A high-speed linear motor double-parameter online identification method

Abstract

The application provides a high-speed linear motor double-parameter online identification method, and belongs to the technical field of high-speed linear motor parameter identification. The method comprises the following steps: a discrete flux linkage model of a stator segmented high-speed linear induction motor is established, two independent artificial neural network identification branches are constructed, and a preliminary identification result is output at each sampling time; a flux linkage prediction residual square loss function is constructed to derive a second-order decoupling update law based on a Hessian matrix inverse, and the update amount of a stator resistance and a magnetizing inductance is calculated; a plurality of candidate estimation sets are constructed by full cross combination of the updated identification result, a covariance matrix of a flux linkage residual vector is estimated online based on the plurality of candidate estimation sets, the plurality of candidate estimation sets are weighted and fused to obtain a final parameter identification result. The application can effectively improve the problems of slow convergence speed, strong double-parameter interference and easy oscillation in the identification process of the traditional identification algorithm, and provides a more accurate parameter source for high-performance control of the motor.

Description

Technical Field

[0001] This invention belongs to the field of high-speed linear motor parameter identification technology, specifically relating to an online identification method for dual parameters of a high-speed linear motor. Background Technology

[0002] High-speed linear motors possess outstanding advantages such as high thrust, fast response, and precise controllability, and have broad application prospects in key fields such as rail transit and electromagnetic propulsion. However, under extreme operating conditions such as high current and strong magnetic fields, the motor is affected by factors such as edge effects, magnetic circuit saturation, and changes in coupling coefficients caused by the rapid and frequent entry and exit of the mover into and out of the stator section. As a result, multiple motor parameters will experience significant real-time perturbations, which seriously restrict the control accuracy and system stability. Therefore, it is urgent to study a multi-parameter identification method.

[0003] Currently, regarding the parameter identification problem of linear motors, patent CN115632590A discloses a deadbeat thrust predictive control method, which improves the parameter robustness of linear induction motors by identifying the motor's excitation inductance and integrating it into the control strategy. Patent CN119070680A proposes an offline parameter identification method for superconducting linear motors, which achieves accurate identification of stator resistance and stator inductance by injecting DC and AC currents and calculating the effective values ​​of voltage and current. Patent CN116780981A discloses a model predictive control method for linear induction motors based on extended Kalman filtering. This method establishes an equivalent model of the linear induction motor considering edge effects and constructs a fuzzy extended Kalman filter observer to identify speed, flux linkage, and motor parameters for model predictive control. However, the above parameter identification methods are mostly applicable to low- and medium-speed linear motor scenarios, and the identified parameters are relatively simple, making it difficult to meet the requirements for rapid and synchronous identification of multiple parameters under ultra-high-speed operating conditions. Summary of the Invention

[0004] This invention provides a method for online identification of two parameters of a high-speed linear motor, which is used to solve the problem that the high-performance control of a high-speed linear induction motor requires high accuracy of motor parameters.

[0005] To achieve the above objectives, this invention provides a two-parameter online identification method for high-speed linear motors. The method includes: Step S1, establishing a discrete flux linkage model of a stator-segmented high-speed linear induction motor, constructing two independent artificial neural network identification branches based on the discrete flux linkage model, and performing identification through dual-branch separation, outputting preliminary identification results at each sampling time; Step S2, based on the two independent artificial neural network identification branches, constructing a flux linkage prediction residual squared loss function to derive a second-order decoupling update law based on the Hessian matrix inverse, and applying this law to the two independent artificial neural network identification branches. The updating process of the stator resistance and magnetizing inductance inside the identification branch is decoupled to obtain the updated values ​​of the stator resistance and magnetizing inductance; in step S3, the updated identification results are obtained based on the updated values ​​of the stator resistance and magnetizing inductance and the preliminary identification results. Multiple candidate estimation sets are constructed by performing full cross-combination on the updated identification results. Based on the multiple candidate estimation sets, the covariance matrix of the flux linkage residual vector is estimated online using a sliding window with a forgetting factor. The multiple candidate estimation sets are weighted and fused with the criterion of minimizing the trace of the fused covariance matrix to obtain the final parameter identification results.

[0006] The beneficial effects of this invention are as follows:

[0007] The traditional artificial neural network and model reference adaptive algorithm fusion identification method is improved from the aspects of identification structure and gradient update mechanism. It realizes fast and stable online identification of stator resistance and excitation inductance, providing reliable parameter support for subsequent motor control performance optimization. Specifically, it includes: (1) the adopted dual-parameter gradient decoupling update rate can effectively improve the problem of asynchronous convergence of dual parameters; (2) the adopted variable learning rate strategy related to the operating conditions can effectively improve the problem of oscillation of identification results; (3) the adopted dual-branch ANN separation identification structure can effectively improve the convergence speed of the identification algorithm. Attached Figure Description

[0008] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings:

[0009] Figure 1 A flowchart of the online dual-parameter identification method for high-speed linear motors provided by the present invention;

[0010] Figure 2 The block diagram of the two-parameter online identification structure based on ANN-MRAS (Artificial Neural Network-Model Reference Adaptive System) provided by this invention;

[0011] Figure 3 The results of online stator resistance identification under high-speed operating conditions provided by this invention;

[0012] Figure 4 The results of online identification of excitation inductance under high-speed operating conditions provided by this invention. Detailed Implementation

[0013] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, this invention adopts the following technical solution.

[0014] Figure 1 The flowchart of the online dual-parameter identification method for high-speed linear motors provided by the present invention is as follows: Figure 1 As shown, the method includes:

[0015] Step S1: Construct a dual-branch artificial neural network separation and identification structure, specifically including: establishing a discrete flux linkage model of the stator segmented high-speed linear induction motor, constructing two independent artificial neural network identification branches based on the discrete flux linkage model, and outputting preliminary identification results at each sampling time through dual-branch separation and identification.

[0016] Step S2, designing a two-parameter gradient decoupling update law, specifically includes: constructing a flux linkage prediction residual squared loss function based on two independent artificial neural network identification branches, in order to derive a second-order decoupling update law based on the inverse of the Hessian matrix, decoupling the update process of the stator resistance and excitation inductance inside the two independent artificial neural network identification branches, so as to obtain the update amount of the stator resistance and excitation inductance.

[0017] Step S3 introduces the covariance matrix to achieve the fusion of dual-branch identification results. Specifically, it includes: obtaining updated identification results based on the updated values ​​of stator resistance and excitation inductance and the preliminary identification results; constructing multiple candidate estimation sets by performing full cross-combination on the updated identification results; and estimating the covariance matrix of the flux linkage residual vector online using a sliding window with a forgetting factor based on the multiple candidate estimation sets. Taking the minimum trace of the fused covariance matrix as the criterion, the multiple candidate estimation sets are weighted and fused to obtain the final parameter identification results.

[0018] Figure 2 The block diagram of the two-parameter online identification structure based on ANN-MRAS provided by this invention is as follows: Figure 2 As shown, Figure 2The online identification method for two parameters based on the fusion of artificial neural networks and model reference adaptive algorithms provided by this invention has the following overall identification approach: Figure 2 As shown below, in conjunction with Figure 1 and Figure 2 The present invention will be described in detail.

[0019] In step S1, the discrete flux linkage model includes a reference model based on a current model and an adjustable model based on a voltage model. Step S1 includes: constructing two independent artificial neural network identification branches for the d-axis and q-axis of the adjustable model respectively, so as to utilize the complementarity of dq-axis information, and outputting the preliminary identification results of the d-axis and q-axis in parallel at each sampling time by performing dual-branch separation identification.

[0020] The discretization expression of the reference model based on the current model is established based on the reference mover flux linkages of the d-axis and q-axis at time k, the reference mover flux linkages of the d-axis and q-axis at time k-1, the stator currents of the d-axis and q-axis at time k, the mover self-inductance, the mover resistance, the slip angular frequency, and the sampling period.

[0021] The adjustable model based on the voltage model is established based on the d-axis and q-axis mover flux linkages at time k, the d-axis and q-axis mover flux linkages at time k-1, the d-axis and q-axis voltages of the nth stator segment at time k, the d-axis and q-axis currents of the nth stator segment at time k, the d-axis and q-axis currents of the nth stator segment at time k-1, the mover coverage ratio of the stator at time k, the stator length coefficient at time k, the sampling period, the stator resistance, the equivalent stator leakage inductance at time k, and the supply angular frequency at time k.

[0022] First, a discrete flux linkage model suitable for a stator-segmented high-speed linear induction motor is established. In the synchronous rotating dq coordinate system, a reference model based on the current model and an adjustable model based on the voltage model are constructed respectively. Their discretized scalar expressions are shown in equations (1) and (2), where equation (1) is the discretized scalar expression of the reference model based on the current model, and equation (2) is the discretized scalar expression of the adjustable model based on the voltage model.

[0023] (1)

[0024] in, and These are the reference motor flux linkages along the d-axis and q-axis at time k. and These are the reference motor flux linkages along the d-axis and q-axis at time k-1. and Let be the d-axis and q-axis currents of the stator at time k, respectively. For the sake of the child's own feelings, For the moving part resistance, T is the slip angular frequency. s The sampling period.

[0025] The discretization equation of the adjustable model is:

[0026] (2)

[0027] In the formula, and These are the motor flux linkages along the d-axis and q-axis at time k, respectively. and These are the motor flux linkages along the d-axis and q-axis at time k-1, respectively. and Let be the d-axis and q-axis voltages of the nth stator segment at time k, respectively. and Let be the d-axis and q-axis currents of the nth stator segment at time k, respectively. and Let be the d-axis and q-axis currents of the nth stator segment at time k-1, respectively. Let the ratio of the motor covering the stator be the value at time k. The stator length coefficient at time k is... The sampling period is For stator resistance, The equivalent stator leakage inductance at time k is and , Let be the power supply angular frequency at time k. For magnetizing inductance, For stator inductance. To avoid Too small a value can cause singularities, especially for values ​​containing 1 / Regularize the terms to... The ratio of mover coverage to stator coverage, where It is a positive constant much less than 1.

[0028] To fully utilize the complementarity of d-axis and q-axis information and suppress the impact of single-axis error fluctuations on the identification results, two independent artificial neural network (ANN) identification branches are constructed for the d-axis and q-axis of the adjustable model, respectively. Each network consists only of an input layer and an output layer. The input vector of the d-axis ANN is... , , , , , It consists of a total of 6 node components, and the output is: The input vector of the q-axis ANN is... , , , , , It consists of a total of 6 node components, and the output is: The interlayer connection weights of the d-axis and q-axis are determined by equation (2), which are respectively and Among them, the stator resistance to be identified implicitly included excitation inductor It is embedded as an adjustable inter-layer connection weight, and the remaining inter-layer connection weights are determined by a known parameter a. n b n T s L s , To be determined jointly.

[0029] After obtaining the input vector at each sampling time, a dual-branch separation and identification is performed using an error backpropagation algorithm driven by the flux linkage residual, to output preliminary identification results. These preliminary identification results include the preliminary identification results along the d-axis. Preliminary identification results of the q-axis ,in and These are the preliminary identification values ​​of the stator resistance along the d-axis and q-axis, respectively. and These are the initial identification values ​​of the excitation inductance along the d-axis and q-axis, respectively, thus providing four sets of candidate parameter estimates for subsequent data fusion.

[0030] Step S2 includes: constructing a loss function with the sum of squared residuals of magnetic flux as the objective; obtaining the gradient vector by taking the first-order partial derivative of the loss function, and continuing to take the partial derivative to obtain the Hessian matrix H; obtaining the explicit decoupling update formula according to the second-order decoupling update law based on the inverse of the Hessian matrix; and obtaining the update amounts of stator resistance and excitation inductance according to the explicit decoupling update formula.

[0031] The loss function targeting the sum of squared flux linkage residuals is constructed based on the reference flux linkages of the d-axis and q-axis at time k output by the reference model based on the current model and the d-axis and q-axis at time k output by the adjustable model based on the voltage model.

[0032] Based on the constructed dual-branch ANN separation and identification structure, the internal stator resistance of a single branch is addressed. And excitation inductance To address the mutual coupling problem during the update process, a squared loss function for the magnetic flux prediction residual is constructed, and based on this, a second-order decoupling update law based on the inverse of the Hessian matrix is ​​derived.

[0033] First, a loss function is constructed for each sampling period, targeting the sum of squared flux linkage residuals:

[0034] (3)

[0035] in, and The reference motor flux linkages at time k based on the current model in equation (1) are the d-axis and q-axis reference flux linkages at time k. and The d-axis and q-axis motor flux linkages at time k are respectively the output of the adjustable model based on the voltage model in equation (2).

[0036] At each sampling time, the flux linkage output is subjected to first-order local linearization around the current parameter estimation point, which can be approximated as:

[0037] (4)

[0038] In the formula, and These are the known terms for the d-axis and q-axis, respectively, without the parameter to be identified. and These are the sensitivity coefficients of the d-axis and q-axis flux linkages to the stator resistance, respectively. and These are the sensitivity coefficients of the magnetizing inductance to the d-axis and q-axis flux linkages, respectively.

[0039] Taking the first-order partial derivative of equation (3), we obtain the gradient vector of the loss function:

[0040] (5)

[0041] Taking the partial derivative of the gradient vector, we obtain the Hessian matrix H corresponding to the loss function:

[0042] (6)

[0043] off-diagonal elements of the Hessian matrix This reflects the degree of cross-coupling between the two parameters. To weaken this coupling, a second-order decoupling update law based on the inverse of the Hessian matrix (e.g., a second-order corrected update rule) is adopted. A local quadratic approximation is made near the current parameter point, and the updated gradient is set to zero, thus yielding the stator resistance. And excitation inductance The explicit decoupling update formula at each time step:

[0044] (7)

[0045] In the formula, and Stator resistance The update amounts at time k on the d-axis and q-axis. and They are magnetizing inductors The update amounts at time k on the d-axis and q-axis. Let be the learning rate at time k. The regularized Hessian matrix and , The regularization coefficient is . It is a second-order identity matrix. This is the determinant of the Hessian matrix after regularization.

[0046] The online identification method for high-speed linear motors with two parameters provided by the present invention further includes: dynamically adjusting the learning rate of the second-order decoupling update law according to the ratio of the mover covering the stator and the power supply angular frequency, so as to suppress the oscillation of the identification results caused by the high-speed operation of the motor or the change of the mover position, and realize the decoupling of the variable learning rate and the two-parameter gradient.

[0047] The learning rate is calculated based on the ratio of the mover to the stator and the power supply angular frequency, combined with the reference learning rate, the adjustment coefficient of the electric angular velocity term, and the adjustment coefficient of the coverage rate change term.

[0048] Due to the power supply angular frequency at time k during the motion's acceleration operation The frequency will continue to increase, and the ratio of the mover covering the stator changes periodically when entering and exiting the stator segment. A fixed learning rate can easily lead to increased gradient fluctuations, causing oscillations in the initial identification results at medium and high speeds. Therefore, this invention designs a power supply angular frequency at time k. The ratio of the motor covering the stator at time k. The relevant variable learning rate mechanism is expressed as follows:

[0049] (8)

[0050] in, Let be the learning rate at time k. As the baseline learning rate, This is the adjustment coefficient for the electric angular velocity term. This is the adjustment coefficient for the coverage change term. Let the ratio of the motor covering the stator be the value at time k. The ratio of the motor covering the stator at time k-1. Let be the power supply angular frequency at time k.

[0051] Step S3 includes: updating the preliminary identification results based on the update amounts of stator resistance and excitation inductance to obtain updated identification results for the d-axis and q-axis at each sampling time; constructing multiple candidate estimation sets by performing full cross-combination of the updated identification results; calculating the corresponding flux linkage residual vector for each candidate estimation in the multiple candidate estimation sets; estimating the covariance matrix of the flux linkage residual vector online using a sliding window with a forgetting factor; and weighted fusing the multiple candidate estimation sets based on the criterion of minimizing the trace of the fused covariance matrix to obtain the final parameter identification results.

[0052] The covariance matrix of the flux linkage residual vector is calculated as follows: Based on the d-axis and q-axis reference mover flux linkage and the stator resistance and excitation inductance output corresponding to the candidate estimates, the flux linkage residual vector corresponding to the candidate estimates is obtained; based on the flux linkage residual vector, the sliding window length, and the forgetting factor, the covariance matrix of the flux linkage residual vector is obtained.

[0053] After obtaining the stator resistance And excitation inductance After updating the identification results for the d-axis and q-axis, four candidate estimates can be obtained by performing a full cross-combination of the updated identification results. , , , The four candidate estimation sets are as follows:

[0054] (9)

[0055] in, and The stator resistance at time k is updated for the d-axis and q-axis, respectively. , , and The stator resistance at time k is updated for the d-axis and q-axis, respectively. , .

[0056] For the i-th candidate estimate (i=1,2,3,4), define the flux linkage residual vector corresponding to the i-th candidate estimate at time k. as follows:

[0057] (10)

[0058] In the formula, and These are the d-axis and q-axis predicted flux linkages of the stator resistance and magnetizing inductance outputs corresponding to the i-th candidate estimates, respectively.

[0059] To evaluate the stability of each candidate estimate over historical periods, a sliding window with a forgetting factor is used to estimate the covariance matrix of the flux linkage residual vector online. :

[0060] (11)

[0061] In the formula, N is the length of the sliding window, and n is the index of the historical time within the sliding window. Let be the forgetting factor at the j-th historical moment within the sliding window, and let covariance matrix be . This is a 2×2 matrix, where the diagonal elements reflect the fluctuation range of the residuals along the d-axis and q-axis, and the off-diagonal elements reflect the correlation between the residuals along the two axes. The smaller the covariance, the more stable the prediction accuracy and the higher the reliability of the candidate estimates.

[0062] Using the criterion of minimizing the trace of the fused covariance matrix, the optimal weights of each candidate estimate are solved. Let the covariance matrix corresponding to the final fusion result be... Its information matrix (Right now The inverse matrix is ​​the weighted sum of the information matrices of each candidate:

[0063] (12)

[0064] In the formula, for The inverse matrix, The fusion weights corresponding to the i-th candidate estimation results at time k are solved using a discrete search method to make the covariance matrix... trace tr( Minimum weight combination This leads to the final fusion result:

[0065] (13)

[0066] In the formula, This represents the optimal fused estimated vector at time k, which is the final parameter identification result. This represents the estimated stator resistance after optimal fusion at time k. This represents the optimal fused excitation inductance estimate at time k. Let i be the candidate estimation set at time k.

[0067] To verify the effectiveness of the proposed two-parameter identification method, a corresponding simulation model was built. The technical solution provided by this invention is employed. Figure 3 Stator resistance under high-speed operating conditions Online identification results Figure 4 Magnetizing inductor for high-speed operation Online identification results, stator resistance And excitation inductance The identification results on the high-speed section are as follows: Figure 3 and Figure 4 As shown, simulation results indicate that when the mover operates in the high-speed range of 220~240 m / s, the stator resistance R s And excitation inductance L m The maximum identification errors were only 0.89% and 0.98%, respectively.

[0068] The optional embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the embodiments of the present invention are not limited to the specific details in the above embodiments. Within the scope of the technical concept of the embodiments of the present invention, various simple modifications can be made to the technical solutions of the embodiments of the present invention, and these simple modifications all fall within the protection scope of the embodiments of the present invention.

[0069] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the embodiments of the present invention will not describe the various possible combinations separately.

[0070] Furthermore, various different implementations of the present invention can be combined arbitrarily, as long as they do not violate the spirit of the present invention, they should also be regarded as the content disclosed in the present invention.

Claims

1. A method for online identification of two parameters of a high-speed linear motor, characterized in that, The method includes: Step S1: Establish a discrete flux linkage model of the stator segmented high-speed linear induction motor, construct two independent artificial neural network identification branches based on the discrete flux linkage model, and separate the identification through the dual branches, outputting the preliminary identification results at each sampling time. Step S2: Based on two independent artificial neural network identification branches, construct the squared loss function of flux linkage prediction residuals to derive the second-order decoupling update law based on the inverse of the Hessian matrix, decouple the update process of stator resistance and excitation inductance inside the two independent artificial neural network identification branches, and obtain the update amount of stator resistance and excitation inductance. Step S3: Based on the updated values ​​of the stator resistance and excitation inductance and the preliminary identification results, the updated identification results are obtained. By performing full cross-combination on the updated identification results, multiple candidate estimation sets are constructed. Based on the multiple candidate estimation sets, the covariance matrix of the flux linkage residual vector is estimated online using a sliding window with a forgetting factor. The multiple candidate estimation sets are weighted and fused with the criterion of minimizing the trace of the fused covariance matrix to obtain the final parameter identification results.

2. The online dual-parameter identification method for high-speed linear motors according to claim 1, characterized in that, In step S1, the discrete flux linkage model includes a reference model based on a current model and an adjustable model based on a voltage model. Step S1 includes: Two independent artificial neural network identification branches are constructed for the d-axis and q-axis of the adjustable model, respectively, to take advantage of the complementarity of d- and q-axis information. By performing dual-branch separation identification, the preliminary identification results of the d-axis and q-axis are output in parallel at each sampling time.

3. The online dual-parameter identification method for high-speed linear motors according to claim 2, characterized in that, The discretization expression of the reference model based on the current model is established based on the reference mover flux linkages of the d-axis and q-axis at time k, the reference mover flux linkages of the d-axis and q-axis at time k-1, the stator currents of the d-axis and q-axis at time k, the mover self-inductance, the mover resistance, the slip angular frequency, and the sampling period.

4. The online dual-parameter identification method for high-speed linear motors according to claim 3, characterized in that, The adjustable model based on the voltage model is established based on the d-axis and q-axis mover flux linkages at time k, the d-axis and q-axis mover flux linkages at time k-1, the d-axis and q-axis voltages of the nth stator segment at time k, the d-axis and q-axis currents of the nth stator segment at time k, the d-axis and q-axis currents of the nth stator segment at time k-1, the mover coverage ratio of the stator at time k, the stator length coefficient at time k, the sampling period, the stator resistance, the equivalent stator leakage inductance at time k, and the supply angular frequency at time k.

5. The online dual-parameter identification method for high-speed linear motors according to claim 4, characterized in that, Step S2 includes: Construct a loss function with the sum of squared flux linkage residuals as the objective; The gradient vector is obtained by taking the first-order partial derivative of the loss function, and the Hessian matrix H is obtained by taking the partial derivatives again. Based on the second-order decoupling update law based on the inverse of the Hessian matrix, the explicit decoupling update formula is obtained. The update values ​​of stator resistance and magnetizing inductance are obtained based on the explicit decoupling update formula.

6. The online dual-parameter identification method for high-speed linear motors according to claim 5, characterized in that, The loss function targeting the sum of squared flux linkage residuals is constructed based on the reference flux linkages of the d-axis and q-axis at time k output by the reference model based on the current model and the d-axis and q-axis at time k output by the adjustable model based on the voltage model.

7. The online dual-parameter identification method for high-speed linear motors according to claim 6, characterized in that, The method also includes: The learning rate of the second-order decoupling update law is dynamically adjusted based on the ratio of the mover covering the stator and the power supply angular frequency to suppress oscillations in the identification results caused by high-speed motor operation or changes in the mover position.

8. The online dual-parameter identification method for high-speed linear motors according to claim 7, characterized in that, The learning rate is calculated based on the ratio of the mover to the stator and the power supply angular frequency, combined with the reference learning rate, the adjustment coefficient of the electric angular velocity term, and the adjustment coefficient of the coverage rate change term.

9. The online dual-parameter identification method for high-speed linear motors according to claim 8, characterized in that, Step S3 includes: After updating the initial identification results based on the update amounts of stator resistance and excitation inductance, the updated identification results of the d-axis and q-axis at each sampling time are obtained. By performing a full cross-combination of the updated identification results, multiple candidate estimation sets are constructed; For each candidate estimate in the multiple candidate estimate sets, calculate the corresponding flux linkage residual vector; The covariance matrix of the flux linkage residual vector is estimated online using a sliding window with a forgetting factor. Using the minimum trace of the fused covariance matrix as the criterion, multiple candidate estimation sets are weighted and fused to obtain the final parameter identification result.

10. The online dual-parameter identification method for high-speed linear motors according to claim 9, characterized in that, The covariance matrix of the flux linkage residual vector is calculated as follows: Based on the d-axis and q-axis reference mover flux linkage and the stator resistance and excitation inductance output corresponding to the candidate estimates, the flux linkage residual vector corresponding to the candidate estimates is obtained by predicting the flux linkage on the d-axis and q-axis. The covariance matrix of the flux linkage residual vector is obtained from the flux linkage residual vector, the sliding window length, and the forgetting factor.

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