Long stator linear synchronous motor speed measurement method based on extended Kalman filter

Abstract

The invention relates to a long-stator linear synchronous motor speed measurement method based on an extended Kalman filter, which is applied to a double-end power supply long-stator linear synchronous motor and comprises the following steps: firstly, in a two-phase synchronous rotating coordinate system d-q, calculating the speed of the long-stator linear synchronous motor; constructing a double-end power supply long stator linear synchronous motor model based on the power supply stator current, the angular velocity and the electrical angle at the two ends of the motor; and then, the model is substituted into an extended Kalman filtering algorithm, and speed estimation of the double-end power supply long stator linear synchronous motor is carried out in real time. Compared with the prior art, the real-time performance and accuracy of position and speed estimation of the double-end power supply long stator linear synchronous motor can be improved, speed sensorless control is achieved, operation is easy and convenient, cost is low, and meanwhile the anti-interference capability is high.

Description

Technical Field

[0001] The invention belongs to the technical field of speed measurement without a speed sensor, and in particular relates to a speed measurement method for a long-stator linear synchronous motor based on an extended Kalman filter. Background Art

[0002] In the high-speed maglev system, the traction system and the suspension system both use long-stator linear synchronous motors. The long-stator linear synchronous motors with double-end power supply can provide a larger driving current, reduce the output capacity of a single converter and ensure the reliability of power supply, improve the flexibility of the system, and meet the needs of high-speed operation of maglev trains. The stable operation of maglev trains requires accurate position detection. When the train runs in a low-speed section, the speed and position information can be obtained through the position sensor and sent to the ground control system through the wireless transmission system; however, when the train runs in a high-speed section, the update cycle of the wireless transmission system is too long to meet the real-time requirements of the traction control system. Therefore, a speed sensorless control method must be used at high speeds to observe and calculate the speed and position of the train in real time to achieve precise control of the train.

[0003] Kalman filter is an optimal prediction estimation method in the sense of minimum variance, which can effectively weaken the influence of random interference and measurement noise. Extended Kalman filter is the promotion and application of linear Kalman filter in nonlinear system, which is often used in rail transportation, navigation and other fields. Its estimated speed range is very wide, and when the system is noisy, it can still estimate the speed and position. At present, there are studies on the application of extended Kalman filter in the detection of linear motor speed and angle. For example, the Chinese invention patent with publication number CN111193448B proposes a permanent magnet synchronous motor load torque observation method based on extended Kalman filter, a surface-mounted permanent magnet synchronous motor load torque observation method based on extended Kalman filter, and uses the extended Kalman filter algorithm to realize real-time monitoring of the load torque of the surface-mounted permanent magnet synchronous motor. However, there is no relevant application method of extended Kalman filter in the double-end powered long stator linear synchronous motor. Therefore, it is urgent to design a long stator linear synchronous motor speed measurement method based on extended Kalman filter to further improve the real-time and accuracy of the position and speed estimation of the double-end powered long stator linear synchronous motor. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a long-stator linear synchronous motor speed measurement method based on an extended Kalman filter, so as to further improve the real-time and accuracy of position and speed estimation of a double-ended powered long-stator linear synchronous motor.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] The present invention provides a long-stator linear synchronous motor speed measurement method based on an extended Kalman filter, which is applied to a double-end powered long-stator linear synchronous motor, and comprises the following steps:

[0007] S1. In a two-phase synchronous rotating coordinate system dq, a double-end powered long stator linear synchronous motor model is constructed based on a state vector, an input vector and an output vector, wherein the state vector includes the output current, angular velocity and electrical angle of the power supply at both ends of the long stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq, the input vector includes the voltage of the power supply at both ends of the long stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq, and the output vector includes the output current of the power supply at both ends of the long stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq;

[0008] S2. Substitute the model constructed in step S1 into the extended Kalman filter algorithm to perform speed estimation of the dual-end power supply long stator linear synchronous motor, specifically including a prediction stage and a correction stage. In the prediction stage, the state vector and output vector at the next moment are predicted according to the input vector and the estimated state vector at the previous moment; in the correction stage, the covariance matrix and gain matrix at the next moment are calculated according to the estimated covariance matrix at the previous moment, and the estimated covariance matrix at the next moment is calculated for use in the next correction stage, and the estimated state vector at the next moment is calculated for use in the next prediction stage, and the real-time speed of the dual-end power supply long stator linear synchronous motor is calculated according to the angular velocity and electrical angle in the estimated state vector.

[0009] Furthermore, in step S1, the specific process of constructing the double-end powered long stator linear synchronous motor model is as follows:

[0010] S101, constructing a voltage equation of a double-end powered long-stator linear synchronous motor in a two-phase synchronous rotating coordinate system dq, and then obtaining a current equation of the double-end powered long-stator linear synchronous motor;

[0011] S102, on the premise of constant angular velocity, rewriting the current equation of the double-end powered long-stator linear synchronous motor into a state equation based on a state vector, an input vector and an output vector;

[0012] S103, discretizing the state equation, adding system noise and measurement noise, and obtaining a double-end powered long-stator linear synchronous motor model.

[0013] Furthermore, in step S101, the voltage equation of the double-end powered long-stator linear synchronous motor is specifically expressed as follows:

[0014]

[0015] Among them, u d1 、uq1 and u d2 、u q2 are the voltages of the two-end power supply of the long stator linear synchronous motor at both ends in the two-phase synchronous rotating coordinate system dq, i d1 、i q1 and i d2 、i q2 are the output currents of the power supplies at both ends of the double-ended long stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq, i d 、i q is the stator current of the double-ended power supply long stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq, i d =i d1 +i d2 ,i q =i q1 +

[0016] i q2 , ψ d , q is the magnetic flux of the stator of the double-ended long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq, ψ d =L d i d +ψ f , ψ q =L q i q , ψ f The rotor flux of the double-ended long-stator linear synchronous motor is

[0017] L d is the d-axis inductance, L q is the q-axis inductance, R k1 , L k1 and R k2 , L k2 are the resistance and inductance of the feeder cable from the power supply at both ends of the double-ended long-stator linear synchronous motor to the stator section of the motor, R s is the stator winding resistance of the double-end powered long stator linear synchronous motor, ω is the angular velocity, θ is the electrical angle.

[0018] Furthermore, in step S101, the current equation of the double-end powered long-stator linear synchronous motor is specifically expressed as follows:

[0019]

[0020] Furthermore, in step S102, the expression of the state equation is specifically as follows:

[0021]

[0022] y=Cx

[0023] Where x is the state vector, u is the input vector, y is the output vector,

[0024]

[0025] Furthermore, in step S103, the expression of the double-end powered long stator linear synchronous motor model is specifically as follows:

[0026] x(k+1)=x(k)+Tf(x(k))+TBu(k)+W(k)

[0027] y(k)=Cx(k)+V(k)

[0028] Where W(k) is the system noise, V(k) is the measurement noise, T is the sampling period, and k represents the time.

[0029] Furthermore, in step S2, in the prediction stage, the expressions for predicting the state vector and output vector at the next moment are specifically as follows:

[0030]

[0031] in, is the predicted state vector at time (k+1), is the estimated state vector at time k, u(k) is the input vector at time k, T is the sampling period, is the predicted output vector at time (k+1).

[0032] Furthermore, in the correction stage, the expressions for calculating the covariance matrix and the gain matrix at the next moment are specifically as follows:

[0033]

[0034] in, and K(k+1) are the prediction covariance matrix and gain matrix at time (k+1), respectively. is the estimated covariance matrix at time k, Q is the covariance matrix of the system noise W(k), R is the covariance matrix of the measurement noise V(k), C(k+1) is the Jacobian matrix,

[0035]

[0036] Furthermore, in the correction stage, the expression for calculating the estimated covariance matrix at the next moment is specifically as follows:

[0037]

[0038] Furthermore, in the correction phase, the expression for calculating the estimated state vector at the next moment is specifically as follows:

[0039]

[0040] Among them, y(k+1) is the measurement state vector.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] The present invention proposes a speed sensorless speed measurement method based on an extended Kalman filter for a double-end powered long-stator linear synchronous motor. Firstly, in a two-phase synchronous rotating coordinate system dq, system noise and measurement noise are considered, and a double-end powered long-stator linear synchronous motor model is constructed based on a state vector, an input vector and an output vector, wherein the state vector includes the output current, angular velocity and electrical angle of the power supply at both ends of the long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq, the input vector includes the voltage of the power supply at both ends of the long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq, and the output vector includes the voltage of the power supply at both ends of the long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq. Output current; Then, the equation is substituted into the extended Kalman filter algorithm to estimate the speed of the double-end powered long-stator linear synchronous motor, which specifically includes a prediction stage and a correction stage. In the prediction stage, the state vector and output vector of the next moment are predicted according to the estimated state vector and input vector of the previous moment; in the correction stage, the covariance matrix and gain matrix of the next moment are calculated according to the estimated covariance matrix of the previous moment, and the estimated covariance matrix of the next moment is calculated for the next correction stage, and the estimated state vector of the next moment is calculated for the next prediction stage, and the real-time speed of the double-end powered long-stator linear synchronous motor is calculated according to the angular velocity and electrical angle in the estimated state vector. The above method can not only improve the real-time and accuracy of the position and speed estimation of the long-stator linear synchronous motor under the double-end power supply mode, realize speed sensorless control, but also is easy to operate, low cost, and has strong anti-interference ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 The equivalent circuit diagram of the double-end power supply mode of the long stator linear synchronous motor;

[0044] Figure 2 This is the algorithm flow of the extended Kalman filter speed measurement method. DETAILED DESCRIPTION

[0045] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0046] Example:

[0047] This embodiment takes a long-stator linear motor used in a high-speed maglev transportation system as an example and provides a long-stator linear synchronous motor speed measurement method based on an extended Kalman filter.

[0048] High-speed maglev trains need to use a dual-end power supply when running at high speeds. This is because dual-end power supply can provide a larger drive current to meet the requirements of acceleration and deceleration during high-speed operation. At the same time, it can reduce the output capacity of a single converter and ensure the reliability of power supply, thereby improving the redundancy of the system. The equivalent circuit diagram of a long-stator linear synchronous motor using a dual-end power supply mode is shown in the figure below. Figure 1 As shown. a1 、u b1 、u c1 and i a1 、i b1 、i c1 are the three-phase output voltage and current of the converter on one side, u a2 、u b2 、u c2 and i a2 、i b2 、i c2 are the three-phase output voltage and current of the converter on the other side, i a 、i b 、i c is the three-phase current of the stator winding of the linear motor, ψ a , b , c is the three-phase flux of the stator winding of the linear motor, R k1 , L k1 and R k2 , L k2 are the resistance and inductance of the feeder cables from the converters on both sides to the stator windings of the linear motor, R s is the stator winding resistance of the linear motor.

[0049] The technical solution provided in this embodiment is to realize the speed measurement of the long-stator linear synchronous motor with double-end power supply by adopting an extended Kalman filter. The extended Kalman filter is essentially a random observer. The system noise and measurement noise are considered in the design process, so it is more robust to the motor parameters. The method proposed in this embodiment includes the following steps:

[0050] S1. Construct a double-end powered long stator linear synchronous motor model. The specific process is:

[0051] S101, according to Figure 1 The equivalent circuit diagram of the long stator linear synchronous motor double-end power supply mode is shown, and the following voltage and current equations are obtained:

[0052]

[0053] In the two-phase synchronous rotating coordinate system dq, the voltage equation of the double-end powered long stator linear synchronous motor is constructed:

[0054]

[0055] Among them, u d1 、u q1 and u d2 、u q2 are the voltages of the two-end power supply of the long stator linear synchronous motor at both ends in the two-phase synchronous rotating coordinate system dq, i d1 、i q1 and i d2 、i q2 are the output currents of the power supplies at both ends of the double-ended long stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq, i d 、i q is the stator current of the double-ended long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq, ψ d , q is the magnetic flux of the stator of the double-ended long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq, ψ f The rotor flux of the double-ended long-stator linear synchronous motor, L d is the d-axis inductance, L q is the d-axis inductance, R k1 , L k1 and R k2 , L k2 are the resistance and inductance of the feeder cable from the power supply at both ends of the double-ended long-stator linear synchronous motor to the stator section of the motor, R s is the stator winding resistance of the double-ended long-stator linear synchronous motor, and ω is the angular velocity.

[0056] Combining formulas (4)-(6), the current equation of the double-end powered long stator linear synchronous motor can be obtained:

[0057]

[0058] S102. Considering that the electrical time constant of the long-stator linear synchronous motor is much smaller than the mechanical time constant, when the sampling period is small, it can be considered that the speed remains unchanged, that is, the change in speed is 0, as follows:

[0059]

[0060] The electrical angle of the long stator linear synchronous motor is:

[0061]

[0062] Formulas (7)-(9) can be rewritten to obtain the following state equation:

[0063]

[0064] Formula (10) can be further expressed as:

[0065]

[0066] y=Cx (11)

[0067] Where x is the state vector, u is the input vector, y is the output vector, According to formula (10) (11), we can get:

[0068]

[0069] S103. In order to construct an extended Kalman filter state observer, equation (11) is discretized:

[0070] x(k+1)=x(k)+Tf(x(k))+TBu(k)

[0071] y(k)=Cx(k) (15)

[0072] Where T is the sampling period. Considering the uncertainty and variability of model parameters in actual systems, measurement noise is inevitable in stator voltage and current. The above formula can be further written as:

[0073] x(k+1)=x(k)+Tf(x(k))+TBu(k)+W(k)

[0074] y(k)=Cx(k)+V(k) (16)

[0075] Where W(k) is the system noise and V(k) is the measurement noise.

[0076] S2. Substitute the model constructed in step S1 into the extended Kalman filter algorithm to estimate the speed of the double-ended power supply long stator linear synchronous motor, including the prediction stage and the correction stage. The specific algorithm flow is as follows: Figure 2 As shown, the following steps are included:

[0077] S201, Status Prediction

[0078] The goal of state prediction is to estimate the state from the previous state. To get the next estimate But in obtaining First, we need to calculate the predicted value The predicted value can only be obtained after the feedback correction in the second stage to obtain the final estimated value. The state prediction can be expressed as:

[0079]

[0080] in, is the predicted state vector at time (k+1), is the estimated state vector at time k, u(k) is the input vector at time k, T is the sampling period, is the predicted output vector at time (k+1).

[0081] S202. Calculate the covariance matrix

[0082] The covariance matrix is ​​used to obtain the gain matrix K(k+1) Therefore, before entering the correction phase, the covariance matrix must be calculated

[0083]

[0084] in, is the prediction covariance matrix at time (k+1), Q is the covariance matrix of the system noise W(k), is the estimated covariance matrix at time k, G(k+1) is the Jacobian matrix, specifically:

[0085]

[0086] From the above formula, we can see that the covariance matrix is the covariance matrix of the previous Plus the newly obtained forecast status information It is determined together with the system noise covariance matrix Q. The system noise Q includes not only the measurement noise introduced by the stator voltage sensor and the quantization error caused by the A / D conversion, but also parameter uncertainty and system disturbances.

[0087] S203, calculate the gain matrix K(k+1)

[0088]

[0089] The gain matrix K(k+1) is mainly used to correct the state vector estimation. R is the covariance matrix of the measurement noise V(k). The measurement noise mainly includes the measurement error of the current sensor and the quantization error caused by the A / D chip.

[0090] S204, state vector estimation

[0091]

[0092] in, represents the (k+1)th state vector estimate, y(j+1) is the measured state vector, is the predicted output vector, the above formula completes arrive According to the estimated angular velocity in the state vector and electrical angle The real-time speed of a double-ended long-stator linear synchronous motor can be calculated.

[0093] S205. Calculate the estimated covariance matrix

[0094]

[0095] in, is the estimated covariance matrix, which reflects the error size of the current estimated state. From step S202 to step S204, it can be seen that The covariance matrix is ​​used in the state estimation of Therefore, in this estimation, the To be called for the next state estimation.

[0096] The above method realizes state estimation by adopting the extended Kalman filter, which not only ensures the estimation accuracy of position and velocity, but also has the advantages of low cost, strong robustness and strong anti-interference ability.

[0097] If the above method is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program codes.

[0098] The above description of the embodiments is to facilitate the understanding and use of the invention by those skilled in the art. It is obvious that those skilled in the art can easily make various modifications to these embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above embodiments, and improvements and modifications made by those skilled in the art based on the disclosure of the present invention without departing from the scope of the present invention should be within the scope of protection of the present invention.

Claims

1. A method for measuring speed of a long-stator linear synchronous motor based on an extended Kalman filter, characterized in that: Applied to double-end powered long stator linear synchronous motor, including the following steps: S1. In a two-phase synchronous rotating coordinate system dq, a double-end powered long stator linear synchronous motor model is constructed based on a state vector, an input vector and an output vector, wherein the state vector includes the output current, angular velocity and electrical angle of the power supply at both ends of the long stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq, the input vector includes the voltage of the power supply at both ends of the long stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq, and the output vector includes the output current of the power supply at both ends of the long stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq; S2. Substitute the model constructed in step S1 into the extended Kalman filter algorithm to perform speed estimation of the dual-end power supply long stator linear synchronous motor, specifically including a prediction stage and a correction stage. In the prediction stage, the state vector and output vector at the next moment are predicted according to the input vector and the estimated state vector at the previous moment; in the correction stage, the covariance matrix and gain matrix at the next moment are calculated according to the estimated covariance matrix at the previous moment, and the estimated covariance matrix at the next moment is calculated for use in the next correction stage, and the estimated state vector at the next moment is calculated for use in the next prediction stage, and the real-time speed of the dual-end power supply long stator linear synchronous motor is calculated according to the angular velocity and electrical angle in the estimated state vector.

2. The method for measuring speed of a long-stator linear synchronous motor based on an extended Kalman filter according to claim 1, characterized in that: In step S1, the specific process of constructing the double-end powered long stator linear synchronous motor model is as follows: S101, constructing a voltage equation of a double-end powered long-stator linear synchronous motor in a two-phase synchronous rotating coordinate system dq, and then obtaining a current equation of the double-end powered long-stator linear synchronous motor; S102, on the premise of constant angular velocity, rewriting the current equation of the double-end powered long-stator linear synchronous motor into a state equation based on a state vector, an input vector and an output vector; S103, discretizing the state equation, adding system noise and measurement noise, and obtaining a double-end powered long-stator linear synchronous motor model.

3. The method for measuring speed of a long-stator linear synchronous motor based on an extended Kalman filter according to claim 2, characterized in that: In step S101, the voltage equation of the double-end powered long-stator linear synchronous motor is specifically expressed as follows: Among them, u d1 、u q1 and u d2 、u q2 are the voltages of the two-end power supply of the long stator linear synchronous motor at both ends in the two-phase synchronous rotating coordinate system dq, i d1 、i q1 and i d2 、i q2 are the output currents of the power supplies at both ends of the double-ended long stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq, i d 、i q is the stator current of the double-ended power supply long stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq, i d =i d1 +i d2 ,i q =i q1 +i q2 , ψ d , q is the magnetic flux of the stator of the double-ended long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq, ψ d =L d i d +ψ f , ψ q =L q i q , ψ f The rotor flux of the double-ended long-stator linear synchronous motor, L d is the d-axis inductance, L q is the q-axis inductance, R k1 , L k1 and R k2 , L k2 are the resistance and inductance of the feeder cable from the power supply at both ends of the double-ended long-stator linear synchronous motor to the stator section of the motor, R s is the stator winding resistance of the double-end powered long stator linear synchronous motor, ω is the angular velocity, θ is the electrical angle.

4. The method for measuring speed of a long-stator linear synchronous motor based on an extended Kalman filter according to claim 3, characterized in that: In step S101, the current equation of the double-end powered long-stator linear synchronous motor is specifically expressed as follows:

5. The method for measuring speed of a long-stator linear synchronous motor based on an extended Kalman filter according to claim 4, characterized in that: In step S102, the expression of the state equation is specifically as follows: y=Cx Where x is the state vector, u is the input vector, y is the output vector, 6. The method for measuring speed of a long-stator linear synchronous motor based on an extended Kalman filter according to claim 5, characterized in that: In step S103, the expression of the double-end powered long stator linear synchronous motor model is as follows: x(k+1)=x(k)+Tf(x(k))+TBu(k)+W(k) y(k)=Cx(k)+V(k) Where W(k) is the system noise, V(k) is the measurement noise, T is the sampling period, and k represents the time.

7. The method for measuring speed of a long-stator linear synchronous motor based on an extended Kalman filter according to claim 5, characterized in that: In step S2, in the prediction stage, the expressions for predicting the state vector and output vector at the next moment are as follows: in, is the predicted state vector at time (k+1), is the estimated state vector at time k, u(k) is the input vector at time k, T is the sampling period, is the predicted output vector at time (k+1).

8. The method for measuring speed of a long-stator linear synchronous motor based on an extended Kalman filter according to claim 7, characterized in that: In the correction stage, the expressions for calculating the covariance matrix and gain matrix at the next moment are as follows: in, and K(k+1) are the prediction covariance matrix and gain matrix at time (k+1), respectively. is the estimated covariance matrix at time k, Q is the covariance matrix of the system noise W(k), R is the covariance matrix of the measurement noise V(k), G(k+1) is the Jacobian matrix, 9. The method for measuring speed of a long-stator linear synchronous motor based on an extended Kalman filter according to claim 8, characterized in that: In the correction stage, the expression for calculating the estimated covariance matrix at the next moment is specifically as follows:

10. The method for measuring speed of a long-stator linear synchronous motor based on an extended Kalman filter according to claim 8, characterized in that: In the correction phase, the expression for calculating the estimated state vector at the next moment is specifically as follows: Among them, y(k+1) is the measured state vector at time (k+1).

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