阅读说明：本技术 一种pmsm无速度传感器转子检测方法 (PMSM speed sensorless rotor detection method ) 是由 杜昭平 吴伟 李伟 王伟然 杨晓飞 伍雪冬 于 2019-11-08 设计创作，主要内容包括：本发明涉及一种PMSM无速度传感器转子检测方法,针对扩展卡尔曼算法在永磁同步电机转子估计上的局限性,在电机的转子估计上使用一种基于Sage-Husa滤波算法,和平方根无迹卡尔曼滤波算法相结合,得到改进无迹卡尔曼算法。改进无迹卡尔曼算法能够在线估计过程噪声或者测量噪声的协方差矩阵,避免了传统卡尔曼滤波器由于仅假设估计过程中存在高斯白噪声而导致的滤波估计性能降低,甚至可能导致滤波发散等问题,利用无迹变换可以使得估算值的精度达到二阶精度,这使得获得的转子位置和电机转速的精度提高,平方根算法也可以使得状态协方差的半正定性得到保证,这也使得滤波的稳定性得到保证。(The invention relates to a PMSM rotor detection method without a speed sensor, aiming at the limitation of an extended Kalman algorithm on the estimation of a permanent magnet synchronous motor rotor, a Sage-Husa based filtering algorithm is used on the estimation of the motor rotor, and the improved unscented Kalman algorithm is obtained by combining a square root unscented Kalman filtering algorithm. The improved unscented Kalman algorithm can estimate the covariance matrix of process noise or measurement noise on line, and avoids the problems that the traditional Kalman filter has reduced filtering estimation performance and even possibly causes filtering divergence due to the fact that Gaussian white noise exists in the estimation process, the accuracy of the estimated value can reach second-order accuracy by using unscented transformation, so that the accuracy of the obtained rotor position and the motor rotating speed is improved, the semipositive property of state covariance can be ensured by using the square root algorithm, and the stability of filtering is also ensured.)

1. A PMSM no-speed sensor rotor detection method comprises the following steps:

step 1: obtaining d-q axis component i of stator current and voltage of permanent magnet synchronous motor_d、i_qAnd u_d、u_q；

Step 2: constructing a mathematical model of the motor system, i_α、i_βRotational speed of rotor omega_rAnd rotor electrical angle theta_eAs a motor system state variable x; will u_α、u_βAs a motor system control variable u; will i_α、i_βAs the motor system output variable y;

and step 3: selecting the weight of an unscented Kalman Sigma sampling point, initializing a state equation according to a Sage-Husa self-adaptive algorithm and an unscented Kalman algorithm, and calculating a measurement noise covariance matrix R at the initial moment₀And cholesky decomposition factor S of covariance₀；

And 4, step 4: according to the decomposition factor S₀Obtaining a construction matrix of the unscented Kalman Sigma sampling points, carrying out nonlinear transformation on the construction matrix of the unscented Kalman Sigma sampling points, and obtaining the square root of the state and the variance, and the estimated state value chi at the next moment_i,k/k-1Estimated state value weighted sum

And 5: cholesky decomposition factor S based on covariance₀Reconstructing a matrix of unscented Kalman Sigma sampling points, and then carrying out nonlinear transformation on the constructed matrix of the unscented Kalman Sigma sampling points to obtain an output value vector estimated at the next moment

Step 6: for the measurement noise covariance matrix R₀Carrying out re-estimation;

and 7: according to the state value χ_i,k/k-1Weighted sum of state valuesVector of output values

2. The PMSM rotor detection method of claim 1, wherein the formula for selecting the weights of unscented kalman Sigma sampling points in step 3 is as follows:

wherein: omega^m、ω^cIs weight value, λ is proportional parameter, λ is (α)²-1) -n, α being the degree of deviation from the state value, 10^-4≤α≤1；L＝2n+1。

3. The PMSM speed sensorless rotor detection method of claim 2, wherein the β in the formula is 2.

4. The PMSM speed sensorless rotor detection method of claim 1, wherein the covariance matrix R of measurement noise in step 6₀The formula for re-estimation is as follows:

wherein: d (k) (1-b)/(1-bk + 1); b is a forgetting factor, and b is more than 0 and less than 1;

Technical Field

The invention relates to the technical field of permanent magnet synchronous motor control, in particular to a PMSM speed sensorless rotor detection method.

Background

The permanent magnet synchronous motor has the advantages of high torque ratio, high efficiency and high power density, so far, the permanent magnet synchronous motor is widely used in a high-performance speed regulating system and has the excellent characteristics of high efficiency, reliable operation, good speed regulating performance and the like as a common alternating current motor because of the advantages of the permanent magnet synchronous motor, and meanwhile, the permanent magnet synchronous motor also has the advantages of long service life, light weight, simple structure and the like of a brushless motor. Generally speaking, the permanent magnet synchronous motor system is convenient to develop towards the direction of small size, light weight, high performance, high efficiency and energy conservation.

In order to ensure the stability of the permanent magnet synchronous motor to be controlled in operation performance, the detection of actual data of the rotor position and the rotating speed of the motor by a permanent magnet synchronous motor mounting position sensor is an indispensable step in closed-loop control. In the current development of permanent magnet synchronous motors, a sensor is generally arranged on one side of the motor to detect information required to be detected, such as hardware circuit devices such as a rotary transformer and a photoelectric encoder. This is a method in which the position and rotational speed of the rotor are detected in real time by sensors and then the data is transmitted to a control loop. From the above, the existence of modern sensors is very helpful for controlling the motor, but the existence of sensors also necessarily increases the complexity of the mechanical structure and the manufacturing cost of the motor, which necessarily reduces the reliability and robustness advantages of the system, and simultaneously limits the use of the permanent magnet synchronous motor in some special environments due to external objective factors such as some environment humidity, too high or too low temperature, motor vibration, dust and the like.

In recent years, domestic and foreign scholars put forward speed-sensorless control to motors one after another, and have a high-frequency injection method and a low-frequency injection method in a zero low-speed region and a model reference adaptive method, a sliding-mode observer method, an extended Kalman algorithm, an intelligent algorithm and the like in a middle high-speed region.

Although the extended Kalman filter algorithm can realize the estimation of the speed and the position of the motor rotor, the method is complex in calculation and omits the second order and the above items, so that the calculation precision is reduced.

Disclosure of Invention

The invention provides a PMSM speed sensorless rotor detection method, which aims to solve the technical problem of low calculation accuracy in the prior art.

The invention provides a PMSM speed sensorless rotor detection method, which comprises the following steps:

step 1: obtaining d-q axis component i of stator current and voltage of permanent magnet synchronous motor_d、i_qAnd u_d、u_q；

Step 2: constructing a mathematical model of the motor system, i_α、i_βRotational speed of rotor omega_rAnd rotor electrical angle theta_eAs a motor system state variable x; will u_α、u_βAs a motor system control variable u; will i_α、i_βAs the motor system output variable y;

and step 3: selecting the weight of an unscented Kalman Sigma sampling point, initializing a state equation according to a Sage-Husa self-adaptive algorithm and an unscented Kalman algorithm, and calculating a measurement noise covariance matrix R at the initial moment₀And cholesky decomposition factor S of covariance₀；

And 4, step 4: according to the decomposition factor S₀Obtaining a construction matrix of the unscented Kalman Sigma sampling points, carrying out nonlinear transformation on the construction matrix of the unscented Kalman Sigma sampling points, and obtaining the square root of the state and the variance, and the estimated state value chi at the next moment_i,k/k-1Estimated state value weighted sumAnd cholesky decomposition factor S of the estimated state variable covariance_k/k-1；

And 5: cholesky decomposition factor S based on covariance₀Reconstructing a matrix for unscented Kalman Sigma sampling points and then reconstructing the unscented Kalman Sigma sampling pointsCarrying out nonlinear transformation on a constructed matrix of trace Kalman Sigma sampling points to obtain an output value vector estimated at the next moment

Then the weight is given to

The weighted sum of the products yields a vector of output values at the next time instant

Finally, subtracting the vector of the output value at the next moment from the output variable y of the motor system at the next moment

Obtaining a measurement residual value e_k；

Step 6: for the measurement noise covariance matrix R₀Carrying out re-estimation;

and 7: according to the state value χ_i,k/k-1Weighted sum of state values

Vector of output values

Estimated vector of output values

And measuring the noise covariance matrix R₀Calculating a filter gain K_kThen through said filter gain K_kAnd measuring the residual value e_kCalculating an estimated corrected state value

Sum state variance S_kAnd finishing the rotation speed acquisition and returning to the step 5.

Further, the formula for selecting the weight of the unscented kalman Sigma sampling point in step 3 is as follows:

wherein: omega^m、ω^cIs weight value, λ is proportional parameter, λ is (α)²-1) -n, α being the degree of deviation from the state value, 10^-4≤α≤1；L＝2n+1。

Further, the β is 2.

Further, the covariance matrix R of the measured noise in step 6₀The formula for re-estimation is as follows:

wherein: d (k) (1-b)/(1-bk + 1); b is a forgetting factor, and b is more than 0 and less than 1;

b ═ diag (a), where B is the column vector consisting of the elements on the a diagonal.

The invention has the beneficial effects that:

1. the estimation accuracy of the system reaches the second order by utilizing the unscented transformation, so that the accuracy of the obtained rotor position and the obtained rotating speed is improved.

2. The unscented Kalman is improved without estimating process noise or measuring a noise variance matrix in advance, and the method is more suitable for practical application.

3. The semi-positivity of the state covariance can be ensured by utilizing a square root algorithm, so that the stability of filtering can be ensured, and the speed and the position of the rotor of the motor can be estimated more accurately.

Drawings

The features and advantages of the present invention will be more clearly understood by reference to the accompanying drawings, which are illustrative and not to be construed as limiting the invention in any way, and in which:

FIG. 1 is a flow chart of an improved unscented Kalman algorithm.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

The embodiment of the invention provides a PMSM rotor detection method without a speed sensor, which comprises the following steps:

step 1: obtaining d-q axis component i of stator current and voltage of permanent magnet synchronous motor_d、i_qAnd u_d、u_q；

Step 2: constructing a mathematical model of the motor system, i_α、i_βRotational speed of rotor omega_rAnd rotor electrical angle theta_eAs a motor system state variable x; will u_α、u_βAs a motor system control variable u; will i_α、i_βAs the motor system output variable y; the method specifically comprises the following steps:

step 21: establishment of static coordinate-based and surface-mounted three-phase permanent magnet synchronous motor (L)_d＝L_q＝L_s) The mathematical model of (2):

wherein: l is_SIs a stator inductance; r_SIs a stator resistor; omega_eIs the electrical angular velocity; i.e. i_α、i_βCurrent components of the stator current on α and β axes respectively;

a stator flux linkage; theta_eIs the rotor position.

Step 22: selecting stator current i_α、i_βRotational speed of rotor ω_rAnd rotor electrical angle theta_eSelecting a voltage u as a state variable x of the electric machine system_α、u_βStator current i as motor system control variable u_α、i_βAs the motor system output variable y. Therefore, the state equation and the measurement equation of the permanent magnet synchronous motor in the two-phase static coordinate system can be obtained, and the equations are as follows:

suppose that the sampling period T is_sWhen the speed is small, the change of the rotating speed is negligible, and the following relation can be obtained:

further, the coefficients of the state space expression can be calculated as follows:

x＝[i_αi_βω_rθ_e]^T,u＝[u_αu_β]^T,y＝[i_αi_β]^T,

wherein: l is_SIs a stator inductance; r_SIs a stator resistor; omega_eIs the electrical angular velocity; i.e. i_α、i_βCurrent components of the stator current on α and β axes respectively;

a stator flux linkage; theta_eIs the rotor position.

And step 3: selecting the weight of an unscented Kalman Sigma sampling point, initializing a state equation according to a Sage-Husa self-adaptive algorithm and an unscented Kalman algorithm, and calculating a measurement noise covariance matrix R at the initial moment₀And cholesky decomposition factor S of covariance₀(ii) a The method comprises the following specific steps:

step 31, selecting the weight of the unscented kalman Sigma sampling point:

wherein: omega^m、ω^cAre all weighted and used to calculate the mean and covariance, respectively, λ is a scaling parameter, typically λ ═ (α)²-1) -n, determining the distribution of points around the Sigma sampling points, and α indicating the degree of deviation from the state value, generally set to 10^-4α is not less than 1, L is 2n +1, and contains prior information of unscented Kalman Sigma sampling point distribution, when the unscented Kalman Sigma sampling point is Gaussian distribution, β optimal value is 2, and the fourth order error term is minimum.

Step 32, initializing the state:

wherein:

is in an initial state; s₀Cholesky decomposition factor as covariance;

is the initial measured noise covariance matrix.

And 4, step 4: according to a decomposition factor S₀Obtaining a construction matrix of the unscented Kalman Sigma sampling points, carrying out nonlinear transformation on the construction matrix of the unscented Kalman Sigma sampling points, and obtaining the square root of the state and the variance, and the estimated state value chi at the next moment_i,k/k-1Estimated state value weighted sum

And cholesky decomposition factor S of the estimated state variable covariance_k/k-1(ii) a The method comprises the following specific steps:

step 41: according to a decomposition factor S₀Calculating an unscented Kalman Sigma point construction matrix:

wherein: the subscript k-1 is the value at time k-1, and k is the value at time k.

Step 42: prediction of the nonlinear state equation and calculation of the square root of the state covariance matrix:

wherein: chi shape_i,k/k-1Represents the estimated state value at time k, estimated from the ith Sigma point estimated from the state estimate at time k-1,

representing the sum of weighted values of the state estimates, Q is the process noise matrix of the system,cholesky factor, which is the covariance of the state variable, is an upper triangular matrix because

May be less than 0, soPositive and negative of

To decide, using a formula

To overcome the semi-positive nature of the matrix.

And 5: according to a decomposition factor S₀Obtaining a construction matrix of the unscented Kalman Sigma sampling points, carrying out nonlinear transformation on the construction matrix of the unscented Kalman Sigma sampling points, and obtaining an output value vector at the next moment

The weight is summed with

Vector of estimated output values at next time subtracted from weighted values of products

Obtaining a measurement residual value e_k(ii) a The method comprises the following specific steps:

step 51: unscented kalman Sigma sampling point reconstruction matrix:

step 52: carrying out nonlinear transformation on the unscented Kalman Sigma sampling point, and then carrying out calculation of a measurement residual error:

wherein: h2]Representing a non-linear transformation;

the vector of the output value estimated at the moment k is shown, and the value of the vector is calculated by each Sigma point of the state quantity;

the method comprises the following steps of (1) representing an estimated value output at the moment k, wherein the value is obtained by calculating an ith unscented Kalman Sigma point;

the expression is the sum of the weights, which is calculated by the weights of all the estimated values, and the value is used as the output estimated value of the new moment.

Step 6: for the measurement noise covariance matrix R₀Carrying out re-estimation; the specific formula is as follows:

wherein: d (k) (1-b)/(1-bk + 1); b is a forgetting factor, usually 0 < b < 1;

b ═ diag (a), where B is the column vector consisting of the elements on the a diagonal;

and

is to estimate

And ensures its stability.

And 7: according to the state value χ_i,k/k-1Weighted sum of state values

Vector of output values

Estimated vector of output values

And measuring the noise covariance matrix R₀Calculating a filter gain K_kAnd then filtering the wave gain K_kAnd measuring the residual value e_kCalculating an estimated corrected state value

Sum state variance S_kAnd 5, finishing the rotation speed acquisition and returning to the step 5; the method comprises the following specific steps:

step 71: calculating a filter gain:

wherein: p_xy,kIs composed of

Andcross covariance; s_yFor the square root factor predictor of the autocovariance matrix, consider

Possibly negative values so usedTo ensure a semi-positive determination of the matrix;

step 72, estimating the corrected state value:

and 73, updating the state variance:

wherein: u represents a weighted sum of the state variances for updating the state variances.

Wherein QR { A } in the above formula represents a QR decomposition of matrix A; s is the cholesky factor for P, denoted as S ═ chol { P }, and is generally referred to as P

The cholesky factor of (c) is called cholesky first-order update, and is simplified to choledate { S, u, ± r }, where u is a matrix, and columns recur in order and undergo cholesky first-order update.

The invention updates the state information when the system obtains the return value, thereby obtaining new rotor information, and the measured covariance matrix system automatically updates without setting an estimated value in advance by using a trial and error method, thereby reducing the workload and being more suitable for practical application.

Although the embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art may make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations fall within the scope defined by the appended claims.