online identification of three-phase unbalanced resistance.

[0048] Example 2 This embodiment is basically the same as Embodiment 1, except that it simulates a two-phase asymmetrical fault condition. Specifically, at t=0.3s, insulation degradation occurs simultaneously in phases A and B, and the actual resistance value of phase A becomes 0.8 times the ideal value. =0.16Ω), the actual resistance of phase B becomes 0.9 times the ideal value ( =0.18Ω), phase C remains healthy ( =0.2Ω). This embodiment aims to verify the identification performance of the method when multiple asymmetric faults occur simultaneously.

[0049] Figure 4 (a) shows the observed dq voltage residual under a two-phase asymmetrical fault. Compared with a single-phase fault, the amplitude and waveform of the voltage residual have changed accordingly, reflecting the superposition effect of multiphase asymmetrical faults. Figure 4 (b) shows the identification results of the three-phase asymmetry parameters. It can be seen that... and Both can quickly converge to their respective set values ​​of 0.2 and 0.1, without faulty phases. Keeping the value near 0, the identification error also does not exceed 3%.

[0050] Variations 1. Besides using the pole placement method to determine the error feedback gain matrix L of the Romberg observer, the linear quadratic regulator (LQR) method can also be used for optimal observer design. In this case, the optimal gain matrix L can be automatically solved by minimizing a performance index that includes state estimation error and control cost. This variation is suitable for situations with higher optimization requirements for the observer's dynamic performance.

[0051] 2. In practical applications, the process noise covariance Q c and observation noise covariance R c The value may change over time. Adaptive Kalman filtering algorithms, such as those based on maximum likelihood estimation or covariance matching, can be used to estimate and adjust Q online. c and R c This is to further improve the robustness of parameter identification.

[0052] 3. This method focuses on the identification of three-phase resistance asymmetry parameters, but it can be combined with other parameter identification methods, such as inductance identification based on signal injection and flux linkage identification based on model reference adaptation, to construct a complete online motor parameter identification system. In this case, the three-phase resistance values ​​provided by this method can be used as known parameter inputs for other identification modules, thereby improving the identification accuracy of the entire system.

[0053] 4. The state equations and observation equations of this invention can be discretized using different methods, such as zero-order hold (ZOH) discretization, first-order forward Euler discretization, or bilinear transform (Tustin) discretization. Those skilled in the art can select an appropriate discretization method based on the sampling period and real-time requirements of the actual control system. When the sampling frequency is sufficiently high, satisfactory discretization accuracy can be obtained using a simple forward Euler method.

[0054] 5. This method can be deployed on various hardware platforms, including but not limited to: digital signal processors (DSPs), field-programmable gate arrays (FPGAs), ARM Cortex-M series microcontrollers, and industrial PCs. For applications with extremely high real-time requirements, FPGAs can be used to implement parallel computation of the Kalman filter to meet higher frequency control needs.

[0055] In summary, this invention establishes an accurate mathematical model of three-phase resistance asymmetry, defines the voltage residual, and adopts a series architecture combining a Luneburg observer and a Kalman filter to achieve high-precision and robust online identification of three-phase asymmetrical resistance.

[0056] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for identifying the three-phase asymmetrical resistance of a permanent magnet synchronous motor based on voltage residual decoupling, characterized in that, Includes the following steps: S1: Establish a mathematical model for a three-phase resistive asymmetry permanent magnet synchronous motor. Define the difference between the actual measured dq voltage and the dq voltage based on the three-phase symmetrical model as the dq voltage residual Y, and derive the relationship between the dq voltage residual Y and the three-phase asymmetry parameters. The parsing mapping relationship between them: ;;in, For d-axis current, For q-axis current, For rotor electrical angle, The rotor's electric angular velocity, This represents the common factor in the resistance disturbance matrix caused by three-phase resistance asymmetry; S2: Based on the Luneburger observer, the system state is reconstructed using the input and output of the permanent magnet synchronous motor, and the dq voltage residual Y is estimated in real time to obtain the observed value of the dq voltage residual. S3: Based on the Kalman filter, establish the three-phase asymmetry parameters... A stochastic linear discrete state-space model with state variables and the observed values ​​of the dq voltage residuals as observation vectors is used to recursively process the three-phase asymmetry parameters. Perform online identification; S4: Based on the identified three-phase asymmetry parameters And the theoretical symmetrical value R of the three-phase resistance, calculate the actual three-phase resistance value of the permanent magnet synchronous motor: .

2. The method according to claim 1, characterized in that, In S2, the error feedback gain matrix L of the Luneburger observer is determined by the pole placement method, which places the poles of the observer system in the left half of the complex plane and makes them 3 to 5 times the reciprocal of the electrical time constant of the motor.

3. The method according to claim 1, characterized in that, In S3, the stochastic linear discrete state-space model is specifically as follows: State transition equation: Among them, state variables A=I 3×3 w is a unit state transition matrix. k This is the process noise vector; Observation equation: , where the observation vector Let v be the observed value of the dq voltage residual. k For the observation noise vector, the observation matrix .

4. The method according to claim 3, characterized in that, The state transition equation adopts a first-order random walk model, which assumes that the current state depends only on the superposition of the previous state and the process uncertainty; the process noise vector w k It follows a pattern with a mean of 0 and a covariance of Q. k The Gaussian distribution of the observation noise vector v k It follows a pattern with a mean of 0 and a covariance of R. k The Gaussian distribution.

5. The method according to claim 3, characterized in that, In S3, the recursive algorithm of the Kalman filter follows a closed-loop iterative logic of prediction-correction, specifically including: Prior state estimation: Kalman gain calculation: Posterior state correction: Among them, Q c and R c These are the discretized process noise covariance matrix and the observation noise covariance matrix, respectively.

6. The method according to claim 4, characterized in that, The process noise covariance matrix Q k The resistance parameter is set according to the expected rate of change: for step faults, Q... k Set as a diagonal matrix, with diagonal elements taken as... Order of magnitude; for slowly varying faults, Q k Set as a diagonal matrix, with diagonal elements taken as... Order of magnitude; the observation noise covariance matrix R k The setting is based on the signal-to-noise ratio of the voltage residual signal.

7. The method according to claim 1, characterized in that, When the motor is operating at extremely low speed or zero speed, the optimization step also includes injecting a high-frequency sinusoidal voltage signal with a small amplitude into the d-axis. The frequency of the injected signal is much higher than the fundamental frequency of the motor, which is used to enhance the fault characteristic components in the voltage residual.

8. The method according to claim 1, characterized in that, In S2, the error feedback gain matrix L of the Luneburg observer is determined using the linear quadratic regulator method. The optimal gain matrix L is obtained by minimizing the performance index that includes the state estimation error and the control cost.

9. The method according to claim 4, characterized in that, The process noise covariance Q k and observation noise covariance R k An adaptive Kalman filter algorithm is used for online estimation and adjustment. The adaptive Kalman filter algorithm is based on the maximum likelihood estimation or covariance matching method.

10. The method according to claim 1, characterized in that, The state equation and observation equation are discretized using any one of the following methods: zero-order hold discretization, first-order forward Euler discretization, or bilinear transformation discretization.

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