Double-vector model predictive control method and system for brushless direct current motor

Abstract

The invention discloses a double-vector model predictive control method and system for a brushless direct current motor. The method comprises the following steps: establishing a mathematical model of the brushless direct current motor aiming at a back electromotive force waveform similar to a sine wave; a current prediction model is obtained by using forward Euler, reference voltages of a d axis and a q axis are obtained according to a deadbeat theory, and finally a current reference value at a (k + 1) moment is obtained by using a Lagrange extrapolation method. On the basis of classic double-vector model prediction, a sine theorem is utilized to consider errors of a reference voltage vector and an actual double-vector combination trajectory, and a combination with the minimum error is selected as an optimal actual output vector combination; and the selected current prediction formula of the optimal double-vector combination is substituted into the value function, and the minimum result is solved, so that the optimal action time of the two vectors in one period is correspondingly obtained.

Description

Technical Field

[0001] The invention relates to a control method of a brushless DC motor, and in particular to a dual-vector model predictive control method and system for a brushless DC motor. Background Art

[0002] The traditional control method of brushless DC motor (BLDCM) is square wave drive. However, the structural design of small and medium-sized brushless DC motors usually uses short-pitch fractional slot windings. The waveform of the back electromotive force of such motors is closer to a sine wave. If it is still driven by square wave current, it will produce a large commutation torque pulsation, which will cause motor vibration and more noise. The existing sinusoidal current drive uses vector control, and vector control is composed of several PI controllers cascaded into a control system. It is relatively easy to implement, but it is difficult to ensure that each controller is in the optimal state. At the same time, due to the linear characteristics of the PI controller, the accuracy is not high enough, and it is difficult to meet the high performance requirements of the brushless DC motor control system. Model Predictive Control (MPC) can replace several PI controller cascades with a single model predictive control, and can perform rolling optimization in each sampling period to ultimately achieve optimal control.

[0003] Classic dual-vector model predictive current control, which is the classic dual-vector model prediction by traversing all 49 possible dual voltage vector combinations of three-phase VSI and the optimal vector combination of action time, has higher dynamic response performance. FCS-MPC has limitations. First, there is only one switch state acting on the VSI in one sampling cycle. When the switch state changes, it will cause large current fluctuations, which will affect the steady-state performance of the entire system. Secondly, the exhaustive method adopted will bring a large computational load, which will affect the performance of the control system. Although the dual-vector model prediction has significant advantages in dynamic response performance, it also has some limitations. Although it can effectively improve the control accuracy, it leads to a significant increase in the amount of calculation. Such high computational load may cause delays in actual real-time control, affecting the response speed and overall performance of the system. This is largely due to the fact that the algorithm needs to traverse all 49 possible dual voltage vector combinations of three-phase VSI, which requires a lot of calculations. In addition, although the use of ordinary simplified calculation methods can reduce the amount of calculation, it often sacrifices certain efficiency and performance, resulting in a decrease in control accuracy. Summary of the invention

[0004] Purpose of the invention: In view of the above problems, the present invention proposes a dual-vector model predictive control method and system for a brushless DC motor, which improves computational efficiency and reduces the amount of calculation while maintaining control accuracy and avoiding performance loss caused by simplified calculation methods.

[0005] Technical solution: The technical solution adopted by the present invention is a dual-vector model predictive control method for a brushless DC motor, comprising the following steps:

[0006] Step 1, establishing a mathematical model for a brushless DC motor with a back electromotive force waveform similar to a sine wave;

[0007] Step 2, according to the mathematical model of the brushless DC motor, the forward Euler method is used to obtain the current prediction model; according to the current prediction model, the deadbeat theory is used to obtain the d and q axis reference voltages; in the calculation process of the d and q axis reference voltages, the current reference value at the time (k+1) is obtained by the Lagrange extrapolation method;

[0008] Step 3, synthesize a reference voltage vector according to the d and q axis reference voltages; construct a vector space according to the trajectory of the dual-vector synthesized voltage vector actually output, and divide the vector space into multiple sub-regions; determine the region in which the synthesized reference voltage vector falls in the vector space; output the optimal dual-vector combination according to the region in which the synthesized reference voltage vector falls in the vector space;

[0009] Step 4: Based on the optimal dual-vector combination, find the optimal action time of the two vectors in one cycle when the value function is minimized.

[0010] Any mathematical model of a brushless DC motor can be used. The mathematical model of a brushless DC motor preferably used in this solution is:

[0011]

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

[0013] Furthermore, the first-order forward Euler method is used to discretize the above equation to obtain the predicted current model:

[0014]

[0015] Where, T s is the sampling period of the control system; i d (k), i q (k) are the current sampling period values ​​of the stator d and q axis currents, i 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; u d (k),u q (k) are the current sampling period values ​​of the stator d and q axis voltages respectively.

[0016] According to the current prediction model, the deadbeat theory is used to obtain the d and q axis reference voltages. The calculation formula is:

[0017]

[0018] In the formula, is the stator d and q axis reference voltage, are the current reference values ​​of the stator d and q axes at time k+1, are the current reference values ​​of the stator d and q axes at time k respectively.

[0019] Among them, in the calculation process of the d and q axis reference voltages, the current reference value at the time (k+1) is obtained by the Lagrange extrapolation method, and the calculation formula is:

[0020]

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

[0022] A vector space is constructed according to the trajectory of the voltage vector synthesized by the dual vectors that are actually output, and the vector space is divided into a plurality of sub-areas, including: the trajectory of the voltage vector synthesized by the dual vectors that are actually output constitutes a hexagonal space; the center point of the hexagon is connected to each vertex, and each vertex is connected to other vertices, and each of the 18 connecting lines formed is a voltage vector combination; the vector space is divided into a triangular area every 60° with u1 (100) as the starting point, and in the four areas divided by the connecting lines in the triangular area, the angular parallel lines of the angles formed by the intersection of every two voltage vector combinations intersect at one point, and the four areas are divided into a plurality of sub-areas again; the triangular area is divided into a total of 14 sub-areas.

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

[0024] (1) Calculate the phase angle of the reference voltage vector, and determine the triangular area where the end of the reference voltage vector is located according to the phase angle of the reference voltage vector;

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

[0026] If the phase angle of the reference voltage vector is divided by an integer multiple of 60° and the residual angle is between 0° and 30°, by comparing the length of the reference voltage vector with L N1 and L N2 The approximate range of the triangular area where the end of the reference voltage vector is located is determined by the size relationship; the approximate range of the triangular area includes: N_0 and N_1 area, N_2 and N_3 and N_4 area, N_5 and N_6 area;

[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 the N_2, N_3 and N_4 regions, 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 It is then determined that the end of the reference voltage vector is in the N_5 and N_6 regions; is the length of the reference voltage vector;

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

[0029]

[0030] Among them, L N1 is the distance from the intersection of the boundary line between N_1 and N_2 regions and the reference voltage vector to the origin, L N2 is the distance from the intersection of the boundary line between N_4 and N_5 regions and the reference voltage vector to the origin; U dc 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 sub-region location where the end of the reference voltage vector is located, including:

[0032] The reference voltage vector ends are in the N_0 and N_1 regions. If It is determined that the end of the reference voltage vector is in the N_0 region. It is then determined that the end of the reference voltage vector is in the N_1 region;

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

[0034] The reference voltage vector ends are in the N_5 and N_6 regions. If It is determined that the end of the reference voltage vector is in the N_5 region. It is then determined that the end of the reference voltage vector is in the N_6 region;

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

[0036]

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

[0038] According to the area where the synthesized reference voltage vector falls in the vector space, the optimal dual-vector combination is outputted correspondingly through the sub-area corresponding vector selection table.

[0039] The value function is:

[0040]

[0041] s.tu s (k)∈{u1,u2,…,u7,u8}

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

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

[0044] i d (k+1), iq The calculation formula for (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) are the current sampling period values ​​of the stator d and q axis currents respectively; T con is the system control period; t nct1 is the action time of the first voltage vector in the optimal dual vector combination in one control cycle, and the action time of the second voltage vector t act2 T con -t act1 ; i′ d1 (k), i′ q1 (k) represents the ramp component caused by the d and q axis components of the first voltage vector, i′ d2 (k), i′ q2 (k) are the ramp components caused by the d-axis and q-axis components of the second voltage vector, respectively, and the calculation formula is:

[0048]

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

[0050] The present 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 and q axis reference voltages according to the current prediction model; in the process of calculating the d and q axis reference voltages, the current reference value at the time (k+1) is obtained by the Lagrange extrapolation method; and synthesize the reference voltage vector according to the d and q axis reference voltages;

[0052] The determination area unit is used to: construct a vector space according to the trajectory of the double-vector synthesized voltage vector actually output, and divide the vector space into a plurality of sub-areas; determine the area where the synthesized reference voltage vector falls in the vector space;

[0053] A voltage vector combination unit is selected, which is used to: output an optimal dual-vector combination according to an area where the synthesized reference voltage vector falls in the vector space;

[0054] The optimal action time calculation unit is used to: solve the optimal action time of two vectors corresponding to the minimum value function within one cycle according to the optimal double vector combination;

[0055] The pulse generator sends the corresponding control switch state to the inverter according to the optimal dual-vector combination and the optimal action time of the two vectors in one cycle, and finally the inverter sends the input voltage to control the brushless DC motor.

[0056] Beneficial effects: Compared with the prior art, the present invention has the following advantages: The present invention proposes a reference vector judgment algorithm for the dual-vector model predictive current control of a brushless DC motor, which simplifies the selection of the optimal vector combination and the calculation of the action time of each vector for the dual-vector model predictive current control of a brushless DC motor with a back electromotive force waveform similar to a sine wave, while maintaining control accuracy. Based on the classic dual-vector model predictive current control of a brushless DC motor, the present invention only needs to perform two reference vector judgment calculations instead of the original forty-nine prediction operations to achieve the control effect. The present invention makes comparisons based on 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. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0058] Figure 2 It is the actual voltage vector combination output trajectory diagram of the present 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 is a first sector reference vector error comparison diagram according to the present invention;

[0061] Figure 5 It is a simulated stator current and torque waveform diagram of a brushless DC motor of the dual vector model predictive control and the classic single vector model predictive control described in the present invention;

[0062] Figure 6 It is a comparison diagram of the simulated speed of the brushless DC motor under the dual-vector model predictive control of the present invention and the classic single-vector model predictive control;

[0063] Figure 7 It is a brushless DC motor simulation A-phase current and its harmonic analysis diagram of the dual-vector model predictive control described in the present invention and the classic single-vector model predictive control. DETAILED DESCRIPTION

[0064] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0065] Example 1

[0066] The dual-vector model predictive control method of the brushless DC motor of the present invention comprises the following steps:

[0067] Step 1, establishing 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 Lagrangian extrapolation method to obtain the current reference value at time (k+1).

[0069] Step 3: Based on the prediction of the classic dual-vector model, the sine theorem is used to consider the error between the reference voltage vector and the actual dual-vector combination trajectory, and the combination with the minimum error is selected as the optimal 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 the minimum result, the optimal action time of the two vectors in one cycle is obtained.

[0071] The main steps are further described below.

[0072] First, for the brushless DC motor whose back electromotive force waveform is similar to a sine wave, we can refer to the PMSM when establishing the mathematical model, make idealized processing, and make the following assumptions: the stator winding connection is star-shaped, and the three-phase winding is distributed in space at an electrical angle of 120°; the saturation effect of the stator core is ignored, and the air gap magnetic field between the stator and the rotor is a sinusoidal distribution; the hysteresis and turbine losses of the stator and rotor are ignored, and there is no damping effect on the rotor and the permanent magnet.

[0073] Under ideal conditions, the mathematical model of the surface-mounted BLDCM in the synchronous rotating coordinate system has a stator voltage equation as follows:

[0074]

[0075] In the above formula: u d 、u q are the stator d and q axis voltage components respectively; i d 、i q They are the stator d-axis and q-axis current components respectively; R s is the motor stator resistance; L s is the stator inductance; ω n is the motor angular velocity; is the permanent magnet flux of the motor.

[0076] According to the stator voltage equation, the motor current i is selected d 、i q As the state variable, the state equation of BLDCM is obtained:

[0077]

[0078] By discretizing the above equation using the first-order forward Euler method, we can get the predicted current model:

[0079]

[0080] T s is the sampling period of the control system; i d (k), i q (k), i d (k+1), i q (k+1) is the current sampling period value of the stator d and q axis current and the predicted value of the next sampling period; u d (k),u q (k) is the value of the stator d and q axis voltage in the current sampling period.

[0081] The core concept of classic MPCC is to select the voltage vector that can minimize the error between the d-axis and q-axis currents and the reference given current as the optimal voltage vector through the value function. The deviation between the stator d-axis and q-axis currents and the reference given current is used as an indicator. Under the action of different vectors, the value functions of the motor stator d-axis and q-axis current feedback are compared to find the optimal one. The formula is as follows:

[0082]

[0083] In the above formula, are the reference values ​​of the motor stator d-axis and q-axis currents (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, u8 are two zero vectors. The 8 switching states are used to predict the d and q axis currents respectively, and the predicted results are substituted into formula (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] The present invention takes the classical model predictive current control theory as the cornerstone and proposes a control algorithm that selects two voltage vectors to work together within one sampling period. According to the motor stator d and q axis current prediction model of formula (3), it can be known that:

[0085]

[0086] According to the deadbeat control theory, Then there is and You can know:

[0087]

[0088] In this and Stator d and q axis reference voltages are synthesized into a reference voltage vector Again In traditional processing, the reference value can be approximated as and However, this will result in a one-beat delay in the reference given signal. To address this problem, a Lagrangian extrapolation method is considered to obtain the current reference value of (k+1):

[0089]

[0090] The control strategy adopted is dual-vector model predictive control. In each control cycle, only two voltage vectors act, which can be a single effective voltage, two effective voltage vectors, or an effective voltage vector and a zero vector. Because the action time is limited, the synthetic voltage vector trajectory actually output by the DV-MPCC should present a star-shaped specific trajectory. In order to select two appropriate voltage vectors and consider the complexity of the algorithm, the present invention judges the synthetic reference voltage vector based on the specific trajectory of the synthetic voltage vector actually output. The two voltage vectors to be output are selected based on which region they fall in.

[0091] like Figure 2 As shown, the actual output synthetic voltage vector trajectory diagram is divided into six areas every 60° with u1(100) as the starting point. Figure 3As shown in the figure, taking the I sector as an example, the I sector is divided into 14 sub-regions, namely I_0, I_1, I_2…I_13, and the remaining five sectors are similar to the I sector. Therefore, the entire voltage plane is divided into 6 sectors and 84 sub-regions. The goal of the sub-region division is to have a unique trajectory with the shortest error distance in each sub-region; the division principle uses the angle bisector (dashed line) of the angle formed by the intersection of the synthetic voltage vector combination straight line trajectory. According to the property of the angle bisector, each point on the line is equal to the two sides of the angle, that is, the areas on both sides of the angle bisector are the closest to the two sides of the corresponding angle (i.e., the synthetic voltage vector trajectory). Starting from the corresponding angle, the area is evenly divided. In this way, each sub-region divided by each dotted angle bisector corresponds to a unique voltage vector combination with the smallest error. It is only necessary to determine the sub-region where the voltage reference point is located, and the optimal voltage vector combination can be directly selected. Then, by calculating the time allocation of the two voltage vector combinations, the optimal action point in the trajectory of the optimal action voltage vector combination in 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 with the voltage reference point.

[0092] Assume that the synthetic reference voltage vector In the I_6 area Figure 4 (a), error voltage vector Δu (in this case Δu is ) is greater than u1 and The minimum error between the two is d0, which shows that DV-MPCC has better control accuracy than the classic single-vector MPCC. Figure 4 middle The vertical distance d1 from the synthetic trajectory of u1+u2, and the vertical distance d2 of the synthetic trajectory of u3+u1, where Figure 4 In (a), d0, d1, and d2 are the smallest compared to d1, indicating that The optimal voltage vector combination output in this sub-area should be u1 and u2. The selection of the optimal voltage vector combination will change when the voltage reference point crosses a certain dotted line, that is, when the voltage reference point is in another sub-area, such as Figure 4 In (b), d2 is the smallest at this time, and the optimal voltage vector combination should be u1 and u3. When located in the I_0, I_1, and I_3 sub-areas, the vector combinations are u1 and u8, u2 and u6, and u1 and u8 respectively.

[0093] Determine which sub-area the voltage reference point is in. First, set the reference voltage angle. The distance from the origin to the boundary between the N_1 area and the N_2 area in the reference voltage direction is K. N1 , the distance to the boundary between N_4 and N_5 is K N2 (N=Ⅰ, Ⅱ……VI is used for sector counting), according to the sine theorem:

[0094]

[0095] Among them U dc is the DC bus voltage, M = 1 to 6, corresponding to the first to sixth sectors, for example, N is the first sector, and M is 1. First, The phase angle θ replaces θ′ in the formula and divides it by k60° (k is an arbitrary integer). When the complementary angle is between 0° and 30°, by comparing With L N1 and L N2 The size relationship of In which of the three approximate areas are N_0 and N_1, N_2 and N_3 and N_4, N_5 and N_6? Greater than L N1 and less than L N2 Then judge at this time In the general area of ​​N_2, N_3, N_4. After determining the general area, Perform detailed area judgment. Let the distance from the origin to the boundary between N_0 and N_1 be L 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 N_3 and N_4 is L N2 , the distance to the boundary between N_5 and N_6 is L N31 According to the sine theorem, we know that:

[0096]

[0097] When the previous step determines When in N_0 and N_1 areas, by comparing With L N11 Relationship judgment Which sub-region is it located in? If it is in the N_0 region, u1 and u8 are selected as the optimal voltage. When it is in the N_2 region, N_3 region and N_4 region, compare With L N2 , L N22 , L N23 Relationship judgment. and <L N22 When , it is determined that in the N_2 area, u2 and u6 are selected. and When it is judged in N_3 area, u1 and u8 are selected. and When it is judged that it is in the N_4 area, u1 and u3 are selected. When in the approximate area of ​​N_5 and N_6, the judgment method is similar to that in N_0 and N_1. With L N31 When θ′ is divided by k60°, and the complementary angle is between 30° and 60°, the judgment method is similar to that between 0° and 30°. The following table shows the vector combination corresponding to each sub-area of ​​sector I.

[0098] Table 1 Sub-area corresponding vector selection table

[0099]

[0100]

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

[0102]

[0103] Among them, T con is the control period, t act1 is the action time of the first voltage vector in one control cycle, then the action time of the second voltage vector t act2 T con -t act1 . i′ d1 (k), i′ q1 (k), i′ d2 (k), i′ q2 (k) are the ramp components caused by the d-axis and q-axis components of the two voltage vectors, respectively, and can be calculated:

[0104]

[0105] Where: n = 1, 2; u dn 、u qn It is the d and q axis voltage vector output by the two selected 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 get the new function CE(t act1 ) and is a quadratic function of one variable, and in the rectangular coordinate system the curve opens upward and has a minimum value, so that:

[0107]

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

[0109]

[0110] 1) When Tcon >t act1 >0, function CE(t act1 ) has a minimum value at (0,T con ), so the minimum value of CE in this interval is a very minimum value. At this time, there are two voltage vector effects in one control cycle.

[0111] 2) When 0>t act1 , function CE(t act1 ) has a minimum value at (0,T con ) interval, so that t act1 =0, the minimum value CE(0) can be obtained. At this time, only one second voltage vector acts within one control cycle.

[0112] 3) When t act1 >T con , function CE(t act1 ) has a minimum value at (0,T con ) interval, so that t act1 =T con , we can get the minimum value CE(T con ). At this time, only one first voltage vector acts in one control cycle.

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

[0114] Example 2

[0115] The dual vector model predictive control system of the present invention has a control block diagram as shown in Figure 1 As shown, including:

[0116] The reference voltage vector calculation unit is used to: calculate the d and q axis reference voltages according to the current prediction model; in the process of calculating the d and q axis reference voltages, the current reference value at the time (k+1) is obtained by the Lagrange extrapolation method; and synthesize the reference voltage vector according to the d and q axis reference voltages;

[0117] The determination area unit is used to: construct a vector space according to the trajectory of the double-vector synthesized voltage vector actually output, and divide the vector space into a plurality of sub-areas; determine the area where the synthesized reference voltage vector falls in the vector space;

[0118] A voltage vector combination unit is selected, which is used to: output an optimal dual-vector combination according to an area where the synthesized reference voltage vector falls in the vector space;

[0119] The optimal action time calculation unit is used to: solve the optimal action time of two vectors corresponding to the minimum value function within one cycle according to the optimal double vector combination;

[0120] The pulse generator obtains the corresponding control switch state according to the optimal dual-vector combination and the optimal action time of the two vectors in one cycle and sends it to the inverter;

[0121] Inverter, which controls the input voltage to the brushless DC motor.

[0122] Experimental verification:

[0123] In order to verify the effect 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 a simulation experiment was performed. The brushless DC motor parameters used in the simulation are given in the table below. The control frequency of the model is set to 10kHz, U dc It is 310V.

[0124] Table 2 Motor parameters

[0125]

[0126] Figure 5 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 given in the figure. The simulation experiment setting conditions are: the brushless DC motor starts at no load at 0s, and is given 1 / 4 rated speed. At 0.2s, the speed is stepped to 1 / 2 rated speed. At 0.4s, the rated load is applied instantaneously. At 0.6s, the speed setting is suddenly changed to the rated speed, and it ends at 1s. Figure 5 It can be concluded that under the same working conditions, MPCC has good dynamic and static performance, while the torque pulsation of the classic single-vector MPCC is significantly greater than that of the DV-MPCC. This shows that the classic MPCC has only one voltage vector in a control cycle, which may cause under-regulation or over-regulation of current tracking. By selecting a suitable dual-vector combination, the torque pulsation can be effectively reduced, and the effect is more obvious when encountering sudden loads, indicating that the latter has better anti-interference ability than the former. Figure 6 The speed response of the two strategies under simulation conditions is compared. When the speed step changes during no-load operation from 0s to 0.4s, DV-MPCC can respond to the speed step faster than the classic MPCC, and has a smaller overshoot. When the rated load is applied at 0.4s, the speed oscillation of the former is smaller than that of the latter, and the speed can be restored more quickly. When the speed steps from the rated load operation state to the rated speed at 0.6s, DV-MPCC has a more obvious dynamic response advantage and reaches the target speed faster than the classic MPCC, while having a smaller steady-state error. Overall, the DV-MPCC control strategy performs better than the classic MPCC in terms of the dynamic response and load capacity of the motor, and can better adapt to load changes and achieve stable operation. Figure 7The steady-state current analysis of the two MPC strategies when the motor is running at rated conditions shows that the harmonic distortion rate of the A-phase current is reduced from 8.32% (classic MPCC) to 2.30% (using DV-MPCC) through simulation analysis. This shows that DV-MPCC is more accurate in regulating current than classic MPCC, responds to load changes more quickly, and reduces the generation of harmonics. The present invention proposes a dual-vector model predictive current control strategy for a brushless DC motor based on classic MPCC. This method re-divides the voltage vector plane in detail according to the synthetic voltage vector trajectory of the actual output, and predicts the voltage vector combination and respective action time of the next cycle based on a given reference voltage vector, which can significantly improve the target current control accuracy. DV-MPCC can effectively reduce motor current harmonics and torque pulsation. In terms of control strategy, this method does not need to enumerate all switch states to continuously evaluate the value function, but selects the vector combination by judging the area where the reference voltage vector is located. The simulation experimental results show that the control strategy proposed by the present invention has excellent dynamic and static performance in a large speed range. By comparing the classic MPCC and DV-MPCC, the latter has good motor dynamic response and efficiency.

Claims

1. A dual-vector model predictive control method for a brushless DC motor, characterized in that: The following steps are involved: Step 1, establishing a mathematical model for a brushless DC motor with a back electromotive force waveform similar to a sine wave; Step 2, according to the mathematical model of the brushless DC motor, the forward Euler method is used to obtain the current prediction model; according to the current prediction model, the deadbeat theory is used to obtain the d and q axis reference voltages; in the calculation process of the d and q axis reference voltages, the current reference value at the time (k+1) is obtained by the Lagrange extrapolation method; Step 3, synthesizing a reference voltage vector according to the d-axis and q-axis reference voltages; constructing a vector space according to the trajectory of the dual-vector synthesized voltage vector actually output, and dividing the vector space into a plurality of sub-regions; determining the region in which the synthesized reference voltage vector falls in the vector space; and outputting an optimal dual-vector combination according to the region in which the synthesized reference voltage vector falls in the vector space; Step 4: Based on the optimal dual-vector combination, find the optimal action time of the two vectors in one cycle when the value function is minimized.

2. The dual-vector model predictive control method for a brushless DC motor according to claim 1, characterized in that: The mathematical model of the brushless DC motor is: In the formula, u d 、u q are the stator d and q axis voltage components respectively; i d 、i q are the stator d and q axis current components respectively; R s is the motor stator resistance; L s is the stator inductance; ω n is the motor angular velocity; is the permanent magnet flux of the motor; t is the time.

3. The dual-vector model predictive control method for a brushless DC motor according to claim 2, characterized in that: By discretizing the above equation using the first-order forward Euler method, we can get the predicted current model: Where, T s is the sampling period of the control system; i d (k), i q (k) are the current sampling period values ​​of the stator d and q axis currents, i 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; u d (k),u q (k) are the current sampling period values ​​of the stator d and q axis voltages respectively.

4. The dual-vector model predictive control method for a brushless DC motor according to claim 3, characterized in that: According to the current prediction model, the deadbeat theory is used to obtain the d and q axis reference voltages. The calculation formula is: In the formula, is the stator d and q axis reference voltage, are the current reference values ​​of the stator d and q axes at time k+1, They are the current reference values ​​of the stator d and q axes at time k respectively.

5. The dual-vector model predictive control method for a brushless DC motor according to claim 4, characterized in that: In the calculation process of the d and q axis reference voltages, the current reference value at the time (k+1) is obtained by the Lagrange extrapolation method, and the calculation formula is: In the formula, are the current reference values ​​of the stator d and q axes at time k-1, They are the current reference values ​​of the stator d and q axes at time k-2 respectively.

6. The dual-vector model predictive control method for a brushless DC motor according to claim 1, characterized in that: A vector space is constructed according to the trajectory of the voltage vector synthesized by the dual vectors actually output, and the vector space is divided into a plurality of sub-areas, including: the trajectory of the voltage vector synthesized by the dual vectors actually output constitutes a hexagonal space; the center point of the hexagon is connected to each vertex, and each vertex is connected to other vertices, and each of the 18 connecting lines formed is a voltage vector combination; the vector space is divided into a triangular area every 60° with u1 (100) as the starting point, and in the four areas divided by the connecting lines, the angular parallel lines of the angles formed by the intersection of every two voltage vector combinations intersect at one point, and the four areas are divided into a plurality of sub-areas again; the triangular area is divided into a total of 14 sub-areas.

7. The dual-vector model predictive control method for a brushless DC motor according to claim 6, characterized in that: Determining the region where the synthesized reference voltage vector falls in the vector space includes the following steps: (1) Calculate the phase angle of the reference voltage vector, and determine the triangular area where the end of the reference voltage vector is located according to the phase angle of the reference voltage vector; (2) Determine the approximate range of the triangular area where the end of the reference voltage vector is located, including: If the phase angle of the reference voltage vector is divided by an integer multiple of 60° and the residual angle is between 0° and 30°, by comparing the length of the reference voltage vector with L N1 and L N2 The approximate range of the triangular area where the end of the reference voltage vector is located is determined by the size relationship; the approximate range of the triangular area includes: N_0 and N_1 area, N_2 and N_3 and N_4 area, N_5 and N_6 area; if Greater than L N1 and less than L N2 Then the reference voltage vector end is judged to be in the N_2, N_3 and N_4 regions. If Less than L N1 Then the reference voltage vector end is judged to be in the N_0 and N_1 regions. If Greater than L N2 It is then determined that the end of the reference voltage vector is in the N_5 and N_6 regions; is the length of the reference voltage vector; L N1 and L N2 The calculation formula is: Among them, L N1 is the distance from the intersection of the boundary line between N_1 and N_2 regions and the reference voltage vector to the origin, L N2 is the distance from the intersection of the boundary line between N_4 and N_5 regions and the reference voltage vector to the origin; U dc is the DC bus voltage, θ′ is the phase angle of the reference voltage vector; M = 1 to 6, corresponding to the first to sixth sectors; (3) Determine the sub-region location where the end of the reference voltage vector is located, including: The reference voltage vector ends are in the N_0 and N_1 regions. If It is determined that the end of the reference voltage vector is in the N_0 region. It is then determined that the end of the reference voltage vector is in the N_1 region; The reference voltage vector ends are in the N_2, N_3 and N_4 regions. If Head Then it is determined that the end of the reference voltage vector is in the N_2 region; if and Then it is determined that the end of the reference voltage vector is in the N_3 region; if and Then it is determined that the end of the reference voltage vector is in the N_4 region; The reference voltage vector ends are in the N_5 and N_6 regions. If It is determined that the end of the reference voltage vector is in the N_5 region. It is then determined that the end of the reference voltage vector is in the N_6 region; L N1 , L N21 , L N22 , L N23 , L N31 The calculation formula is: Where, L N11 is the distance from the intersection of the boundary line between N_0 and N_1 regions and the reference voltage vector to the origin, L N21 is the distance from the intersection of the boundary line between N_2 and N_3 regions and the reference voltage vector to the origin, L N22 is the distance from the intersection of the boundary line between N_2 and N_4 regions and the reference voltage vector to the origin, L N23 is the distance from the intersection of the boundary line between N_3 and N_4 regions and the reference voltage vector to the origin, L N31 is the distance from the intersection of the boundary line between the N_5 region and the N_6 region and the reference voltage vector to the origin; According to the area where the synthesized reference voltage vector falls in the vector space, the optimal dual-vector combination is outputted correspondingly through the sub-area corresponding vector selection table.

8. The dual-vector model predictive control method for a brushless DC motor according to claim 1, characterized in that: The value function is: s.t u s (k)∈{u1,u2,...,u7,u8} In the formula, i 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; are the reference values ​​of the motor stator d and q axis currents, u s (k) is the voltage vector at time k; u1, u2, ..., u6 are effective voltage vectors used to synthesize the actual output voltage vector; u7, u8 are two zero vectors.

9. The dual-vector model predictive control method for a brushless DC motor according to claim 1, characterized in that: The calculation formula for the predicted value of the stator d and q axis current in the next sampling period is: i d (k+1)=i d (k)+i′ d1 (k)t act1 +i′ d2 (k)(T con -t act1 ) i q (k+1)=i q (k)+i′ q1 (k)t act +i′ q2 (k)(T con -t act1 ) In the formula, i d (k), i q (k) are the current sampling period values ​​of the stator d and q axis currents respectively; T con is the system control period; t act1 is the action time of the first voltage vector in the optimal dual vector combination in one control cycle, and the action time of the second voltage vector t act2 T con -t act1 ; i′ d1 (k), i′ q1 (k) represents the ramp component caused by the d and q axis components of the first voltage vector, i′ d2 (k), i′ q2 (k) are the ramp components caused by the d-axis and q-axis components of the second voltage vector, respectively, and the calculation formula is: In the formula, i′ dn (k), i′ qn (k) represents the ramp component caused by the d and q axis components of the nth voltage vector in the optimal dual vector combination, u dn 、u qn represents the d-axis and q-axis components of the voltage vector in the optimal dual-vector combination, n represents the nth voltage vector in the optimal dual-vector combination; R s is the motor stator resistance; L s is the stator inductance; ω n is the motor angular velocity; is the permanent magnet flux of the motor.

10. 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 and q axis reference voltages according to the current prediction model; in the process of calculating the d and q axis reference voltages, the current reference value at the time (k+1) is obtained by the Lagrange extrapolation method; and synthesize the reference voltage vector according to the d and q axis reference voltages; A determination area unit is used to: construct a vector space according to the trajectory of the double-vector synthetic voltage vector actually output, and divide the vector space into a plurality of sub-areas; and determine the area in which the synthetic reference voltage vector falls in the vector space; A voltage vector combination unit is selected, which is used to: output an optimal dual-vector combination according to an area where the synthesized reference voltage vector falls in the vector space; The optimal action time calculation unit is used to: solve the optimal action time of two vectors corresponding to the minimum value function within one cycle according to the optimal double vector combination; The pulse generator obtains the corresponding control switch state according to the optimal dual-vector combination and the optimal action time of the two vectors in one cycle and sends it to the inverter; Inverter, which controls the input voltage to the brushless DC motor.

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