A method and system for analytical modeling of rotary transformer signals under multiple operating conditions

Abstract

This invention relates to the field of resolver signal processing technology and discloses a method and system for analytical modeling of resolver signals that integrates multi-condition coupling. It aims to solve the technical problems of existing modeling methods that do not fully consider the coupling effect of eccentricity and electromagnetic interference, have insufficient model accuracy, and limited applicability. This method constructs an integrated equivalent circuit of the electric drive system and the resolver, analyzes the coupling mechanism between electromagnetic interference and resolver eccentricity, and establishes analytical expressions for multi-field coupled signals including dynamic eccentricity, static eccentricity, and differential common-mode electromagnetic interference. Ultimately, it achieves accurate modeling of resolver signals under complex operating conditions. This invention integrates the electromagnetic interference coupling path with the eccentric air gap magnetic field distortion law into a unified model, making it applicable to complex electric drive scenarios such as electric vehicles. It provides accurate theoretical support for resolver signal error compensation and control performance optimization. Through parameter calibration, it can be adapted to different types of resolvers, demonstrating strong practicality.

Description

Technical Field

[0001] This invention relates to the field of rotary transformer signal processing technology, specifically to a method and system for analytical modeling of rotary transformer signals that integrates multi-condition coupling. Background Technology

[0002] As a high-precision angular position sensor, the rotary transformer detects rotor position signals through electromagnetic coupling between the excitation winding and the output winding. The accuracy of its output signal directly determines the performance of the motor control system. In practical applications, rotary transformers often face the coupling effects of multiple complex operating conditions:

[0003] (1) Eccentric working condition: Installation error, bearing wear, etc. cause the stator and rotor geometric center to shift, forming static eccentricity (constant eccentricity) or dynamic eccentricity (eccentricity changes periodically with rotor rotation), causing air gap magnetic field distortion, resulting in output signal amplitude fluctuation and phase shift.

[0004] (2) Electromagnetic interference: The high-frequency switching action of power devices in the electric drive system generates differential mode and common mode interference, which is coupled to the resolver signal through cable conduction or spatial radiation, resulting in a decrease in signal-to-noise ratio;

[0005] (3) Vibration condition: Rotor torsional vibration causes periodic perturbations to superimpose on the actual position angle, further aggravating signal error.

[0006] Existing technologies have some limitations:

[0007] (1) Single-condition modeling methods (such as considering only eccentricity or electromagnetic interference) cannot reflect the coupling effect of multiple factors, and the model accuracy is insufficient;

[0008] (2) Although numerical simulation methods can simulate complex working conditions, they have low computational efficiency and are difficult to apply to real-time control systems.

[0009] (3) Structural optimization schemes (such as stator balance hole design) can only passively reduce interference and cannot achieve accurate prediction and compensation of signal error from the mechanism level.

[0010] Therefore, there is an urgent need for a signal analysis modeling method for rotary transformers that can integrate the coupling effects of multiple operating conditions, has high accuracy, and is highly practical.

[0011] To address this, we propose a method and system for analytical modeling of rotary transformer signals that integrates multi-condition coupling. Summary of the Invention

[0012] The purpose of this invention is to provide a method and system for analytical modeling of rotary transformer signals that integrates multi-condition coupling, thereby solving the problems mentioned in the background art.

[0013] To achieve the above objectives, the present invention provides the following technical solution: a method for analytical modeling of rotary transformer signals that integrates multi-condition coupling, comprising the following steps:

[0014] S1. Construct an integrated equivalent circuit for the electric drive system and the rotary transformer. This equivalent circuit includes a power device switching model, a permanent magnet synchronous motor armature winding model, and a coupling model of the rotary transformer's excitation winding and output winding. Define the winding resistance. , self-awareness Mutual induction and ratio Parameters;

[0015] S2. Establish a mathematical model for the eccentric operation of the rotary transformer. Based on the air gap magnetic flux density distribution equation, derive the static eccentricity (eccentricity amount). (constant value) and dynamic eccentricity (eccentricity) With rotor rotation angle Air gap length distribution function under periodic variation ;

[0016] S3. Analyze the electromagnetic interference coupling mechanism of the electric drive system, identify the coupling paths of differential-mode interference conducted through cables and common-mode interference transmitted through electromagnetic radiation, and establish the interference voltage amplitude. With frequency Mathematical description;

[0017] S4. Based on the winding function method, combined with the eccentric model of S2 and the interference model of S3, the induced electromotive force of the sinusoidal output winding of the rotary transformer under coupled conditions is obtained. Cosine output winding induced electromotive force The parsing expression;

[0018] S5. Introduce vibration correction coefficient The influence of rotor torsional vibration on signal phase was compensated, and a complete analytical model of the rotary transformer signal was finally formed. The accuracy of the model was verified through experiments.

[0019] Preferably, in S1, the voltage equation expression for the excitation winding of the rotary transformer is:

[0020] ;

[0021] The voltage equations of the output winding coupling model are divided into sinusoidal output winding voltage equations and cosine output winding voltage equations.

[0022] The expression for the sinusoidal output winding voltage equation is as follows:

[0023] ;

[0024] The expression for the cosine output winding voltage equation is as follows:

[0025] ;

[0026] in: , These are the terminal voltage and current of the excitation winding, respectively;

[0027] , These are the terminal voltage and current of the sinusoidal output winding, respectively;

[0028] , These are the terminal voltage and current of the cosine output winding, respectively;

[0029] , , These are the DC resistances of each winding;

[0030] , , These are the self-inductances of each winding;

[0031] This refers to the mutual inductance between the excitation winding and the sinusoidal output winding.

[0032] This refers to the mutual inductance between the excitation winding and the cosine output winding.

[0033] It represents the first derivative of the current with respect to time, reflecting the induced electromotive force component of the winding.

[0034] Preferably, in S2, the air gap length distribution function The expression is:

[0035] ;

[0036] in: This represents the average air gap length without eccentricity, in meters.

[0037] Eccentricity, which is the distance between the geometric center of the stator and the geometric center of the rotor, is expressed in meters (m).

[0038] The rotor angle, measured in rad, is defined as the angle between the rotor axis and the reference axis.

[0039] The eccentric phase angle (in rad) is defined as the angle between the line connecting the centers of the stator and rotor and the reference axis.

[0040] Eccentricity under dynamic eccentricity conditions It changes periodically over time, and the expression is:

[0041] ;

[0042] in: This is the static eccentricity component, in meters (m).

[0043] This represents the dynamic eccentricity amplitude, in meters (m).

[0044] This represents the rotor angular velocity, in rad / s.

[0045] The time unit is seconds (s).

[0046] Preferably, in step S3, the mathematical expression for the electromagnetic interference signal is:

[0047] ;

[0048] in: The value represents the amplitude of the interference voltage, expressed in volts (V).

[0049] The interference frequency is expressed in Hz.

[0050] The initial phase angle of the interference signal is expressed in rad.

[0051] Preferably, in S4, the analytical expression for the induced electromotive force is divided into an expression for the induced electromotive force of the sinusoidal output winding and an expression for the induced electromotive force of the cosine output winding.

[0052] The expression for the induced electromotive force of the sinusoidal output winding is:

[0053] ;

[0054] The expression for the induced electromotive force of the cosine output winding is:

[0055] ;

[0056] in: This refers to the turns ratio of a rotary transformer, specifically the ratio of the number of turns in the output winding to the number of turns in the excitation winding.

[0057] This represents the excitation voltage amplitude, in volts (V).

[0058] The excitation voltage angular frequency, , This is the excitation frequency, measured in rad / s.

[0059] Time, in seconds;

[0060] The rotor angle is expressed in rad.

[0061] The eccentricity influence coefficient is dimensionless and related to the rate of change of air gap permeability.

[0062] This refers to the eccentricity, expressed in meters (m).

[0063] This is the eccentric phase angle, measured in rad.

[0064] is the interference coupling coefficient, which is dimensionless and reflects the coupling strength of electromagnetic interference to the resolver winding. It is related to the distance from the interference source and the coupling area of ​​the winding.

[0065] This refers to the amplitude of electromagnetic interference voltage, measured in volts (V).

[0066] The interference frequency is expressed in Hz.

[0067] The initial phase angle of the interference signal is expressed in rad.

[0068] Preferably, in step S5, the vibration correction coefficient The expression is:

[0069] ;

[0070] in: The amplitude of the vibration effect is dimensionless and reflects the maximum modulation amplitude of the signal by the vibration, with a value range of 0-0.1.

[0071] The frequency of vibration. , The vibration frequency is expressed in rad / s.

[0072] t represents time, measured in seconds (s).

[0073] The initial phase angle of the vibration, in rad;

[0074] The vibration-corrected resolver output voltage is:

[0075] ;

[0076] ;

[0077] in: , These are the induced electromotive forces of the sine and cosine output windings before correction, respectively, in V;

[0078] , These are the sine and cosine output voltages after vibration correction, respectively, in volts (V).

[0079] Preferably, in step S5, data is collected through an experimental platform, and the eccentricity influence coefficient is calibrated using the least squares method. Interference coupling coefficient and vibration amplitude parameter.

[0080] A rotary transformer signal processing system, comprising:

[0081] Signal acquisition module: configured to acquire the excitation voltage signal, sine output winding voltage signal, cosine output winding voltage signal, rotor speed signal and vibration acceleration signal of the rotary transformer;

[0082] Parameter identification module: configured to identify the eccentricity influence coefficient based on the acquired signal using a Kalman filter algorithm. Interference coupling coefficient and vibration amplitude Model parameters;

[0083] Model calculation module: configured to call the analytical model described in claims 1-7, input the collected raw signals and identified parameters, and calculate the theoretical output voltage under multi-condition coupling;

[0084] Error compensation module: configured to compare the actual acquired output voltage with the theoretical voltage calculated by the model, generate error compensation amount, correct the original output voltage, and output a high-precision position signal;

[0085] Storage and communication module: configured to store model parameters, collected data and compensation results, and to perform real-time data interaction with external controllers.

[0086] This invention provides a method for analytical modeling of rotary transformer signals that integrates multi-condition coupling. This method for analytical modeling of rotary transformer signals that integrates multi-condition coupling has the following advantages:

[0087] (1) Multi-condition coupled modeling: For the first time, the coupled effects of eccentricity, electromagnetic interference and vibration are integrated, covering the main error sources of resolver signals, and the model has a wider range of applications;

[0088] (2) Analytical expression: The signal characteristics under complex working conditions are described by analytical expression, which has high computational efficiency and can be directly integrated into the real-time control system;

[0089] (3) Scalability: It can be adapted to different models of resolvers through parameter calibration, making it highly practical;

[0090] (4) Clear mechanism: It reveals the influence of each working condition on the signal, providing theoretical support for the optimization of the resolver structure and the suppression of interference. Attached Figure Description

[0091] Figure 1 Flowchart of analytical modeling method for multi-condition coupled signals;

[0092] Figure 2 Flowchart for implementing analytical modeling of resolver signals under complex operating conditions. Detailed Implementation

[0093] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described with reference to the accompanying drawings.

[0094] like Figure 1-2 As shown, the present invention has the following specific embodiments.

[0095] This embodiment takes the rotary transformer of a certain electric vehicle drive system as the research object. Its rated parameters and operating parameters are as follows:

[0096] 1. Basic parameter configuration

[0097] (1) Core parameters of the rotary transformer:

[0098] Excitation voltage amplitude =12V, excitation frequency =10kHz, excitation angular frequency rad / s; turns ratio =0.5, the ratio of the number of turns in the output winding to the number of turns in the excitation winding;

[0099] Winding resistance: =10Ω, = =8Ω;

[0100] Winding self-inductance: =5 mH, = =3 mH;

[0101] Mutual intuition: = =2 mH.

[0102] (2) Parameters for eccentric working condition:

[0103] Uneccentric average air gap length =0.2 mm;

[0104] Static eccentricity component =0.03 mm, dynamic eccentricity amplitude =0.01 mm;

[0105] Eccentric phase angle ;

[0106] Rotor angular velocity =314 rad / s, corresponding to a rotational speed of 5000 rpm, therefore the dynamic eccentricity is:

[0107]

[0108] Air gap length distribution function:

[0109]

[0110] (3) Electromagnetic interference parameters:

[0111] Interference voltage amplitude =0.5V, interference frequency =20kHz, interference angular frequency = =1.256×10⁵ rad / s;

[0112] Interference phase angle ;

[0113] Interference Coupling Coefficient =0.1.

[0114] (4) Vibration parameters:

[0115] Vibration Amplitude =0.02, vibration angular frequency =628 rad / s, corresponding to 100Hz vibration;

[0116] Vibration phase angle ;

[0117] Vibration correction factor:

[0118]

[0119] (5) Simulation time parameters:

[0120] Simulation duration =0.02 s, time step .

[0121] 2. Calculation process of multi-condition coupled signals

[0122] Based on the analytical model of this invention, the calculation steps for the resolver output signal are as follows:

[0123] (1) Calculation of rotor position angle:

[0124] The rotor position angle changes linearly with time (uniform rotation):

[0125]

[0126] (2) Calculation of the fundamental terms of induced electromotive force:

[0127] Under ideal operating conditions, the fundamental term of the induced electromotive force of the sine / cosine winding is:

[0128]

[0129]

[0130] Substituting the parameters, we get:

[0131]

[0132]

[0133] (3) Superposition of eccentricity effect terms:

[0134] Eccentricity influence coefficient =0.8, then the eccentricity correction term is:

[0135]

[0136]

[0137] Substituting the parameters, we get:

[0138]

[0139]

[0140] (4) Superposition of electromagnetic interference terms:

[0141] The interference items are:

[0142]

[0143]

[0144] Substituting the parameters, we get:

[0145]

[0146]

[0147] (5) Multi-condition coupled induced electromotive force:

[0148] By superimposing the basic term, the eccentric term, and the interference term, we obtain the induced electromotive force before correction:

[0149]

[0150]

[0151] (6) Vibration correction:

[0152] Introducing vibration correction factor The final output voltage is obtained as follows:

[0153]

[0154]

[0155] 3. Simulation Results and Experimental Verification

[0156] Based on the above formula, numerical calculations are performed using Matlab software. The core code logic is as follows:

[0157] (1) Parameter initialization: Define all the above electrical parameters, operating parameters and time vector;

[0158] (2) Iterative calculation: For each time step Calculate in sequence , , And substitute into the analytical expression to solve. , and the corrected voltage;

[0159] (3) Results visualization: plot the time-domain waveform of the signal and compare local details.

[0160] This embodiment demonstrates that the analytical modeling method of the present invention can accurately describe the characteristics of resolver signals under eccentricity, electromagnetic interference, and vibration coupling, providing an accurate theoretical model for signal error compensation under complex working conditions.

[0161] The above description is merely an illustrative embodiment of the present invention and is not intended to limit the scope of the invention. Any equivalent changes and modifications made by those skilled in the art without departing from the concept and principles of the present invention should fall within the scope of protection of the present invention. Furthermore, it should be noted that the components of the present invention are not limited to the overall application described above. Each technical feature described in the specification can be used individually or in combination as needed. Therefore, the present invention naturally covers other combinations and specific applications related to this case.

Claims

1. A method for analytical modeling of rotary transformer signals that integrates multi-condition coupling, characterized in that, Includes the following steps: S1. Construct an integrated equivalent circuit for the electric drive system and the rotary transformer. This equivalent circuit includes a power device switching model, a permanent magnet synchronous motor armature winding model, and a coupling model of the rotary transformer's excitation winding and output winding. Define the winding resistance. , self-awareness Mutual induction and ratio Parameters; S2. Establish a mathematical model for the eccentric operation of the rotary transformer. Based on the air gap magnetic flux density distribution equation, derive the static eccentricity (eccentricity amount). (constant value) and dynamic eccentricity (eccentricity) With rotor rotation angle Air gap length distribution function under periodic variation ; S3. Analyze the electromagnetic interference coupling mechanism of the electric drive system, identify the coupling paths of differential-mode interference conducted through cables and common-mode interference transmitted through electromagnetic radiation, and establish the interference voltage amplitude. With frequency Mathematical description; S4. Based on the winding function method, combined with the eccentric model of S2 and the interference model of S3, the induced electromotive force of the sinusoidal output winding of the rotary transformer under coupled conditions is obtained. Cosine output winding induced electromotive force The parsing expression; S5. Introduce vibration correction coefficient The influence of rotor torsional vibration on signal phase was compensated, and a complete analytical model of the rotary transformer signal was finally formed. The accuracy of the model was verified through experiments.

2. The method for analytical modeling of rotary transformer signals integrating multi-condition coupling as described in claim 1, characterized in that: In S1, the voltage equation expression for the excitation winding of the rotary transformer is: ； The voltage equations of the output winding coupling model are divided into sinusoidal output winding voltage equations and cosine output winding voltage equations. The expression for the sinusoidal output winding voltage equation is as follows: ； The expression for the cosine output winding voltage equation is as follows: ； in: , These are the terminal voltage and current of the excitation winding, respectively; , These are the terminal voltage and current of the sinusoidal output winding, respectively; , These are the terminal voltage and current of the cosine output winding, respectively; , , These are the DC resistances of each winding; , , These are the self-inductances of each winding; This refers to the mutual inductance between the excitation winding and the sinusoidal output winding. This refers to the mutual inductance between the excitation winding and the cosine output winding. It represents the first derivative of the current with respect to time, reflecting the induced electromotive force component of the winding.

3. The method for analytical modeling of rotary transformer signals integrating multi-condition coupling as described in claim 1, characterized in that: In S2, the air gap length distribution function The expression is: ； in: This represents the average air gap length without eccentricity, in meters. Eccentricity, which is the distance between the geometric center of the stator and the geometric center of the rotor, is expressed in meters (m). The rotor angle, measured in rad, is defined as the angle between the rotor axis and the reference axis. The eccentric phase angle (in rad) is defined as the angle between the line connecting the centers of the stator and rotor and the reference axis. Eccentricity under dynamic eccentricity conditions It changes periodically over time, and the expression is: ； in: This is the static eccentricity component, in meters (m). This represents the dynamic eccentricity amplitude, in meters (m). ω represents the rotor angular velocity, in rad / s. The time unit is seconds (s).

4. The method for analytical modeling of rotary transformer signals integrating multi-condition coupling as described in claim 1, characterized in that: In S3, the mathematical expression for the electromagnetic interference signal is: ； in: The value represents the amplitude of the interference voltage, in volts (V). The interference frequency is expressed in Hz. The initial phase angle of the interference signal is expressed in rad.

5. The method for analytical modeling of rotary transformer signals integrating multi-condition coupling according to claim 1, characterized in that: In S4, the analytical expression of induced electromotive force is divided into the induced electromotive force expression of sinusoidal output winding and the induced electromotive force expression of cosine output winding. The expression for the induced electromotive force of the sinusoidal output winding is: ； The expression for the induced electromotive force of the cosine output winding is: ； in: This refers to the turns ratio of a rotary transformer, specifically the ratio of the number of turns in the output winding to the number of turns in the excitation winding. This represents the excitation voltage amplitude, in volts (V). The excitation voltage angular frequency, , This is the excitation frequency, measured in rad / s. Time, in seconds; The rotor angle is expressed in rad. The eccentricity influence coefficient is dimensionless and related to the rate of change of air gap permeability. This refers to the eccentricity, expressed in meters (m). This is the eccentric phase angle, measured in rad. is the interference coupling coefficient, which is dimensionless and reflects the coupling strength of electromagnetic interference to the resolver winding. It is related to the distance from the interference source and the coupling area of ​​the winding. This refers to the amplitude of electromagnetic interference voltage, measured in volts (V). The interference frequency is expressed in Hz. The initial phase angle of the interference signal is expressed in rad.

6. The method for analytical modeling of rotary transformer signals integrating multi-condition coupling according to claim 1, characterized in that: In S5, the vibration correction coefficient The expression is: ； in: The amplitude of the vibration effect is dimensionless and reflects the maximum modulation amplitude of the signal by the vibration, with a value range of 0-0.

1. The frequency of vibration. , The vibration frequency is expressed in rad / s. t represents time, measured in seconds (s). The initial phase angle of the vibration, in rad; The vibration-corrected resolver output voltage is: ； ； in: , These are the induced electromotive forces of the sine and cosine output windings before correction, respectively, in V; , These are the sine and cosine output voltages after vibration correction, respectively, in volts (V).

7. The method for analytical modeling of rotary transformer signals integrating multi-condition coupling according to claim 1, characterized in that: In step S5, data is collected through an experimental platform, and the eccentricity influence coefficient is calibrated using the least squares method. Interference coupling coefficient and vibration amplitude parameter.

8. A signal processing system for a rotary transformer, characterized in that, The resolver signal analytical model is constructed using the resolver signal analytical modeling method integrating multi-condition coupling as described in any one of claims 1-7, wherein the system comprises: Signal acquisition module: configured to acquire the excitation voltage signal, sine output winding voltage signal, cosine output winding voltage signal, rotor speed signal and vibration acceleration signal of the rotary transformer; Parameter identification module: configured to identify the eccentricity influence coefficient based on the acquired signal using a Kalman filter algorithm. Interference coupling coefficient and vibration amplitude Model parameters; Model calculation module: configured to call the analytical model described in claims 1-7, input the collected raw signals and identified parameters, and calculate the theoretical output voltage under multi-condition coupling; Error compensation module: configured to compare the actual acquired output voltage with the theoretical voltage calculated by the model, generate error compensation amount, correct the original output voltage, and output a high-precision position signal; Storage and communication module: configured to store model parameters, collected data and compensation results, and to perform real-time data interaction with external controllers.

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