Motor non-inductive control method based on improved cubature Kalman filter

Abstract

The application relates to the technical field of motor control, in particular to a motor non-inductive control method based on improved cubature Kalman filtering. The method comprises the following steps: acquiring motor data, constructing a motor non-inductive control state space model based on the motor data, obtaining a state vector and a measurement vector according to the motor non-inductive control state space model; initializing filtering parameters; performing state estimation through improved cubature Kalman filtering based on the filtering parameters, the state vector and the measurement vector; and performing non-inductive control on the motor according to the optimization result of state estimation. In this way, the tracking sensitivity of the motor can be improved, the strong tracking triggering opportunity can be accurately judged, and the method has the advantages of strong robustness.

Description

Technical Field

[0001] This invention generally relates to the field of motor control technology, and more specifically, to a sensorless motor control method based on improved capacitive Kalman filtering. Background Technology

[0002] Sensorless motor control, which eliminates the need for position sensors (such as encoders or Hall sensors), offers significant advantages such as low cost, high reliability, compact structure, and adaptability to harsh environments, and has become one of the mainstream development directions in the field of motor control.

[0003] Capacitive Kalman Filtering (CKF), as an efficient nonlinear state estimation algorithm, can effectively solve the problem of speed and rotor position estimation in sensorless motor control by approximating Gaussian distribution through volume sampling. It is currently a widely used core technology.

[0004] However, the traditional CKF has the following prominent technical pain points in the practical application of sensorless motor control: (1) Tracking lag problem: When the motor speed rises rapidly during the start-up phase, or when the load changes suddenly or the parameters change over time, the system state will change drastically. The traditional CKF uses a fixed gain or a simple fading factor, which cannot dynamically adjust the filter sensitivity according to the state change, resulting in tracking lag for the state change, increasing the deviation between speed and position estimation, and affecting the control accuracy. (2) Inaccurate strong tracking judgment: The existing strong tracking triggering mechanism mostly relies on a single threshold judgment, which is easily affected by factors such as observation noise and electromagnetic interference, resulting in false triggering or missed triggering. False triggering will increase filter redundancy and reduce steady-state accuracy; missed triggering will not be able to respond to the state change in time, causing estimation deviation. (3) Insufficient robustness: During the operation of the motor, parameters such as stator resistance and inductance will drift with temperature and load changes. The traditional CKF has weak adaptability to parameter changes, and the filter accuracy is easily affected. In severe cases, it may lead to control instability. Summary of the Invention

[0005] This invention provides a sensorless motor control method based on an improved capacitive Kalman filter. This method can improve the tracking sensitivity of the motor, thereby accurately determining the timing of strong tracking triggering, and also has the advantage of strong robustness.

[0006] The method includes:

[0007] Acquire motor data, construct a sensorless control state space model of the motor based on the motor data, and obtain state vectors and measurement vectors according to the sensorless control state space model of the motor.

[0008] Initialize the filter parameters; based on the filter parameters, state vector, and measurement vector, perform state estimation using an improved capacitive Kalman filter;

[0009] Sensorless control of the motor is performed based on the optimization results of the state estimation.

[0010] Furthermore, the state-space model includes:

[0011]

[0012] in, This is the current state vector; This is the state transition function; This is the state vector from the previous time step; The control input vector from the previous time step; This is the noise vector from the previous time step; For measurement vectors; For measurement functions; This is the observed noise vector.

[0013] Furthermore, the state estimation based on the filter parameters, state vector, and measurement vector, using an improved capacitive Kalman filter, includes:

[0014] Time updates are performed based on the filter parameters, state vector, and measurement vector.

[0015] The measurement is updated based on the time-updated results to obtain the predicted value of the measurement vector and the square root of the target error feature.

[0016] The predicted value of the measurement vector is detected by chi-square detection, and the measurement vector that passes the detection is used as the target measurement vector.

[0017] State estimation is performed based on the target measurement vector and the square root of the target error feature.

[0018] Further, the time update based on the filter parameters, state vector, and measurement vector includes:

[0019] The initial error covariance matrix is ​​decomposed by Cholesky. Based on the Cholesky decomposition results and the state vector, the volume points are calculated. The volume points are then input into the state transition function to obtain the propagation volume points. The propagation volume points are weighted and averaged to obtain the predicted state vector values. The state prediction residual volume point matrix is ​​constructed based on the propagation volume points and the predicted state vector values.

[0020] The fading factor is calculated based on UT transform and Mahalanobis distance;

[0021] The process noise characteristic square root is obtained based on the initial process noise covariance matrix; then, the error characteristic square root is predicted and estimated based on the state prediction residual volume point matrix, the process noise characteristic square root, and the fading factor, and the predicted error characteristic square root is obtained, and the predicted error characteristic square root is used as the result of time update.

[0022] Among them, the initial error covariance matrix and the initial process noise covariance matrix are filtering parameters.

[0023] Furthermore, the calculation of the fading factor based on UT transform and Mahalanobis distance includes:

[0024] The measurement vector residual is calculated based on the measurement vector, and the residual sequence covariance matrix is ​​constructed based on the measurement vector residual. Then, the residual sequence covariance matrix and the observation noise vector are subjected to UT transformation to obtain the first correction and the second correction. Among them, the process noise vector and the observation noise vector belong to the motor data.

[0025] The fading factor is initialized based on the first and second correction values; then the Mahalanobis distance between the state vector and the predicted state vector is calculated, and the initialized fading factor is updated using the Mahalanobis distance to obtain the fading factor.

[0026] Furthermore, after constructing the residual sequence covariance matrix based on the measurement vector residuals, the method further includes:

[0027] A first constraint condition for the strong tracking filter is preset, and the state vector is constrained based on the first constraint condition for the strong tracking filter to obtain the minimum value of the state prediction covariance.

[0028] A second constraint condition for the strong tracking filter is preset, and the measurement vector is constrained based on the second constraint condition for the strong tracking filter to obtain a residual orthogonal sequence;

[0029] The residual sequence covariance matrix is ​​adjusted based on the minimum state prediction covariance and the orthogonal residual sequence, thereby achieving strong tracking and indirect control of the fading factor.

[0030] Further, the step of updating the measurement of the time-updated results to obtain the predicted value of the measurement vector and the square root of the target error feature includes:

[0031] The volume points are updated based on the predicted values ​​of the state vector and the square root of the prediction error characteristics to obtain the measurement propagation volume points;

[0032] Measurement prediction is performed based on the measurement propagation volume point to obtain the predicted value of the measurement vector.

[0033] Construct a measurement prediction residual volume point matrix based on the measurement vector prediction value and the measurement propagation volume point;

[0034] The measurement noise feature square root is obtained based on the initial measurement noise covariance matrix; then, the error feature square root is estimated based on the measurement prediction residual volume point matrix, the measurement noise feature square root, and the fading factor to obtain the target error feature square root; the measurement vector prediction value and the target error feature square root are used as the measurement update result; where the initial measurement noise covariance matrix is ​​a filtering parameter.

[0035] Furthermore, the chi-square detection includes:

[0036] Calculate the observation residuals of the measurement vector and the predicted values ​​of the measurement vector; then obtain the chi-square statistic based on the observation residuals.

[0037] If the chi-square statistic is less than the warning threshold, then maintain the normal filtering.

[0038] If the chi-square statistic is not less than the warning threshold and is less than the trigger threshold, then the warning mode is activated;

[0039] If the chi-square statistic is not less than the trigger threshold, then the strong tracking mode is activated.

[0040] Further, the state estimation based on the target measurement vector and the square root of the target error feature includes:

[0041] The cross-covariance is estimated based on the state prediction residual volume point matrix and the measurement prediction residual volume point matrix to obtain the cross-covariance matrix;

[0042] The gain is estimated based on the cross-covariance matrix and the square root of the target error characteristics to obtain the Kalman filter gain.

[0043] The state vector prediction value is updated based on the Kalman filter gain, the state vector prediction value, and the target measurement vector.

[0044] The target error square root is updated based on the characteristic square root of the Kalman filter gain, the state prediction residual volume point matrix, the measurement prediction residual volume point matrix, and the prediction noise covariance matrix.

[0045] The updated state vector prediction and the updated target error feature square root are used as the results of state estimation.

[0046] Furthermore, after performing state estimation by improving the capacitive Kalman filter, the algorithm is further optimized by using the Sage-Husa estimator.

[0047] The Sage-Husa estimator includes:

[0048] Adaptive compensation is used to update the process noise covariance matrix;

[0049] The updated state vector prediction value is compensated by adaptive filtering of the nonlinear system;

[0050] A pre-defined inflation factor is used to compensate for the updated target error feature square root based on the inflation factor.

[0051] Compared with the prior art, the present invention has the following beneficial technical effects:

[0052] (1) In response to the tracking lag problem caused by the fixed gain or simple fading factor of the traditional CKF (Cubature Kalman Filter), this invention innovatively adopts the adaptive fading factor of Mahalanobis distance to dynamically adapt to the drastic state change scenarios such as motor start-up and load change.

[0053] (2) Existing strong tracking uses strong tracking regardless of whether it is applicable, thereby increasing the complexity of the algorithm; while the present invention uses threshold judgment for dynamic processing, and in order to address the defects of single threshold judgment being prone to false triggering and missed triggering, it innovatively uses a dual-constraint strong tracking control combined with a chi-square detection hierarchical triggering mechanism to achieve accurate determination of the timing of strong tracking.

[0054] (3) To address the problem of weak adaptability of traditional CKF to parameter drift and noise interference, this invention relies on the adaptive compensation of the Sage-Husa estimator to significantly enhance the robustness of the algorithm, comprehensively surpassing traditional solutions and significantly improving the accuracy and stability of sensorless motor control. It should be understood that the content described in the Summary of the Invention is not intended to limit the key or important features of the embodiments of this invention, nor is it intended to limit the scope of this invention. Other features of this invention will become readily apparent from the following description. Attached Figure Description

[0055] The above and other features, advantages, and aspects of the various embodiments of the present invention will become more apparent from the accompanying drawings and the following detailed description. In the drawings, the same or similar reference numerals denote the same or similar elements, wherein:

[0056] Figure 1 A flowchart of a sensorless motor control method based on an improved capacitive Kalman filter according to an embodiment of the present invention is shown;

[0057] Figure 2 A flowchart of an improved capacitive Kalman filter according to an embodiment of the present invention is shown;

[0058] Figure 3 A flowchart of time updates according to an embodiment of the present invention is shown;

[0059] Figure 4 A flowchart illustrating the calculation of the fading factor according to an embodiment of the present invention is shown;

[0060] Figure 5 A flowchart illustrating the strong tracking filter constraint according to an embodiment of the present invention is shown;

[0061] Figure 6 A flowchart of measurement updates according to an embodiment of the present invention is shown;

[0062] Figure 7 A flowchart of state estimation according to an embodiment of the present invention is shown;

[0063] Figure 8 A flowchart illustrating the optimization of the state estimation algorithm according to an embodiment of the present invention is shown. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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.

[0065] Furthermore, the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0066] In this invention, state estimation is performed using an improved Kalman filter, and then sensorless control of the motor is achieved based on the state estimation results. This approach enables dynamic tracking of state changes, precise triggering of strong tracking, and improved robustness.

[0067] Figure 1 A flowchart of a sensorless motor control method based on an improved voluminous Kalman filter according to an embodiment of the present invention is shown.

[0068] The method includes:

[0069] S101. Obtain motor data, construct a sensorless control state space model of the motor based on the motor data, and obtain the state vector and measurement vector according to the sensorless control state space model of the motor.

[0070] In this embodiment, the state-space model is a nonlinear discrete-time system state-space model, used to clarify the state mapping relationship between the motor and the filtering algorithm. Specifically, the model includes:

[0071]

[0072] in, Let this be the current state vector. , This refers to the rotor speed; For rotor angle; for Shaft stator current; for Shaft stator current; The state transition function describes the evolution of the motor state over time. The state transition function is derived based on the mathematical model of the dq axis of the permanent magnet synchronous motor. This is the state vector from the previous time step; The control input vector from the previous time step; This is the noise vector from the previous time step; For measurement vectors, ; for shaft current; for shaft current; This is a measurement function used to map the motor state vector to the measurement vector; This is the observed noise vector.

[0073] The state vector and measurement vector are obtained through the state space model described above, thereby clarifying the nonlinear mapping relationship between the motor state and the measurement, accurately characterizing core parameters such as rotor speed, angle and current, providing a reliable data foundation for subsequent filtering state estimation, and improving the initial adaptability of sensorless control.

[0074] S102, Initialize filter parameters; such as Figure 2 As shown, based on the filter parameters, state vector, and measurement vector, state estimation is performed through improved capacitive Kalman filtering, including steps S201-S204:

[0075] S201, such as Figure 3 As shown, time updates are performed based on the filter parameters, state vector, and measurement vector, including S301~S303:

[0076] S301. Perform Cholesky decomposition on the initial error covariance matrix. Calculate the volume points based on the Cholesky decomposition results and the state vector. Input the volume points into the state transition function to obtain the propagation volume points. Perform a weighted average on the propagation volume points to obtain the predicted state vector values. Construct a state prediction residual volume point matrix based on the propagation volume points and the predicted state vector values. The initial error covariance matrix is ​​a filtering parameter.

[0077] In this embodiment, the initial error covariance matrix is ​​decomposed using Cholesky method, including:

[0078]

[0079] in, The initial value is the eigenvalue square root of the initial error covariance matrix; It is a decomposition function; The initial error covariance matrix; This is the transpose symbol.

[0080] As some optional implementation methods of this embodiment, it is assumed that the initial error covariance matrix is... After decomposing it using the above formula .

[0081] In this embodiment, the volume point is calculated based on the Cholesky decomposition results and the state vector, and then the volume point is input into the state transition function to obtain the propagation volume point, including:

[0082]

[0083]

[0084]

[0085] in, for k At time -1, the first One volume point; for k The characteristic square root of the error at time -1; For the first Unit volume points; for k The state vector at time -1; For the first The propagated volume point is obtained by propagating the volume points through the state transition function; This is the control input vector at time k-1; This refers to the number of volume points; This is the index of the volume point.

[0086] As some optional implementations of this embodiment, it is assumed that the Cholesky decomposition results State vector The volume point obtained through the above formula is: The propagation volume point obtained after transferring the volume point using a turntable is: .

[0087] In this embodiment, a weighted average is performed on the propagation volume points to obtain the predicted state vector value, including:

[0088]

[0089] in, for k Time based k Predicted state vector value at time -1; This refers to the number of volume points; The index of the volume point; For the first The propagation volume point is obtained by propagating the volume points through the state transition function.

[0090] As some optional implementation methods in this embodiment, it is assumed that the broadcast volume point is The predicted state vector value obtained after weighted averaging is .

[0091] In this embodiment, constructing a state prediction residual volume point matrix based on the propagation volume points and the predicted state vector values ​​includes:

[0092]

[0093] in, for k Time based k The state prediction residual volumetric point matrix constructed from information at time -1; This refers to the number of volume points; For the first propagation volume point ( k Time based k (Results of volumetric point propagation of information at time -1) This is the second propagation volume point; For the first m One propagation volume point.

[0094] As some optional implementation methods in this embodiment, it is assumed that the broadcast volume point is The predicted state vector value is Then the state prediction residual volume point matrix is .

[0095] S302, such as Figure 4 As shown, the fading factors are calculated based on UT transform and Mahalanobis distance, including S401~S402:

[0096] S401. Calculate the measurement vector residual based on the measurement vector, and construct the residual sequence covariance matrix according to the measurement vector residual; then perform UT transformation on the residual sequence covariance matrix and the observation noise vector to obtain the first correction and the second correction; wherein, the process noise vector and the observation noise vector belong to the motor data.

[0097] In this embodiment, calculating the measurement vector residual based on the measurement vector includes:

[0098]

[0099] in, for k Time-measured vector residual; for k Time based k Predicted value of the measurement vector obtained from the information at time -1; This is the measurement vector.

[0100] As some optional implementation methods of this embodiment, it is assumed that the measurement vector is The predicted value of the measurement vector is The calculated measurement vector residual is .

[0101] In this embodiment, constructing the residual sequence covariance matrix based on the measurement vector residuals includes:

[0102]

[0103] in, for k Covariance matrix of time-residual sequences; The measurement vector residual at time 1; This is the transpose matrix of the measurement vector residual at time 1; Forgetting factor; for k The covariance matrix of the residual sequence at time -1; This is the index for the discrete time step.

[0104] As some optional implementation methods of this embodiment, it is assumed that the measurement vector residual is The covariance matrix of the constructed residual sequence is then... .

[0105] In this embodiment, as Figure 5 As shown, after constructing the covariance matrix of the residual sequence based on the measurement vector residuals, steps S501~S503 are also included:

[0106] S501. A first constraint condition for the strong tracking filter is preset. Based on the first constraint condition for the strong tracking filter, the state vector is constrained to obtain the minimum state prediction covariance, including:

[0107]

[0108] in, This represents the minimum value of the state prediction covariance. The initial state vector; This is the estimated state vector value at the initial moment.

[0109] S502. A second constraint condition for the preset strong tracking filter is used to constrain the measurement vector based on the second constraint condition of the strong tracking filter to obtain a residual orthogonal sequence, including:

[0110]

[0111] in, The residuals are orthogonal sequences; for k + j The measurement vector residual at time step; for k The transpose matrix of the time-time measurement vector residuals; For the index of the discrete time step; This is the offset of the time step.

[0112] S503. Based on the minimum value of the state prediction covariance and the orthogonal sequence of residuals, adjust the covariance matrix of the residual sequence to achieve strong tracking and indirect control of the fading factor.

[0113] Specifically, the first constraint of the strong tracking filter is used to ensure that the state estimate is optimal in the mean square sense; the second constraint of the strong tracking filter is used to ensure that the residuals at different times are orthogonal to each other. When the system model is accurate and the state is normal, the filter can simultaneously satisfy both the first and second constraints of the strong tracking filter; when the system model is mismatched or the state changes abruptly, the filter may only satisfy one of the first and second constraints of the strong tracking filter. In this case, the strong tracking effect is needed to force the residual sequences to restore orthogonality.

[0114] Based on the strong tracking filter condition, the fading factor is indirectly controlled. Constrained by residual orthogonality and minimizing error covariance, precise adaptive adjustment of the fading factor is achieved, solving the problems of traditional methods relying on empirical thresholds and control lag. When the motor state changes abruptly or the model mismatches, the factor responds quickly by increasing, reducing interference from historical data; in steady state, it converges smoothly, balancing accuracy and stability. Compared to the weak anti-interference of traditional CKF and the susceptibility of EKF (Extended Kalman Filter) to linearization divergence, this control method is more robust, ensuring the reliability and real-time performance of state estimation even under complex operating conditions, and significantly improving tracking accuracy.

[0115] In this embodiment, the UT transformation includes:

[0116]

[0117] in, This is the first correction amount; As a weakening factor; For the observed noise vector; This is the second correction amount; for k Time based k The characteristic square root of the covariance matrix obtained from the information at time -1.

[0118] S402. Initialize the fading factor based on the first correction amount and the second correction amount; then calculate the Mahalanobis distance between the state vector and the predicted state vector value, and update the initialized fading factor through the Mahalanobis distance to obtain the fading factor.

[0119] In this embodiment, initializing the fading factor based on the first correction amount and the second correction amount includes:

[0120]

[0121] in, The fading factor is used for initialization.

[0122] As some optional implementation methods of this embodiment, it is assumed that the first correction amount is The second correction vector is Then the initial fading factor is .

[0123] In this embodiment, calculating the Mahalanobis distance between the state vector and the predicted state vector includes:

[0124]

[0125] in, The Mahalanobis distance; This is the current state vector; For the first The historical state vector at any given time; For the first The inverse of the time error covariance matrix.

[0126] In this embodiment, the initial fading factor is updated using Mahalanobis distance to obtain the fading factor, including:

[0127] 1. Adaptive weights are calculated based on Mahalanobis distance from motor state variables.

[0128]

[0129] in, For adaptive weights; The Mahalanobis distance; Preset a threshold for Mahalanobis distance; This is the scale parameter.

[0130] Specifically, when the Mahalanobis distance is greater than a preset threshold (e.g., 1.2), the adaptive weights... Approaching 1 enhances the effect of the diminishing returns factor; when the Mahalanobis distance is less than the preset threshold, the adaptive weights... Approaching 0 weakens the effect of the fading factor.

[0131] 2. The initial fading factor is updated by combining the "segmented fading + recovery mechanism".

[0132] In this embodiment, the segmented fading and recovery mechanism includes:

[0133] (1) The "segmented gradual elimination" mechanism is as follows:

[0134] 1) During periods of rapid change such as motor startup and sudden load changes, the fading factor remains at a high value of 1.2-1.5;

[0135] 2) During the steady-state operation phase, the decay factor decreases to 1.0-1.1;

[0136] (2) The “recovery mechanism” is: when the rate of change of the state is less than the preset value for 3 consecutive sampling periods, the fading factor is restored to the steady state value; thus, the updated Markovian fading factor is obtained.

[0137] Specifically, the update formula for the fading factor is:

[0138]

[0139] in, For adaptive weights; It is the Markovnikov diminishing factor; This is the initial fading factor.

[0140] This invention precisely addresses the three major pain points of traditional CKF (Continuous Calorie Flow) by using UT (Ultimate Time Transform) transformation and Mahalanobis distance to optimize the calculation of the fading factor: (1) By using UT transformation to process the residual covariance matrix and observation noise, a correction amount is generated to initialize the fading factor, avoiding the experience dependence of traditional methods and conforming to the actual operating conditions of the motor. (2) By combining the Mahalanobis distance update factor, the interference of multivariable dimensions and correlations is eliminated. (3) The combination of the two can also filter out electromagnetic interference and parameter drift, solving the problem of insufficient robustness of traditional methods and ensuring accurate state tracking of the motor under all operating conditions.

[0141] S303. Obtain the square root of the process noise feature based on the initial process noise covariance matrix; then, predict and estimate the square root of the error feature based on the state prediction residual volume point matrix, the square root of the process noise feature, and the fading factor to obtain the square root of the prediction error feature, and use the square root of the prediction error feature as the result of time update. The initial process noise covariance matrix is ​​a filtering parameter.

[0142] In this embodiment, obtaining the square root of the process noise feature based on the initial process noise covariance matrix means inversely deriving the square root of the process noise feature using the construction formula of the initial process noise covariance matrix, where the construction formula of the initial process noise covariance matrix is:

[0143]

[0144] in, for k The initial process noise covariance matrix at time -1; for k The square root of the process noise characteristic at time -1; for k The square root transpose of the process noise characteristics at time -1.

[0145] As some optional implementations of this embodiment, it is assumed that the initial process noise covariance matrix is... The square root of the process noise characteristic is .

[0146] In this embodiment, the predicted error square root is estimated based on the state prediction residual volume point matrix, the process noise characteristic square root, and the fading factor, including:

[0147]

[0148]

[0149] in, It is an orthogonal matrix; It is an upper triangular matrix; for k Time based k The eigenvalue of the prediction error covariance matrix obtained from the information at time -1; For the state dimension.

[0150] As some optional implementations of this embodiment, it is assumed that the square root of the process noise characteristic is The state prediction residual volumetric point matrix is: Then the characteristic square root of the prediction error of the prediction estimate is .

[0151] The improved capacitive Kalman filter achieves state estimation, which has the following advantages over existing technologies: (1) It eliminates the need for linearization of the Jacobian matrix in traditional EKF, avoiding linearization errors and improving the estimation accuracy of nonlinear scenarios. (2) It incorporates the Mahalanobis fading factor to solve the problems of low tracking accuracy and model mismatch in traditional CKF for maneuvering targets. (3) By dynamically adjusting the filtering parameters, it adapts to multi-dimensional state changes such as motor speed and current, and has stronger resistance to noise and parameter drift. Under complex working conditions such as startup and sudden load changes, its estimation stability and response speed far exceed those of existing schemes that rely on fixed models or single adaptive mechanisms.

[0152] S202, such as Figure 6 As shown, the measurement is updated based on the time-updated results to obtain the predicted value of the measurement vector and the square root of the target error feature, including S601~S604:

[0153] S601. Update the volume points based on the predicted state vector values ​​and the square root of the prediction error characteristics to obtain the measurement propagation volume points, including:

[0154]

[0155]

[0156] in, for k Time based k -1 time information time number One volume point; for k Time based k The square root of the error characteristic of the information at time -1; For the first Unit volume points; for k Time based k The state vector of information at time -1; for k Time based k -1 time information time number One measurement propagation volume point; This is the measurement function.

[0157] S602. Based on the measurement propagation volume point, perform measurement prediction to obtain the predicted value of the measurement vector, including:

[0158]

[0159] in, for k Time based k Predicted value of the measurement vector obtained from the information at time -1; This refers to the number of volume points; This is the index of the volume point.

[0160] S603. Construct a measurement prediction residual volume point matrix based on the predicted values ​​of the measurement vector and the measurement propagation volume points, including:

[0161]

[0162] in, for k Time based k The measurement prediction residual volume point matrix is ​​obtained from the information at time -1. This refers to the number of volume points; for k Time based k The first measurement propagation volume point obtained from the information at time -1; for k Time based k The second measurement propagation volume point obtained from the information at time -1; for k Time based k The information obtained at time -1 One measurement propagation volume point.

[0163] S604. Obtain the square root of measurement noise characteristics based on the initial measurement noise covariance matrix; then estimate the square root of error characteristics based on the measurement prediction residual volume point matrix, the square root of measurement noise characteristics, and the fading factor to obtain the target square root of error characteristics; use the predicted value of the measurement vector and the target square root of error characteristics as the result of measurement update; wherein the initial measurement noise covariance matrix is ​​a filtering parameter.

[0164] In this embodiment, obtaining the square root of the measurement noise feature based on the initial measurement noise covariance matrix means inversely deriving the square root of the measurement noise feature using the construction formula of the initial measurement noise covariance matrix. The construction formula of the initial measurement noise covariance matrix is ​​as follows:

[0165]

[0166] in, for k The initial measurement noise covariance matrix at time t; for k The characteristic square root of the measurement noise covariance matrix at time; for k The transpose of the eigenvalues ​​of the measurement noise covariance matrix at time t.

[0167] In this embodiment, the target error characteristic square root is obtained by estimating the error characteristic square root based on the measurement prediction residual volume point matrix, the measurement noise characteristic square root, and the fading factor, including:

[0168]

[0169]

[0170] in, It is an orthogonal matrix; It is an upper triangular matrix; for k Time based k The eigenvalue of the covariance matrix obtained from the information at time -1; The dimension of the measurement vector.

[0171] Specifically, when the system model parameters change abruptly, the observation error (the difference between measurement vectors) will increase, the fading factor and the square root of the target error feature will also increase, while the Kalman gain will decrease, the proportion of the state vector estimate will increase, and the proportion of the observation error will decrease, thereby avoiding divergence caused by parameter changes and enhancing the stability of the algorithm.

[0172] The measurement update in this invention is optimized through multi-dimensional means, and has the following advantages: (1) It integrates the measurement prediction residual matrix and the square root of the noise feature, and dynamically adjusts the filter gain to avoid the linearization error of the traditional EKF and the problem of insufficient utilization of measurement information in the UKF. (2) It combines the fading factor and the measurement dimension adaptation mechanism to suppress the influence of electromagnetic interference, outliers, etc., and can quickly respond to sudden changes in motor state, while maintaining the estimation accuracy in steady state. (3) Compared with the defects of weak anti-interference and lagging update of the traditional CKF, this update method is more robust and significantly improves the state estimation accuracy under complex working conditions, achieving dual optimization of stability and real-time performance.

[0173] S203. The predicted value of the measurement vector is detected by chi-square detection, and the measurement vector that passes the detection is used as the target measurement vector.

[0174] In this embodiment, the chi-square detection includes:

[0175] Calculate the observation residuals of the measurement vector and the predicted values ​​of the measurement vector; then obtain the chi-square statistic based on the observation residuals; if the chi-square statistic is less than the warning threshold, maintain the normal filtering; if the chi-square statistic is not less than the warning threshold and is less than the trigger threshold, start the warning mode; if the chi-square statistic is not less than the trigger threshold, start the strong tracking mode.

[0176] In this embodiment, calculating the observation vector residuals of the measurement vector and the predicted values ​​of the measurement vector includes:

[0177]

[0178] in, for k The residual of the observed vector at each moment; for k Time based k The predicted value of the measurement vector obtained from the information at time -1.

[0179] In this embodiment, the chi-square statistic is obtained based on the observed residuals, including:

[0180]

[0181] in, This is the chi-square statistic.

[0182] As some optional implementation methods of this embodiment, the warning threshold can be 90% and the trigger threshold can be 99%.

[0183] Specifically, after obtaining the chi-square statistic from the observed residuals, the process also includes direction determination. The specific direction determination process is as follows:

[0184] Based on the rate of change of the current state rate of change from the previous time step By comparing the signs, it is determined whether the direction of the state change is consistent. If the direction is consistent for two consecutive sampling periods and the chi-square statistic is not less than the trigger threshold, then strong tracking triggering is confirmed to avoid false triggering.

[0185] Specifically, the rate of change of the current state is:

[0186]

[0187] Specifically, the rate of change at the previous moment was:

[0188]

[0189] in, for k The state vector at any given time; for k The state vector at time -1; for k The state vector at time -2; The fixed sampling period of the system (determined by the hardware acquisition frequency).

[0190] Chi-square detection has the following advantages in detecting the predicted value of measurement vectors: (1) By calculating the observation residual and chi-square statistic, and using 90% and 99% dual thresholds for hierarchical judgment, it can accurately distinguish between occasional anomalies such as electromagnetic interference and sensor noise and real state changes such as sudden changes in motor load. Compared with the traditional single threshold, false triggering is greatly reduced, avoiding the decline in steady-state accuracy. (2) Chi-square detection constructs a three-level response mechanism, dynamically switching between conventional filtering, early warning adjustment, and strong tracking mode according to the size of the statistic, overcoming the drawback of the traditional filtering "all or nothing", and reducing the response delay to within 2 sampling periods under complex motor conditions. (3) Combined with the discrimination of the direction of the rate of change of state, false changes are further filtered. Even if the motor parameters drift due to temperature, the measurement vector can still be stably screened. Compared with the traditional filtering without a detection mechanism, the estimation accuracy is improved, and the robustness and control stability of the algorithm are greatly enhanced.

[0191] S204, such as Figure 7 As shown, state estimation is performed based on the target measurement vector and the square root of the target error feature, including S701~S705:

[0192] S701. Based on the state prediction residual volume point matrix and the measurement prediction residual volume point matrix, perform cross-covariance estimation to obtain the cross-covariance matrix, including:

[0193]

[0194] in, for k Time based k The cross-covariance matrix of information at time -1.

[0195] S702. Based on the cross-covariance matrix and the square root of the target error characteristic, the gain is estimated to obtain the Kalman filter gain, including:

[0196]

[0197] in, This represents the Kalman filter gain.

[0198] As some optional implementation methods of this embodiment, it is assumed that the square root of the target error feature is Then the Kalman filter gain is .

[0199] S703. Update the state vector prediction value based on the Kalman filter gain, the state vector prediction value, and the target measurement vector, including:

[0200]

[0201] in, for k The predicted state vector value at time t; for k Time based k Predicted state vector value at time -1; For measurement vectors; for k Time based k The predicted value of the measurement vector obtained from the information at time -1.

[0202] S704. Update the target error characteristic square root based on the characteristic square root of the Kalman filter gain, the state prediction residual volume point matrix, the measurement prediction residual volume point matrix, and the prediction noise covariance matrix, including:

[0203]

[0204]

[0205] in, for k The eigenvalue of the covariance matrix of the prediction error at time t; For the state dimension.

[0206] S705. The updated state vector prediction and the updated target error characteristic square root are used as the results of state estimation.

[0207] The state estimation method has the following advantages through multi-dimensional fusion optimization: (1) First, the cross-covariance matrix is ​​accurately estimated, and then the Kalman gain is dynamically adjusted by combining the square root of the target error feature, avoiding the defects of linearization error and fixed gain of traditional EKF. (2) The update process simultaneously optimizes the predicted value of the state vector and the square root of the error feature, adapting to the multi-state coupling characteristics of motor speed, current and other factors. The estimation accuracy is higher in steady state and the response is faster in sudden changes. (3) Compared with the traditional CKF, which has weak anti-interference and poor parameter drift adaptation, this method is more robust and can effectively suppress noise and interference under complex working conditions. The state estimation error is reduced, which is far superior to the stability and accuracy of existing technologies.

[0208] This invention uses improved capacitive Kalman filtering for state estimation, which has the following advantages: (1) It integrates UT transform, Mahalanobis distance and strong tracking constraint to optimize the fading factor, solves the tracking lag problem of traditional CKF fixed gain, and improves the response speed when the state changes abruptly. (2) It combines chi-square detection to screen measurement vectors in a graded manner, which reduces the false trigger rate compared with the traditional single threshold method and improves steady-state accuracy.

[0209] In this embodiment, after performing state estimation by improving the capacitive Kalman filter, the state estimation algorithm is further optimized by using the Sage-Husa estimator.

[0210] Specifically, such as Figure 8As shown, the Sage-Husa estimator includes S801~S803:

[0211] S801. The process noise covariance matrix is ​​updated using adaptive compensation, including:

[0212]

[0213] in, for k The initial process noise covariance matrix at time t; The forgetting factor has a value of 0.95. for k The initial process noise covariance matrix at time -1; This represents the Kalman filter gain. for k The residual of the observed vector at each moment; for k The transpose of the observation vector residuals at time t; This is the transpose matrix of the Kalman filter gain; for k The state error covariance matrix at time t; For the state dimension; For weights; for k Time based k Information at time -1 Each state predicts residual volumetric points; This is the estimated value of the state vector.

[0214] As some optional implementations of this embodiment, the initial process noise covariance matrix is: Then, the measurement noise covariance is obtained through state vector compensation. .

[0215] S802. Compensating the updated state vector prediction value through adaptive filtering of the nonlinear system, including:

[0216]

[0217]

[0218] Among them, To correct the gain matrix; The global scaling factor is set to 0.8. It is a diagonal matrix; For the measurement noise covariance matrix R k+1 The square root of the first diagonal element represents the noise standard deviation of the first measurement component; For the measurement noise covariance matrix R k+1 The square root of the second diagonal element represents the noise standard deviation of the second measurement component; For the measurement noise covariance matrix R k+1 The m The square root of the i-th diagonal element represents the... m The noise standard deviation of each measurement component; The state vector after compensation; for k +1 time based on k The predicted state vector value based on the time information; for k The observation vector residual at time +1.

[0219] As some optional implementations of this embodiment, it is assumed that the corrected gain matrix is... Then the compensated state vector is .

[0220] Specifically, the modified gain matrix This is used to measure the magnitude of noise, which directly reflects the reliability of the sensor data; the direction of high noise (i.e., The direction with larger diagonal element values ​​indicates that the measurement data is unreliable and the correction should be conservative (i.e., low gain); conversely, the direction with less noise can be more aggressive (i.e., high gain).

[0221] S803. A preset inflation factor is used to compensate for the updated target prediction error feature square root based on the inflation factor, including:

[0222]

[0223] in, for k +1 time based on k The characteristic square root of the target prediction error covariance matrix obtained from time-series information; It is the expansion factor. ; for k Time based k -1 time information error characteristic square root.

[0224] By dynamically compensating for noise and errors through the Sage-Husa estimator, its ability to resist parameter drift far exceeds that of traditional EKF and UKF. Under complex motor operating conditions, the state estimation error is reduced, achieving synergistic optimization of tracking sensitivity, robustness and accuracy.

[0225] S103. Perform sensorless control of the motor based on the optimization results of the state estimation, including:

[0226] (1) Collect measured data such as stator voltage and current during motor operation, construct a nonlinear discrete state space model based on motor characteristics, extract state vector (including rotor speed, angle and d / q axis current) and measurement vector (including α / β axis current), and prepare initial filtering parameters (initial error covariance matrix, process noise and measurement noise covariance matrix).

[0227] (2) The state vector, measurement vector and initial filtering parameters are input into the improved capacitive Kalman filter module. The module performs internal processing such as time update, measurement update, chi-square detection and state optimization, and outputs accurate state estimation results (optimized estimates of rotor speed, rotor angle and stator current).

[0228] (3) Based on the accurate state estimation results, motor control signals are generated to achieve sensorless control of rotor position and speed without the need for hardware such as encoders, thus ensuring stable operation of the motor.

[0229] According to embodiments of the present invention, the following advantages are available compared to the prior art:

[0230] (1) An improved capacitive Kalman filter architecture integrating multiple mechanisms is constructed, which integrates square root filtering, strong tracking constraints, Sage-Husa adaptive estimator and chi-square detection to form a three-in-one framework of "noise adaptation-anomaly screening-state tracking", breaking through the limitations of traditional single filtering. In addition, square root filtering ensures the non-negative qualitative nature of the covariance matrix, and Sage-Husa estimator dynamically adapts to noise changes, reducing the state estimation error. In this way, the problems of easy divergence and insufficient accuracy of traditional filtering are solved. Strong tracking control reduces the response delay of state change to within 2 sampling periods, and the hierarchical mechanism avoids the drawback of "all or nothing". The maximum error of load change is optimized, thus breaking through the tracking lag bottleneck.

[0231] (2) A hierarchical measurement screening mechanism is designed, which adopts a dual-threshold chi-square detection with 90% early warning and 99% trigger, combined with the discrimination of the direction of the rate of change of state in two consecutive sampling periods, to accurately distinguish between occasional interference and real mutation. In addition, multi-dimensional screening reduces the false trigger rate, can still estimate stably in the face of parameter drift, improves robustness, avoids control instability, and improves anti-interference and robustness.

[0232] (3) A dynamic collaborative parameter control strategy is proposed. The fading factor is indirectly controlled through strong tracking constraints. A Mahalanobis adaptive mechanism is introduced into the fading factor, and the noise covariance matrix is ​​updated in real time with the Sage-Husa estimator to achieve "factor self-adaptation-noise self-compensation".

[0233] (4) This invention does not require additional sensors. It achieves precise and seamless control through algorithm optimization, taking into account stability under all working conditions and computational efficiency, reducing application costs and expanding applicable scenarios.

[0234] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, because according to the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are all optional embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0235] The above is an introduction to the method embodiments. The following describes the solution of the present invention further through an apparatus embodiment that has the same inventive concept as the method in the foregoing embodiments.

[0236] It should be understood that the various forms of processes shown above can be used, with steps reordered, added, or deleted. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this invention can be achieved, and this is not limited herein.

[0237] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A sensorless motor control method based on improved capacitive Kalman filtering, characterized in that, include: Acquire motor data, construct a sensorless control state space model of the motor based on the motor data, and obtain state vectors and measurement vectors according to the sensorless control state space model of the motor. Initialize the filter parameters; based on the filter parameters, state vector, and measurement vector, perform state estimation using an improved capacitive Kalman filter; Sensorless control of the motor is performed based on the optimization results of the state estimation; The state estimation based on the filter parameters, state vector, and measurement vector, using an improved capacitive Kalman filter, includes: updating the time based on the filter parameters, state vector, and measurement vector; updating the measurement vector based on the updated time result to obtain the predicted value of the measurement vector and the square root of the target error feature; detecting the predicted value of the measurement vector using chi-square detection, and using the detected measurement vector as the target measurement vector; and performing state estimation based on the target measurement vector and the square root of the target error feature. The time update based on the filter parameters, state vector, and measurement vector includes: performing Cholesky decomposition on the initial error covariance matrix; calculating volume points based on the Cholesky decomposition results and state vectors; inputting the volume points into the state transition function to obtain propagation volume points; performing a weighted average on the propagation volume points to obtain predicted state vector values; constructing a state prediction residual volume point matrix based on the propagation volume points and predicted state vector values; calculating the fading factor based on UT transform and Mahalanobis distance; obtaining the process noise characteristic square root based on the initial process noise covariance matrix; then predicting and estimating the error characteristic square root based on the state prediction residual volume point matrix, the process noise characteristic square root, and the fading factor to obtain the predicted error characteristic square root, and using the predicted error characteristic square root as the result of the time update; wherein, the initial error covariance matrix and the initial process noise covariance matrix are filter parameters. The calculation of the fading factor based on UT transformation and Mahalanobis distance includes: calculating the measurement vector residual based on the measurement vector; constructing the residual sequence covariance matrix based on the measurement vector residual; performing UT transformation on the residual sequence covariance matrix and the observation noise vector to obtain a first correction and a second correction; wherein the process noise vector and the observation noise vector belong to the motor data; initializing the fading factor based on the first correction and the second correction; calculating the Mahalanobis distance between the state vector and the predicted state vector value, and updating the initialized fading factor using the Mahalanobis distance to obtain the fading factor.

2. The method according to claim 1, characterized in that, The state-space model includes: in, This is the current state vector; This is the state transition function; This is the state vector from the previous time step; The control input vector from the previous time step; This is the noise vector from the previous time step; For measurement vectors; For measurement functions; This is the observed noise vector.

3. The method according to claim 1, characterized in that, After constructing the covariance matrix of the residual sequence based on the measurement vector residuals, the method further includes: A first constraint condition for the strong tracking filter is preset, and the state vector is constrained based on the first constraint condition for the strong tracking filter to obtain the minimum value of the state prediction covariance. A second constraint condition for the strong tracking filter is preset, and the measurement vector is constrained based on the second constraint condition for the strong tracking filter to obtain a residual orthogonal sequence; The residual sequence covariance matrix is ​​adjusted based on the minimum state prediction covariance and the orthogonal residual sequence, thereby achieving strong tracking and indirect control of the fading factor.

4. The method according to claim 1, characterized in that, The step of updating the measurement results after the time update to obtain the predicted value of the measurement vector and the square root of the target error feature includes: The volume points are updated based on the predicted values ​​of the state vector and the square root of the prediction error characteristics to obtain the measurement propagation volume points; Measurement prediction is performed based on the measurement propagation volume point to obtain the predicted value of the measurement vector. Construct a measurement prediction residual volume point matrix based on the measurement vector prediction value and the measurement propagation volume point; The measurement noise feature square root is obtained based on the initial measurement noise covariance matrix; then, the error feature square root is estimated based on the measurement prediction residual volume point matrix, the measurement noise feature square root, and the fading factor to obtain the target error feature square root; the measurement vector prediction value and the target error feature square root are used as the measurement update result; where the initial measurement noise covariance matrix is ​​a filtering parameter.

5. The method according to claim 1, characterized in that, The chi-square test includes: Calculate the observation residuals of the measurement vector and the predicted values ​​of the measurement vector; then obtain the chi-square statistic based on the observation residuals. If the chi-square statistic is less than the warning threshold, then maintain the normal filtering. If the chi-square statistic is not less than the warning threshold and is less than the trigger threshold, then the warning mode is activated; If the chi-square statistic is not less than the trigger threshold, then the strong tracking mode is activated.

6. The method according to claim 4, characterized in that, The state estimation based on the target measurement vector and the square root of the target error feature includes: The cross-covariance is estimated based on the state prediction residual volume point matrix and the measurement prediction residual volume point matrix to obtain the cross-covariance matrix; The gain is estimated based on the cross-covariance matrix and the square root of the target error characteristics to obtain the Kalman filter gain. The state vector prediction value is updated based on the Kalman filter gain, the state vector prediction value, and the target measurement vector. The target error square root is updated based on the characteristic square root of the Kalman filter gain, the state prediction residual volume point matrix, the measurement prediction residual volume point matrix, and the prediction noise covariance matrix. The updated state vector prediction and the updated target error feature square root are used as the results of state estimation.

7. The method according to claim 1, characterized in that, After improving the capacitive Kalman filter for state estimation, the algorithm is further optimized by using the Sage-Husa estimator. The Sage-Husa estimator includes: Adaptive compensation is used to update the process noise covariance matrix; The updated state vector prediction value is compensated by adaptive filtering of the nonlinear system; A pre-defined inflation factor is used to compensate for the updated target error feature square root based on the inflation factor.

Images