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

Abstract

The application 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, a double-end power supply long-stator linear synchronous motor model is constructed based on motor two-end power supply stator current, angular velocity and electric angle in a two-phase synchronous rotating coordinate system d-q; then, the model is substituted into an extended Kalman filter algorithm, and real-time speed estimation of the double-end power supply long-stator linear synchronous motor is carried out. Compared with the prior art, the application can improve the real-time performance and accuracy of double-end power supply long-stator linear synchronous motor position and speed estimation, realize speed sensorless control, is simple and convenient to operate, low in cost, and has strong anti-interference capability.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of speed sensorless speed measurement, and particularly relates to a long-stator linear synchronous motor speed measurement method based on an extended Kalman filter. BACKGROUND

[0002] In a high-speed magnetic suspension system, a long-stator linear synchronous motor is used in the traction system and the suspension system. The long-stator linear synchronous motor with double-end power supply can provide greater driving current, reduce the output capacity of a single converter, ensure the reliability of power supply, improve the flexibility of the system, and meet the needs of the magnetic suspension train in high-speed operation. Precise position detection is required for the stable operation of the magnetic suspension train. When the train is running in the 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 is running in the 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 to observe and calculate the speed and position of the train in real time to achieve precise control of the train.

[0003] The Kalman filter is a minimum variance optimal prediction estimation method that can effectively reduce the influence of random interference and measurement noise. The extended Kalman filter is a generalization of the linear Kalman filter in nonlinear systems and is often used in rail transportation, navigation, and other fields. It has a wide range of speed estimation and can estimate the speed and position of the system even when there is noise. Currently, the extended Kalman filter has been applied in the detection of linear motor speed and angle. For example, a permanent magnet synchronous motor load torque observation method based on an extended Kalman filter is disclosed in Chinese Patent No. CN111193448B. The method 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 related application method of the extended Kalman filter in the long-stator linear synchronous motor with double-end power supply. Therefore, it is necessary to design a long-stator linear synchronous motor speed measurement method based on an extended Kalman filter to further improve the real-time performance and accuracy of the position and speed estimation of the long-stator linear synchronous motor with double-end power supply. SUMMARY

[0004] The purpose of the present application is to overcome the shortcomings of the prior art and provide a long-stator linear synchronous motor speed measurement method based on an extended Kalman filter to further improve the real-time performance and accuracy of the position and speed estimation of the long-stator linear synchronous motor with double-end power supply.

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

[0006] The application provides 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.

[0007] S1. In a two-phase synchronous rotating coordinate system d-q, a double-end power supply long-stator linear synchronous motor model is constructed based on a state vector, an input vector and an output vector, wherein the state vector comprises output currents, angular velocities and electric angles of the double-end power supply long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system d-q, the input vector comprises voltages of the double-end power supply long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system d-q, and the output vector comprises output currents of the double-end power supply long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system d-q.

[0008] S2. The model constructed in step S1 is substituted into an extended Kalman filter algorithm to estimate the speed of the double-end power supply long-stator linear synchronous motor, which comprises a prediction stage and a correction stage, in the prediction stage, the state vector and the output vector at the next moment are predicted according to the input vector and the estimated state vector at the last moment, in the correction stage, the covariance matrix and the gain matrix at the next moment are calculated according to the estimated covariance matrix at the last moment, the estimated covariance matrix at the next moment is calculated for use in the next correction stage, the estimated state vector at the next moment is calculated for use in the next prediction stage, and the real-time speed of the double-end power supply long-stator linear synchronous motor is calculated according to the angular velocity and the electric angle in the estimated state vector.

[0009] Further, in step S1, the specific process of constructing the double-end power supply long-stator linear synchronous motor model is as follows.

[0010] S101. In a two-phase synchronous rotating coordinate system d-q, a voltage equation of the double-end power supply long-stator linear synchronous motor is constructed to obtain a current equation of the double-end power supply long-stator linear synchronous motor.

[0011] S102. The current equation of the double-end power supply long-stator linear synchronous motor is rewritten into a state equation based on the state vector, the input vector and the output vector on the premise that the angular velocity is constant.

[0012] S103. The state equation is discretized and system noise and measurement noise are added to obtain the double-end power supply long-stator linear synchronous motor model.

[0013] Further, in step S101, the expression of the voltage equation of the double-end power supply long-stator linear synchronous motor is as follows.

[0014]

[0015] Wherein, u d1 , uq1 and u d2 , u q2 are the voltages of the two-end power supply of the long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system d-q, respectively, d1 , i q1 and i d2 , i q2 are the output currents of the two-end power supply of the long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system d-q, respectively, d , i q are the currents of the stator of the long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system d-q, respectively, d = i d1 + i d2 , i q = i q1 +

[0016] i q2 , ψ d , ψ q are the flux linkages of the stator of the long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system d-q, respectively, d = L d i d + ψ f , ψ q = L q i q , ψ f is the rotor flux linkage of the long-stator linear synchronous motor,

[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 feeding cable from the two-end power supply of the long-stator linear synchronous motor to the stator segment, respectively, R s is the stator winding resistance of the long-stator linear synchronous motor, ω is the angular velocity, θ is the electrical angle.

[0018] Further, in step S101, the expression of the current equation of the long-stator linear synchronous motor is specifically as follows:

[0019]

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

[0021]

[0022] y = Cx

[0023] where x is a state vector, u is an input vector, y is an output vector,

[0024]

[0025] Further, in step S103, the expression of the double-ended power supply long-stator linear synchronous motor model is 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 a system noise, V(k) is a measurement noise, T is a sampling period, and k represents a time.

[0029] Further, in step S2, in the prediction stage, the expressions of the predicted state vector and output vector at the next time are as follows:

[0030]

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

[0032] Further, in the correction stage, the expressions of the covariance matrix and gain matrix at the next time are as follows:

[0033]

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

[0035]

[0036] Further, in the correction stage, the expression of the estimated covariance matrix at the next time is as follows:

[0037]

[0038] Further, in the correction stage, the expression of the estimated state vector of the next moment is specifically as follows:

[0039]

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

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

[0042] The present application provides a speed sensorless speed measurement method based on an extended Kalman filter applied to a double-ended power supply long-stator linear synchronous motor, first, in the two-phase synchronous rotating coordinate system d-q, considering the system noise and the measurement noise, a double-ended power supply long-stator linear synchronous motor model is constructed based on the state vector, the input vector and the output vector, wherein the state vector includes the output current, the angular velocity and the electric angle of the double-ended power supply long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system d-q, the input vector includes the voltage of the double-ended power supply long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system d-q, and the output vector includes the output current of the double-ended power supply long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system d-q; then, the equation is substituted into the extended Kalman filter algorithm to estimate the speed of the double-ended power supply long-stator linear synchronous motor, which specifically includes a prediction stage and a correction stage, in the prediction stage, the state vector and the output vector of the next moment are predicted according to the estimated state vector and the input vector of the last moment; in the correction stage, the covariance matrix and the gain matrix of the next moment are calculated according to the estimated covariance matrix of the last moment, the estimated covariance matrix of the next moment is calculated for use in the next correction stage, the estimated state vector of the next moment is calculated for use in the next prediction stage, and the real-time speed of the double-ended power supply long-stator linear synchronous motor is calculated according to the angular velocity and the electric angle in the estimated state vector. The above-mentioned method not only can improve the real-time performance and accuracy of the position and speed estimation of the long-stator linear synchronous motor under the double-ended power supply mode, realize speed sensorless control, but also is simple and convenient to operate, low in cost, and has strong anti-interference ability. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 It is an equivalent circuit diagram of the double-ended power supply mode of the long-stator linear synchronous motor.

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

[0045] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection 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 to provide a speed measurement method for a long stator linear synchronous motor based on an extended Kalman filter.

[0048] High-speed maglev trains require dual-end power supply for high-speed operation. This is because dual-end power supply can provide a larger drive current to meet the acceleration and deceleration requirements at high speeds, while also reducing the output capacity of individual converters, ensuring power supply reliability, and improving system redundancy. The equivalent circuit diagram of a long-stator linear synchronous motor using dual-end power supply mode is shown below. Figure 1 As shown. Where u a1 u b1 u c1 and i a1 i b1 i c1 These represent the three-phase output voltage and current of one side of the converter, u a2 u b2 u c2 and i a2 i b2 i c2 These represent the three-phase output voltage and current of the converter on the other side, i a i b i c ψ is the three-phase current of the stator winding of the linear motor. a ψ b ψ c R is the three-phase flux linkage of the stator winding of a linear motor. k1 L k1 and R k2 L k2 R represents the resistance and inductance of the feed cables from the two converters to the stator windings of the linear motor. s This refers to the resistance of the stator winding of a linear motor.

[0049] The technical solution provided in this embodiment is to achieve speed measurement of a dual-powered long-stator linear synchronous motor by using an extended Kalman filter. The extended Kalman filter is essentially a stochastic observer, and its design takes into account system noise and measurement noise, thus exhibiting strong robustness to motor parameters. The method proposed in this embodiment includes the following steps:

[0050] S1. Construct a model of a dual-powered long stator linear synchronous motor. The specific process is as follows:

[0051] S101、According to the equivalent circuit diagram of the long-stator linear synchronous motor double-ended power supply mode as shown in Figure 1 The following voltage and current equations are obtained:

[0052]

[0053] In the two-phase synchronous rotating coordinate system d-q, the voltage equation of the double-ended power supply long-stator linear synchronous motor is constructed:

[0054]

[0055] where u d1 , u q1 , and u d2 , u q2 are the voltages of the double-ended power supply long-stator linear synchronous motor at both ends in the two-phase synchronous rotating coordinate system d-q, i d1 , i q1 , and i d2 , i q2 are the output currents of the double-ended power supply long-stator linear synchronous motor at both ends in the two-phase synchronous rotating coordinate system d-q, i d , i q are the currents of the double-ended power supply long-stator linear synchronous motor stator in the two-phase synchronous rotating coordinate system d-q, ψ d , ψ q are the fluxes of the double-ended power supply long-stator linear synchronous motor stator in the two-phase synchronous rotating coordinate system d-q, ψ f is the rotor flux of the double-ended power supply 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 feeding cable from the double-ended power supply long-stator linear synchronous motor to the motor stator section, R s is the stator winding resistance of the double-ended power supply long-stator linear synchronous motor, and ω is the angular velocity.

[0056] By combining formulas (4)-(6), the current equation of the double-ended power supply 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, in the case of small sampling period, it can be considered that the speed remains unchanged, i.e. the change of speed is 0, as follows:

[0059]

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

[0061]

[0062] The formula (7)-(9) can be rewritten to obtain the state equation as follows:

[0063]

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

[0065]

[0066] y=Cx (11)

[0067] wherein x is a state vector, u is an input vector, y is an output vector, According to the formula (10) (11), we can obtain:

[0068]

[0069] S103, in order to construct the extended Kalman filter state observer, the formula (11) is discretized:

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

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

[0072] wherein T is a sampling period. Considering that in the actual system, the model parameters have uncertainty and variability, and the measurement noise is inevitably present in the stator voltage and current, the above formula is 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] wherein W(k) is a system noise, and V(k) is a measurement noise.

[0076] S2, the model constructed in step S1 is substituted into the extended Kalman filter algorithm, and the speed estimation of the double-ended power supply long-stator linear synchronous motor is carried out, including the prediction stage and the correction stage, and the specific algorithm process is as shown in Figure 2 , including the following steps:

[0077] S201, state prediction

[0078] The target of state prediction is to obtain the next estimation from the last state estimation But before obtaining the prediction value must be calculated The final estimation value can be obtained after the prediction value is corrected by the feedback of the second stage The state prediction can be expressed as:

[0079]

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

[0081] S202, calculation of covariance matrix

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

[0083]

[0084] wherein, is the predicted covariance matrix at (k+1) time, Q is the covariance matrix of the system noise W(k), is the estimation covariance matrix at k time, and G(k+1) is the Jacobian matrix, which is specifically:

[0085]

[0086] As can be seen from the above formula, the covariance matrix is determined by the last covariance matrix plus the newly obtained prediction state information and the system noise covariance matrix Q. In addition to the measurement noise introduced by the stator voltage sensor and the quantization error caused by A / D conversion, the system noise Q also includes parameter uncertainty and system disturbance.

[0087] S203, calculation of gain matrix K(k+1)

[0088]

[0089] The gain matrix K(k+1) is mainly used to complete the correction of the state vector estimation, and R is the covariance matrix of the measurement noise V(k), which 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] wherein, represents the (k+1)th state vector estimation value, y(j+1) is the measured state vector, is the predicted output vector, and the above formula completes the state estimation from to According to the angular velocity and the electric angle in the estimated state vector, the real-time speed of the double-ended long-stator linear synchronous motor can be calculated.

[0093] S205, calculation of estimated covariance matrix

[0094]

[0095] wherein, is the estimated covariance matrix, which reflects the error size of the current estimation state. As can be seen from steps S202 to S204, the covariance matrix is used in the state estimation of Therefore, in the current estimation, the covariance matrix should also be calculated in advance for the next state estimation.

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

[0097] If the above method is realized in the form of a software function 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 solutions of the present application or the part of the prior art that essentially contributes or the part of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in various embodiments of the present application. The aforementioned storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various media that can store program codes.

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

Claims

1. A speed measurement method for a long stator linear synchronous motor based on an extended Kalman filter, characterized in that, For use in dual-ended power supply long stator linear synchronous motors, the following steps are included: S1. In the two-phase synchronous rotating coordinate system dq, a dual-powered long stator linear synchronous motor model is constructed based on the state vector, input vector, and output vector. 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. 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 estimate the speed of the dual-powered long stator linear synchronous motor. This includes a prediction stage and a correction stage. In the prediction stage, the state vector and output vector of the next moment are predicted based on the input vector and estimated state vector of the previous moment. In the correction stage, the covariance matrix and gain matrix of the next moment are calculated based on the estimated covariance matrix of the previous moment. The estimated covariance matrix of the next moment is then calculated for use in the next correction stage. The estimated state vector of the next moment is calculated for use in the next prediction stage. The real-time speed of the dual-powered long stator linear synchronous motor is calculated based on the angular velocity and electrical angle in the estimated state vector. In step S1, the specific process of constructing the dual-end power supply long stator linear synchronous motor model is as follows: S101. Under the two-phase synchronous rotating coordinate system dq, construct the voltage equation of the dual-end power supply long stator linear synchronous motor, and then obtain the current equation of the dual-end power supply long stator linear synchronous motor. S102. Under the premise of constant angular velocity, the current equation of the dual-end power supply long stator linear synchronous motor is rewritten as a state equation based on state vector, input vector and output vector. S103. Discretize the state equation and add system noise and measurement noise to obtain a dual-powered long stator linear synchronous motor model. In step S102, the expression for the state equation is as follows: in, For state vectors, , For the input vector, , For output vector, ; in, , and , These represent the voltages of the power supplies at both ends of a dual-powered long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq. , and , These are the output currents of the power supplies at both ends of the dual-powered long stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq. , The current in the stator of a dual-ended power-supply long-stator linear synchronous motor in the two-phase synchronous rotating coordinate system dq. , , , The magnetic flux linkage of the stator in a two-phase synchronous rotating coordinate system dq for a dual-ended power supply long stator linear synchronous motor. ， , Rotor flux linkage for a dual-ended power supply long stator linear synchronous motor For d-axis inductance, It is the q-axis inductance. , and , These represent the resistance and inductance of the feed cables from the two ends of the power supply to the stator section of the dual-powered long stator linear synchronous motor. Stator winding resistance for a dual-ended power supply long stator linear synchronous motor Angular velocity, , It is an electrical angle.

2. The speed measurement method for a long stator linear synchronous motor based on an extended Kalman filter according to claim 1, characterized in that, In step S101, the specific expression of the voltage equation for the dual-ended power supply long stator linear synchronous motor is as follows: 。 3. The speed measurement method for a long stator linear synchronous motor based on an extended Kalman filter according to claim 2, characterized in that, In step S101, the specific expression of the current equation for the dual-ended power-supply long stator linear synchronous motor is as follows: 。 4. The speed measurement method for a long stator linear synchronous motor based on an extended Kalman filter according to claim 1, characterized in that, In step S103, the specific expression of the dual-end power supply long stator linear synchronous motor model is as follows: in, For system noise, To measure noise, The sampling period is Indicates the time.

5. The speed measurement method for a long stator linear synchronous motor based on an extended Kalman filter according to claim 1, characterized in that, In step S2, during the prediction phase, the expressions for predicting the state vector and output vector at the next moment are as follows: in, For prediction The state vector at time t, for The estimated state vector at time t, for The input vector at time t, The sampling period is For prediction The output vector at time step.

6. The speed measurement method for a long stator linear synchronous motor based on an extended Kalman filter according to claim 5, characterized in that, During the correction phase, the expressions for calculating the covariance matrix and gain matrix at the next time step are as follows: in, and They are respectively The prediction covariance matrix and gain matrix at time step, for The estimated covariance matrix at time t. For system noise The covariance matrix, To measure noise The covariance matrix, For Jacobian matrices, 。 7. The speed measurement method for a long stator linear synchronous motor based on an extended Kalman filter according to claim 6, characterized in that, During the correction phase, the expression for calculating the estimated covariance matrix at the next time step is as follows: 。 8. The speed measurement method for a long stator linear synchronous motor based on an extended Kalman filter according to claim 6, characterized in that, During the correction phase, the expression for calculating the estimated state vector at the next moment is as follows: in, for The measured state vector at time t.

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