Permanent magnet synchronous motor off-line inductance identification method and system
Patent Information
- Application Number
- CN202611197505.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-07
- Publication Date
- 2026-10-20
Smart Images
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Abstract
Description
Technical Field
[0001] This invention belongs to the technical field of motor parameter identification, and more specifically, relates to an offline inductance identification method and system for permanent magnet synchronous motors. Background Technology
[0002] Permanent magnet synchronous motors (PMSMs) are widely used in electric vehicles, industrial servos, robot actuators, and precision transmissions due to their high power density, fast dynamic response, and high efficiency. The d-axis and q-axis inductances are crucial parameters in the PMSM control model, and their accuracy directly affects control performance, including current loop tuning, torque estimation, field weakening control, rotor position estimation, and condition monitoring. Traditional PMSM inductance parameters are typically obtained from manufacturer-specified values, offline measurements, or online identification algorithms. Offline PMSM inductance identification methods allow for the injection of test signals when the motor is stationary or at low speeds, and the inductance parameters can be calculated by measuring the voltage and current responses. Since the offline identification process does not rely on the motor's normal load operation, it reduces the impact of operating conditions on the identification results. However, this method requires measuring voltage and current response. Low-cost drive systems generally do not have additional terminal voltage sensors. In this case, the actual terminal voltage cannot be obtained directly. The terminal voltage can only be reconstructed from the duty cycle, DC bus voltage, and control commands. However, due to the influence of inverter dead zone, power device conduction voltage drop, bus voltage sampling error, cable resistance, winding resistance variation, and current sampling noise, there will be a deviation between the reconstructed voltage and the actual terminal voltage, which will cause inductor identification error.
[0003] To address the issue of offline inductance identification errors in permanent magnet synchronous motors (PMSMs), current main methods involve injecting specific test signals and establishing compensation models. The paper "Offline Inductance Identification of IPMSM With Sequence-Pulse Injection" proposes an embedded offline inductance identification method for PMSMs based on sequence pulse injection, extracting d-axis and q-axis inductance information through pulse voltage and current responses. The paper "Offline Inductance Identification of PMSM With Adaptive Inverter Nonlinearity Compensation" proposes an offline inductance identification method for PMSMs with adaptive inverter nonlinearity compensation, improving identification accuracy by compensating for inverter nonlinearity. However, these current offline inductance identification methods typically require designing specific excitation processes, relying on relatively accurate inverter nonlinearity models or prior compensation parameters, and still suffer from significant inductance identification errors in scenarios with unknown parameters, limited hardware costs, and varying parasitic impedance.
[0004] Therefore, how to accurately identify the inductance of a permanent magnet synchronous motor without setting a terminal voltage sensor and without knowing the model parameters is a technical problem that urgently needs to be solved. Summary of the Invention
[0005] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides an offline inductance identification method and system for permanent magnet synchronous motors, the purpose of which is to achieve accurate identification of the inductance of permanent magnet synchronous motors without setting up a terminal voltage sensor and without knowing the model parameters.
[0006] According to a first aspect of the present invention, an offline inductance identification method for a permanent magnet synchronous motor is provided, comprising: When the permanent magnet synchronous motor locks the rotor, a step command is injected into the current axis to be identified. The current response generated by the current axis to be identified under the step command excitation is collected, and the voltage response of the current axis to be identified is reconstructed to obtain its reconstructed voltage. The current axis to be identified is either the d-axis or the q-axis. The first stage of training is performed using the current response and reconstructed voltage within the steady-state window as inputs to the steady-state model. The steady-state model is used to acquire the current response and reconstructed voltage at the k-th time point and to calculate the estimated current response at the k-th time point based on the parametric equivalent circuit relationship. The parameter equivalent circuit consists of the reconstructed gain voltage. Equivalent resistance Nonlinear disturbance voltage and the inductor to be identified It is formed by connecting the dots; where the subscripts are... The identifier indicates the axis to be identified. This is the gain correction factor. It is a nonlinear disturbance voltage. Indicates about nonlinear functions, , These are the reconstructed voltage and current responses acquired at the k-th time point, respectively. , , and The parameters are to be trained; the first stage of training includes freezing the inductor to be identified. ,renew , , The first stage of training ends when the first-stage loss of the steady-state model converges to a preset level. The first-stage loss includes the estimated current response output by the steady-state model. With the acquired current response Similarity loss between them; The second stage of training is performed using the transient recursive model based on the current response and reconstructed voltage input within the transient window; the transient recursive model calls the steady-state model trained beforehand. , , This is used to obtain the current response and reconstructed voltage at the k-th time point, and to calculate the estimated current response at the (k+1)-th time point based on the parametric equivalent circuit relationship. The second phase of training includes freezing... , , ,renew The second stage of training ends when the second-stage loss of the transient recursive model converges to a preset level. The second-stage loss includes the estimated current response output by the transient recursive model. With the acquired current response The similarity loss between them; updated after the second training phase. This serves as the inductance identification result for the current axis to be identified.
[0007] According to a second aspect of the present invention, an offline inductor identification system for a permanent magnet synchronous motor is provided. The system is used to implement the offline inductor identification method for a permanent magnet synchronous motor as described in any of the preceding claims. Specifically, it includes a training data acquisition unit, a first-stage training unit, and a second-stage training unit. The training data acquisition unit is used to acquire training data, the first-stage training unit is used to perform a first-stage training, and the second-stage training unit is used to perform a second-stage training.
[0008] According to a third aspect of the invention, a computer-readable storage medium is provided having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the method described in any of the preceding claims.
[0009] Overall, compared with the prior art, the technical solutions conceived in this invention have the following beneficial effects.
[0010] This invention addresses the problems of traditional offline inductor identification methods, such as reliance on additional voltage sensors, susceptibility to inverter dead zones and voltage drops in power devices, and decreased identification accuracy in the presence of sampling and quantization noise. A novel offline inductor identification method is proposed: First, under rotor-locked conditions, a single-axis step command is injected into the shaft to be identified, the current response is collected, and the voltage is reconstructed to obtain training data; second, a gain correction coefficient is introduced. Nonlinear disturbance voltage and equivalent resistance The trainable static compensation parameters are constructed including the reconstructed gain voltage. Equivalent resistance Nonlinear disturbance voltage and the inductor to be identified The parameter equivalent circuit, reconstructed gain voltage Used to correct the reconfiguration voltage calculated from the inverter duty cycle and bus voltage, equivalent resistance This is a linear voltage drop term used to absorb winding resistance, cable resistance, and device on-resistance; it is a nonlinear disturbance voltage. Used to approximate current polarity-dependent disturbances such as inverter dead zone and device voltage drop. , , The introduction of this method, combined with the subsequent training process, allows for the absorption of the differences between the ideal linear model and the actual system behavior through mathematical means, decoupling the dynamic characteristics of the target inductor parameters from complex environmental disturbances. Based on the relationship embodied in the equivalent circuit of the above parameters, a steady-state model and a transient recursive model can be established. Subsequently, a two-stage gradient training strategy is adopted. In the first stage, the steady-state model is trained using training data from the steady-state window, freezing the inductor and updating the static compensation parameters. The fitting results of the steady-state segment can reflect the absorption effect of the static compensation parameters on the voltage drop error, thus obtaining accurate static compensation parameters. In the second stage, the transient recursive model is trained using training data from the transient window, locking the static compensation parameters and updating the inductor. The fitting results in the transient window can reflect the influence of the inductor on the current slope, thus obtaining accurate inductor identification results. The above scheme can complete offline inductor identification without setting up an additional terminal voltage sensor and without knowing the motor parameters, making it suitable for offline self-tuning of low-cost drivers.
[0011] Furthermore, the mapping of the parameters to be trained is achieved through a neural network, and the learnable weights of each mapping layer are trained to achieve the desired parameters. , , and This update can speed up the training process and quickly obtain accurate inductance identification results. Attached Figure Description
[0012] Figure 1 This is a flowchart of the steps of an offline inductance identification method for a permanent magnet synchronous motor according to an embodiment of the present invention.
[0013] Figure 2 This is a schematic diagram of injecting a step command into the current axis to be identified in one embodiment of the present invention.
[0014] Figure 3 These are, in one embodiment of the present invention, the applied current step curve, the acquired current response sequence, and the reconstructed voltage sequence; wherein, (a) is the current step curve, (b) is the acquired current response sequence, and (c) is the reconstructed voltage sequence.
[0015] Figure 4 This is a schematic diagram of the parameter equivalent circuit in one embodiment of the present invention.
[0016] Figure 5 This is a structural diagram of the steady-state model and the transient recursive model in one embodiment of the present invention.
[0017] Figure 6 This is a flowchart illustrating the steps of performing two-stage training in one embodiment of the present invention.
[0018] Figure 7 This is a graph showing the fitting effect of the d-axis current in the verification example.
[0019] Figure 8 This is a graph showing the q-axis current fitting effect in the verification example.
[0020] Figure 9 This is a diagram showing the convergence effect of the d-axis and q-axis inductors in the second stage of the verification example.
[0021] Figure 10 This is a statistical chart of the d-axis and q-axis inductance identification results under different noise intensities in the verification example.
[0022] Figure 11 This is a surface plot of the identification error under different combinations of d-axis and q-axis inductance in the verification example. Detailed Implementation
[0023] 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.
[0024] Example 1 like Figure 1 The diagram shows a flowchart of the offline inductance identification method for a permanent magnet synchronous motor according to an embodiment of the present invention, which includes steps S1 to S3. Each step is described in detail below.
[0025] Step S1: With the permanent magnet synchronous motor in the locked rotor state, inject a step command into the current axis to be identified, collect the current response generated by the current axis to be identified under the step command excitation, and reconstruct the voltage response of the current axis to be identified to obtain its reconstructed voltage; wherein, the current axis to be identified is the d-axis or the q-axis.
[0026] Specifically, the voltage equation of the permanent magnet synchronous motor in the dq rotating coordinate system is: ; In step S1, the permanent magnet synchronous motor is placed in a rotor-locked state. This avoids the kinetic electromotive force introduced by rotor rotation from contaminating the voltage-current relationship, and also prevents the torque generated by the injected current on the shaft to be identified from causing slight rotor movement, which would lead to position θ drift and Park transformation distortion. This ensures that the response under step excitation purely reflects the winding inductance and resistance characteristics, and that the offline inductance identification results are not affected by speed, position estimation errors, and back EMF modeling errors. At this time, the electric angular velocity in the voltage equation of the dq rotating coordinate system of the permanent magnet synchronous motor is... Forced to zero, and electric angular velocity With the relevant terms disappearing, the voltage equation of the permanent magnet synchronous motor in the dq rotating coordinate system simplifies to: ; In the formula, Indicates the current identification axis. To identify the current axis voltage, To identify the current axis current, For stator resistance, To identify the shaft inductance at present.
[0027] With the terminal voltage sensor in place, the inductance of the current identification axis can be calculated by measuring the current identification axis voltage and current, substituting them into the above equation, thus achieving inductance identification.
[0028] However, without a terminal voltage sensor, it is impossible to obtain the actual value of the current identification axis voltage. In this case, voltage reconstruction is usually achieved based on existing reconstruction algorithms. For example, the current identification axis voltage is estimated based on the known DC bus voltage, the current PWM duty cycle, and inverter nonlinear compensation. The reconstructed voltage of the current identification axis is obtained by subtracting the dead zone, tube voltage drop, line loss, and other non-ideal inverter terms from "duty cycle × bus voltage". This reconstructed voltage is not directly sampled by the voltage sensor, so it has a certain deviation. If this reconstructed voltage is used directly for calculation, it will lead to a large error in inductor identification.
[0029] In one embodiment, such as Figure 2 The diagram illustrates the injection of a step command into the current axis to be identified in one embodiment of the present invention. Specifically, this embodiment involves injecting a current step command into the current axis to be identified: under rotor-locked conditions, during the control cycle, the current command (or current step command) of the current axis to be identified (d-axis or q-axis) in the current control loop is... or The value changes from zero to a preset amplitude I. step The current command for the other axis remains zero, causing the PI regulator of the currently identified axis to automatically output the corresponding axis voltage command, which is applied to the inverter via reverse Park and SVPWM. This induces a current response determined by the inductance and resistance in the winding of the currently identified axis to power inductor identification.
[0030] like Figure 3 The diagram shows the applied current step curve, the acquired current response sequence, and the reconstructed voltage sequence in one embodiment of the present invention; wherein (a) is the current step curve, (b) is the acquired current response sequence, and (c) is the reconstructed voltage sequence. It should be noted that only one axis, either the d-axis or the q-axis, is selected for identification each time; therefore, the applied current step, the acquired current response sequence, and the reconstructed voltage sequence are all relative to the axis to be identified.
[0031] Step S2: Using the time-aligned current response and reconstructed voltage within the steady-state window as the first set of training data, input them into the steady-state model to perform the first stage of training; the steady-state model is used to obtain the current response and reconstructed voltage collected at the k-th time point, and calculate the estimated value of the current response at the k-th time point based on the parametric equivalent circuit relationship. The first phase of training includes freezing the inductors to be identified. ,renew , , The first stage of training ends when the first-stage loss of the steady-state model converges to a preset level.
[0032] The first-stage loss includes the current response estimate from the steady-state model output. With the acquired current response The similarity loss between them.
[0033] Step S3: Using the time-aligned current response and reconstructed voltage within the transient window as the second set of training data, input them into the transient recursive model to perform the second stage of training; the transient recursive model calls the data trained by the steady-state model. , , This is used to obtain the current response and reconstructed voltage at the k-th time point, and to calculate the estimated current response at the (k+1)-th time point based on the parametric equivalent circuit relationship. The second phase of training includes freezing. , , ,renew The second stage of training ends when the second-stage loss of the transient recursive model converges to a preset level; the updated value after the second training stage ends... This serves as the inductance identification result for the current axis to be identified.
[0034] The second-stage loss includes the current response estimate from the transient recursive model output. With the acquired current response The similarity loss between them.
[0035] The step response first passes through a transient window and then enters a steady-state window. Understandably, in the offline identification method for inductor parameters under static conditions of a permanent magnet synchronous motor, the transient window refers to the period from the moment the step current command is injected until the winding current response completes its main exponential rise phase and the rate of change of current has not yet decayed below a preset threshold. Within this window, the current satisfies the transient differential equation relationship. The steady-state window refers to the continuous period during which the current response enters di / dt≈0 and the measured current has only switching ripple in the neighborhood of the command value. In engineering, the two windows can be jointly divided based on the time constant τ=L / R and the slope threshold.
[0036] Specifically, the models for steps S2 and S3 above both rely on the parametric equivalent circuit. For example... Figure 4 The diagram shown is a parameter equivalent circuit diagram according to an embodiment of the present invention. This parameter equivalent circuit consists of a reconstructed gain voltage. Equivalent resistance Inductor to be identified Nonlinear disturbance voltage Series connection, reconstructed gain voltage Used to correct the reconfiguration voltage calculated from the inverter duty cycle and bus voltage, equivalent resistance The linear voltage drop term is used to absorb winding resistance, cable resistance, and device on-resistance. The nonlinear disturbance voltage drop term is composed of... This indicates that it is used to approximate current polarity-related disturbances such as inverter dead zone and device voltage drop in a differentiable manner. , , The introduction of this method, combined with the subsequent training process, allows for the absorption of the differences between the ideal linear model and the actual system behavior through mathematical means, thereby decoupling the dynamic characteristics of the target inductance parameters from complex environmental disturbances.
[0037] Among them, regarding nonlinear functions The function can be selected from hyperbolic tangent, smooth sign function, piecewise differentiable saturated function, or differentiable polar function. The following explanation uses the hyperbolic tangent as an example, but other functions can also be used.
[0038] At this point, the parametric equivalent circuit can be expressed as: ; Among them, subscript The identifier indicates the axis to be identified. This is the gain correction factor. It is a nonlinear disturbance voltage. , These are the reconstructed voltage and current responses acquired at the k-th time point, respectively. The hyperbolic tangent smoothing coefficient is... , , and These are the parameters to be trained.
[0039] Based on the equivalent circuit with the above parameters, the response current at the current timing point and the response current at the next timing point can be estimated.
[0040] First, the equivalent resistance The voltage across the two ends is denoted as the effective voltage. Its expression is: .
[0041] At this point, the steady-state model calculates the estimated current response at the k-th time point based on the parametric equivalent circuit relationship. The calculation formula is: .
[0042] The transient recursive model calculates the estimated current response at time point k+1 based on the parametric equivalent circuit relationship. The calculation formula is: ;
[0043] In the formula, These are all intermediate parameters. This is the sampling step size.
[0044] like Figure 5 The diagram shows the structure of the steady-state model and the transient recursive model in one embodiment of the present invention. The steady-state model and the transient recursive model share the same effective voltage calculation module. The steady-state model also includes a steady-state calculation module, and the transient recursive model also includes a transient calculation module. The effective voltage calculation module is used to obtain the current response collected at the k-th time point. and reconstructed voltage And calculate the effective voltage The steady-state calculation module is used to obtain the effective voltage. And calculate the estimated current response value. The transient calculation module is used to obtain the current response acquired at the k-th time point. and effective voltage And calculate the estimated current response value. .
[0045] In one embodiment, the method maps the parameters to be trained using a neural network. Specifically, it sets the neural network as four parallel mapping layers, namely the first to fourth mapping layers. The first mapping layer maps its learnable weights to gain correction coefficients. The second mapping layer maps its learnable weights to equivalent resistance. The third mapping layer maps its learnable weights to nonlinear perturbation voltages. The fourth mapping layer maps its learnable weights to the inductance to be identified. The trainable parameters are achieved by training the learnable weights of each mapping layer. , , and Update.
[0046] More specifically, the first mapping layer assigns its learnable weights Mapped to gain correction coefficient The mapping formula is: ; More specifically, the second mapping layer uses its learnable weights Mapped to equivalent resistance The mapping formula is: ; More specifically, the third mapping layer uses its learnable weights Mapped to nonlinear disturbance voltage The mapping formula is: ; More specifically, the fourth mapping layer uses its learnable weights Mapped to the inductor to be identified The mapping formula is: ; In the formula, These are all boundary parameters pre-defined in the first mapping layer. These are all boundary parameters pre-defined in the second mapping layer. The boundary parameters pre-defined for the third mapping layer, This is the Sigmoid function.
[0047] In one embodiment, the loss function of the first stage loss Loss function of the second stage loss The calculation formula is: ; ; In the formula, Represents the steady-state window. This indicates a transient window.
[0048] like Figure 6 The diagram shows a flowchart of the two-stage training process in one embodiment of the present invention. After training begins, parameters are initialized. In Phase I, the static gate opens, and the model is updated. , , and Simultaneously, freezing is achieved through a gradient mask. When the steady-state loss rate of change is less than a threshold, Phase II begins. In Phase II, the transient gate opens, and the model is updated. Simultaneously lock , and The loss is then calculated and backpropagation is performed until the maximum number of training epochs is reached or the convergence condition is met. Based on the above steps, the final inductance to be identified is obtained after training is complete. The result is its identification result.
[0049] The following is a verification through specific experiments.
[0050] A 1.57 kW built-in permanent magnet synchronous motor was used for verification. The motor has a rated torque of approximately 3.75 Nm, 4 pole pairs, a rated speed of approximately 2500 rpm, and a rated current of approximately 6 A. The driver uses a three-phase voltage source inverter with a switching frequency and current sampling frequency of 10 kHz. To obtain the true reference values, the d-axis and q-axis inductances were measured using a high-precision LCR meter before the experiment. During the identification process, step current commands were injected into the d-axis and q-axis respectively under rotor-locked conditions. For example, approximately -1A step current was injected during d-axis identification, and approximately 1A step current was injected during q-axis identification. The controller recorded the complete current response sequence. During data preprocessing, 10% of the maximum current amplitude was used as the trigger threshold to determine the step trigger point, and 20 sampling points were traced back to extract 400 sampling points as effective training samples, corresponding to a data window of approximately 40 ms.
[0051] like Figure 7 The image shown is a graph illustrating the fitting effect of the d-axis current in a verification example. Figure 8 The image shown is a graph illustrating the q-axis current fitting effect in the verification example. From... Figure 7 and Figure 8 It can be seen that the predicted current in the transient window and steady-state segment of the trained model highly overlaps with the measured current, indicating that the trained model can reproduce the step response process of the d-axis and q-axis well, which means that the parameter identification results are highly accurate and closely match the actual parameters of the motor.
[0052] like Figure 9The figure shows the convergence results of the d-axis and q-axis inductances in the second stage of the verification example. During the second stage of training, the inductance parameters gradually converge under the constraint of the loss function. Experimental data shows that the d-axis inductance can converge to approximately 4.749 mH, and the q-axis inductance can converge to approximately 7.922 mH, with errors relative to the LCR instrument reference values of approximately 3.87% and 1.54%, respectively. This result demonstrates that the present invention can achieve high-precision offline inductance identification without an additional phase voltage sensor.
[0053] Table 1 below records the d-axis and q-axis inductance identification results under different noise intensities. Figure 10 The figure shows the statistical results of d-axis and q-axis inductance identification under different noise intensities in the verification example. To verify the noise immunity, Gaussian white noise with an intensity of 1% to 10% was added to the current signal and the training was repeated. Experimental data shows that under 10% noise conditions, the drift of the mean d-axis inductance relative to the noise-free reference is approximately 0.77%, and the drift of the mean q-axis inductance relative to the noise-free reference is approximately 1.81%. The drift of both axis parameters is controlled within 2%, indicating that the present invention has good robustness to current measurement noise and quantization noise.
[0054] Table 1:
[0055] Table 2 below records the identification errors in the verification examples under different combinations of d-axis and q-axis inductances. Figure 11 The figure shows the identification error surface plots under different d-axis and q-axis inductance combinations in the verification example. To verify the generalization ability, a... , and The parameter scan dataset covers near-surface-mounted permanent magnet synchronous motors. The application scenarios also cover high salient pole ratio built-in permanent magnet synchronous motors. Experimental data shows that, in 49 parameter combinations, the average error of the d-axis inductance is approximately 2.31%, and the average error of the q-axis inductance is approximately 2.51%, indicating that the present invention has good applicability under different inductor combinations.
[0056] Table 2:
[0057] Example 2 The present invention also relates to an offline inductor identification system for permanent magnet synchronous motors. The system is used to implement the offline inductor identification method for permanent magnet synchronous motors as described in Embodiment 1. Specifically, it includes a training data acquisition unit, a first-stage training unit, and a second-stage training unit. The training data acquisition unit is used to acquire training data, the first-stage training unit is used to perform the first-stage training, and the second-stage training unit is used to perform the second-stage training.
[0058] Example 3 The present invention also relates to a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the offline inductance identification method for permanent magnet synchronous motors described in Embodiment 1.
[0059] Specifically, the memory may include high-speed random access memory, as well as non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart media cards (SMC), secure digital (SD) cards, flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.
[0060] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. It should be noted that the terms "in one embodiment," "for example," and "again" are intended to illustrate the present invention and are not intended to limit the present invention.
[0061] The above embodiments merely illustrate several implementation methods of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention.
Claims
1. A method for offline inductance identification of a permanent magnet synchronous motor, characterized in that, include: When the permanent magnet synchronous motor locks the rotor, a step command is injected into the current axis to be identified. The current response generated by the current axis to be identified under the step command excitation is collected, and the voltage response of the current axis to be identified is reconstructed to obtain its reconstructed voltage. The current axis to be identified is either the d-axis or the q-axis. The first stage of training is performed using the current response and reconstructed voltage within the steady-state window as inputs to the steady-state model. The steady-state model is used to acquire the current response and reconstructed voltage at the k-th time point and to calculate the estimated current response at the k-th time point based on the parametric equivalent circuit relationship. The parameter equivalent circuit consists of the reconstructed gain voltage. Equivalent resistance Nonlinear disturbance voltage and the inductor to be identified It is formed by connecting the dots; where the subscripts are... The identifier indicates the axis to be identified. This is the gain correction factor. It is a nonlinear disturbance voltage. Indicates about nonlinear functions, , These are the reconstructed voltage and current responses acquired at the k-th time point, respectively. , , and The parameters are to be trained; the first stage of training includes freezing the inductor to be identified. ,renew , , The first stage of training ends when the first-stage loss of the steady-state model converges to a preset level. The first-stage loss includes the estimated current response output by the steady-state model. With the acquired current response Similarity loss between them; The second stage of training is performed using the transient recursive model based on the current response and reconstructed voltage input within the transient window; the transient recursive model calls the steady-state model trained beforehand. , , This is used to obtain the current response and reconstructed voltage at the k-th time point, and to calculate the estimated current response at the (k+1)-th time point based on the parametric equivalent circuit relationship. The second phase of training includes freezing... , , ,renew The second stage of training ends when the second-stage loss of the transient recursive model converges to a preset level. The second-stage loss includes the estimated current response output by the transient recursive model. With the acquired current response The similarity loss between them; updated after the second training phase. This serves as the inductance identification result for the current axis to be identified.
2. The offline inductance identification method for permanent magnet synchronous motors as described in claim 1, characterized in that, When acquiring training data, a step command is injected into the current axis to be identified, including a current step command: under rotor-locked conditions, the current command of the current axis to be identified in the current control loop is stepped from zero to a preset amplitude during the control cycle, while the current command of the other axis remains zero. This causes the PI regulator of the current axis to be identified to automatically output the corresponding axis voltage command, which is then applied to the inverter via inverse Park transformation and SVPWM, thereby exciting a current response in the winding of the current axis to be identified.
3. The offline inductance identification method for permanent magnet synchronous motors as described in claim 1, characterized in that, The steady-state model calculates the estimated current response at time point k. The calculation formula is: ； ； The transient recursive model calculates the estimated current response at time point k+1. The calculation formula is: ； ； ； In the formula, Equivalent resistance The effective voltages at both ends are intermediate parameters. This is the sampling step size.
4. The offline inductance identification method for permanent magnet synchronous motors as described in claim 3, characterized in that, The steady-state model and the transient recursive model share the same effective voltage calculation module. The steady-state model also includes a steady-state calculation module, and the transient recursive model also includes a transient calculation module. The effective voltage calculation module is used to obtain the current response collected at the k-th time point. and reconstructed voltage And calculate the effective voltage. ; The steady-state calculation module is used to obtain the effective voltage. And calculate the estimated current response value. ; The transient calculation module is used to obtain the current response collected at the k-th time point. and the effective voltage And calculate the estimated current response value. .
5. The offline inductance identification method for permanent magnet synchronous motors as described in claim 1, characterized in that, The method uses a neural network to map the parameters to be trained. Specifically, it sets the neural network into four parallel mapping layers, namely the first to fourth mapping layers. The first mapping layer maps its learnable weights to gain correction coefficients. The second mapping layer maps its learnable weights to equivalent resistance. The third mapping layer maps its learnable weights to nonlinear perturbation voltages. The fourth mapping layer maps its learnable weights to the inductance to be identified. ; The trainable parameters are achieved by training the learnable weights of each mapping layer. , , and Update.
6. The offline inductance identification method for permanent magnet synchronous motors as described in claim 5, characterized in that, The first mapping layer assigns its learnable weights Mapped to gain correction coefficient The mapping formula is: ； The second mapping layer uses its learnable weights Mapped to equivalent resistance The mapping formula is: ； The third mapping layer incorporates its learnable weights. Mapped to nonlinear disturbance voltage The mapping formula is: ； The fourth mapping layer incorporates its learnable weights. Mapped to the inductor to be identified The mapping formula is: ； In the formula, These are all boundary parameters pre-defined in the first mapping layer. These are all boundary parameters pre-defined in the second mapping layer. The boundary parameters pre-defined for the third mapping layer, This is the Sigmoid function.
7. The offline inductance identification method for permanent magnet synchronous motors as described in any one of claims 1 to 6, characterized in that, Loss function of the first stage and the loss function of the second stage loss The calculation formula is: ； ； In the formula, Represents the steady-state window. This indicates a transient window.
8. The offline inductance identification method for a permanent magnet synchronous motor as described in any one of claims 1 to 6, characterized in that, about nonlinear functions Selected from hyperbolic tangent function, smooth sign function, piecewise differentiable saturated function, or differentiable polar function.
9. An offline inductance identification system for a permanent magnet synchronous motor, characterized in that, The system is used to implement the offline inductor identification method for permanent magnet synchronous motors as described in any one of claims 1 to 8, specifically including a training data acquisition unit, a first-stage training unit, and a second-stage training unit. The training data acquisition unit is used to acquire training data, the first-stage training unit is used to perform a first-stage training, and the second-stage training unit is used to perform a second-stage training.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 8.