A Vector Optimization Prediction Control Method for Permanent Magnet Brushless DC Motors

Abstract

The present invention relates to a vector optimal prediction control method for a permanent magnet brushless DC motor, which includes steps such as discretization of the current state equation, prediction of the ideal voltage vector at the next moment, sector division, judgment and selection of the optimal voltage vector, calculation of the action time of the optimal voltage vector, and acquisition of the drive pulse signal, etc.; the design method increases the number of voltage vectors applied in each sampling period, flexibly selects and adjusts two voltage vectors and their respective action times, making the prediction result closer to the ideal voltage vector, improving the system stability, reducing the torque ripple, and obtaining better control effects; this method judges the position of the ideal voltage vector through twelve-sector division, directly selects two optimal voltage vectors, and there is no need to use the cost function to select the second optimal voltage vector by traversing all vectors, thus greatly reducing the calculation amount and making the model predictive control method more practical and universal.

Description

Technical Field

[0001] The present invention relates to a vector optimal prediction control method for a permanent magnet brushless DC motor, belonging to the technical field of motor control. Background Art

[0002] The surface-mounted brushless DC motor has the characteristics of high efficiency, small volume, large power density, simple structure, etc., and is widely used in many technical fields such as industrial production, daily life, aerospace, etc. The more traditional control methods of brushless DC motors mainly include vector control and direct torque control. The main idea of vector control is to perform vector transformation. Although it has good dynamic performance, it has problems such as strong dependence on motor parameters and difficult complete decoupling. Although direct torque control abandons the idea of decoupling and adopts the method of stator flux orientation, with simple structure and fast torque response, it also has problems of large calculation amount and poor low-speed performance. In order to further improve the control performance of brushless DC motors, model predictive control has received extensive attention from scholars. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a vector optimal prediction control method for a permanent magnet brushless DC motor, which can expand the action range of voltage vectors, reduce the torque ripple of the motor, effectively reduce the calculation amount of motor control, and improve the real-time performance of current control.

[0004] The present invention adopts the following technical solutions to solve the above technical problems: The present invention designs a vector optimal prediction control method for a permanent magnet brushless DC motor, which is used for predictive control of a permanent magnet brushless DC motor in a three-phase full-bridge drive mode, including the following steps:

[0005] Step A. According to the second-order Euler discretization, using the stator current state equation in the rotating coordinate system, obtain the predicted values of the direct and quadrature axis currents after prediction and correction at the next moment, and adopt the deadbeat prediction control idea to obtain the ideal voltage vector at the current moment after delay compensation, and then enter Step B;

[0006] Step B. Based on the decomposition values of the ideal voltage vector at the current moment after delay compensation on the α-axis and β-axis, obtain the angle corresponding to the ideal voltage vector at the current moment through the arctangent function, and combine the candidate voltage vectors in each of the twelve sectors divided by the equal angles corresponding to the motor space voltage vectors to obtain the first optimal voltage vector and the second optimal voltage vector corresponding to the ideal voltage vector at the current moment, and then enter Step C;

[0007] Step C. According to the first optimal voltage vector and the second optimal voltage vector corresponding to the ideal voltage vector at the current moment, obtain the action durations corresponding to the first optimal voltage vector and the second optimal voltage vector respectively according to the sum of the action durations corresponding to the two optimal voltage vectors being equal to the sampling period, and then enter Step D;

[0008] Step D. Construct a modulation wave with the ratio of the action duration corresponding to one of the first optimal voltage vector and the second optimal voltage vector to the sampling period, combine it with the upper triangular carrier of the preset frequency, divide the duration intervals of the action of the first optimal voltage vector and the second optimal voltage vector respectively in the sampling period to which the current moment belongs, and then combine the switching states of each bridge arm in the three-phase full bridge corresponding to the ideal voltage vector in each sector respectively, and the preset first optimal voltage vector and the second optimal voltage vector, to obtain the drive pulse signal of the three-phase full bridge corresponding to the sampling period to which the current moment belongs, so as to realize the drive of the permanent magnet brushless DC motor.

[0009] As a preferred technical solution of the present invention: the said step A includes the following steps A1 to A3;

[0010] Step A1. According to the second-order Euler discretization, according to the following formula:

[0011]

[0012] In the formula

[0013]

[0014] Obtain the theoretical exact value i s (k + 1) of the current at the next moment k + 1, where i s (k) represents the theoretical exact value of the current at the current moment k, e s (k) represents the back electromotive force at the current moment k, L s represents the stator inductance in the permanent magnet brushless DC motor, R s represents the stator resistance in the permanent magnet brushless DC motor, T s represents the sampling period, and then enter step A2;

[0015] Step A2. Use the stator current state equation in the rotating coordinate system, as follows:

[0016]

[0017] Obtain the decomposition values i d (k + 1) and i q (k + 1) of the predicted and corrected AC and DC axis current prediction values at the next moment k + 1 on the d-axis and q-axis respectively, where i d0 (k) and i q0 (k) respectively represent the decomposition values of the current i s0 (k) on the d-axis and q-axis respectively, u d (k) and u q(k) represents the decomposition values of the selected effective voltage vectors corresponding to the current sampling period at the k-th moment on the d-axis and q-axis respectively; then proceed to step A3;

[0018] Step A3. Adopt the deadbeat predictive control idea and combine According to the following formula:

[0019]

[0020] Obtain the decomposition values of the ideal voltage vector at the current k-th moment after delay compensation on the d-axis and q-axis respectively Among them, respectively represent the decomposition values of the current given values of the AC and DC axis currents on the d-axis and q-axis respectively.

[0021] As a preferred technical solution of the present invention: The said step B includes the following steps B1 to B3;

[0022] Step B1. According to the decomposition values of the ideal voltage vector at the current k-th moment after delay compensation on the d-axis and q-axis respectively According to the following formula:

[0023]

[0024] Obtain the decomposition values of the ideal voltage vector at the current k-th moment on the α-axis and β-axis respectively Among them, θ represents the rotor position angle of the permanent magnet brushless DC motor, and then proceed to step B2;

[0025] Step B2. Through the arctangent function as follows:

[0026]

[0027] Obtain the angle γ corresponding to the ideal voltage vector at the current k-th moment, and then proceed to step B3;

[0028] Step B3. According to each candidate voltage vector in the twelve sectors divided by equal angles corresponding to the motor space voltage vector, obtain the first optimal voltage vector U vec1 and the second optimal voltage vector U vec2 .

[0029] As a preferred technical solution of the present invention: The twelve sectors divided by equal angles corresponding to the basic voltage vector of the motor are obtained by the following operations;

[0030] Operation: First, based on the various candidate voltage vectors corresponding to the α-axis and β-axis decomposition of the motor basic voltage vector, a six-sector division with an interval of 60 degrees between adjacent candidate voltage vectors is constructed; then, according to the position of the ideal voltage vector in the six-sector division, the corresponding first optimal voltage vector and the second optimal voltage vector are selected, and the voltage vector motion trajectory in the six-sector division after the ideal voltage vector is decomposed is constructed according to this rule; then, according to the voltage vector motion trajectory, the motor basic voltage vector is further divided into twelve sectors with an interval of 30 degrees between adjacent sectors based on the six-sector division.

[0031] As a preferred technical solution of the present invention: the step C includes the following steps C1 to C3;

[0032] Step C1. According to the following formula:

[0033]

[0034] Obtain the slope of the quadrature axis current h0 when the zero vector is applied, L s represents the stator inductance of the permanent magnet brushless DC motor, R s represents the stator resistance in the permanent magnet brushless DC motor, ω r represents the permanent magnet brushless DC motor rotor angular velocity, ψ f represents the permanent magnet flux of the permanent magnet brushless DC motor, and then enters step C2;

[0035] Step C2: Based on the slope h0 of the quadrature axis current when the zero vector acts, combined with the first optimal voltage vector U vec1 , the second optimal voltage vector U vec2 The decomposition values ​​U on the q axis q_vec1 , U q_vec2 , according to the following formula:

[0036]

[0037] Get the first optimal voltage vector U vec1 , the second optimal voltage vector U vec2 The slope of the quadrature axis current h vec1 、h vec2 , then proceed to step C3;

[0038] Step C3. According to the following formula:

[0039]

[0040] Get the first optimal voltage vector U vec1 , the second optimal voltage vector U vec2 The corresponding action time t vec1 ,t vec2 , Indicates the quadrature-axis current reference value, i q (k) represents the decomposed value of the theoretical exact value of the direct and quadrature-axis currents at the current k-th moment on the q-axis.

[0041] 1. The vector optimal prediction control method for a permanent magnet brushless DC motor according to claim 1, characterized in that: the step D includes the following steps D1 to D3;

[0042] Step D1. Using the action duration t vec1 corresponding to the first optimal voltage vector U vec1 and the sampling period T s to construct a modulation wave T cm , and then enter step D2;

[0043] Step D2. Based on the upper triangular carrier wave with a preset frequency, determine that the period when the modulation wave T cm is greater than the upper triangular carrier wave is the action duration interval of the first optimal voltage vector in the sampling period to which the current moment belongs, and the period when the modulation wave T cm is less than the upper triangular carrier wave is the action duration interval of the second optimal voltage vector in the sampling period to which the current moment belongs, that is, determine the action duration intervals of the first optimal voltage vector and the second optimal voltage vector in the sampling period to which the current moment belongs respectively, and then enter step D3;

[0044] Step D3. According to the action duration intervals of the first optimal voltage vector and the second optimal voltage vector in the sampling period to which the current moment belongs respectively, combined with the switching states of each bridge arm in the three-phase full bridge corresponding to the ideal voltage vectors in each sector respectively and the preset first optimal voltage vector and the second optimal voltage vector, obtain the drive pulse signal of the three-phase full bridge corresponding to the sampling period to which the current moment belongs, and realize the drive of the permanent magnet brushless DC motor.

[0045] As a preferred technical solution of the present invention: Based on S a , S b , S c respectively represent the switching states of each bridge arm in the three-phase full bridge, the states of the upper and lower power switching tubes of each bridge arm are complementary, and it is defined that the switching state of "1" corresponds to the conduction of the upper-bridge-arm power switching tube and the cut-off of the lower-bridge-arm power switching tube, and the switching state of "0" corresponds to the cut-off of the upper-bridge-arm power switching tube and the conduction of the lower-bridge-arm power switching tube; the switching states of each bridge arm of S a , S b , S c corresponding to the ideal voltage vectors in each sector respectively and the preset first optimal voltage vector and the second optimal voltage vector in the three-phase full bridge are as follows:

[0046] When the ideal voltage vector is in the first sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridgea , S b , S c The switching states of each bridge arm are 1, 0, 0 in sequence. The preset second optimal voltage vector corresponds to S a , S b , S c in the three-phase full-bridge. The switching states of each bridge arm are 0, 1, 0 in sequence;

[0047] When the ideal voltage vector is in the second sector, the preset first optimal voltage vector corresponds to S a , S b , S c in the three-phase full-bridge. The switching states of each bridge arm are 1, 1, 0 in sequence. The preset second optimal voltage vector corresponds to S a , S b , S c in the three-phase full-bridge. The switching states of each bridge arm are 1, 0, 1 in sequence;

[0048] When the ideal voltage vector is in the third sector, the preset first optimal voltage vector corresponds to S a , S b , S c in the three-phase full-bridge. The switching states of each bridge arm are 1, 1, 0 in sequence. The preset second optimal voltage vector corresponds to S a , S b , S c in the three-phase full-bridge. The switching states of each bridge arm are 0, 1, 1 in sequence;

[0049] When the ideal voltage vector is in the fourth sector, the preset first optimal voltage vector corresponds to S a , S b , S c in the three-phase full-bridge. The switching states of each bridge arm are 0, 1, 0 in sequence. The preset second optimal voltage vector corresponds to S a , S b , S c in the three-phase full-bridge. The switching states of each bridge arm are 1, 0, 0 in sequence;

[0050] When the ideal voltage vector is in the fifth sector, the preset first optimal voltage vector corresponds to S a , S b , S c in the three-phase full-bridge. The switching states of each bridge arm are 0, 1, 0 in sequence. The preset second optimal voltage vector corresponds to S a , S b , S c in the three-phase full-bridge. The switching states of each bridge arm are 0, 0, 1 in sequence;

[0051] When the ideal voltage vector is in the sixth sector, the preset first optimal voltage vector corresponds to S a , S b, S c The switching states of each bridge arm are 0, 1, 1 in sequence. The preset second optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 1, 1, 0 in sequence;

[0052] When the ideal voltage vector is in the seventh sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 0, 1, 1 in sequence. The preset second optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 1, 0, 1 in sequence;

[0053] When the ideal voltage vector is in the eighth sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 0, 0, 1 in sequence. The preset second optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 0, 1, 0 in sequence;

[0054] When the ideal voltage vector is in the ninth sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 0, 0, 1 in sequence. The preset second optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 1, 0, 0 in sequence;

[0055] When the ideal voltage vector is in the tenth sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 1, 0, 1 in sequence. The preset second optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 0, 1, 1 in sequence;

[0056] When the ideal voltage vector is in the eleventh sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S cThe switching states of each bridge arm are 1, 0, 1 in sequence. The preset second optimal voltage vector corresponds to S in the three-phase full bridge a 、S b 、S c The switching states of each bridge arm are 1, 1, 0 in sequence;

[0057] When the ideal voltage vector is in the twelfth sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridge a 、S b 、S c The switching states of each bridge arm are 1, 0, 0 in sequence. The preset second optimal voltage vector corresponds to S in the three-phase full bridge a 、S b 、S c The switching states of each bridge arm are 0, 0, 1 in sequence.

[0058] For the vector optimal prediction control method of a permanent magnet brushless DC motor according to the present invention, compared with the prior art by adopting the above technical solutions, the following technical effects are achieved:

[0059] For the vector optimal prediction control method of a permanent magnet brushless DC motor designed by the present invention, by increasing the number of voltage vectors applied in each sampling period, flexibly selecting and adjusting two voltage vectors and their respective action times, the prediction result is closer to the ideal voltage vector, the system stability is improved, the torque ripple is reduced, and better control effects are obtained; the design method judges the position of the ideal voltage vector through the division of twelve sectors, directly selects two optimal voltage vectors, and there is no need to select the second optimal voltage vector by traversing using a value function, greatly reducing the calculation amount and making the model predictive control method more practical and general. Description of the Drawings

[0060] Figure 1 is the system block diagram of the model predictive control method of the permanent magnet brushless DC motor designed by the present invention;

[0061] Figure 2 is the schematic diagram of the decomposition of the ideal voltage vector in the design of the present invention;

[0062] Figure 3 is the schematic diagram of the voltage vector motion trajectory in the design of the present invention;

[0063] Figure 4 is the schematic diagram of the sector division in the design of the present invention;

[0064] Figure 5 is the schematic diagram of the modulation rule in the design of the present invention.

[0065] In the figure: i a , i b , i c are the three-phase winding currents of the motor; i α, \(i_{\alpha\beta}\) is the current of the motor on the \(\alpha\beta\) axis; \(i\) d , \(i\) q is the current of the motor on the rotating coordinate axis; is the reference value of the direct and quadrature axis currents; represents the ideal voltage vector; \(\omega\) r is the reference angular velocity and the actual angular velocity of the motor; \(U\) vec1 、\(U\) vec2 are the two optimal voltage vectors selected; \(t\) vec1 、\(t\) vec2 are the action times of the optimal voltage vectors; Sampling period \(T\) s ; \(i\) a , \(i\) b , \(i\) c are the currents of the three-phase windings of the motor. **Specific Embodiment**

[0066] The following further elaborates on the specific embodiment of the present invention in conjunction with the accompanying drawings of the specification.

[0067] The present invention designs a vector optimal prediction control method for a permanent magnet brushless DC motor, which is used for predictive control of a permanent magnet brushless DC motor in a three-phase full-bridge drive mode. In practical applications, as Figure 1 shown, the following specific steps A to D are executed.

[0068] Step A. According to the second-order Euler discretization, using the stator current state equation in the rotating coordinate system, obtain the predicted values of the direct and quadrature axis currents after prediction and correction at the next moment, and adopt the deadbeat prediction control idea to obtain the ideal voltage vector at the current moment after delay compensation, and then enter Step B.

[0069] The stator current state equation of the surface-mounted brushless DC motor in the rotating coordinate system can be expressed as Equation (1):

[0070]

[0071] In the formula, \(u\) s represents the direct and quadrature axis voltages; \(i\) s represents the direct and quadrature axis currents; \(L\) s is the stator inductance; \(R\) s is the stator resistance; \(e\) s is the back electromotive force. The back electromotive force in the rotating coordinate system can be directly calculated as:

[0072]

[0073] In the formula, \(\omega\) r is the rotor angular velocity; \(\varPsi\) f is the permanent magnet flux linkage.

[0074] Perform forward Euler discretization on Equation (1), and replace the derivative with a forward difference quotient to obtain the discrete mathematical model of the surface-mounted brushless DC motor, which is:

[0075]

[0076] where \(i\) sp (k) is the current sampled value of the current, and \(i\) sp (k + 1) is the next sampled value of the current, and \(i\) s (k + 1) is the exact theoretical value of the current at the next moment, and \(T\) s is the sampling period. The next sampled value of the current \(i\) sp (k + 1) can be approximately expressed as:

[0077]

[0078] For forward Euler discretization, when \(k = 1, 2, \cdots\), the \(i\) sp (k) on the right side of the formula is approximate. Therefore, there will be a cumulative error in the calculated \(i\) sp (k + 1). Analyzing the cumulative error is relatively complex. Here, we first analyze the simple local truncation error.

[0079] The local truncation error is the difference between the current sampled value \(i\) sp (k + 1) and the exact theoretical value of the current \(i\) s (k + 1). The exact theoretical value of the current \(i\) s (k + 1) at the next moment obtained by Taylor expansion to the quadratic term is:

[0080]

[0081] where \(i\) s (k) is the exact theoretical value of the current at the current moment. Assuming that there is no error in \(i\) sp (k) in Equation (3), that is, \(i\) s (k)= \(i\) sp (k), then subtracting Equation (4) from Equation (5) gives the error between the Euler approximation value and the Taylor exact value:

[0082]

[0083] Substituting Equation (1) into Equations (4) and (6) and further simplifying gives:

[0084]

[0085] Therefore, the second-order Euler discretization form of the predicted-corrected current state equation can be expressed as:

[0086]

[0087] where i sp (k + 1) is the current sampling value at the next moment, serving as the first-step prediction estimation result, and i s (k + 1) the theoretically accurate value of the current serves as the second-step correction result.

[0088] Equation (8) can be further simplified to:

[0089]

[0090] where u s (k - 1) is the effective voltage vector determined in the previous sampling period, and is0 is as shown in the following formula

[0091]

[0092] Then in practical applications, the above-mentioned step A is specifically executed as follows: steps A1 to A3.

[0093] Step A1. According to the second-order Euler discretization, according to the following formula:

[0094]

[0095] where

[0096]

[0097] Obtain the theoretically accurate value of the current i s (k + 1) at the next moment of k + 1, where i s (k) represents the theoretically accurate value of the current at the current moment of k, and e s (k) represents the back electromotive force at the current moment of k, and L s represents the stator inductance in the permanent magnet brushless DC motor, and R s represents the stator resistance in the permanent magnet brushless DC motor, and T s represents the sampling period, and then enter step A2.

[0098] Step A2. Use the stator current state equation in the rotating coordinate system as follows:

[0099]

[0100] Obtain the decomposition values of the predicted and corrected direct and quadrature axis current prediction values at the next moment of k + 1 on the d-axis and q-axis respectively, i d (k + 1), i q (k + 1), where i d0 (k), i q0 (k) represent the decomposition values of the current i s0 (k) on the d-axis and q-axis respectively, and u d (k), uq (k) represents the decomposition values of the selected effective voltage vectors corresponding to the current sampling period at the k-th moment on the d-axis and q-axis respectively; then proceed to step A3.

[0101] Step A3. Adopt the deadbeat predictive control idea and combine According to the following formula:

[0102]

[0103] Obtain the decomposition values of the ideal voltage vector at the current k-th moment after delay compensation on the d-axis and q-axis respectively where respectively represent the decomposition values of the current k-th moment AC-DC axis current given values on the d-axis and q-axis respectively.

[0104] Further, perform the following operations to obtain the twelve sectors divided at equal angles corresponding to the basic voltage vector of the motor.

[0105] Operations: First, based on each candidate voltage vector decomposed along the α-axis and β-axis corresponding to the basic voltage vector of the motor, construct a six-sector division with a 60-degree interval between adjacent candidate voltage vectors; then, according to the position of the ideal voltage vector in the six-sector division, select the corresponding first optimal voltage vector and second optimal voltage vector, and construct the voltage vector motion trajectory of the ideal voltage vector after decomposition in the six-sector division according to this rule; then, based on the voltage vector motion trajectory, further divide the basic voltage vector of the motor into a twelve-sector division with a 30-degree interval between adjacent ones.

[0106] And specifically analyze that for the selection of the two optimal voltage vectors in the dual-vector model predictive control, since there are only two effective voltage vectors U vec1 , U vec2 acting in the dual-vector model predictive control, therefore, the action times of the two optimal voltage vectors satisfy t vec1 + t vec2 = T s . Below, take the selection of the first optimal voltage vector U 100 as an example for analysis, as Figure 2 shown. From when the ideal voltage vector is located at the position shown in Figure 2 (a), according to the principle of minimum error, the first optimal voltage vector is selected as U 100 . For the selection of the second optimal voltage vector, by using the fact that the action times of the two optimal voltage vectors are exactly equal to the sampling period time, decompose the ideal voltage vector . It can be seen that when the optimal voltage vector is selected as U 010 , since θ3 = θ4, the action times of the two optimal voltage vectors are exactly equal to the sampling period. Similarly is located atFigure 2 The position shown in (b).

[0107] For Figure 2 the decomposition of the ideal voltage vector, it can be seen that when the ideal voltage vector is located on both sides of the six basic voltage vectors, the selection of the second optimal voltage vector is exactly the interval vector of the first optimal voltage vector on the same side as the location point of the ideal voltage vector. According to this rule, the voltage vector motion trajectory after the decomposition of the ideal voltage vector can be drawn, as Figure 3 shown.

[0108] According to Figure 3 the voltage vector motion trajectory, the space voltage vector is divided into sectors. It can be seen that at the intersection of the dotted lines of the voltage vector motion trajectory, it is exactly the switching point of the first optimal voltage vector. Then, using the arctangent function formula (16), the space voltage vector is decomposed into twelve sectors. In the counterclockwise direction, each 30° with the α-axis as the reference is a sector, as Figure 4 shown.

[0109]

[0110] According to the angle calculated by the arctangent function and Figure 4 the sector where the ideal voltage vector is located, the two optimal voltage vectors can be directly judged. The optimal voltage vector table corresponding to different sectors is shown in Table 1.

[0111] Table 1

[0112]

[0113]

[0114] The basis for the selection of the action time of the two effective voltage vectors in the dual-vector model predictive control. According to the deadbeat control strategy, the action time t vec1 and t vec2 of the combination of the two effective voltage vectors are allocated. Since only two optimal voltage vectors act during the entire control period. Therefore, from the stator current state equation (1), it can be obtained that the action time of the two optimal voltage vectors satisfies the condition:

[0115]

[0116] Among them, is the reference value of the quadrature-axis current, h vec1 and h vec2 are the slopes of the quadrature-axis current when the two effective voltage vectors U vec1 and U vec2 act, and t vec1 and t vec2 are the action times of the two effective voltage vectors. The effective voltage vector U vec1The relationship between the corresponding direct-axis and quadrature-axis voltage vectors and the inverter switch states can be expressed as:

[0117]

[0118] Similarly, for the effective voltage vector U vec2 the corresponding relational expression can be expressed as:

[0119]

[0120] where Sa, Sb, and Sc represent the inverter switch states. The states of the upper and lower switching devices of each bridge arm are complementary. Here, "1" is defined as the upper-arm power switching device being on and the lower-arm power switching device being off; conversely, "0" is the upper-arm power switching device being off and the lower-arm power switching device being on.

[0121] According to Equation (1), h vec1 and h vec2 can be respectively expressed as:

[0122]

[0123] In the formula, h0 is the slope of the quadrature-axis current when the zero vector acts. According to Equations (1) and (2), when the zero vector acts and u s = 0, the slope h0 of the quadrature-axis current can be expressed as:

[0124]

[0125] According to Equation (17), the action times t vec1 and t vec2 of the two effective voltage vectors can be expressed as:

[0126]

[0127] Substitute the h vec1 and h vec2 obtained from Equation (19) into Equation (21), and the action times of the two effective voltage vectors can be directly calculated.

[0128] There are two cases for the voltage vector combination of the double-vector model predictive control. One is that the action times of the two effective voltage vectors are both not 0 or T s , and the other is that the action time of one of the two effective voltage vectors is 0 or T s . When the selected voltage vector combination is the second case, it becomes the single-vector model predictive voltage control, and all single-vector model predictive voltage controls are a special case of the double-vector model predictive control.

[0129] Based on the above analysis, continue to execute the following steps.

[0130] Step B. Based on the decomposition values of the ideal voltage vector at the current moment after delay compensation on the α-axis and β-axis, obtain the angle corresponding to the ideal voltage vector at the current moment through the arctangent function, and combine the candidate voltage vectors in each of the twelve sectors divided by the equal angles corresponding to the motor space voltage vector, to obtain the first optimal voltage vector and the second optimal voltage vector corresponding to the ideal voltage vector at the current moment, and then enter Step C.

[0131] Then in practical applications, the above Step B is specifically executed as Steps B1 to B3 as follows.

[0132] Step B1. According to the decomposition values of the ideal voltage vector at the current k moment after delay compensation on the d-axis and q-axis According to the following formula:

[0133]

[0134] Obtain the decomposition values of the ideal voltage vector at the current k moment on the α-axis and β-axis where θ represents the rotor position angle of the permanent magnet brushless DC motor, and then enter Step B2.

[0135] Step B2. Through the arctangent function as follows:

[0136]

[0137] Obtain the angle γ corresponding to the ideal voltage vector at the current k moment, and then enter Step B3.

[0138] Step B3. According to the candidate voltage vectors in each of the twelve sectors divided by the equal angles corresponding to the motor space voltage vector, obtain the first optimal voltage vector U vec1 and the second optimal voltage vector U vec2 .

[0139] Step C. According to the first optimal voltage vector and the second optimal voltage vector corresponding to the ideal voltage vector at the current moment, and based on the sum of the action durations corresponding to the two optimal voltage vectors being equal to the sampling period, obtain the action durations corresponding to the first optimal voltage vector and the second optimal voltage vector respectively, and then enter Step D.

[0140] Furthermore, in practical applications, the above Step C is specifically executed as Steps C1 to C3;

[0141] Step C1. According to the following formula:

[0142]

[0143] Obtain the slope h0 of the quadrature-axis current when the zero vector acts, L sDenote the stator inductance in the permanent magnet brushless DC motor, R s Denote the stator resistance in the permanent magnet brushless DC motor, ω r Denote the angular velocity of the rotor of the permanent magnet brushless DC motor, ψ f Denote the permanent magnet flux linkage of the permanent magnet brushless DC motor, and then enter step C2.

[0144] Step C2. According to the slope h0 of the quadrature-axis current when the zero vector acts, combined with the decomposition values U vec1 of the first optimal voltage vector U vec2 and the second optimal voltage vector U q_vec1 on the q-axis respectively, U q_vec2 , according to the following formula:

[0145]

[0146] Obtain the slopes h vec1 of the quadrature-axis current when the first optimal voltage vector U vec2 and the second optimal voltage vector U vec1 act, h vec2 , and then enter step C3.

[0147] Step C3. According to the following formula:

[0148]

[0149] Obtain the action durations t vec1 corresponding to the first optimal voltage vector U vec2 and the second optimal voltage vector U vec1 respectively, t vec2 , Denote the reference value of the quadrature-axis current, i q (k) represents the decomposition value of the theoretical accurate value of the direct and quadrature-axis currents at the current kth moment on the q-axis.

[0150] Step D. Using the ratio of the action duration corresponding to one of the first optimal voltage vector and the second optimal voltage vector to the sampling period to construct a modulation wave, combined with the upper triangular carrier wave of the preset frequency, divide the duration intervals of the action of the first optimal voltage vector and the second optimal voltage vector respectively in the sampling period to which the current moment belongs, and then combined with the switching states of each bridge arm in the three-phase full bridge corresponding to the ideal voltage vectors respectively in each sector, obtain the drive pulse signal of the three-phase full bridge corresponding to the sampling period to which the current moment belongs, and realize the drive of the permanent magnet brushless DC motor.

[0151] In practical applications, the above step D is specifically executed as steps D1 to D3 as follows.

[0152] Step D1. Using the first optimal voltage vector Uvec1 The corresponding action duration t vec1 and the sampling period T s to construct a modulation wave T cm , and then enter step D2.

[0153] Step D2. Based on the upper triangular carrier wave with a preset frequency, determine the modulation wave T cm The period when it is greater than the upper triangular carrier wave is the duration interval of the action of the first optimal voltage vector in the sampling period to which the current moment belongs, and the modulation wave T cm The period when it is less than the upper triangular carrier wave is the duration interval of the action of the second optimal voltage vector in the sampling period to which the current moment belongs, that is, determine the duration intervals of the actions of the first optimal voltage vector and the second optimal voltage vector in the sampling period to which the current moment belongs, and then enter step D3.

[0154] Step D3. According to the duration intervals of the actions of the first optimal voltage vector and the second optimal voltage vector in the sampling period to which the current moment belongs, combined with the switching states of each bridge arm in the three-phase full bridge corresponding to the ideal voltage vectors in each sector respectively and the preset first optimal voltage vector and the second optimal voltage vector, obtain the drive pulse signal of the three-phase full bridge corresponding to the sampling period to which the current moment belongs, and realize the drive of the permanent magnet brushless DC motor.

[0155] Among them, based on S a , S b , S c respectively represent the switching states of each bridge arm in the three-phase full bridge. The states of the upper and lower power switching tubes of each bridge arm are complementary, and it is defined that the switching state of "1" corresponds to the conduction of the upper bridge arm power switching tube and the cut-off of the lower bridge arm power switching tube, and the switching state of "0" corresponds to the cut-off of the upper bridge arm power switching tube and the conduction of the lower bridge arm power switching tube; the switching states of each bridge arm corresponding to the preset first optimal voltage vector and the second optimal voltage vector in each sector where the ideal voltage vector is located respectively and S a , S b , S c each bridge arm are as follows:

[0156] When the ideal voltage vector is in the first sector, the switching states of each bridge arm corresponding to the preset first optimal voltage vector in the three-phase full bridge are 1, 0, 0 in sequence, and the switching states of each bridge arm corresponding to the preset second optimal voltage vector in the three-phase full bridge are 0, 1, 0 in sequence; a , S b , S c When the ideal voltage vector is in the second sector, the switching states of each bridge arm corresponding to the preset first optimal voltage vector in the three-phase full bridge are 0, 1, 0 in sequence, and the switching states of each bridge arm corresponding to the preset second optimal voltage vector in the three-phase full bridge are 1, 0, 0 in sequence; a , S b , S c When the ideal voltage vector is in the second sector, the switching states of each bridge arm corresponding to the preset first optimal voltage vector in the three-phase full bridge are 0, 1, 0 in sequence, and the switching states of each bridge arm corresponding to the preset second optimal voltage vector in the three-phase full bridge are 1, 0, 0 in sequence;

[0157] When the ideal voltage vector is in the second sector, the switching states of each bridge arm corresponding to the preset first optimal voltage vector in the three-phase full bridge are S a , Sb , S c The switching states of each bridge arm are 1, 1, 0 in sequence, and the preset second optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 1, 0, 1 in sequence;

[0158] When the ideal voltage vector is in the third sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 1, 1, 0 in sequence, and the preset second optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 0, 1, 1 in sequence;

[0159] When the ideal voltage vector is in the fourth sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 0, 1, 0 in sequence, and the preset second optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 1, 0, 0 in sequence;

[0160] When the ideal voltage vector is in the fifth sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 0, 1, 0 in sequence, and the preset second optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 0, 0, 1 in sequence;

[0161] When the ideal voltage vector is in the sixth sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 0, 1, 1 in sequence, and the preset second optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 1, 1, 0 in sequence;

[0162] When the ideal voltage vector is in the seventh sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S cThe switching states of each bridge arm are 0, 1, 1 in sequence. The preset second optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 1, 0, 1 in sequence;

[0163] When the ideal voltage vector is in the eighth sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 0, 0, 1 in sequence. The preset second optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 0, 1, 0 in sequence;

[0164] When the ideal voltage vector is in the ninth sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 0, 0, 1 in sequence. The preset second optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 1, 0, 0 in sequence;

[0165] When the ideal voltage vector is in the tenth sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 1, 0, 1 in sequence. The preset second optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 0, 1, 1 in sequence;

[0166] When the ideal voltage vector is in the eleventh sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 1, 0, 1 in sequence. The preset second optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are 1, 1, 0 in sequence;

[0167] When the ideal voltage vector is in the twelfth sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S cThe switching states of each bridge arm are successively 1, 0, 0, and the preset second optimal voltage vector corresponds to S in the three-phase full bridge a , S b , S c The switching states of each bridge arm are successively 0, 0, 1.

[0168] That is, in practical applications, according to the switching states of each bridge arm in the three-phase full bridge corresponding to the preset first optimal voltage vector and the second optimal voltage vector respectively under each sector where the above ideal voltage vectors are located, the drive pulse signals corresponding to the three-phase full bridge in the current sampling period are obtained, so as to realize the drive of the permanent magnet brushless DC motor.

[0169] In the application of the permanent magnet brushless DC motor model predictive control method designed by the above technical solution, by increasing the number of voltage vectors applied in each sampling period, flexibly selecting and adjusting the two voltage vectors and their respective action times, the prediction result is closer to the ideal voltage vector, the system stability is improved, the torque ripple is reduced, and a better control effect is obtained; the design method judges the position of the ideal voltage vector through twelve-sector division, directly selects two optimal voltage vectors, and there is no need to use the value function to select the second optimal voltage vector by traversing, which greatly reduces the calculation amount and makes the model predictive control method more practical and universal.

[0170] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge scope of those of ordinary skill in the art.

Claims

1. A vector optimal prediction control method for a permanent magnet brushless DC motor, which is used for predictive control of a permanent magnet brushless DC motor under a three-phase full-bridge drive mode, is characterized in that, It includes the following steps: Step A. According to the second-order Euler discretization, using the stator current state equation in the rotating coordinate system, obtain the predicted values of the direct and quadrature axis currents after prediction and correction at the next moment, and adopt the deadbeat prediction control idea to obtain the ideal voltage vector at the current moment after delay compensation, and then enter Step B; Step B. Based on the decomposition values of the ideal voltage vector at the current moment after delay compensation on the α-axis and β-axis, obtain the angle corresponding to the ideal voltage vector at the current moment through the arctangent function, and combine the candidate voltage vectors in the twelve sectors corresponding to the equal angle division of the motor space voltage vector to obtain the first optimal voltage vector and the second optimal voltage vector corresponding to the ideal voltage vector at the current moment, and then enter Step C; The above Step B includes the following Steps B1 to B3; Step B1. According to the decomposition values of the ideal voltage vector at the current k-th moment after delay compensation on the d-axis and q-axis According to the following formula: Obtain the decomposition values of the ideal voltage vector at the current k moment on the α-axis and β-axis respectively where θ represents the rotor position angle of the permanent magnet brushless DC motor, and then proceed to step B2; Step B2. Through the arctangent function as follows: Obtain the angle γ corresponding to the ideal voltage vector at the current moment k, and then enter Step B3; Step B3. Obtain the first optimal voltage vector U corresponding to the ideal voltage vector at the current moment according to each candidate voltage vector in the lower twelve sectors divided by equal angles corresponding to the motor space voltage vector vec1 , the second optimal voltage vector U vec2 ; Step C. According to the first optimal voltage vector and the second optimal voltage vector corresponding to the ideal voltage vector at the current moment, make the sum of the action durations corresponding to the two optimal voltage vectors equal to the sampling period to obtain the action durations corresponding to the first optimal voltage vector and the second optimal voltage vector respectively, and then enter Step D; The above Step C includes the following Steps C1 to C3; Step C1. According to the following formula: Obtain the slope h0,L of the quadrature-axis current when the zero vector acts s Denote the stator inductance in the permanent magnet brushless DC motor, R s Denote the stator resistance in the permanent magnet brushless DC motor, ω r Denote the rotor angular velocity of the permanent magnet brushless DC motor, ψ f Denote the permanent magnet flux linkage of the permanent magnet brushless DC motor, and then enter step C2; Step C2. According to the slope h0 of the quadrature-axis current when the zero vector acts, combined with the decomposition values U vec1 and U vec2 of the first optimal voltage vector and the second optimal voltage vector on the q-axis respectively, U q_vec1 and U q_vec2 , according to the following formula: Obtain the first optimal voltage vector U vec1 , the second optimal voltage vector U vec2 The slope h of the quadrature-axis current when acting vec1 , h vec2 , and then enter step C3; Step C3. According to the following formula: Obtain the first optimal voltage vector U vec1 and the second optimal voltage vector U vec2 respectively corresponding action durations t vec1 and t vec2 , represents the quadrature-axis current reference value, and i q (k) represents the decomposition value of the theoretical exact value of the direct and quadrature-axis currents at the current k-th moment on the q-axis; Step D. Construct a modulation wave with the ratio of the action duration corresponding to one of the first optimal voltage vector and the second optimal voltage vector to the sampling period, combine it with the upper triangular carrier of the preset frequency, divide the duration intervals of the first optimal voltage vector and the second optimal voltage vector acting respectively in the sampling period to which the current moment belongs, and then combine the switching states of each bridge arm in the three-phase full bridge corresponding to the ideal voltage vector in each sector and the preset first optimal voltage vector and the second optimal voltage vector respectively to obtain the drive pulse signal of the three-phase full bridge corresponding to the sampling period to which the current moment belongs, so as to realize the drive of the permanent magnet brushless DC motor.

2. The vector optimal prediction control method for a permanent magnet brushless DC motor according to claim 1, wherein: The above Step A includes the following Steps A1 to A3; Step A1. According to the second-order Euler discretization, according to the following formula: In the formula Obtain the exact theoretical value \(i_{(k + 1)}\) of the current at the next \(k + 1\) moment, where \(i_{(k)}\) represents the exact theoretical value of the current at the current \(k\) moment, \(e_{(k)}\) represents the back electromotive force at the current \(k\) moment, \(L\) represents the stator inductance in the permanent magnet brushless DC motor, \(R\) represents the stator resistance in the permanent magnet brushless DC motor, \(T\) represents the sampling period, and then proceed to step A2; s (k + 1), where s (k) represents the exact theoretical value of the current at the current k moment, e s (k) represents the back electromotive force at the current k moment, L s represents the stator inductance in the permanent magnet brushless DC motor, R s represents the stator resistance in the permanent magnet brushless DC motor, T s represents the sampling period, and then enter step A2; Step A2. Using the stator current state equation in the rotating coordinate system, as follows: Obtain the decomposition values of the predicted corrected direct-axis and quadrature-axis current prediction values at the next k+1 moment on the d-axis and q-axis, i d (k+1) and i q (k+1), where i d0 (k) and i q0 (k) respectively represent the decomposition values of the current i s0 (k) on the d-axis and q-axis, u d (k) and u q (k) represent the decomposition values of the selected effective voltage vectors corresponding to the current sampling period at the current k moment on the d-axis and q-axis respectively; then enter step A3; Step A3. Adopt the deadbeat predictive control idea and combine with According to the following formula: The decomposed values of the ideal voltage vector at the current k-th moment after obtaining the delay compensation on the d-axis and q-axis respectively wherein respectively represent the decomposed values of the current reference values of the AC and DC axes at the current k-th moment on the d-axis and q-axis respectively.

3. A vector optimal prediction control method for a permanent magnet brushless DC motor according to claim 1, characterized in that: The twelve sectors corresponding to the equal angle division of the motor space voltage vector are obtained by the following operations; Operation: First, based on the candidate voltage vectors obtained by decomposing the basic voltage vector of the motor on the α-axis and β-axis, construct a six-sector division with a 60-degree interval between adjacent candidate voltage vectors; then, according to the position of the ideal voltage vector in the six-sector division, select the corresponding first optimal voltage vector and the second optimal voltage vector, and construct the voltage vector motion trajectory of the decomposed ideal voltage vector in the six-sector division according to this rule; then, according to the voltage vector motion trajectory, further divide the basic voltage vector of the motor into a twelve-sector division with a 30-degree interval between adjacent ones.

4. The vector optimal prediction control method for a permanent magnet brushless DC motor according to claim 1, wherein: The above Step D includes the following Steps D1 to D3; Step D1. Using the action duration t vec1 corresponding to the first optimal voltage vector U vec1 and the sampling period T s to construct a modulation wave T cm , and then proceed to Step D2; Step D2. Determine the modulation wave T based on the upper triangular carrier wave with a preset frequency cm The time period greater than the upper triangular carrier wave is the duration interval during which the first optimal voltage vector acts in the sampling period to which the current moment belongs, and the modulation wave T cm The time period less than the upper triangular carrier wave is the duration interval during which the second optimal voltage vector acts in the sampling period to which the current moment belongs, that is, determine the duration intervals during which the first optimal voltage vector and the second optimal voltage vector act in the sampling period to which the current moment belongs respectively, and then enter step D3; Step D3. According to the duration intervals of the first optimal voltage vector and the second optimal voltage vector acting respectively in the sampling period at the current moment, combined with the switching states of each bridge arm in the three-phase full bridge corresponding to the preset first optimal voltage vector and the second optimal voltage vector respectively in each sector where the ideal voltage vector is located, obtain the drive pulse signal of the three-phase full bridge corresponding to the sampling period at the current moment, and realize the drive of the permanent magnet brushless DC motor.

5. The vector optimal prediction control method for a permanent magnet brushless DC motor according to claim 1 or 4, characterized in that: Based on S a , S b , S c respectively represent the switching states of each arm in the three-phase full bridge. The states of the upper and lower power switching transistors in each arm are complementary. It is defined that the switching state of "1" corresponds to the conduction of the upper-arm power switching transistor and the turn-off of the lower-arm power switching transistor, and the switching state of "0" corresponds to the turn-off of the upper-arm power switching transistor and the conduction of the lower-arm power switching transistor; the ideal voltage vectors in each sector respectively, the preset first optimal voltage vector and the second optimal voltage vector respectively correspond to S a , S b , S c The switching states of each arm are as follows: When the ideal voltage vector is in the first sector, the preset first optimal voltage vector corresponds to S in the three-phase full bridge a 、S b 、S c The switching states of each bridge arm are 1, 0, 0 in sequence. The preset second optimal voltage vector corresponds to S in the three-phase full bridge a 、S b 、S c The switching states of each bridge arm are 0, 1, 0 in sequence; When the ideal voltage vector is in the second sector, the switching states of the switches in the three-phase full-bridge corresponding to the preset first optimal voltage vector for S a , S b , S c in each bridge arm are 1, 1, 0 in sequence, and the switching states of the switches in the three-phase full-bridge corresponding to the preset second optimal voltage vector for S a , S b , S c in each bridge arm are 1, 0, 1 in sequence; When the ideal voltage vector is in the third sector, the switching states of the S a , S b , S c arms of the three-phase full-bridge are successively 1, 1, 0, and the switching states of the S a , S b , S c arms of the preset second optimal voltage vector corresponding to the three-phase full-bridge are successively 0, 1, 1; When the ideal voltage vector is in the fourth sector, the preset first optimal voltage vector corresponds to S in the three-phase full-bridge a , S b , S c The switching states of each bridge arm are 0, 1, 0 in sequence. The preset second optimal voltage vector corresponds to S in the three-phase full-bridge a , S b , S c The switching states of each bridge arm are 1, 0, 0 in sequence; When the ideal voltage vector is in the fifth sector, the switching states of the S a , S b , S c arms of the three-phase full bridge are successively 0, 1, 0, and the switching states of the S a , S b , S c arms of the second optimal voltage vector corresponding to the three-phase full bridge are successively 0, 0, 1; When the ideal voltage vector is in the sixth sector, the switching states of the S a , S b , S c arms of the three-phase full-bridge are sequentially 0, 1, 1, and the switching states of the S a , S b , S c arms of the preset second optimal voltage vector corresponding to the three-phase full-bridge are sequentially 1, 1, 0; When the ideal voltage vector is in the seventh sector, the switching states of the S a , S b , S c arms of the three-phase full-bridge are sequentially 0, 1, 1, and the switching states of the S a , S b , S c arms of the second optimal voltage vector corresponding to the three-phase full-bridge are sequentially 1, 0, 1; When the ideal voltage vector is in the eighth sector, the switching states of the S a , S b , S c arms of the three-phase full-bridge are successively 0, 0, 1, and the switching states of the S a , S b , S c arms of the preset second optimal voltage vector corresponding to the three-phase full-bridge are successively 0, 1, 0; When the ideal voltage vector is in the ninth sector, the switching states of the switches in the three-phase full-bridge corresponding to the preset first optimal voltage vector for S a , S b , S c in each bridge arm are 0, 0, 1 in sequence, and the switching states of the switches in the three-phase full-bridge corresponding to the preset second optimal voltage vector for S a , S b , S c in each bridge arm are 1, 0, 0 in sequence; When the ideal voltage vector is in the tenth sector, the switching states of the S a , S b , S c arms of the three-phase full-bridge are successively 1, 0, 1. The switching states of the S a , S b , S c arms of the three-phase full-bridge corresponding to the preset second optimal voltage vector are successively 0, 1, 1; When the ideal voltage vector is in the eleventh sector, the preset first optimal voltage vector corresponds to S in the three-phase full-bridge a , S b , S c The switching states of each bridge arm are 1, 0, 1 in sequence. The preset second optimal voltage vector corresponds to S in the three-phase full-bridge a , S b , S c The switching states of each bridge arm are 1, 1, 0 in sequence; When the ideal voltage vector is in the twelfth sector, the switch states of each arm of the preset first optimal voltage vector corresponding to the three-phase full-bridge for S a , S b , S c are 1, 0, 0 in sequence, and the switch states of each arm of the preset second optimal voltage vector corresponding to the three-phase full-bridge for S a , S b , S c are 0, 0, 1 in sequence.

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