A cross-optimization-based permanent magnet synchronous motor predictive control method

Abstract

The application discloses a kind of permanent magnet synchronous motor prediction control methods based on cross optimization, it is related to motor control field, specific method is, the stator flux, stator current and electromagnetic torque prediction equation of permanent magnet synchronous motor discrete model are established;In each control cycle, the torque and flux linkage corresponding to all stator voltage vectors in inverter respectively are predicted, the normalized torque error and normalized flux linkage error corresponding to all stator voltage vectors respectively are calculated, each normalized torque error, flux linkage error is arranged in ascending order respectively, and the first 50% stator voltage vector of sorting is selected as flux linkage and torque optimal set respectively;Then the cross error in each optimal set is calculated, and finally the stator voltage vector with minimum cross error is selected as the optimal voltage vector.

Description

Technical Field

[0001] This invention relates to the field of motor control, and more specifically to a predictive control method for permanent magnet synchronous motors based on cross-optimization. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) have been widely used in modern industrial drive and servo control fields due to their advantages such as high power density and high efficiency. Finite control set model predictive control (FMCM) FCS - MPC As an advanced control strategy, it combines the ideas of modern control theory with the characteristics of discrete control of power converters. Through predictive models, rolling optimization and feedback correction, it exhibits excellent dynamic performance and has become one of the current research hotspots.

[0003] In traditional FCS - MPC In this context, a cost function is typically used to evaluate the performance of different voltage vectors. This cost function usually contains multiple control objectives (such as torque control and flux linkage control), which need to be balanced using weighting factors. The selection of these weighting factors has a significant impact on the control effect: improper values ​​can lead to the deterioration of the performance of a certain control objective. Furthermore, the tuning process of the weighting factors is cumbersome, requiring repeated adjustments based on load and operating conditions, which can disrupt the overall control performance. FCS - MPC Simplicity. Furthermore, traditional... FCS - MPC The methods generally employ offline and online search methods. Offline search is cumbersome and disrupts the workflow. FCS - MPC The original simplicity of the online search method is compromised by its large computational cost and strong dependence on the model, while the simplified cost function method is sensitive to changes in model parameters and has weak robustness.

[0004] In view of this, this application has conducted in-depth research on this basis, resulting in this case. Summary of the Invention

[0005] The purpose of this invention is to provide a predictive control method for permanent magnet synchronous motors based on cross-optimization, which does not require cumbersome weighting factor tuning and has low computational cost and complexity.

[0006] To achieve the above objectives, the solution of the present invention is:

[0007] A predictive control method for permanent magnet synchronous motors (PMSMs) based on cross-optimization is proposed. First, stator flux prediction equations, stator current prediction equations, and electromagnetic torque prediction equations are established for a discrete model of the PMSM. Then, in each control cycle, the torque and flux linkage corresponding to all stator voltage vectors in the two-level three-phase inverter are predicted. The normalized torque error and normalized flux linkage error corresponding to each stator voltage vector are calculated. The normalized torque errors are sorted in ascending order, and the top 50% of the stator voltage vectors are selected as the torque optimization set. Similarly, the normalized flux linkage errors are sorted in ascending order, and the top 50% of the stator voltage vectors are selected as the flux linkage optimization set. Then, the cross-error between the normalized flux linkage error and the minimum flux linkage error corresponding to each stator voltage vector in the torque optimization set is calculated. The cross-error between the normalized torque error and the minimum torque error corresponding to each stator voltage vector in the flux linkage optimization set is also calculated. Finally, the stator voltage vector with the smallest cross-error is selected as the optimal voltage vector and output to the PMSM through the two-level three-phase inverter.

[0008] Includes the following steps:

[0009] Step 1: Establish the prediction equations for the discrete model of the permanent magnet synchronous motor. The established stator flux prediction equation is as follows:

[0010] ,

[0011] ,

[0012] ,

[0013] In the formula, Indicates in The predicted value of the stator flux at any given time. This represents the magnetic flux value at time k. Indicates the control cycle. Represents the stator voltage vector. express The voltage drop across the stator circuit at any given moment. Represents the stator current vector. express Stator current vector at any given moment Indicates stator resistance. This represents the rate of change of magnetic flux;

[0014] The established stator current prediction equation is as follows: ,in, , In the formula, express The predicted value of the stator current vector at time t. Indicates the leakage coefficient. Indicates stator inductance, Indicates rotor inductance, Indicates mutual intuition. Indicates rotor resistance. Represents the time constant. Indicates the rotor angular velocity;

[0015] The established electromagnetic torque prediction equation is as follows:

[0016] In the formula, express The predicted value of the electromagnetic torque at time t. express Predicted value of the direct-axis component of stator flux linkage at time step. express Predicted values ​​of the cross-axis component of the stator flux linkage at any given time. express Predicted value of the direct-axis component of the stator current at any given time. express Predicted value of stator current quadrature-axis component at time step It is an extreme logarithm.

[0017] Step 2, the model prediction control crossover method is as follows;

[0018] Step 2-1: Sort and filter the two evaluation indicators. The calculation formulas for the two evaluation indicators are as follows:

[0019] ,

[0020] ,

[0021] In the formula, This represents the normalized torque error; Indicates the use of the first When the stator voltage vector is The predicted value of the electromagnetic torque at time t, where, This indicates the current state of the switch. =1, 2, ..., 6, 7; Indicates the normalized flux linkage error. This indicates the set torque reference value. This indicates the rated torque of the motor; Indicates the use of the first When the stator voltage vector is The predicted magnitude of the stator flux linkage vector at time t. This indicates the set stator flux linkage reference modulus. This indicates the rated flux linkage modulus of the motor;

[0022] Calculate the normalized torque error and normalized flux linkage error corresponding to all the stator voltage vectors respectively, then sort the normalized torque error and normalized flux linkage error in ascending order respectively, and select the top 50% of the stator voltage vectors in each evaluation index to form the torque optimization set and flux linkage optimization set respectively.

[0023] Step 2-2: Calculate the cross error. Calculate the cross error between the normalized flux linkage error and the minimum flux linkage error corresponding to each stator voltage vector in the preferred torque set. At the same time, calculate the cross error between the normalized torque error and the minimum torque error corresponding to each stator voltage vector in the preferred flux linkage set. Then select the stator voltage vector with the smallest cross error as the optimal voltage vector.

[0024] Step 3: Input the optimal voltage vector into the two-level three-phase inverter, and output it to the permanent magnet synchronous motor through the conversion of the two-level three-phase inverter.

[0025] The stator voltage vector output by the two-level three-phase inverter and the stator current vector Each is obtained through a sliding mode observer in real time. The stator flux value at a given time is used as a prediction. Stator flux at time +1 and The basic input for torque at time +1.

[0026] With the above structure, the present invention has the following beneficial effects: In each control cycle, the priority control target of torque or flux linkage is automatically switched according to the magnitude of the cross error. That is, the priority is dynamically determined by the cross error, and the control is adjusted according to the deviation of the actual torque and flux linkage errors in each cycle. This avoids flux linkage runaway caused by traditional fixed screening rules, eliminates weighting factors, adapts to the requirements of all working conditions and changes in working conditions, and overcomes the difficulties of screening rules not being suitable for working conditions and insufficient coordination of multiple targets. Furthermore, since the normalized torque error and normalized flux linkage error are sorted separately, only the stator voltage vector of the first half of the region is taken. Therefore, the problem of large calculation volume of full sorting is avoided, and the optimal stator voltage vector is not missed. Attached Figure Description

[0027] Figure 1 This is a block diagram illustrating the principle of the predictive control method of the present invention. Detailed Implementation

[0028] To further explain the technical solution of the present invention, the present invention will be described in detail below through specific embodiments.

[0029] A predictive control method for permanent magnet synchronous motors based on cross-optimization is proposed. This method is based on common drive systems for controlling permanent magnet synchronous motors, such as... Figure 1 As shown, the drive system includes an inverter, which is a conventional two-level three-phase inverter. The inverter comprises three phase arms, corresponding to phases a, b, and c as described below. Each phase has two switching transistors, located on the upper and lower arms of each phase arm. It should be noted that because the inverter is a two-level three-phase inverter, it has eight switching states. Since a two-level three-phase inverter has two equivalent zero-voltage vectors, for ease of calculation, the two equivalent zero-voltage vectors are combined, i.e. =1, 2, 3, 4, 5, 6, 7 This indicates the current state of the switch.

[0030] In addition, the aforementioned drive system also includes a PI regulator, and each input quantity can be obtained by conventional means in the art or by the methods described below, so it will not be described in detail here.

[0031] In this embodiment, the predictive control method for the permanent magnet synchronous motor is as follows: First, the stator flux prediction equation, stator current prediction equation, and electromagnetic torque prediction equation of the discrete model of the permanent magnet synchronous motor are established. Then, in each control cycle, the torque and flux linkage corresponding to all stator voltage vectors in the two-level three-phase inverter are predicted according to the above prediction equations. The normalized torque error and normalized flux linkage error corresponding to all stator voltage vectors are calculated. The normalized torque errors are sorted in ascending order, and the top 50% of the stator voltage vectors are taken as the torque optimization set. The normalized flux linkage errors are sorted in ascending order, and the top 50% of the stator voltage vectors are taken as the flux linkage optimization set. Then, the cross error between the normalized flux linkage error and the minimum flux linkage error corresponding to each stator voltage vector in the torque optimization set is calculated. The cross error between the normalized torque error and the minimum torque error corresponding to each stator voltage vector in the flux linkage optimization set is calculated. Finally, the stator voltage vector with the smallest cross error is selected as the optimal voltage vector and output to the permanent magnet synchronous motor through the two-level three-phase inverter.

[0032] To elaborate, this embodiment includes the following steps.

[0033] Step 1: Establish the prediction equations for the discrete model of the permanent magnet synchronous motor.

[0034] Step 1-1, the established stator flux prediction equation is:

[0035] ,

[0036] ,

[0037] ,

[0038] In the formula, Indicates in The predicted value of the stator flux at any given time. This represents the magnetic flux value at time k. This indicates the control interval, also known as the control cycle. Represents the stator voltage vector; Indicates stator resistance and Stator current vector at time The product of, which represents The voltage drop across the stator circuit is a core component of the motor stator voltage balance equation. Represents the stator current vector. express Stator current vector at any given moment Indicates stator resistance. It represents the rate of change of magnetic flux.

[0039] Step 1-2, the established stator current prediction equation is as follows:

[0040] ,

[0041] in, , .

[0042] In the formula, express Predicted stator current vector value at time 10:00. Indicates the leakage coefficient. Indicates stator inductance, Indicates rotor inductance, Indicates mutual intuition. Indicates rotor resistance. Represents the time constant. This indicates the rotor angular velocity.

[0043] Steps 1-3, the established electromagnetic torque prediction equation is as follows:

[0044] ,

[0045] In the formula, This represents the predicted value of the electromagnetic torque at time k+1. express Predicted value of the direct-axis component of stator flux linkage at time step. express Predicted values ​​of the cross-axis component of the stator flux linkage at any given time. This represents the predicted value of the direct-axis component of the stator current at time k+1. This represents the predicted value of the quadrature-axis component of the stator current at time k+1; The pole pair number is used to reflect the amplification effect of the number of magnetic pole pairs on torque; the coefficient 1.5 originates from the conversion from a three-phase system to a two-phase system. d-q Coordinate transformation of the system.

[0046] It is worth mentioning that electromagnetic torque is caused by d shaft flux and q The interaction of shaft currents and q shaft flux and d The interaction of the shaft currents produces the currents together, and since they are in opposite directions, the difference is taken.

[0047] Furthermore, based on the stator voltage vector output of a two-level three-phase inverter and stator current vector By using existing conventional sliding mode observers, in order to acquire in real time The stator flux value at a given time is used as a prediction. Stator flux at time +1 (i.e. ) and torque (i.e. The basic input.

[0048] Step 2, the model prediction control crossover method is as follows:

[0049] Step 2-1: Sort and filter the two evaluation indicators. The calculation formulas for the two evaluation indicators are as follows:

[0050] ,

[0051] ,

[0052] In the formula, This represents the normalized torque error; Indicates the use of the first When the stator voltage vector is The predicted value of the electromagnetic torque at time t, where, =1, 2, ..., 6, 7; This indicates the set torque reference value; This indicates the rated torque of the motor, used to normalize torque error and eliminate the influence of the magnitude of the torque value on error judgment.

[0053] Indicates the normalized flux linkage error. Indicates the use of the first When the stator voltage vector is The predicted magnitude of the stator flux linkage vector at time t. This indicates the stator flux linkage reference modulus set by the drive system; This indicates the rated flux linkage modulus of the motor, used to normalize flux linkage error to ensure consistency with the measurement scale of torque error.

[0054] Then, in each control cycle, according to the calculation formula of the above evaluation index, the normalized torque error and normalized flux linkage error corresponding to all stator voltage vectors are calculated respectively. The normalized torque error and normalized flux linkage error are arranged in ascending order respectively, and the top 50% of stator voltage vectors in each evaluation index are selected to form the torque optimization set and flux linkage optimization set respectively.

[0055] Furthermore, in this embodiment, the top 50% of the stator voltage vectors in each evaluation index (i.e. There are 3, namely, there are 3 stator voltage vectors in both the torque optimization and flux optimization sets.

[0056] Furthermore, in step 2-1, following the principle of minimizing the normalized error, that is, for the two control criteria of torque error and magnetic flux error, the stator voltage vector is respectively... Arranged in ascending order of normalized error values ​​according to the corresponding criteria; the smaller the error, the higher the ranking and the higher the priority.

[0057] It's worth mentioning that the top 50% of stator voltage vectors for each evaluation criterion are selected to avoid missing the optimal solution. Specifically, this operation considers the worst-case scenario, ensuring that even if the top 3 vectors with the smallest normalized torque error are completely different from the top 3 vectors with the smallest normalized flux error, all potential optimal stator voltage vectors are covered. This avoids missing the optimal solution by only selecting the top 2. The bottom 50% of stator voltage vectors are excluded in the subsequent calculation of cross-error and selection of the optimal stator voltage vector. This is because the core principle of ranking is ascending order of normalized error; the smaller the error, the higher the ranking. The torque error or flux error corresponding to the bottom half of the stator voltage vectors is significantly larger than the top 3. Even if they participate in the selection, their cross-error with the other control criterion will inevitably be larger, making it impossible for them to be the optimal solution that minimizes the error of both control criteria.

[0058] Step 2-2: Calculate the cross error. Calculate the cross error between the normalized flux linkage error and the minimum flux linkage error for each stator voltage vector in the torque optimization set obtained in Step 2-1. Calculate the cross error between the normalized torque error and the minimum torque error for each stator voltage vector in the flux linkage optimization set obtained in Step 2-1. Then select the stator voltage vector with the smallest cross error as the optimal voltage vector.

[0059] To elaborate further, the stator voltage vector corresponding to the normalized error (i.e., normalized flux linkage error or normalized torque error) corresponding to the minimum cross error is selected as the optimal voltage vector.

[0060] Step 3: Input the optimal voltage vector obtained in step 2-2 into a two-level three-phase inverter, and output it to the permanent magnet synchronous motor through the conversion of the two-level three-phase inverter.

[0061] It should be noted that after each selection of the optimal voltage vector and output to the inverter, the next control cycle will begin, and the cycle will start again from acquiring new stator voltage and current, and the observer will estimate new stator flux. That is, steps 2-3 will be repeated in each control cycle.

[0062] This invention provides a predictive control method for permanent magnet synchronous motors that eliminates the need for cumbersome weighting factor tuning and avoids performance degradation due to improper weighting. It uses cross-error to dynamically adjust the priority of torque and flux linkage, enabling the control strategy to adapt to different operating conditions and ensuring global optimization. Furthermore, the calculation process only involves error sorting and cross-error calculation, resulting in low computational load and complexity. It should be noted that in experimental verification, the method outperforms traditional methods in terms of torque ripple, flux linkage ripple, and stator current total harmonic distortion.

[0063] Furthermore, the normalized torque error and normalized flux linkage error are sorted separately, and then only the stator voltage vector of the first half of the region is taken. This avoids the problem of large computational load of full sorting, while ensuring that the optimal stator voltage vector is not missed.

[0064] Furthermore, this invention replaces the previous fixed priority mechanism with a dynamic priority judgment mechanism based on cross-error. It dynamically balances the objectives through cross-error, eliminating the need for subjectively setting weighting factors. In each control cycle, it automatically switches the priority objective (i.e., switching the priority control objective of torque or flux linkage) based on the magnitude of the cross-error. It also calculates the deviation of the priority objective from the other objective through the cross-error, avoiding suboptimal solutions. Specifically, in this embodiment, the two control objectives are torque (corresponding to the criterion). ) and magnetic flux (corresponding criteria) However, it does not fix which is the priority target and which is another target. The priority target is "dynamically switched" and determined by the real-time cross error. By judging which target's priority selection has less impact on the other target through the cross error, the priority target is dynamically switched. This avoids the non-optimal solution of "one target is optimal but the other target deviates significantly" in the traditional method. The tuning process is simple. It only requires calculating the cross error and does not need to be repeatedly adjusted according to the load and operating conditions.

[0065] The above description is only a preferred embodiment of this invention. Any equivalent changes and modifications made that fall within the scope of the claims of this invention shall be deemed to fall within the scope of the claims of this invention.

Claims

1. A predictive control method for permanent magnet synchronous motors based on cross-optimization, characterized in that: First, the stator flux prediction equation, stator current prediction equation, and electromagnetic torque prediction equation of the discrete model of the permanent magnet synchronous motor are established. Then, in each control cycle, the torque and flux linkage corresponding to all stator voltage vectors in the two-level three-phase inverter are predicted. The normalized torque error and normalized flux linkage error corresponding to all stator voltage vectors are calculated. The normalized torque errors are sorted in ascending order, and the top 50% of the stator voltage vectors are taken as the torque optimization set. The normalized flux linkage errors are sorted in ascending order, and the top 50% of the stator voltage vectors are taken as the flux linkage optimization set. Then, the cross error between the normalized flux linkage error and the minimum flux linkage error corresponding to each stator voltage vector in the torque optimization set is calculated. The cross error between the normalized torque error and the minimum torque error corresponding to each stator voltage vector in the flux linkage optimization set is calculated. Finally, the stator voltage vector with the smallest cross error is selected as the optimal voltage vector, which is output to the permanent magnet synchronous motor through the two-level three-phase inverter. Includes the following steps: Step 1: Establish the prediction equations for the discrete model of the permanent magnet synchronous motor. The established stator flux prediction equation is as follows: ， ， ， In the formula, Indicates in The predicted value of the stator flux at any given time. express The magnetic flux value at time t. Indicates the control period. Represents the stator voltage vector. express The voltage drop across the stator circuit at any given moment. Represents the stator current vector. express Stator current vector at any given moment Indicates stator resistance. This represents the rate of change of magnetic flux; The established stator current prediction equation is as follows: ,in, , In the formula, express The predicted value of the stator current vector at time t. Indicates the leakage coefficient. Indicates stator inductance, Indicates rotor inductance, Indicates mutual intuition. Indicates rotor resistance. Represents the time constant. Indicates the rotor angular velocity; The established electromagnetic torque prediction equation is as follows: In the formula, express The predicted value of the electromagnetic torque at time t. express Predicted value of the direct-axis component of stator flux linkage at time step. express Predicted values ​​of the cross-axis component of the stator flux linkage at any given time. express Predicted value of the direct-axis component of the stator current at any given time. express Predicted value of stator current quadrature-axis component at time step It is the extreme logarithm; Step 2, the model prediction control crossover method is as follows; Step 2-1: Sort and filter the two evaluation indicators. The calculation formulas for the two evaluation indicators are as follows: ， ， In the formula, This represents the normalized torque error; Indicates the use of the first When the stator voltage vector is The predicted value of the electromagnetic torque at time t, where, This indicates the current state of the switch. =1, 2, ..., 6, 7; Indicates the normalized flux linkage error. This indicates the set torque reference value. This indicates the rated torque of the motor; Indicates the use of the first When the stator voltage vector is The predicted magnitude of the stator flux linkage vector at time t. This indicates the set stator flux linkage reference modulus. This indicates the rated flux linkage modulus of the motor; Calculate the normalized torque error and normalized flux linkage error corresponding to all the stator voltage vectors respectively, then sort the normalized torque error and normalized flux linkage error in ascending order respectively, and select the top 50% of the stator voltage vectors in each evaluation index to form the torque optimization set and flux linkage optimization set respectively. Step 2-2: Calculate the cross error. Calculate the cross error between the normalized flux linkage error and the minimum flux linkage error corresponding to each stator voltage vector in the preferred torque set. At the same time, calculate the cross error between the normalized torque error and the minimum torque error corresponding to each stator voltage vector in the preferred flux linkage set. Then select the stator voltage vector with the smallest cross error as the optimal voltage vector. Step 3: Input the optimal voltage vector into the two-level three-phase inverter, and output it to the permanent magnet synchronous motor through the conversion of the two-level three-phase inverter.

2. The predictive control method for a permanent magnet synchronous motor based on cross-optimization according to claim 1, characterized in that: The stator voltage vector output by the two-level three-phase inverter and the stator current vector Each is obtained through a sliding mode observer in real time. The stator flux value at a given time is used as a prediction. Stator flux at time +1 The basic input for torque at time +1.

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