High-speed surface-mounted permanent magnet synchronous motor online parameter identification method based on zero-order retainer and current double sampling

Abstract

The invention relates to a high-speed surface-mounted permanent magnet synchronous motor online parameter identification method based on a zero-order retainer and current double sampling, and belongs to the technical field of permanent magnet synchronous motor control. The method comprises the following steps: firstly, establishing a continuous mathematical model of the surface-mounted permanent magnet synchronous motor by considering a rotor displacement effect, solving a discrete mathematical model of the surface-mounted permanent magnet synchronous motor by adopting a zero-order retainer discretization method, and simplifying the discrete mathematical model; secondly, current parameters of the motor are collected in a current double-sampling mode, and the current parameters are used for expanding the dimensionality of the discrete mathematical model; then, based on the discrete mathematical model after dimension expansion, parameter identification is carried out through a recursive least square method; and finally, performing nonlinear compensation on the three-phase voltage input into the surface-mounted permanent magnet synchronous motor so as to improve the parameter identification precision. According to the invention, rapid and high-precision online parameter identification of the surface-mounted permanent magnet synchronous motor can be realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of permanent magnet synchronous motor control, and relates to an online parameter identification method for a high-speed surface-mounted permanent magnet synchronous motor based on a zero-order hold and current double sampling. Background Art

[0002] With the rapid development of modern industry and technology, the requirements for motor performance are increasing day by day. High-speed permanent magnet synchronous motors (PMSMs) have been widely used in aerospace, industrial automation, power generation, medical equipment, transportation and other fields due to their excellent performance, such as high efficiency, high power density and excellent dynamic response ability. Therefore, in-depth research on the control technology of high-speed PMSMs is of great significance for promoting the progress of motor technology and meeting the growing industrial demands.

[0003] Common high-speed PMSM control strategies, such as vector control, direct torque control, model predictive control, etc., all rely on some basic parameters of the motor, such as resistance, inductance, permanent magnet flux linkage, etc. However, during the operation of the system, the parameters of the motor will change continuously, and parameter mismatch will lead to a decline in the control performance of the motor or even instability. Therefore, online identification of motor parameters is necessary to ensure the robustness and stability of the control system.

[0004] Online parameter identification is based on the discrete mathematical model of the motor. By collecting electrical quantities such as voltage and current, and combining algorithms to calculate and estimate the motor parameters in real time. However, due to the limited switching frequency of IGBTs, high-speed PMSMs will operate under low carrier ratio conditions. At this time, the change of rotor position within one period cannot be ignored, and the dq-axis coupling of the motor is aggravated. The error of the motor discrete model obtained by the traditional discretization method increases significantly, which in turn leads to a decrease in the control accuracy of the current loop and a slowdown in the dynamic response. In severe cases, it may even become unstable.

[0005] In addition, there are two common problems in parameter identification: 1) When the PMSM operates in a steady state, due to the linear correlation of input variables resulting in under-rank, the identified parameters cannot converge; 2) Since the output voltage of the inverter is not easy to measure, usually the output of the current loop is used as the voltage value to participate in the calculation, and the error therein will seriously affect the parameter identification result.

[0006] For the above-mentioned under-rank problem, the main methods include reducing the identified parameters and signal injection. However, reducing the identified parameters will lead to larger errors. Therefore, signal injection is generally adopted at present. Signal injection includes rotor position signal injection and voltage and current signal injection. Although signal injection can achieve the effect of increasing the rank and improving the parameter identification accuracy, it will also affect the operation performance of the motor, such as generating torque ripple. Summary of the Invention

[0007] In view of this, the object of the present invention is to provide an online parameter identification method for a high-speed surface-mounted permanent magnet synchronous motor based on a zero-order hold and current double sampling. By establishing an accurate discrete model of the high-speed PMSM and combining a parameter identification strategy based on current double sampling, the rank is increased and the identification error is reduced.

[0008] To achieve the above object, the present invention provides the following technical solutions:

[0009] An online parameter identification method for a high-speed surface-mounted permanent magnet synchronous motor based on a zero-order hold and current double sampling, the method comprising:

[0010] First, considering the rotor displacement effect, establish a continuous mathematical model of the surface-mounted permanent magnet synchronous motor, use the zero-order hold discretization method to solve the discrete mathematical model of the surface-mounted permanent magnet synchronous motor, and simplify the discrete mathematical model; secondly, collect the current parameters of the motor by means of current double sampling to expand the dimension of the discrete mathematical model; then, based on the discrete mathematical model after dimension expansion, perform parameter identification by the recursive least squares method; finally, perform nonlinear compensation on the three-phase voltage input to the surface-mounted permanent magnet synchronous motor to improve the parameter identification accuracy.

[0011] Furthermore, the established continuous mathematical model of the surface-mounted permanent magnet synchronous motor is expressed as:

[0012]

[0013] where, i dq represents the dq-axis stator current, u dq represents the dq-axis stator voltage, e dq represents the dq-axis back electromotive force term, R represents the stator resistance, L represents the dq-axis stator inductance, ω e represents the electrical angular velocity, ψ f represents the rotor flux linkage.

[0014] Furthermore, use a zero-order hold to discretize the continuous mathematical model of the surface-mounted permanent magnet synchronous motor to obtain a discretized mathematical model:

[0015] i dq (k + 1) = Gi dq (k) + Mu dqref (k) - Fe dq (k)

[0016] G 11 = G 22 = e Tσ cos(Tω e )

[0017] G 12 =-G 12 =e Tσ sin(Tω e )

[0018]

[0019] In the formula, T represents the discretization period; M ij represents the element in the i-th row and j-th column of matrix M, where i = 1, 2, j = 1, 2; F ij represents the element in the i-th row and j-th column of matrix F. G ij represents the element in the i-th row and j-th column of matrix G.

[0020] Furthermore, based on the characteristic that the normal operating speed of the high-speed surface-mounted permanent magnet synchronous motor is very high, the discretized mathematical model is simplified to obtain:

[0021]

[0022] In the formula, A h represents the input data matrix, X h represents the parameter matrix, u dref (k), u qref (k) represent the given voltage values of the d-axis and q-axis respectively; e d , e q represent the back electromotive force terms of the d-axis and q-axis respectively, Δ d (k), Δ q (k) represent the compensation values of the d-axis and q-axis during the identification process respectively.

[0023] Furthermore, the current parameters of the motor are collected by means of double current sampling, and the dimension of the discrete mathematical model is expanded. The expanded discrete mathematical model is expressed as:

[0024]

[0025] In the formula, Δ d (k + 1 / 2), Δ q (k + 1 / 2) are the results after replacing T in Δ d (k), Δ q (k) with T / 2 respectively. T pwm is a PWM period, and T s represents the sampling period, which is 1 / 2 of the PWM period T pwm under double sampling.

[0026] Among them, the double current sampling includes performing a current sampling both at the beginning and the center of the control period of the surface-mounted permanent magnet synchronous motor.

[0027] Furthermore, based on the discrete mathematics model after dimension expansion, parameter identification is performed by the recursive least squares method, including the d-axis and q-axis stator currents and the electrical angle θ of the surface-mounted permanent magnet synchronous motor e to form the input vector of the recursive least squares method, and the parameters to be identified of the surface-mounted permanent magnet synchronous motor are output through iteration, including the stator inductance, the stator resistance, and the rotor permanent magnet flux linkage.

[0028] Furthermore, the non-linear compensation for the three-phase voltage input to the surface-mounted permanent magnet synchronous motor includes calculating the error voltage to be compensated for phase a through the following formula:

[0029]

[0030] In the formula, u aoerr is the error voltage to be compensated for phase a, u sw is the voltage drop across the IGBT, u d ′ is the voltage drop across the freewheeling diode, U dc is the terminal voltage of the surface-mounted permanent magnet synchronous motor, T pwm is a PWM period. T s represents the sampling period, u ao is the actual value of the phase-a phase voltage, is the ideal value of the phase-a phase voltage;

[0031] The error voltages to be compensated for phases b and c are also calculated through the above formula.

[0032] The beneficial effects of the present invention are as follows: Aiming at the problem that the traditional discrete model has a large error due to the lack of high-order terms at a low carrier ratio, the present invention proposes to use zero-order hold discretization to reduce the discrete error. At the same time, considering the rotor rotation displacement within one period, the present invention integrates its rotation matrix into the model of the surface-mounted permanent magnet synchronous motor as a whole for discretization, and finally obtains a zero-order hold model of the surface-mounted permanent magnet synchronous motor considering the rotor position change within the control period, significantly improving the model accuracy.

[0033] In addition, to solve the problem of under-rank caused by linear correlation of the input matrix in the steady state, the present invention proposes a current double-sampling strategy. Utilizing the characteristic that the actual applied voltage significantly deviates from the given value at a low carrier ratio in the high-frequency band, an additional sampling and identification are performed at the center of the PWM period, which can achieve matrix rank augmentation and improve the parameter identification accuracy. At the same time, the parameter identification algorithm selects the recursive least squares method with a forgetting factor, which converges quickly, is easy to implement, and the present invention designs a non-linear compensation strategy suitable for double sampling, significantly improving the online parameter identification accuracy.

[0034] Other advantages, objectives and features of the present invention will be described to some extent in the subsequent specification, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be learned from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following specification. Description of the Drawings

[0035] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be described in preferred detail below in conjunction with the drawings, where:

[0036] Figure 1 is the voltage vector diagram within one control cycle;

[0037] Figure 2 is the schematic diagram of the current double sampling principle;

[0038] Figure 3 is the parameter identification result based on different models;

[0039] Figure 4 is the parameter identification result based on different sampling modes;

[0040] Figure 5 is the structural block diagram of the online parameter identification method for a high-speed surface-mounted permanent magnet synchronous motor based on a zero-order hold and current double sampling. Detailed Embodiment

[0041] The following illustrates the embodiments of the present invention through specific specific examples. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the drawings provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0042] Among them, the drawings are only used for illustrative purposes, showing only schematic diagrams, not physical diagrams, and cannot be understood as a limitation to the present invention; in order to better illustrate the embodiments of the present invention, some components in the drawings will be omitted, enlarged or reduced, which does not represent the size of the actual product; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0043] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc. indicating the orientation or positional relationship, they are based on the orientation or positional relationship shown in the accompanying drawings. This is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the positional relationship in the accompanying drawings are only for illustrative purposes and should not be construed as a limitation of the present invention. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.

[0044] To achieve the online parameter identification of a high-speed surface-mounted permanent magnet synchronous motor, an embodiment of the present invention proposes an identification method based on the zero-order hold model and current double sampling, as Figure 5 shown. This method establishes a more accurate discrete model of a high-speed PMSM. Compared with the traditional discrete model, the error of this model is significantly reduced at a low carrier ratio, and a parameter identification strategy based on double sampling is proposed in combination with the operating characteristics at a low carrier ratio, achieving rank augmentation and effectively reducing the identification error.

[0045] The implementation principle of this method is as follows:

[0046] Considering that the rotor position changes in real time within a control period, as Figure 1 shown, within the k-th period to the k + 1-th period, the actual output voltage should satisfy:

[0047]

[0048] where u dqref represents the given voltage value, u dq represents the actual output voltage value, t represents the time, and ω e represents the electrical angular velocity.

[0049] Combining Equation (1) to discretize the continuous mathematical model of PMSM using a zero-order hold, the improved discrete mathematical model of the permanent magnet synchronous motor can be obtained as:

[0050] i dq (k + 1) = Gi dq (k) + Mu dqref (k) - Fe dq (k) (2)

[0051] where

[0052]

[0053] where L is the dq-axis stator inductance of the surface-mounted PMSM, R is the stator resistance, ω e is the electrical angular velocity, T is the discretization period, ψ f is the rotor flux linkage, i dq is the dq-axis current, e dq is the dq-axis back electromotive force term. M ij represents the element in the i-th row and j-th column of matrix M, i = 1, 2, j = 1, 2. F ij represents the element in the i-th row and j-th column of matrix F. G ij represents the element in the i-th row and j-th column of matrix G.

[0054] Current double sampling, that is, an additional current sampling is performed at the center time of the control period. Denote the center times of the k-th moment and the k + 1-th moment as the k + 1 / 2 moment. Since the high-speed surface-mounted permanent magnet synchronous motor has a high speed, it can be considered that |ω e | >> |σ| and e σT = 1 + σT. After current double sampling, Equation (2) can be expanded as:

[0055]

[0056] where, T pwm is a PWM period.

[0057]

[0058] where, Δ d (k + 1 / 2), Δ q (k + 1 / 2) are the results after replacing T in Δ d (k), Δ q (k) with T / 2. u dref (k), u qref (k) are the given voltage values of the d-axis and q-axis respectively, e d , e q are the d-axis and q-axis back electromotive force terms respectively. A h represents the input data matrix, T s represents the sampling period.

[0059] It can be seen that current double sampling expands the original matrix dimension and solves the problem of underdetermined rank in parameter identification. According to Equation (4), the recursive least squares method can be used to complete the online parameter identification of the high-speed surface-mounted PMSM.

[0060] Embodiment 1

[0061] Based on the above principle, this embodiment provides an online parameter identification method for a high-speed surface-mounted permanent magnet synchronous motor based on a zero-order hold and current double sampling. The method includes:

[0062] S1. Establish a continuous mathematical model of the permanent magnet synchronous motor, which can be expressed as:

[0063]

[0064] where u d and u q represent the d-axis and q-axis stator voltages respectively, L d and L q represent the d-axis and q-axis stator inductances respectively, and i d and i q represent the d-axis and q-axis stator currents respectively.

[0065] For the surface-mounted PMSM, L d = L q = L. The equation (7) can be written in matrix form:

[0066]

[0067] And i dq = [i d i q T 、u dq = [u d u q T 、e dq = [0 ω e T .

[0068] S2. Incorporate the rotor displacement effect into the mathematical model and rewrite the continuous mathematical model of the PMSM to obtain:

[0069]

[0070] S3. Use the zero-order hold discretization method to solve the discrete mathematical model of the surface-mounted permanent magnet synchronous motor, and the solution is shown in (2).

[0071] S4. Simplify the discrete mathematical model. Specifically, since the normal operating speed of the high-speed surface-mounted permanent magnet synchronous motor is very high, it can be considered that ω e 2 ≥10σ 2 . Therefore, the discrete mathematical model shown in equation (2) is simplified to obtain:

[0072]

[0073] Based on the simplified discrete mathematical model, the recursive least squares method can be used for parameter identification. Specifically, after each recursion is completed, the current motor parameter values are used to update Δ dq , and the obtained Δ dq ​​​will participate in the next recursion. Since Δ dq is positively correlated with the rotational speed, at the initial stage of identification, the value of Δ dq is small and hardly affects the result of parameter identification. As the recursion progresses, the motor parameters and Δ dq tend to the actual values simultaneously, improving the accuracy of parameter identification at high speeds and low carrier ratios.

[0074] S5. Construct an online parameter identification method based on dual current sampling.

[0075] Among them, the principle of dual current sampling is as shown in Figure 2 , and the values of the midpoint current and the midpoint voltage can be obtained by the following formula:

[0076]

[0077] Among them, the matrix T is the transformation matrix from abc to d-q axis based on the angle θ e +Φ, Φ = ω e (k)T pwm / 2, and T pwm is a PWM period.

[0078] After dual current sampling, the discrete mathematical model shown in Equation (12) can be dimensionally expanded, and the expansion result is shown in Equation (4).

[0079] Subsequently, recursive least squares parameter identification is performed according to the dimensionally expanded discrete mathematical model. The process of recursive least squares is as follows:

[0080]

[0081] Among them, P is the covariance matrix, λ is the forgetting factor, a k is the input vector of the kth period, w k is the output vector of the kth period, and y k is the output of the kth period.

[0082] S6. Perform nonlinear compensation to improve the identification accuracy. Specifically, nonlinear compensation is performed on the voltage as shown in the following formula:

[0083]

[0084] Among them, u aoerr is the error voltage to be compensated for phase a, u sw is the voltage drop across the IGBT, and u d ′ is the voltage drop across the freewheeling diode.

[0085] M a 、M b, M c Both satisfy:

[0086]

[0087] where j = a, b, c. T d is the dead time, T on is the IGBT rise delay, T off is the IGBT turn-off delay.

[0088] For the error voltages that need to be compensated for the b-phase and c-phase, they are also obtained from Equations (16) and (17).

[0089] Program the online parameter identification method provided in Embodiment 1 and embed it in the DSP, and conduct experimental verification on the dual-motor experimental platform.

[0090] Among them, the identification error is defined as:

[0091]

[0092] The flux linkage error and inductance error are the same by analogy.

[0093] Ensure that other conditions are the same, and conduct online parameter identification using the discrete model proposed in Embodiment 1 and the traditional discrete model respectively.

[0094] As Figure 3 shown, it is a comparison of the identification results of the discrete model proposed in Embodiment 1 and the traditional discrete model at high speed and low carrier ratio. It can be seen that at high speed and low carrier ratio, due to the large discrete error of the traditional discrete model, the parameter identification effect is poor, especially the resistance identification result seriously deviates from the actual value. And the identification result obtained based on the discrete model proposed in Embodiment 1 is relatively excellent.

[0095] Ensure that other conditions are the same, and verify the online parameter identification results based on the traditional current single sampling and the current double sampling described in Embodiment 1 respectively. As Figure 4 shown, after adopting the current double sampling, the online parameter identification accuracy of the electrode is significantly improved, which proves that the current double sampling method provides additional data groups for the recursive least squares method, realizes rank augmentation, effectively improves the parameter identification accuracy, and speeds up the convergence rate.

[0096] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the present technical solution, and they should all be covered by the scope of the claims of the present invention.

Claims

1. An online parameter identification method for high-speed surface-mounted permanent magnet synchronous motors based on a zero-order hold and current double sampling, characterized in that The method includes: Firstly, considering the rotor displacement effect, a continuous mathematical model of the surface-mounted permanent magnet synchronous motor is established. The zero-order hold discretization method is used to solve the discrete mathematical model of the surface-mounted permanent magnet synchronous motor, and the discrete mathematical model is simplified. Secondly, the current parameters of the motor are collected by means of current double sampling to expand the dimension of the discrete mathematical model. Then, based on the discrete mathematical model with expanded dimension, parameter identification is carried out by the recursive least squares method. Finally, non-linear compensation is performed on the three-phase voltage input to the surface-mounted permanent magnet synchronous motor to improve the parameter identification accuracy.

2. The method according to claim 1, characterized in that, The established continuous mathematical model of the surface-mounted permanent magnet synchronous motor is expressed as: Wherein, i dq represents the dq-axis stator current, u dq represents the dq-axis stator voltage, e dq represents the dq-axis back electromotive force term, R represents the stator resistance, L represents the dq-axis stator inductance, ω e represents the electrical angular velocity, ψ f represents the rotor flux linkage.

3. The method according to claim 2, characterized in that, The zero-order hold is used to discretize the continuous mathematical model of the surface-mounted permanent magnet synchronous motor, and the discretized mathematical model is obtained: i dq (k + 1) = Gi dq (k) + Mu dqref (k) - Fe dq (k) G 11 = G 22 = e Tσ cos(Tω e ) G 12 = -G 12 = e Tσ sin(Tω e ) where T represents the discretization period; M ij represents the element in the i-th row and j-th column of matrix M, where i = 1, 2 and j = 1, 2; F ij represents the element in the i-th row and j-th column of matrix F. G ij represents the element in the i-th row and j-th column of matrix G.

4. The method according to claim 3, characterized in that, Based on the characteristic that the normal operating speed of the high-speed surface-mounted permanent magnet synchronous motor is very high, the discretized mathematical model is simplified to obtain: Where, A h represents the input data matrix, X h represents the parameter matrix, u dref (k) and u qref (k) respectively represent the given voltage values on the d-axis and q-axis; e d and e q respectively represent the back electromotive force terms on the d-axis and q-axis, Δ d (k) and Δ q (k) respectively represent the compensation values on the d-axis and q-axis during the identification process.

5. The method according to claim 4, characterized in that, The current parameters of the motor are collected by means of current double sampling to expand the dimension of the discrete mathematical model, and the expanded discrete mathematical model is expressed as: where, Δ d (k + 1 / 2) and Δ q (k + 1 / 2) are the results of replacing T in Δ d (k) and Δ q (k) with T / 2 respectively, and T pwm is a PWM period, and T s represents the sampling period, which is 1 / 2 of the PWM period T under double sampling. pwm ​ 6. The method according to claim 1 or 5, characterized in that, The current double sampling includes performing a current sampling both at the start and the center moment of the control period of the surface-mounted permanent magnet synchronous motor.

7. The method according to claim 5, characterized in that, Based on the discrete mathematical model after dimension expansion, parameter identification is carried out by the recursive least squares method, including the d-axis and q-axis stator currents and electrical angle θ of the surface-mounted permanent magnet synchronous motor e to form the input vector of the recursive least squares method, and the parameters to be identified of the surface-mounted permanent magnet synchronous motor are output through iteration, including stator inductance, stator resistance and rotor permanent magnet flux linkage.

8. The method according to claim 1, wherein The non-linear compensation for the three-phase voltage input to the surface-mounted permanent magnet synchronous motor includes calculating the error voltage to be compensated for phase a through the following formula: where, u aoerr is the error voltage to be compensated for phase a, u sw is the voltage drop across the IGBT, u d ′ is the voltage drop across the freewheeling diode, U dc is the terminal voltage of the surface-mounted permanent magnet synchronous motor, T pwm is a PWM period. T s represents the sampling period, which is 1 / 2 of the PWM period T pwm under double sampling, u ao is the actual value of the phase a voltage, is the ideal value of the phase a voltage; The error voltages to be compensated for phase b and phase c are also calculated through the above formula.

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