A permanent magnet synchronous motor rotor position estimation method based on circle fitting technology

Abstract

The application discloses a permanent magnet synchronous motor rotor position estimation method based on circle fitting technology and relates to the technical field of motor control and position detection.The method comprises the following steps: collecting two-way orthogonal signals of a Hall effect position sensor and mapping the signals to a complex domain; adopting circle fitting to extract geometric center parameters of a signal track; performing decentralization processing by using the parameters and constructing a whitening transformation matrix to suppress negative sequence components and random interference, so that corrected orthogonal signals are obtained; extracting a phase according to the corrected signals, performing kinematics state reconstruction by using local polynomial regression, and realizing high-precision estimation of the rotor position.The method combines circle fitting and whitening transformation joint processing, effectively suppresses direct current offset, amplitude imbalance, orthogonal error and random noise, realizes continuous position and angular velocity estimation without phase lag by combining local polynomial regression, and significantly improves detection precision and robustness.

Description

Technical Field

[0001] This invention relates to the field of motor control and position detection technology, and more specifically to a rotor position estimation method for permanent magnet synchronous motors based on circle fitting technology. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in high-performance electromechanical systems due to their high torque density, compact structure, and excellent dynamic response. The control performance of PMSMs is highly dependent on the accuracy of rotor position measurement; therefore, reliable position sensors are essential. Among available position sensing solutions, Hall effect sensors, consisting of two orthogonally arranged Hall elements and a signal processing circuit, are commonly used in conjunction with magnetic blocks in robotic systems due to their low cost and ease of shaft-end mounting. In this application, Hall effect sensors typically operate in a manner similar to incremental encoders. Specifically, the analog signal generated by the Hall element is converted into a digital pulse output, and the accumulated pulse count is used to calculate the rotor position. However, this pulse integration method inherently suffers from discontinuities and cumulative integration drift, which degrades position accuracy over long operating cycles, limiting its applicability in high-precision robotic motors.

[0003] One potential solution to the above problem is to directly reconstruct continuous rotor angles using the raw sine and cosine outputs of the Hall elements. During rotation, orthogonally distributed Hall sensors generate two sinusoidal signals with a 90° phase shift, which can be defined as sine and cosine components. By applying arctangent calculation to these two ideal signals, continuous electrical angles can, in principle, be obtained for each rotor position.

[0004] While theoretically applicable, this method remains difficult to reliably implement in robotic permanent magnet synchronous motors due to various environmental interferences. First, the magnetic field distribution around the Hall sensor is susceptible to interference from the strong electromagnetic field of the motor stator, the non-uniform magnetization of the rotor, and the nearby ferromagnetic casing. These effects can cause signal drift. Second, temperature variations within the compact robot joint modules can cause thermal drift in the Hall element and signal processing circuitry, resulting in random interference and nonlinear gain distortion in the sinusoidal output. Third, mechanical misalignment during assembly is often unavoidable. These errors periodically modulate the signal amplitude and baseline, producing periodic angular ripple after arctangent calculation.

[0005] Therefore, proposing a high-precision rotor position estimation method for permanent magnet synchronous motors that can effectively suppress DC offset, amplitude imbalance, orthogonal error and random interference is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides a rotor position estimation method for permanent magnet synchronous motors based on circle fitting technology. This method analyzes the distortion of sinusoidal-cosine signals under disturbance based on circle theory and develops a circle fitting algorithm to reconstruct ideal orthogonal signals for continuous position estimation. To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, embodiments of the present invention provide a rotor position estimation method for a permanent magnet synchronous motor based on circle fitting technology, comprising the following steps: S1. Acquire two orthogonal analog signals output by the Hall effect position sensor in the permanent magnet synchronous motor, and map the two orthogonal analog signals to the complex domain to generate complex signals; S2. The trajectory of the complex signal in the complex plane is processed using a circle fitting method to identify and extract the geometric center parameters of the signal trajectory; S3. The complex signal is decentered using the geometric center parameter, and a whitening transformation matrix is ​​constructed based on the decentered complex signal. The decentered complex signal is then input into the whitening transformation matrix to obtain the corrected orthogonal signal. S4. Extract phase information based on the corrected orthogonal signal, and use the local polynomial regression method to reconstruct the kinematic state of the phase information to achieve high-precision estimation of the rotor position of the permanent magnet synchronous motor.

[0008] Furthermore, step S2 specifically includes the following steps: S21: Convert the complex signal into a two-dimensional real coordinate representation and establish a linear affine transformation model in the real domain; S22: Construct an algebraic function corresponding to the circular geometric model, and solve for the effective matrix with the goal of enforcing the unit circle constraint; S23: Solve for the geometric center parameters of the signal trajectory using the least squares method.

[0009] Furthermore, in step S21, the establishment of the linear affine transformation model in the real number domain is expressed as:

[0010]

[0011] in, b represents the true value; μ represents the static translation of the signal trajectory in the complex plane; μ represents the principal scaling and rotation of the signal vector. Indicates the ellipticity; It represents the transformation matrix, acting as a bridge between geometric distortion and complex physical parameters.

[0012] Furthermore, the step S22, which involves forcing a unit circle constraint to solve for the effective matrix, specifically includes:

[0013] The effective matrix T is solved from Q, where matrix Q characterizes the signal's geometric distortion properties, reflecting the elliptical shape of the signal trajectory caused by amplitude imbalance and phase shift errors. The linear correction matrix T is obtained from matrix Q and is used for affine transformation and normalization of the orthogonal signal. After normalization, A signal approximating an ideal unit circle passes through Obtain the rotor position from it.

[0014] Furthermore, the step S23, which involves solving for the geometric center parameters using the least squares method, specifically includes: Solve the quadratic curve parameters using singular value decomposition, and then analyze the center coordinates from the parameters. The parameter vector P is identified as corresponding to the minimum singular value. min The right singular vector:

[0015] Among them, geometric center From It is obtained through parsing and extraction.

[0016] Furthermore, step S3 specifically includes the following steps: S31: Calculate the covariance matrix based on the signal samples after removing the geometric center; S32: Construct the whitening transformation matrix based on the analytical decomposition of the signal covariance matrix; S33: The signal is transformed using the whitening transformation matrix, and abnormal sampling points are removed using the truncation criterion.

[0017] Furthermore, the step S32, which involves constructing a whitening transformation matrix based on the analytical decomposition of the signal covariance matrix, specifically includes:

[0018] Where T is the whitening matrix, which is obtained analytically using the Cholesky decomposition of the covariance matrix; Furthermore, step S4 specifically includes the following steps: S41: Approximate the rotor trajectory within the sliding window using a motion polynomial; S42: Transform the position estimation problem into a weighted least squares optimization problem for polynomial coefficients to obtain the corresponding kinematic parameters; S43: Solve the least squares problem to obtain the optimal position and optimal angular velocity corresponding to the current moment.

[0019] Furthermore, in step S41, the rotor trajectory within the sliding window is approximated using a motion polynomial, and expressed as:

[0020] Where n is the current time index, c i Indicates the first i The order of the local kinematics coefficients, where k represents the order of the polynomial.

[0021] Furthermore, in step S43, the optimal position and optimal angular velocity are expressed as follows:

[0022] in, h 0 and h 1 is the projection kernel, which can simultaneously reconstruct the optimal position. and angular velocity .

[0023] As can be seen from the above technical solutions, compared with the prior art, the high-precision position estimation method based on circle fitting technology disclosed in this invention has the following beneficial effects: This invention uses a circle fitting method to identify and extract the geometric center of the signal trajectory in the complex plane. It can physically separate and compensate for multi-source distortions such as DC offset, amplitude imbalance and phase error in the orthogonal signal of the Hall sensor, avoiding the limitations of traditional correction methods based on empirical thresholds or fixed parameters, and providing reliable basic data for subsequent signal processing.

[0024] This invention constructs a whitening transformation matrix based on the decentralized signal, which can effectively suppress negative order components, high-order harmonics and random noise interference in the signal, significantly improve the roundness and orthogonality of orthogonal signals, and maintain stable signal quality even under complex electromagnetic environment and drastic load fluctuation conditions, thus providing a guarantee for high-precision phase extraction.

[0025] This invention employs a local polynomial regression method to reconstruct the kinematic state of phase information, which can simultaneously estimate the rotor position and angular velocity within a sliding time window. This effectively suppresses the influence of noise on phase estimation, avoids the problems of traditional methods being susceptible to signal distortion and having phase jumps and estimation lag, and achieves continuous high-precision rotor position estimation without phase lag.

[0026] The circle fitting, whitening transformation, and local polynomial regression algorithms of this invention are all low-complexity matrix operations and linear optimization problems with moderate computational load. They can be implemented in real time on embedded control platforms without relying on high-precision rotary transformers or photoelectric encoders, which significantly reduces system costs and improves control performance. They are particularly suitable for high-performance, low-cost permanent magnet synchronous motor drive systems.

[0027] This invention describes and processes different types of errors within the same mathematical framework, avoiding the model complexity and parameter coupling problems caused by designing separate compensation stages for different errors in traditional methods. It significantly improves the robustness of position estimation under harmonic interference and noise environments, avoiding the sensitivity of traditional least squares methods to outliers. The method has a clear overall structure, and the computation process can be implemented online, making it suitable for resource-constrained embedded control systems. It can significantly improve the accuracy of permanent magnet synchronous motor rotor position estimation without adding additional hardware sensors, and has high engineering application value. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0029] Figure 1 This is a schematic diagram illustrating the working principle of the Hall effect sensor under both interference-free and interference-affected conditions.

[0030] Figure 2 A flowchart of a permanent magnet synchronous motor rotor position estimation method based on circle fitting technology provided in an embodiment of the present invention.

[0031] Figure 3 The figure shows the results of the geometric correction performance of the permanent magnet synchronous motor rotor position estimation method based on circle fitting technology under distortion conditions according to an embodiment of the present invention.

[0032] Figure 4 The experimental results are for the rotor position estimation method of permanent magnet synchronous motor based on circle fitting technology according to an embodiment of the present invention. Detailed Implementation

[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] To clearly illustrate the improvement approach of this invention for the problem of Hall sensor signal distortion, we will first combine... Figure 1 A direct comparison is provided between the Hall sensor output signals and rotor position estimation results under ideal and actual operating conditions. For example... Figure 1 As shown, Figure 1 The left side shows the motor rotor magnets rotating with the motor, and the Hall element outputting two orthogonal analog signals; Figure 1 The top right shows the ideal sine / cosine signal and the rotor position calculated by the atan2 function; Figure 1 The lower right corner shows the distorted signal under actual working conditions, affected by noise, DC offset, and amplitude imbalance. It can be seen that signal distortion will cause significant errors in rotor position estimation. Therefore, it can be concluded that the influence of environmental interference cannot be ignored in the position estimation of high-precision control of permanent magnet synchronous motors in high-performance electromechanical systems.

[0035] To address the issues of insufficient rotor position estimation accuracy and poor anti-interference capability caused by Hall signal distortion under actual operating conditions, this invention proposes a targeted solution based on circle fitting technology to achieve high-precision and robust estimation of the rotor position of a permanent magnet synchronous motor. For example... Figure 1 As shown in the figure, this invention discloses a rotor position estimation method for a permanent magnet synchronous motor based on circle fitting technology, including the following steps: S1. Acquire two orthogonal analog signals output by the Hall effect position sensor in the permanent magnet synchronous motor, and map the two orthogonal analog signals to the complex domain to generate complex signals; The orthogonal signals output by the Hall position sensor are collected, and the two orthogonal signals are mapped to the complex domain. The main distortion forms caused by installation deviation, magnetic field distortion, amplitude imbalance, phase error and electromagnetic interference in the orthogonal signals of the Hall sensor are uniformly modeled into a generalized linear complex model that includes positive sequence, negative sequence, DC offset and random disturbance.

[0036] S2. The trajectory of the complex signal in the complex plane is processed using a circle fitting method to identify and extract the geometric center parameters of the signal trajectory; The complex signal is converted into a two-dimensional real coordinate representation. A linear affine transformation model in the real domain is established. An algebraic function corresponding to the circular geometric model is constructed and a unit circle constraint is imposed. The parameters of the quadratic curve are solved by singular value decomposition, and the geometric center coordinates of the signal trajectory are extracted analytically from the parameters.

[0037] S3. The complex signal is decentered using the geometric center parameter, and a whitening transformation matrix is ​​constructed based on the decentered complex signal. The whitening transformation matrix is ​​used to suppress the negative order component and random interference in the signal to obtain the corrected orthogonal signal. The original complex signal is decentered using geometric center parameters to eliminate DC offset. The covariance matrix is ​​calculated based on the decentered signal samples. A whitening transformation matrix is ​​constructed by performing Cholesky decomposition on the covariance matrix. Abnormal sampling points are removed by combining the truncation criterion, and negative order components, higher harmonics and random noise are suppressed to obtain the corrected orthogonal signal.

[0038] S4. Extract phase information based on the corrected orthogonal signal, and use the local polynomial regression method to reconstruct the kinematic state of the phase information to achieve high-precision estimation of the rotor position of the permanent magnet synchronous motor. Rotor position phase information is extracted from the corrected orthogonal signal. The rotor motion trajectory is approximated by a low-order motion polynomial within the sliding time window. The position estimation is transformed into a weighted least squares optimization problem of polynomial coefficients. The optimal rotor position and angular velocity at the current moment are reconstructed using the projection kernel, thus achieving high-precision position estimation without phase lag.

[0039] This invention effectively suppresses DC offset, amplitude imbalance, orthogonality error, and random noise in Hall sensor signals through a combined process of circle fitting and whitening transformation. Combined with local polynomial regression kinematic reconstruction, it achieves continuous rotor position and angular velocity estimation without phase lag. Compared to traditional methods, this invention significantly improves the rotor position detection accuracy and system robustness of permanent magnet synchronous motors under electromagnetic interference and non-ideal installation conditions. Furthermore, it is computationally simple, easily implemented in embedded real-time systems, and has high engineering application value.

[0040] The rotor position estimation method for permanent magnet synchronous motors based on circle fitting technology of the present invention will be described in detail below: Step S1: Acquire two orthogonal analog signals output by the Hall effect position sensor in the permanent magnet synchronous motor, and map the two orthogonal signals to the complex domain, specifically including: Step S11, mathematically, the offset caused by the internal magnetic field generated by the stator current, the non-uniform magnetization of the rotor, and the influence of nearby ferromagnetic structures manifests as a static translation of the position trajectory in the complex plane, which is equivalent to adding a zero-sequence DC vector b0:

[0041] Among them, b s and b c Let u(θ) represent the offsets in the (C, S) plane, where u(θ) is an ideal orthogonal signal and j is the imaginary unit.

[0042] Step 12: Interpret amplitude imbalance, phase error, and quadrature mismatch as negative-sequence components, and superimpose the positive and negative rotation components:

[0043] Among them, G P and G n These represent the magnitudes of the positive and negative sequences, respectively. p and n This represents their respective initial phase angles. Specifically, p This indicates a mechanical alignment offset, and n Controls the spatial orientation of elliptic distortion. Item G n Directly quantize the ellipticity. If G n =0 The trajectory is a perfect circle if G n The trajectory ≠0 must be an ellipse. This complex formula provides a unified theoretical basis for simultaneously correcting gain and phase errors, and provides a theoretical basis for circle fitting.

[0044] Step 13 identifies two unavoidable types of interference: periodic harmonics and random noise, and calculates the total interference. ( It can be achieved by adding random additive noise. ( The Fourier series representation of ) is:

[0045] Among them, A k It is a coefficient. ( The value changes over time, providing justification for subsequent whitening and covariance addition stage statistics.

[0046] Step 14: Model the measured signal as a generalized linear transformation of an ideal vector:

[0047] in, and It is by The complex distortion coefficients are derived from the symmetric component decomposition in ), and to maintain mathematical consistency, these coefficients explicitly include phase shift. This represents the main scaling and rotation of the signal vector; Indicates the ellipticity. Amplitude | |=G n The eccentricity is determined by the phase ∠. = n It determines the direction of the major axis of the ellipse. It rigorously maps physical geometric errors to the complex algebraic field, showing that recovering the ideal circle is mathematically equivalent to identifying and eliminating non-holomorphic conjugate terms. And offset b0.

[0048] Using the above modeling method, the system characterizes the main distortion forms in the orthogonal signals of Hall effect sensors caused by installation deviations, magnetic field distortion, amplitude imbalance, phase errors, and electromagnetic interference, and unifies them into a generalized linear complex model that includes positive sequence, negative sequence, DC offset, and random disturbances. This provides a complete and rigorous theoretical foundation for the subsequent design of geometric compensation, robust statistical whitening, and continuous position estimation algorithms based on circle fitting.

[0049] Step S2 involves converting the complex signal into an equivalent two-dimensional real coordinate representation, constructing an algebraic error function corresponding to the circular geometric model, and establishing a system of linear equations about the coordinates of the geometric center of the trajectory with the goal of minimizing the algebraic error. The geometric center parameters of the signal trajectory are obtained by solving the system of linear equations using least squares, specifically including: The nonanalytic complex distortion problem is transformed into a linearly solvable geometric elliptic problem in the real domain. Through robust least squares and SVD methods, the geometric center and shape of the signal trajectory are accurately identified, providing a reliable geometric foundation for subsequent negative order suppression and whitening processes; including: Step S21: Convert the complex signal into a real number representation: By establishing a mapping relationship between complex domain signals and two-dimensional Euclidean space vectors, the amplitude imbalance and phase shift distortion of the Hall sensor are decoupled into a linear affine transformation model in the real domain. This transforms the nonlinear distortion compensation problem into a geometric optimization problem for the coordinates of the center of the signal trajectory.

[0050] in, Let denote a real value, which is a linear affine mapping over the real number field, and vector b corresponds to . The DC offset in the trajectory is the root cause of the overall translational shift.

[0051] Measurement vector, transformation matrix M∈i 2×2 It bears the weight of amplitude imbalance, orthogonality error, and phase coupling, acting as a bridge between geometric distortion and complex physical parameters:

[0052] Step S22: Construct the algebraic function corresponding to the circular geometric model, and solve for the effective matrix with the objective of enforcing the unit circle constraint, expressed as:

[0053] Since the physical matrix M is not unique, directly from Solving for the effective matrix Forced unit circle constraint:

[0054] The effective matrix T is solved from Q, where matrix Q characterizes the signal's geometric distortion properties, reflecting the elliptical shape of the signal trajectory caused by amplitude imbalance and phase shift error. The linear correction matrix T is obtained from matrix Q and is used for affine transformation and normalization of the orthogonal signal. After normalization, A signal approximating an ideal unit circle passes through Obtain the rotor position from it.

[0055] Step S23: Solve the system of linear equations using the least squares method: Center identification on the algebraic manifold of the signal trajectory is formulated as a constrained least squares minimization problem.

[0056] The general equation of a quadratic curve is expressed as: To ensure numerical stability against measurement noise, the design matrix... Singular Value Decomposition (SVD) is employed. The parameters of the quadratic curve are solved using SVD, and the center coordinates are then analytically extracted from the parameters. The parameter vector P is identified as corresponding to the minimum singular value. min The right singular vector:

[0057] Among them, geometric center From It was obtained through parsing.

[0058] Compared with direct matrix inversion, this singular value decomposition-based method has higher robustness in suppressing random sampling noise from sensors and improving the numerical stability of microprocessor computation, and can effectively filter out macroscopic geometric deviations.

[0059] Step S3 involves decentering the original complex signal using the geometric center parameters to eliminate the main DC offset effect. Subsequently, the covariance matrix is ​​calculated for the decentered signal samples, and a whitening transformation matrix is ​​constructed based on this covariance matrix. This effectively reduces the impact of negative-order components, higher harmonics, and random noise on the position estimation accuracy. Specifically, this includes: Step S31, calculate the covariance matrix using the geometric center parameters: The original complex signal is processed using geometric center parameters to reduce the effects of local noise and non-uniform sampling. To improve accuracy, the statistical properties of ideal orthogonal rotation are utilized.

[0060] All elliptic distortions are essentially manifested in the off-diagonal and non-isoaxial nature of the covariance matrix. The collected Hall signals are decentered to calculate the 2×2 covariance matrix ∑y, in preparation for whitening.

[0061] Using the center calibration sample Sample covariance matrix ∑ The energy distribution with generalized linear distortion was captured:

[0062] Where, ∑ The noise floor is represented. To restore unitary orthogonality (i.e., suppress the negative-order component v) and reject non-Gaussian outliers, a robust set of rectified signals is defined by a truncated whitening transform. rect:

[0063] Among them, y raw It is the original measurement set. It is the cutoff threshold, used to automatically identify and remove non-Gaussian anomalous sampling points caused by transient electromagnetic interference.

[0064] Step S32: Calculate the covariance ∑ for each calculation period. Then, calculate ∑ -1 Based on the Cholesky decomposition of the signal covariance matrix to obtain T, a set of virtual orthogonal signals with unitary orthogonality properties is dynamically reconstructed.

[0065]

[0066] equation It has a dual function. The linear operator T effectively "circularizes" the trajectory, eliminating the complex model. Off-diagonal coupling terms in the truncated operator. ∥2≤ It acts as a Mahalanobis distance gate to filter out extreme random outliers caused by transient electromagnetic interference, thereby ensuring statistical robustness.

[0067] Step S33: Using a preset truncation criterion, outlier sampling points that deviate from the statistical distribution are removed, effectively reducing the impact of random noise, higher harmonics and outliers on the accuracy of position estimation, and ensuring that the input data for subsequent kinematic state reconstruction meets the requirements of statistical robustness.

[0068] Step S4 involves extracting the phase of the corrected orthogonal signal to obtain phase information related to the rotor position, and then reconstructing the kinematic state using a local polynomial regression method. Specifically, this includes: By using a weighted least squares method to perform polynomial fitting on the phase sequence within a sliding time window, the optimal estimates of position and angular velocity can be obtained simultaneously at the current moment. Within a sliding time window of a preset length, a local polynomial regression method is used to fit the phase sequence. By jointly utilizing historical sampling points within the window, while suppressing random noise, a continuous, smooth, and lag-free estimate of the rotor position and angular velocity at the current moment can be achieved.

[0069] Includes the following steps: Step S41: Assuming that the rotor motion can be approximated as a low-order polynomial motion within this short time window, the phase estimate value at each sampling moment within the finite time window is... ( The low-order kinematic polynomials are used to approximate the actual motion trajectory of the motor rotor. ( ) is represented as:

[0070] Where n is the current time index, c i Indicates the first The order of the local kinematics coefficients, where k represents the order of the polynomial.

[0071] Step S42: Using statistical information from all historical data within the window, the rotor motion state is optimally estimated, constructing a time index vector τ and a Vandermonde matrix H. A weight matrix W is selected to give greater weight to data closer to the current moment. The position estimation problem is transformed into a weighted least squares optimization problem for polynomial coefficients, obtaining the optimal coefficient vector of the polynomial. This process utilizes statistical information from all data points within the window to combat random noise. ( This achieves a noise reduction effect similar to filtering;

[0072] Where H represents the Vandermonde design matrix, W represents the weighting matrix, and θ is the phase sequence acquired within the window.

[0073] Step S43: At the current moment, in order to simultaneously output the optimal position and angular velocity estimates without introducing phase lag, the optimal position is reconstructed simultaneously using projection kernels h0 and h1. and angular velocity :

[0074] The constant term coefficient C0 of the polynomial is directly taken as the denoised position at the current moment. This value represents the intercept of the fitted trajectory at the current moment, and theoretically there is no phase lag. The first term coefficient C1 is directly taken as the current instantaneous angular velocity, which avoids the noise amplification problem caused by the traditional difference method. While preserving the dynamic characteristics of the motion, it effectively suppresses random harmonics in the signal.

[0075] When using circle fitting technology to estimate the continuous position of a Hall effect sensor for a permanent magnet synchronous motor with high precision, the following steps are taken: First, the orthogonal signals output by the Hall position sensor are acquired and mapped to the complex domain. The trajectory of the Hall sensor signal in the complex plane is processed based on the circle fitting geometric method. Then, the geometric center parameters of the signal trajectory are identified and extracted to effectively estimate and compensate for DC offset and amplitude imbalance errors. Next, robust statistical whitening is introduced. By constructing a whitening transformation matrix and combining it with the truncation criterion, negative order components, random noise, and abnormal sampling points are suppressed. Finally, the kinematic state of the corrected orthogonal signal is reconstructed using the local polynomial regression method. This effectively avoids phase lag in position estimation while suppressing random noise, thus achieving high-precision estimation of the continuous position and angular velocity of the Hall effect sensor for the permanent magnet synchronous motor.

[0076] The optimized result diagram and the comparison diagram before optimization in this embodiment are shown in the reference diagram. Figure 3 As shown. Figure 3 The left side shows the distribution of the signal trajectory over time: the signal trajectory processed by the traditional method (red dashed line) shows obvious divergence and distortion characteristics, the signal trajectory is loose and covers a large area; while the signal trajectory processed by the method proposed in this invention (blue solid line) converges quickly, the trajectory is compact and regular, and the divergence problem caused by signal distortion is effectively eliminated. Figure 3 The right side shows a local magnified comparison and the results of geometric distortion quantification. It can be seen that the traditional method has a wide signal trajectory coverage, corresponding to high geometric distortion, which seriously affects the accuracy of position estimation. In contrast, the method proposed in this invention can strictly constrain the signal trajectory within a low distortion range, and the geometric distortion is significantly reduced.

[0077] The figure demonstrates the combined advantages of geometric modeling and statistical signal processing techniques. Even under non-ideal conditions such as Hall effect sensor offset, amplitude imbalance, and electromagnetic interference, accurate estimation of the continuous position of the motor rotor can still be achieved, demonstrating significant theoretical research value and engineering application potential. This achieves high-precision, low-delay estimation of the rotor position and angular velocity of a permanent magnet synchronous motor, improving the operational stability, control accuracy, and intelligence level of the motor drive system.

[0078] Figure 4The experimental results of the rotor position estimation method for permanent magnet synchronous motors based on circle fitting technology are shown in the figure. Figure (a) shows the rotor position and error waveform calculated based on the ideal signal under ideal conditions, with the position error close to zero. Figure (b) shows the result after processing the distorted signal using the traditional method. It can be seen that the position error fluctuates significantly due to the influence of signal distortion. Figures (c) and (d) show the processing results of the method proposed in this invention under different operating conditions. The comparison shows that the method of this invention can effectively suppress the influence of signal distortion, the position error (C4 channel) is significantly reduced and fluctuates less, and the estimated rotor position (C3 channel) is closer to the ideal linear output. This verifies the significant advantages of this invention in high-precision rotor position estimation.

[0079] The high-precision position estimation method for motors in this embodiment processes the trajectory of the Hall sensor signal in the complex plane based on the circular fitting geometry method, and then identifies and extracts the geometric center parameters of the signal trajectory to achieve effective estimation and compensation for DC offset and amplitude imbalance errors. Then, robust statistical whitening processing is introduced, and finally, the kinematic state is reconstructed by the local polynomial regression method on the corrected orthogonal signal. While suppressing random noise, it effectively avoids the phase lag phenomenon in position estimation, and realizes high-precision estimation of continuous position and angular velocity of the Hall effect sensor of permanent magnet synchronous motor.

[0080] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0081] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A rotor position estimation method for a permanent magnet synchronous motor based on circle fitting technology, characterized in that, Includes the following steps: S1. Acquire two orthogonal analog signals output by the Hall effect position sensor in the permanent magnet synchronous motor, and map the two orthogonal analog signals to the complex domain to generate complex signals; S2. The trajectory of the complex signal in the complex plane is processed using a circle fitting method to identify and extract the geometric center parameters of the signal trajectory; S3. The complex signal is decentered using the geometric center parameter, and a whitening transformation matrix is ​​constructed based on the decentered complex signal. The decentered complex signal is then input into the whitening transformation matrix to obtain the corrected orthogonal signal. S4. Extract phase information based on the corrected orthogonal signal, and use the local polynomial regression method to reconstruct the kinematic state of the phase information to achieve high-precision estimation of the rotor position of the permanent magnet synchronous motor.

2. The method as described in claim 1, characterized in that, Step S2 specifically includes the following steps: S21: Convert the complex signal into a two-dimensional real coordinate representation and establish a linear affine transformation model in the real domain; S22: Construct an algebraic function corresponding to the circular geometric model, and solve for the effective matrix with the goal of enforcing the unit circle constraint; S23: Solve for the geometric center parameters of the signal trajectory using the least squares method.

3. The method as described in claim 2, characterized in that, In step S21, the establishment of the linear affine transformation model in the real number domain is expressed as: in, b represents the true value; μ represents the static translation of the signal trajectory in the complex plane; μ represents the principal scaling and rotation of the signal vector. Indicates the ellipticity; It represents the transformation matrix, acting as a bridge between geometric distortion and complex physical parameters.

4. The method as described in claim 2, characterized in that, The step S22, which involves forcing the unit circle constraint to solve for the effective matrix, specifically includes: The effective matrix T is solved from Q, where matrix Q characterizes the signal's geometric distortion properties, reflecting the elliptical shape of the signal trajectory caused by amplitude imbalance and phase shift error. The linear correction matrix T is obtained from matrix Q and is used for affine transformation and normalization of the orthogonal signal. After normalization, A signal approximating an ideal unit circle passes through Obtain the rotor position from it.

5. The method as described in claim 2, characterized in that, The step S23, which involves solving for the geometric center parameters using the least squares method, specifically includes: Solve the quadratic curve parameters using singular value decomposition, and then analyze the center coordinates from the parameters. The parameter vector P is identified as corresponding to the minimum singular value. min The right singular vector: Among them, geometric center From It is obtained through parsing and extraction.

6. The method as described in claim 1, characterized in that, Step S3 specifically includes the following steps: S31: Calculate the covariance matrix based on the signal samples after removing the geometric center; S32: Construct the whitening transformation matrix based on the analytical decomposition of the signal covariance matrix; S33: The signal is transformed using the whitening transformation matrix, and abnormal sampling points are removed using the truncation criterion.

7. The method as described in claim 6, characterized in that, Step S32, which involves constructing a whitening transformation matrix based on the analytical decomposition of the signal covariance matrix, specifically includes: Where T is the whitening matrix, which is analytically derived using the Cholesky decomposition of the covariance matrix.

8. The method as described in claim 1, characterized in that, Step S4 specifically includes the following steps: S41: Approximate the rotor trajectory within the sliding window using a motion polynomial; S42: Transform the position estimation problem into a weighted least squares optimization problem for polynomial coefficients to obtain the corresponding kinematic parameters; S43: Solve the least squares problem to obtain the optimal position and optimal angular velocity corresponding to the current moment.

9. The method as described in claim 8, characterized in that, In step S41, the rotor trajectory within the sliding window is approximated using a motion polynomial, and expressed as follows: Where n is the current time index, c i Indicates the first i The order of the local kinematics coefficients, where k represents the order of the polynomial.

10. The method as described in claim 8, characterized in that, In step S43, the optimal position and optimal angular velocity are expressed as follows: in, h 0 and h 1 is the projection kernel, which can simultaneously reconstruct the optimal position. and angular velocity .

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