A double vector model predictive control method and system for a brushless direct current motor

Abstract

The application discloses a double-vector model predictive control method and system for a brushless direct current motor, and comprises the following steps: establishing a mathematical model for the brushless direct current motor with back electromotive force waveforms similar to sine waves; obtaining a current prediction model by using a forward Euler method; obtaining d, q axis reference voltages according to a zero beat theory; and finally, obtaining current reference values at a (k+1) time point by using a Lagrange extrapolation method. On the basis of a classical double-vector model prediction, the sine theorem is used to consider the error of a reference voltage vector and an actual double-vector combined track, and the minimum error combination is selected as the best actual output vector combination. By substituting the current prediction formula of the selected optimal double-vector combination into a value function and solving the minimum result, the optimal action time of two vectors in a cycle is obtained.

Description

Technical Field

[0001] This invention relates to a control method for a brushless DC motor, and more particularly to a dual-vector model predictive control method and system for a brushless DC motor. Background Technology

[0002] Traditional brushless DC motors (BLDCMs) are controlled using square wave drive. However, the structural design of small and medium-power brushless DC motors typically uses short-pitch fractional-slot windings. The back electromotive force waveform of these motors is closer to a sine wave. If square wave current drive is still used, it will generate large commutation torque ripples, causing motor vibration and increased noise. Existing sinusoidal current drive uses vector control, which is a control system composed of several cascaded PI controllers. While relatively easy to implement, ensuring that each controller is optimal is quite difficult. Furthermore, the linear characteristics of PI controllers result in insufficient accuracy, making it difficult to meet the high-performance requirements of brushless DC motor control systems. Model Predictive Control (MPC), on the other hand, can replace several cascaded PI controllers with a single model predictive control unit, and can perform rolling optimization in each sampling period to ultimately achieve optimal control.

[0003] Classical two-vector model predictive current control (FCS-MPC) predicts current by traversing all 49 possible combinations of dual voltage vectors for the three-phase VSI and finding the optimal vector combination based on the application time. This results in superior dynamic response performance. However, FCS-MPC has limitations. First, only one switching state applies to the VSI within a single sampling period. Changes in the switching state can cause significant current fluctuations, affecting the steady-state performance of the entire system. Second, the exhaustive method employed introduces a large computational load, impacting control system performance. While FCS-MPC offers significant advantages in dynamic response performance, it also has limitations. Although it effectively improves control accuracy, it leads to a significant increase in computation. This high computational load can cause delays in real-time control, affecting the system's response speed and overall performance. This is largely due to the algorithm's requirement to traverse all 49 possible combinations of dual voltage vectors for the three-phase VSI, necessitating substantial computation. Furthermore, while using simplified calculation methods can reduce computation, it often sacrifices efficiency and performance, leading to decreased control accuracy. Summary of the Invention

[0004] Purpose of the invention: To address the above problems, this invention proposes a dual-vector model predictive control method and system for brushless DC motors, which improves computational efficiency, reduces computational load, maintains control accuracy, and avoids performance loss caused by simplifying the calculation method.

[0005] Technical Solution: The technical solution adopted in this invention is a dual-vector model predictive control method for brushless DC motors, comprising the following steps:

[0006] Step 1: Establish a mathematical model for a brushless DC motor with a back electromotive force waveform similar to a sine wave.

[0007] Step 2: Based on the mathematical model of the brushless DC motor, obtain the current prediction model using the forward Euler method; based on the current prediction model, obtain the d and q axis reference voltages using the deadbeat theory; during the calculation of the d and q axis reference voltages, the current reference value at time (k+1) is obtained using the Lagrange extrapolation method.

[0008] Step 3: Based on the d and q axis reference voltages, synthesize a reference voltage vector; construct a vector space based on the trajectory of the actual output dual-vector synthesized voltage vector, and divide the vector space into multiple sub-regions; determine the region in the vector space where the synthesized reference voltage vector falls; output the optimal dual-vector combination based on the region in the vector space where the synthesized reference voltage vector falls.

[0009] Step 4: Based on the optimal combination of two vectors, solve for the optimal action time of the two vectors within one cycle when the value function is minimized.

[0010] Any mathematical model of a brushless DC motor can be used. In this scheme, the preferred mathematical model for a brushless DC motor is:

[0011]

[0012] In the formula, u d u q These are the stator d-axis and q-axis voltage components, respectively; i d i q These are the stator d-axis and q-axis current components, respectively; R s L is the stator resistance of the motor. s For stator inductance; ω n This refers to the angular velocity of the motor. t represents the permanent magnet flux linkage of the motor; t represents time.

[0013] Furthermore, by discretizing the above equation using the first-order forward Euler method, the predicted current model can be obtained:

[0014]

[0015] In the formula, T s i represents the sampling period of the control system. d (k), i q (k) represent the current sampling period values ​​of the stator d-axis and q-axis currents, respectively, i d(k+1),i q (k+1) represent the predicted values ​​of the stator d-axis and q-axis currents for the next sampling period, respectively; u d (k), u q (k) represents the current sampling period value of the stator d-axis and q-axis voltages, respectively.

[0016] Based on the current prediction model, the d-axis and q-axis reference voltages are obtained using the deadbeat theory, and the calculation formula is as follows:

[0017]

[0018] In the formula, The stator d-axis and q-axis reference voltages, These are the reference values ​​for the stator current along the d and q axes at time k+1, respectively. These are the reference current values ​​for the stator d-axis and q-axis at time k, respectively.

[0019] In the calculation of the d-axis and q-axis reference voltages, the current reference value at time (k+1) is obtained using the Lagrange extrapolation method, and the calculation formula is as follows:

[0020]

[0021] In the formula, These are the reference values ​​for the stator current along the d and q axes at time k-1, respectively. These are the reference current values ​​for the stator d-axis and q-axis at time k-2, respectively.

[0022] A vector space is constructed based on the trajectory of the voltage vector synthesized from the actual output dual vectors. The vector space is divided into multiple sub-regions, including: the trajectory of the voltage vector synthesized from the actual output dual vectors forms a hexagonal space; the center point of the hexagon is connected to each vertex, and each vertex is connected to other vertices. Each of the 18 connecting lines is a combination of voltage vectors; the vector space is divided into a triangular region every 60° starting from u1(100). In the four regions divided by the connecting lines in the triangular region, the angle lines of the angles formed by the intersection of each of the two voltage vector combinations intersect at a point. The four regions are further divided into multiple sub-regions; the triangular region is divided into a total of 14 sub-regions.

[0023] Determining the region in vector space where the synthesized reference voltage vector falls includes the following steps:

[0024] (1) Calculate the phase angle of the reference voltage vector and determine the triangular region where the end of the reference voltage vector is located based on the phase angle of the reference voltage vector;

[0025] (2) Determine the approximate range of the triangular region where the end of the reference voltage vector is located, including:

[0026] If the complementary angle of the phase angle of the reference voltage vector divided by an integer multiple of 60° is between 0° and 30°, then by comparing the length of the reference voltage vector with L... N1 and L N2 Based on the magnitude relationship, determine the approximate range of the triangular region where the end of the reference voltage vector is located; the approximate range of the triangular region includes: regions N_0 and N_1, regions N_2, N_3 and N_4, and regions N_5 and N_6;

[0027] like Greater than L N1 And less than L N2 Then it is determined that the end of the reference voltage vector is in regions N_2, N_3, and N_4, such as... Less than L N1 Then it is determined that the end of the reference voltage vector is in the N_0 and N_1 regions, such as Greater than L N2 Then it is determined that the end of the reference voltage vector is in the N_5 and N_6 regions; The length of the reference voltage vector;

[0028] L N1 and L N2 The formula for calculation is:

[0029]

[0030] Among them, L N1 L is the distance from the origin to the intersection of the boundary line between regions N_1 and N_2 and the reference voltage vector. N2 The distance from the origin to the intersection of the boundary line between regions N_4 and N_5 and the reference voltage vector; U dc It is the DC bus voltage, θ′ is the phase angle of the reference voltage vector; M = 1 to 6, used for sector counting;

[0031] (3) Determine the location of the sub-region where the end of the reference voltage vector is located, including:

[0032] If the reference voltage vector ends in the N_0 and N_1 regions, Then it is determined that the end of the reference voltage vector is in the N_0 region. Then it is determined that the end of the reference voltage vector is in region N_1;

[0033] The reference voltage vector ends in regions N_2, N_3, and N_4, if and Then determine that the end of the reference voltage vector is in region N_2; if and Then determine that the end of the reference voltage vector is in region N_3; if and Then it is determined that the end of the reference voltage vector is in region N_4;

[0034] The reference voltage vector ends in the N_5 and N_6 regions, if Then it is determined that the end of the reference voltage vector is in region N_5. Then it is determined that the end of the reference voltage vector is in region N_6;

[0035] L N11 L N2 L N22 L N23 L N31 The formula for calculation is:

[0036]

[0037] In the formula, L N1 L is the distance from the origin to the intersection of the boundary line between regions N_0 and N_1 and the reference voltage vector. N21 L is the distance from the origin to the intersection of the boundary line between regions N_2 and N_3 and the reference voltage vector. N22 L is the distance from the origin to the intersection of the boundary line between regions N_2 and N_4 and the reference voltage vector. N2 L is the distance from the origin to the intersection of the boundary line between regions N_3 and N_4 and the reference voltage vector. N31 The distance from the origin to the intersection of the boundary line between regions N_5 and N_6 and the reference voltage vector.

[0038] Based on the region in the vector space where the synthesized reference voltage vector falls, the optimal dual-vector combination is output through the corresponding vector selection table for the sub-region.

[0039] The value function is:

[0040]

[0041] s.tu s (k)∈{u1,u2,…,u7,u8}

[0042] In the formula, These are the reference values ​​for the d-axis and q-axis currents of the motor stator, respectively. s (k) is the voltage vector at time k;

[0043] u1, u2, ..., u6 are the effective voltage vectors used to synthesize the actual output voltage vector; u7 and u8 are two zero vectors. d (k+1),i q (k+1) are the predicted values ​​of the stator d-axis and q-axis currents in the next sampling period, respectively.

[0044] i d (k+1),iq The formula for calculating (k+1) is:

[0045] i d (k+1)=i d (k)+i′ d1 (k)t act1 +i′ d2 (k)(T con -t act1 )

[0046] i q (k+1)=i q (k)+i′ q1 (k)t act1 +i′ q2 (k)(T con -t act1 )

[0047] In the formula, i d (k), i q (k) represents the current sampling period values ​​of the stator d-axis and q-axis currents, respectively; T con The system control cycle; t nct1 Let t be the duration of the first voltage vector in the optimal dual-vector combination within one control cycle, then the duration of the second voltage vector is t. act2 For T con -t act1 ;i′ d1 (k), i′ q1 (k) represents the ramp component caused by the first voltage vector d-axis and q-axis components, i′ d2 (k), i′ q2 (k) represents the ramp component caused by the d and q-axis components of the second voltage vector, respectively, and is calculated as follows:

[0048]

[0049] In the formula, i′ dn (k), i′ qn (k) represents the ramp component caused by the d-axis and q-axis components of the nth voltage vector in the optimal two-vector combination, u dn u qn R represents the d-axis and q-axis components of the voltage vector in the optimal two-vector combination, and n represents the nth voltage vector in the optimal two-vector combination. s L is the stator resistance of the motor. s For stator inductance; ω n This refers to the angular velocity of the motor. It is a permanent magnet flux linkage for motors.

[0050] This invention proposes a dual-vector model predictive control system for a brushless DC motor, comprising:

[0051] The reference voltage vector calculation unit is used to: calculate the d-axis and q-axis reference voltages based on the current prediction model; during the calculation of the d-axis and q-axis reference voltages, the current reference value at time (k+1) is obtained using the Lagrange extrapolation method; and synthesize the reference voltage vector based on the d-axis and q-axis reference voltages.

[0052] The region determination unit is used to: construct a vector space based on the trajectory of the actual output dual-vector synthesized voltage vector, divide the vector space into multiple sub-regions, and determine the region in the vector space where the synthesized reference voltage vector falls;

[0053] Select the voltage vector combination unit to: output the optimal dual-vector combination based on the region in the vector space where the synthesized reference voltage vector falls;

[0054] The optimal action time calculation unit is used to: solve for the optimal action time of the two vectors within one period when the value function is minimized based on the optimal combination of two vectors;

[0055] The pulse generator sends corresponding control switch states to the inverter based on the optimal dual-vector combination and the optimal action time of the two vectors within one cycle. Finally, the inverter sends the input voltage to control the brushless DC motor.

[0056] Beneficial Effects: Compared with existing technologies, this invention has the following advantages: This invention proposes a reference vector judgment algorithm for dual-vector model predictive current control of brushless DC motors, which simplifies the selection of the optimal vector combination and the calculation of the action time of each vector in dual-vector model predictive current control of brushless DC motors with back EMF waveforms similar to sine waves, while maintaining control accuracy. Based on the classic dual-vector model predictive current control of brushless DC motors, this invention reduces the original forty-nine prediction calculations to only two reference vector judgment calculations to achieve the desired control effect. This invention compares the actual output voltage trajectory of the dual-vector combination, and the control accuracy is basically consistent with the classic dual-vector model predictive current method. Attached Figure Description

[0057] Figure 1 This is an overall block diagram of the dual-vector model predictive control system for the brushless DC motor described in this invention;

[0058] Figure 2 This is the actual voltage vector combination output trajectory diagram described in this invention;

[0059] Figure 3 This is a schematic diagram of the first sector division of the voltage vector according to the present invention;

[0060] Figure 4 This is a comparison diagram of the reference vector error of the first sector as described in this invention;

[0061] Figure 5 These are the stator current and torque waveforms of a brushless DC motor simulated using the dual-vector model predictive control and classical single-vector model predictive control described in this invention.

[0062] Figure 6 This is a comparison chart of simulated speeds of brushless DC motors using the dual-vector model predictive control described in this invention and the classical single-vector model predictive control.

[0063] Figure 7 This is a simulation diagram of the A-phase current and its harmonics of a brushless DC motor using the dual-vector model predictive control and classical single-vector model predictive control described in this invention. Detailed Implementation

[0064] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0065] Example 1

[0066] The dual-vector model predictive control method for brushless DC motors described in this invention includes the following steps:

[0067] Step 1: Establish a mathematical model for a brushless DC motor with a back electromotive force waveform similar to a sine wave.

[0068] Step 2: Use forward Euler to obtain the current prediction model, obtain the d and q axis reference voltages based on the deadbeat theory, and finally use the Lagrange extrapolation method to obtain the current reference value at time (k+1).

[0069] Step 3: Based on the prediction of the classic two-vector model, the sine theorem is used to consider the error between the reference voltage vector and the actual two-vector combination trajectory, and the combination with the smallest error is selected as the best actual output vector combination.

[0070] Step 4: By substituting the current prediction formula of the selected optimal dual-vector combination into the value function and solving for the minimum result, the optimal action time of the two vectors within one cycle is obtained.

[0071] The main steps are further explained below.

[0072] Firstly, for brushless DC motors with back EMF waveforms resembling sine waves, the mathematical model can be referenced from PMSM and idealized, with the following assumptions: the stator windings are connected in a star configuration, and the three-phase windings are spatially distributed at 120° electrical angles; the saturation effect of the stator core is ignored, and the air gap magnetic field between the stator and rotor is sinusoidally distributed; the hysteresis and turbine losses of the stator and rotor are ignored, and there is no damping effect between the rotor and the permanent magnet.

[0073] In an ideal state, the mathematical model of a surface-mounted BLDCM in a synchronous rotating coordinate system has the following stator voltage equation:

[0074]

[0075] In the above formula: u d u q Each represents the d-axis and q-axis voltage components of the stator; i d i q Each represents the stator d-axis and q-axis current components; R s L is the stator resistance of the motor. s For stator inductance; ω n This refers to the angular velocity of the motor. It is a permanent magnet flux linkage for motors.

[0076] Based on the stator voltage equation, the motor current i is selected. d i q Assuming the state variables are defined, the state equations for BLDCM are obtained as follows:

[0077]

[0078] Discretizing the above equation using the first-order forward Euler method yields the predicted current model:

[0079]

[0080] T s i represents the sampling period of the control system. d (k), i q (k), i d (k+1),i q (k+1) represents the current sampling period value and the predicted value for the next sampling period of the stator d-axis and q-axis currents; u d (k), u q (k) represents the current sampling period of the stator d-axis and q-axis voltages.

[0081] The core concept of the classic MPCC (Multi-Level Capacitor) is to select the voltage vector that minimizes the error between the d-axis and q-axis currents and the reference given current through a value function. The deviation between the stator d-axis and q-axis currents and the reference given current is used as an indicator. The value functions of the motor stator d-axis and q-axis current feedback obtained under different vectors are compared to determine the optimal value. The formula is as follows:

[0082]

[0083] In the above formula, These are the reference values ​​for the d-axis and q-axis currents of the motor stator (i = 1, 2, ..., 7, 8). s(k) is the voltage vector at time k under different switching states; u1, u2, ..., u6 are effective voltage vectors; u7 and u8 are two zero vectors. The d-axis and q-axis currents are predicted for these 8 switching states respectively. The predicted results are substituted into equation (4) for comparison. The voltage vector with the smallest CE is set as the optimal voltage vector, and the optimal switching state is finally output.

[0084] This invention, based on classical model predictive current control theory, proposes a control algorithm that selects two voltage vectors acting together within one sampling period. According to equation (3), the stator d-axis and q-axis current prediction model of the motor shows that:

[0085]

[0086] Based on the theory of deadbeat control, let Then there is and It can be known that:

[0087]

[0088] Among them and The stator d-axis and q-axis reference voltages are combined into a reference voltage vector. Again The location is used to make a judgment. In traditional processing, the reference value can be approximated as... and However, this results in a one-beat delay in the reference signal. To address this issue, consider using a Lagrange extrapolation method to obtain the current reference value for (k+1):

[0089]

[0090] The adopted control strategy is dual-vector model predictive control, where only two voltage vectors act within each control cycle. This can be a single effective voltage vector, two effective voltage vectors, or a combination of one effective voltage vector and a zero vector. Due to time constraints, the actual output composite voltage vector trajectory of the DV-MPCC should exhibit a specific star-shaped trajectory. To select suitable voltage vectors while considering algorithm complexity, this invention determines the composite reference voltage vector based on the specific trajectory of the actual output composite voltage vector. The specific region to be located determines the selection of the two voltage vectors to be output.

[0091] like Figure 2 As shown, the actual output composite voltage vector trajectory is divided into six regions starting from u1(100) and every 60°. Figure 3Taking sector I as an example, sector I is divided into 14 sub-sectors: I_0, I_1, I_2...I_13. The other five sectors are similar to sector I. Therefore, the entire voltage plane is divided into 6 major sectors and 84 sub-sectors. The goal of sub-sector division is to ensure that each sub-sector has a unique trajectory with the shortest error distance. The division principle utilizes the angle bisector (dashed line) formed by the intersection of the straight trajectories of the combined voltage vectors. According to the property of the angle bisector, each point on the bisector is equidistant from both sides of the angle. That is, the regions on both sides of the bisector are closest to the two sides of the corresponding angle (i.e., the trajectory of the combined voltage vector). The regions are evenly divided starting from the corresponding angle. Thus, each sub-sector divided by the dashed bisector corresponds to a unique voltage vector combination with the smallest error. By simply determining the sub-sector where the voltage reference point is located, the optimal voltage vector combination can be directly selected. Then, by combining the calculation of the time allocation of the two voltage vector combinations, the optimal point of action in the trajectory of the optimal action voltage vector combination within the current control cycle can be selected, that is, the point in the trajectory of the optimal action voltage vector combination with the smallest error from the voltage reference point.

[0092] Assuming a synthesized reference voltage vector Located in I_6 zone, such as Figure 4 (a) Error voltage vector Δu (at this time Δu is The assigned value of ) is greater than u1 and The minimum error d0 between the two indicates that the DV-MPCC has better control accuracy compared to the classic single-vector MPCC. Figure 4 middle The perpendicular distance d1 between the composite trajectory of u1 and u2 The perpendicular distance d2 between the composite trajectory of u3 and u1, where in Figure 4 In (a), among d0, d1, and d2, d1 is the smallest, indicating that at this time... When the voltage reference point is in this sub-region, the optimal voltage vector combination should be u1 and u2. The selection of the optimal voltage vector combination changes when the voltage reference point crosses a certain dotted line, i.e., when the voltage reference point is in another sub-region. Figure 4 In (b), d2 is at its minimum at this point, and the optimal voltage vector combination should be u1 and u3. Similarly, when When located in sub-regions I_0, I_1, and I_3, the vector combinations are u1 and u8, u2 and u6, and u1 and u8, respectively.

[0093] To determine which sub-region the voltage reference point is in, first define the distance K from the origin to the boundary between regions N_1 and N_2 based on the reference voltage angle and along the reference voltage direction. N1 The distance to the boundary between region N_4 and region N_5 is K. N2 (N = I, II...VI are used for sector counting), according to the law of sines:

[0094]

[0095] Among them U dc This is the DC bus voltage, M = 1 to 6, corresponding to the first to sixth sectors. For example, if N is sector I, then M is 1. First, The phase angle θ is replaced by θ′ in the formula and divided by k60° (k is any integer). When the complementary angle is between 0° and 30°, it is compared... With L N1 and L N2 First determine the size relationship. Which approximate region among N_0 and N_1, N_2 and N_3 and N_4, N_5 and N_6 does it fall into? For example... Greater than L N1 And less than L N2 Then determine at this time It lies within the approximate region of N_2, N_3, and N_4. After determining the approximate region, then... Perform detailed region determination. Let L be the distance from the origin to the boundary line between N_0 and N_1. N11 The distance to the boundary between N_2 and N_3 is L. N21 The distance to the boundary between N_2 and N_4 is L. N22 The distance to the boundary between region N_3 and region N_4 is L. N2 The distance to the boundary between N_5 and N_6 is L. N31 According to the Law of Sines:

[0096]

[0097] When the previous step determines When in regions N_0 and N_1, by comparison With L N11 Relationship determination Specifically, which sub-region it is located in, such as If the voltage is in region N_0, then u1 and u8 are chosen as the optimal voltages. When the voltage is roughly in regions N_2, N_3, and N_4, a comparison is needed. With L N2 L N22 L N23 Relationship judgment. When and <L N22 When it is determined that the region is N_2, u2 and u6 are selected. and If the condition is in region N_3, select u1 and u8. and If the condition is determined to be in region N_4, then u1 and u3 are selected. When the determination is... When the area is roughly between N_5 and N_6, the method for determining its location is similar to that for the area between N_0 and N_1. With L N31 Comparison. When θ′ divided by k60°, the complementary angle is between 30° and 60°, the judgment method is similar to that for 0° to 30°. The table below shows the vector combinations corresponding to each sub-region of sector I.

[0098] Table 1 Sub-region Corresponding Vector Selection Table

[0099]

[0100]

[0101] The current predicted by the two-vector model for the next control cycle can be expressed as:

[0102]

[0103] In this context, T con To control the period, t act1 Let t be the duration of the first voltage vector in one control cycle, then the duration of the second voltage vector is... act2 For T con -t act1 i′ d1 (k), i′ q1 (k), i′ d2 (k), i′ q2 (k) represents the ramp components caused by the d-axis and q-axis components of the two voltage vectors, respectively. The following can be calculated:

[0104]

[0105] Where: n = 1, 2; u dn u qn These are the d-axis and q-axis voltage vectors output from the selected two voltage vector switching states.

[0106] Substituting formula (10) into the model prediction value function formula (4), we can find the action time of each vector corresponding to the minimum result of the value function. After substitution, we obtain a new function CE(t). act1 And it is a quadratic function in one variable, and in a rectangular coordinate system, the curve opens upwards and has a minimum value, such that:

[0107]

[0108] By solving the above formula, we can find that:

[0109]

[0110] 1) When Tcon >t act1 >0, function CE(t) act1 The minimum value of ) is located in (0,T) con Therefore, the minimum value of CE in this interval is the minimum value, and at this time there are two voltage vectors acting within one control cycle.

[0111] 2) When 0 > t act1 The function CE(t) act1 The minimum value of ) is in (0,T) con To the left of the interval, make t act1 =0, and the minimum value CE(0) can be obtained. At this time, there is only one second voltage vector acting within one control cycle.

[0112] 3) When t act1 >T con The function CE(t) act1 The minimum value of ) is in (0,T) con To the right of the interval, make t act1 =T con The minimum value CE(T) can be obtained. con At this point, only one first voltage vector acts within one control cycle.

[0113] In this way, the actual output vectors and their respective optimal action times are selected from the optimal vector combinations.

[0114] Example 2

[0115] The control block diagram of the dual-vector model predictive control system described in this invention is as follows: Figure 1 As shown, it includes:

[0116] The reference voltage vector calculation unit is used to: calculate the d-axis and q-axis reference voltages based on the current prediction model; during the calculation of the d-axis and q-axis reference voltages, the current reference value at time (k+1) is obtained using the Lagrange extrapolation method; and synthesize the reference voltage vector based on the d-axis and q-axis reference voltages.

[0117] The region determination unit is used to: construct a vector space based on the trajectory of the actual output dual-vector synthesized voltage vector, divide the vector space into multiple sub-regions, and determine the region in the vector space where the synthesized reference voltage vector falls;

[0118] Select the voltage vector combination unit to: output the optimal dual-vector combination based on the region in the vector space where the synthesized reference voltage vector falls;

[0119] The optimal action time calculation unit is used to: solve for the optimal action time of the two vectors within one period when the value function is minimized based on the optimal combination of two vectors;

[0120] The pulse generator obtains the corresponding control switch state based on the optimal dual-vector combination and the optimal action time of the two vectors within one cycle, and sends it to the inverter.

[0121] An inverter controls the input voltage of a brushless DC motor.

[0122] Experimental verification:

[0123] To verify the effectiveness of the designed dual-vector model predictive current control algorithm, a brushless DC motor model predictive control system was built in the Matlab / Simulink environment and simulation experiments were conducted. The brushless DC motor parameters used in the simulation are given in the table below. The control frequency of the model was set to 10kHz, U... dc It is 310V.

[0124] Table 2 Motor Parameters

[0125]

[0126] Figure 5 The simulation results for the A-phase current, motor speed, and torque waveforms of the classic single-vector MPCC strategy and the DV-MPCC strategy designed in this paper are presented respectively. The simulation experiment is set as follows: the brushless DC motor starts under no-load at 0s with a given speed of 1 / 4 of the rated speed; at 0.2s, the speed stepwise changes to 1 / 2 of the rated speed; at 0.4s, the rated load is instantaneously applied; at 0.6s, the speed setpoint abruptly changes to the rated speed; and the simulation ends at 1s. Figure 5 The results show that, under the same operating conditions, MPCC possesses excellent dynamic and static performance, while the torque ripple of the classic single-vector MPCC is significantly greater than that of the DV-MPCC. This indicates that the classic MPCC, with only one voltage vector acting within a control cycle, may experience under- or over-regulation in current tracking. By selecting a suitable dual-vector combination, torque ripple can be effectively reduced, with a more pronounced effect when encountering sudden load changes, demonstrating that the latter has better anti-interference capabilities than the former. Figure 6 To compare the speed response of the two strategies under simulation conditions, during the 0s-0.4s no-load operation and speed step transition, the DV-MPCC responds to the speed step faster than the classic MPCC, while exhibiting smaller overshoot. When the rated load is applied at 0.4s, the former shows less speed oscillation and recovers speed more quickly. When the speed steps from rated load to rated speed at 0.6s, the DV-MPCC demonstrates a significant dynamic response advantage, reaching the target speed faster than the classic MPCC, while also exhibiting smaller steady-state error. Overall, the DV-MPCC control strategy outperforms the classic MPCC in both motor dynamic response and load capacity, better adapting to load changes and achieving stable operation. Figure 7Steady-state current analysis of the two MPC strategies under rated motor operating conditions shows that the harmonic distortion rate of phase A current is reduced from 8.32% (classical MPCC) to 2.30% (using DV-MPCC). This indicates that DV-MPCC provides more precise current regulation, responds faster to load changes, and reduces harmonic generation compared to classical MPCC. This invention proposes a dual-vector model predictive current control strategy for brushless DC motors based on classical MPCC. This method re-divides the voltage vector plane based on the actual output synthetic voltage vector trajectory, predicts the voltage vector combination and its duration for the next cycle based on a given reference voltage vector, significantly improving the target current control accuracy. DV-MPCC effectively reduces motor current harmonics and torque ripple. In terms of control strategy, this method does not require enumerating all switching states and continuously evaluating the value function; instead, it selects vector combinations by determining the region where the reference voltage vector is located. Simulation results show that the proposed control strategy exhibits excellent dynamic and static performance over a wide speed range. By comparing the classic MPCC with the DV-MPCC, the latter has better motor dynamic response and efficiency.

Claims

1. A two-vector model predictive control method for a brushless DC motor, characterized in that: Includes the following steps: Step 1: Establish a mathematical model for a brushless DC motor with a back electromotive force waveform similar to a sine wave. Step 2: Based on the mathematical model of the brushless DC motor, obtain the current prediction model using the forward Euler method; based on the current prediction model, obtain the d and q axis reference voltages using the deadbeat theory; during the calculation of the d and q axis reference voltages, the current reference value at time (k+1) is obtained using the Lagrange extrapolation method. Step 3: Based on the d-axis and q-axis reference voltages, synthesize a reference voltage vector; construct a vector space based on the trajectory of the actual output dual-vector synthesized voltage vector, and divide the vector space into multiple sub-regions; determine the region in the vector space where the synthesized reference voltage vector falls. Based on the region in the vector space where the synthesized reference voltage vector falls, the optimal combination of two vectors is output. The method described above involves constructing a vector space based on the trajectory of the voltage vector synthesized from the actual output dual vectors, and dividing the vector space into multiple sub-regions. This includes: the trajectory of the voltage vector synthesized from the actual output dual vectors forming a hexagonal space; the center point of the hexagon being connected to each vertex, and each vertex being connected to all other vertices, with each of the 18 lines forming a voltage vector combination; and then dividing the vector space into... Starting from (100), a triangular region is divided every 60°. In the four regions divided by the connecting lines of the triangular region, the angle lines of the angles formed by the intersection of the two voltage vector combinations intersect at a point, and the four regions are further divided into multiple sub-regions; the triangular region is divided into a total of 14 sub-regions. The determination of the region in the vector space where the synthesized reference voltage vector falls includes the following steps: (1) Calculate the phase angle of the reference voltage vector, and determine the triangular region where the end of the reference voltage vector is located based on the phase angle of the reference voltage vector; (2) Determine the range of the triangular region where the end of the reference voltage vector is located, including: If the complementary angle of the phase angle of the reference voltage vector divided by an integer multiple of 60° is between 0° and 30°, then by comparing the length of the reference voltage vector with... and Based on the magnitude relationship, the range of the triangular region where the end of the reference voltage vector is located is determined; the range of the triangular region includes: for the sub-region between 0° and 30° in the vector space, 7 regions are defined from the inside out, namely... ~ area; If | |greater than and less than Then determine that the end of the reference voltage vector is at and and Region, if | |less than Then determine that the end of the reference voltage vector is at and Region, if | |greater than Then determine that the end of the reference voltage vector is at and Region; | | represents the length of the reference voltage vector; and The formula for calculation is: ； ； in, for district and The distance from the origin to the intersection of the boundary line of the region and the reference voltage vector. for district and The distance from the origin to the intersection of the boundary line of the zone and the reference voltage vector; It is the DC bus voltage. The phase angle of the reference voltage vector; M = 1~6, corresponding to the first to sixth sectors; (3) Determine the location of the sub-region where the end of the reference voltage vector is located, including: The reference voltage vector is at the end and Region, if | |< Then determine that the end of the reference voltage vector is at District, | |> Then determine that the end of the reference voltage vector is at district; The reference voltage vector is at the end and and Region, if | |< And| |< Then determine the end of the reference voltage vector at District; if | |> And| |< Then determine the end of the reference voltage vector at District; if | |> And| |> Then determine the end of the reference voltage vector at district; The reference voltage vector is at the end and Region, if | |< Then determine that the end of the reference voltage vector is at District, | |> Then determine that the end of the reference voltage vector is at district; , , , , The formula for calculation is: ； ； ； ； ； In the formula, for district and The distance from the origin to the intersection of the boundary line of the region and the reference voltage vector. for district and The distance from the origin to the intersection of the boundary line of the region and the reference voltage vector. for district and The distance from the origin to the intersection of the boundary line of the region and the reference voltage vector. for district and The distance from the origin to the intersection of the boundary line of the region and the reference voltage vector. for district and The distance from the origin to the intersection of the boundary line of the zone and the reference voltage vector; Step 4: Based on the optimal combination of two vectors, solve for the optimal action time of the two vectors within one cycle when the value function is minimized.

2. The two-vector model predictive control method for brushless DC motors according to claim 1, characterized in that: The mathematical model for a brushless DC motor is as follows: ； In the formula, , stator , Axis voltage components; , stator Axis current components; This refers to the stator resistance of the motor. For stator inductance; This refers to the angular velocity of the motor. t represents the permanent magnet flux linkage of the motor; t represents time.

3. The dual-vector model predictive control method for brushless DC motors according to claim 2, characterized in that: Discretizing the above equation using the first-order forward Euler method yields the predicted current model: ； ； In the formula, The sampling period of the control system; , stator , Current sampling period value of shaft current , stator , Predicted value of shaft current in the next sampling period; , stator , The current sampling period value of the shaft voltage.

4. The two-vector model predictive control method for brushless DC motors according to claim 3, characterized in that: Based on the current prediction model, the d-axis and q-axis reference voltages are obtained using the deadbeat theory, and the calculation formula is as follows: ； ； In the formula, , For stator , Shaft reference voltage, , Stator at time k+1 , Shaft current reference value, , Stator at time k , Reference value for shaft current.

5. The dual-vector model predictive control method for brushless DC motors according to claim 4, characterized in that: In the calculation of the d-axis and q-axis reference voltages, the current reference value at time (k+1) is obtained using the Lagrange extrapolation method, and the calculation formula is as follows: ； ； In the formula, , Stator at time k-1 , Shaft current reference value, , Stator at time k-2 , Reference value for shaft current.

6. The two-vector model predictive control method for brushless DC motors according to claim 1, characterized in that: The value function is: ； s.t ; In the formula, , stator , Predicted value of shaft current in the next sampling period; , These are the motor stator , Reference value for shaft current. It is the voltage vector at time k; This is the effective voltage vector used to synthesize the actual output voltage vector; There are two zero vectors.

7. The two-vector model predictive control method for brushless DC motors according to claim 1, characterized in that: stator , The formula for calculating the predicted value of the shaft current in the next sampling period is: ； ； In the formula, , stator , Current sampling period value of shaft current; For system control cycle; Let the duration of the first voltage vector in the optimal dual-vector combination be the duration of action of the second voltage vector within one control cycle. for ; , Represents the first voltage vector , The oblique wave component caused by the axial component. , The second voltage vector , The slope component caused by the axial component is calculated as follows: ； ； In the formula, , Represents the nth voltage vector in the optimal two-vector combination. , The oblique wave component caused by the axial component. , Represents the voltage vector in the optimal two-vector combination. , Axis component, n represents the nth voltage vector in the optimal two-vector combination; This refers to the stator resistance of the motor. For stator inductance; This refers to the angular velocity of the motor. It is a permanent magnet flux linkage for motors.

8. The two-vector model predictive control method for brushless DC motors according to claim 1, characterized in that: Based on the region in the vector space where the synthesized reference voltage vector falls, the optimal dual-vector combination is output through the corresponding vector selection table for the sub-region.

9. A dual-vector model predictive control system for a brushless DC motor, characterized in that, include: The reference voltage vector calculation unit is used to calculate the d-axis and q-axis reference voltages based on the current prediction model. In the calculation of the d and q axis reference voltages, the current reference value at time (k+1) is obtained by Lagrange extrapolation. Based on the d-axis and q-axis reference voltages, synthesize the reference voltage vector; The region determination unit is used to: construct a vector space based on the trajectory of the actual output dual-vector synthesized voltage vector, divide the vector space into multiple sub-regions, and determine the region in the vector space where the synthesized reference voltage vector falls; Select the voltage vector combination unit to: output the optimal dual-vector combination based on the region in the vector space where the synthesized reference voltage vector falls; The optimal action time calculation unit is used to: solve for the optimal action time of the two vectors within one period when the value function is minimized based on the optimal combination of two vectors; The pulse generator obtains the corresponding control switch state based on the optimal dual-vector combination and the optimal action time of the two vectors within one cycle, and sends it to the inverter. Inverter, which controls the input voltage of a brushless DC motor; The method described above involves constructing a vector space based on the trajectory of the voltage vector synthesized from the actual output dual vectors, and dividing the vector space into multiple sub-regions. This includes: the trajectory of the voltage vector synthesized from the actual output dual vectors forming a hexagonal space; the center point of the hexagon being connected to each vertex, and each vertex being connected to all other vertices, with each of the 18 lines forming a voltage vector combination; and then dividing the vector space into... Starting from (100), a triangular region is divided every 60°. In the four regions divided by the connecting lines of the triangular region, the angle lines of the angles formed by the intersection of the two voltage vector combinations intersect at a point, and the four regions are further divided into multiple sub-regions; the triangular region is divided into a total of 14 sub-regions. The determination of the region in the vector space where the synthesized reference voltage vector falls includes the following steps: (1) Calculate the phase angle of the reference voltage vector, and determine the triangular region where the end of the reference voltage vector is located based on the phase angle of the reference voltage vector; (2) Determine the range of the triangular region where the end of the reference voltage vector is located, including: If the complementary angle of the phase angle of the reference voltage vector divided by an integer multiple of 60° is between 0° and 30°, then by comparing the length of the reference voltage vector with... and Based on the magnitude relationship, the range of the triangular region where the end of the reference voltage vector is located is determined; the range of the triangular region includes: for the sub-region between 0° and 30° in the vector space, 7 regions are defined from the inside out, namely... ~ area; If | |greater than and less than Then determine that the end of the reference voltage vector is at and and Region, if | |less than Then determine that the end of the reference voltage vector is at and Region, if | |greater than Then determine that the end of the reference voltage vector is at and Region; | | represents the length of the reference voltage vector; and The formula for calculation is: ； ； in, for district and The distance from the origin to the intersection of the boundary line of the region and the reference voltage vector. for district and The distance from the origin to the intersection of the boundary line of the zone and the reference voltage vector; It is the DC bus voltage. The phase angle of the reference voltage vector; M = 1~6, corresponding to the first to sixth sectors; (3) Determine the location of the sub-region where the end of the reference voltage vector is located, including: The reference voltage vector is at the end and Region, if | |< Then determine that the end of the reference voltage vector is at District, | |> Then determine that the end of the reference voltage vector is at district; The reference voltage vector is at the end and and Region, if | |< And| |< Then determine the end of the reference voltage vector at District; if | |> And| |< Then determine the end of the reference voltage vector at District; if | |> And| |> Then determine the end of the reference voltage vector at district; The reference voltage vector is at the end and Region, if | |< Then determine that the end of the reference voltage vector is at District, | |> Then determine that the end of the reference voltage vector is at district; , , , , The formula for calculation is: ； ； ； ； ； In the formula, for district and The distance from the origin to the intersection of the boundary line of the region and the reference voltage vector. for district and The distance from the origin to the intersection of the boundary line of the region and the reference voltage vector. for district and The distance from the origin to the intersection of the boundary line of the region and the reference voltage vector. for district and The distance from the origin to the intersection of the boundary line of the region and the reference voltage vector. for district and The distance from the origin to the intersection of the boundary line of the zone and the reference voltage vector.

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