A model predictive fault-tolerant control method for five-phase permanent magnet synchronous motor based on deadbeat

Abstract

The present invention discloses a five-phase permanent magnet synchronous motor model prediction fault-tolerant control method based on deadbeat. The method first discretizes the voltage equation, iterates the discretized voltage equation once, obtains the current at the next moment, and calculates the reference voltage based on the deadbeat idea. Secondly, the voltage cost function is designed. Then, the voltage vector after the fault is synthesized on the principle of suppressing the third harmonic current to zero, and a virtual voltage vector is obtained, and the virtual voltage vector is processed with equal amplitude. Finally, the processed virtual voltage vector is divided into sectors, so that the optimal voltage vector corresponding to the reference voltage vector in each sector is the virtual voltage vector in the sector. The present invention can effectively reduce the calculation amount of the finite set model prediction fault-tolerant control of the five-phase permanent magnet synchronous motor under the open circuit fault, and suppress the torque pulsation and current harmonics caused by the fault, and has a good application prospect.

Description

Technical Field

[0001] The present invention belongs to the field of multi-phase motor fault-tolerant control, and in particular to open-circuit fault-tolerant control of a five-phase permanent magnet synchronous motor (PMSM). The present invention is applicable to occasions such as aerospace, electric vehicles, and ship propulsion that require high motor operation reliability. Background Art

[0002] PMSM has the advantages of high torque density, high efficiency, and high reliability. In recent years, it has been widely used in aerospace, electric vehicles, ship propulsion, etc. Since multi-phase motors have more control freedom than three-phase motors and can be used in situations with high reliability requirements, they have attracted widespread attention from scholars at home and abroad.

[0003] After a multi-phase motor fails, the use of a fault-tolerant control algorithm can keep the motor's performance similar to that of normal operation. At present, the fault-tolerant control algorithm of the five-phase PMSM is mainly based on vector control and direct torque control. The model predictive control algorithm was not taken seriously when it was first proposed because of its large amount of calculation and high hardware requirements. With the maturity of computer technology and power electronics technology, more and more scholars have begun to conduct in-depth research on the model predictive control algorithm.

[0004] The finite set model predictive control for PMSM converts each available voltage vector into a corresponding current value, substitutes it into the current cost function, and iterates to obtain the voltage vector that minimizes the cost function. For a five-phase PMSM, there are 32 available voltage vectors during normal operation. The amount of calculation required for voltage vector screening is greatly increased compared to vector control and direct torque control, which has high hardware requirements and poor steady-state performance. Therefore, some scholars have proposed using virtual voltage vectors to reduce the amount of calculation and introducing duty cycle control to improve the steady-state performance of the algorithm. Although this method can effectively improve control performance, it is mainly aimed at normal operation of the motor. When a motor fails, the current distortion is severe and the torque pulsation becomes larger. The fault-tolerant control algorithm based on model prediction needs further in-depth research.

[0005] When any phase of the motor fails (taking phase A as an example), the available voltage vectors change from 32 to 16, and the amplitude of the fundamental space voltage vector is unequal and unevenly distributed. In order to suppress torque pulsation and reduce the amount of calculation and current harmonic content, Chinese invention patent application No. 201810282582.5 discloses a finite set model predictive fault-tolerant control method based on virtual voltage vectors, which has achieved good fault-tolerant control effects. However, the use of virtual vectors still requires 8 iterations of the current cost function, which takes a long time to calculate. In order to reduce the amount of calculation, the literature IEEE Transactions on Industry Applications, vol.55, no.6, pp.6001-6010, Nov.-Dec.2019 (Performance Improvement of Model Predictive Current Control of Fault-Tolerant Five-Phase Flux-Switching Permanent Magnet Motor Drive) proposed a voltage vector pre-selection control strategy, which reduced the voltage vectors of each iteration from 15 to 3, greatly reducing the amount of calculation; however, the voltage vector finally selected by this strategy is a large vector, and the third harmonic problem is not considered, resulting in a high harmonic content and poor steady-state performance. Therefore, it is necessary to further study model predictive fault-tolerant control to further reduce the amount of calculation and improve the steady-state performance of the algorithm while ensuring that the dynamic performance remains unchanged. Summary of the invention

[0006] In view of the shortcomings and defects of the existing model predictive fault-tolerant control technology, this paper proposes a deadbeat-based model predictive fault-tolerant control strategy for five-phase PMSM. The purpose is to reduce the post-fault model prediction calculation time, simplify the duty cycle calculation method, and ensure that the post-fault model predictive control obtains excellent dynamic and steady-state performance.

[0007] The specific steps of the technical solution of the present invention are as follows: A five-phase permanent magnet synchronous motor PMSM model prediction fault-tolerant control method based on zero-beat includes the following steps:

[0008] Step 1: The actual speed of the five-phase PMSM detected is used as the feedback speed n of the motor and the given speed n of the motor. ref The motor speed error is obtained by subtracting n, and the q-axis current of the motor is obtained through the PI controller, and this current is used as the q-axis reference current. At the same time, i d =0 control, d-axis reference current

[0009] Step 2: Based on the principle of minimum copper loss, reconstruct the fault-tolerant reduced-order transformation matrix of the five-phase PMSM in the case of an open-circuit fault in phase A.

[0010]

[0011] Where: α = 0.4π;

[0012] Step 3: Use the fault-tolerant reduced-order transformation matrix to transform the remaining non-fault phase current i collected by the current sensor into B 、i C 、i D 、i E The current i transformed into the fundamental wave space and harmonic wave space of the two-phase stationary coordinate system α 、i β 、i y , and then the current in the dq coordinate system is obtained by Park transformation

[0013] Step 4: Establish and discretize the voltage equation of the five-phase PMSM with a single-phase open circuit fault in the dq coordinate system to obtain the current value at time k+1 On this basis, the discrete voltage equation is iterated once to obtain the current value at time k+2

[0014]

[0015] Where: R is the stator resistance; L is the stator inductance; ω is the electrical angle; is the permanent magnet flux; T s To control the cycle; is the current at time k+1; is the current at time k+2; is the voltage at time k+1;

[0016] Step 5: Set the reference current on the dq coordinate system and Assign to and Derivation of reference voltage based on deadbeat idea and Then use the Park inverse transformation matrix to transform it to the two-phase stationary coordinate system to obtain the reference voltage on the two-phase stationary coordinate system and The new voltage cost function is designed in the two-phase stationary coordinate system:

[0017]

[0018] Where: is the reference voltage, is the voltage in the stationary coordinate system at time k+1.

[0019] Step 6, using a fault-tolerant reduced-order transformation matrix to transform the non-fault phase voltages corresponding to different switching states of the power devices in the PMSM inverter to a two-phase stationary coordinate system, and obtain voltage vector distribution diagrams in the fundamental wave space and the harmonic wave space after the open circuit fault;

[0020] Step 7: To suppress the third harmonic current i y =0 is the principle to synthesize the voltage vector in the harmonic space of the two-phase stationary coordinate system to zero, and then obtain the synthetic virtual voltage vector in the fundamental wave space of the two-phase stationary coordinate system, and take the virtual voltage vector with the shortest amplitude as the base value, perform equal amplitude processing on the virtual voltage vector, and obtain the processed virtual voltage vector vv i = k(d1u i+ d2u j ), i=1…8, u i is a basic voltage vector synthesized with the virtual voltage vector, u j is another basic voltage vector synthesized with the virtual voltage vector, d1 and d2 are the action coefficients of the two corresponding basic voltage vectors, and k is the coefficient that makes all virtual voltage vectors have the same amplitude;

[0021] Step 8: divide the equal-amplitude virtual voltage vector into sectors in the fundamental wave space. The area enclosed by two adjacent virtual voltage vectors is an isosceles triangle. The vertex bisector of the isosceles triangle is used as the dividing line of each sector. Each isosceles triangle is divided into sectors in equal parts. Each virtual voltage vector falls on the center line of each sector.

[0022] Step 9, according to the reference voltage on the two-phase stationary coordinate system obtained in step 5, calculate the sector where the reference voltage vectors corresponding to the two reference voltages are located, and then according to the voltage cost function in step 5, it can be determined that the virtual voltage vector in the sector where the reference voltage vector is located is the optimal voltage vector to be optimized, and the optimal voltage vector is projected onto the reference voltage vector, and then the optimal action time t of the optimal voltage vector in each control cycle is obtained by the geometric method. opt ;

[0023] Step 10: Convert the selected optimal voltage vector and optimal action time into basic voltage vectors and action time of each basic voltage vector.

[0024]

[0025] Where: t1 is the action time of the first basic voltage vector; t2 is the action time of the second basic voltage vector; t optis the optimal voltage vector action time; d1 is the first basic voltage proportion in the virtual vector; d2 is the second basic voltage proportion in the virtual voltage vector; k is the new virtual voltage amplitude proportional coefficient, T s To control the cycle;

[0026] The selected basic voltage vector and action time are input into the PWM module to generate a PWM waveform, control the on and off of the power devices in the inverter, and realize the fault-tolerant control of the five-phase PMSM.

[0027] Furthermore, the mathematical model of the five-phase PMSM with single-phase open circuit fault in step 4 in the dq coordinate system is discretized by the previous Euler method to obtain

[0028]

[0029] Thus, the current value at time k+2 is obtained by iteration

[0030] Further, the specific process of step 5 is:

[0031] Step 5.1, based on the idea of ​​zero beat, the reference current and and in step 4 and The reference voltage in the dq coordinate system is derived as

[0032]

[0033] Furthermore, the reference current and It can be expressed as

[0034]

[0035] Step 5.2, design the traditional current cost function as

[0036] Step 5.3, add the current at time k+2 in step 4 and the current at time k+2 in step 5.1. and Substituting the expression into the current cost function, the equivalent voltage cost function is obtained:

[0037]

[0038] Step 5.4, use the Park inverse transformation matrix to transform the voltage in the dq coordinate system in the equivalent voltage cost function into the two-phase stationary coordinate system, thereby obtaining a new voltage cost function.

[0039] Further, the specific process of step 6 is:

[0040] Step 6.1, when phase A is open, the voltage of each non-fault phase corresponding to the switching state of the upper bridge arm power device in the five-phase PMSM inverter can be expressed as

[0041]

[0042] Where: U dc is the bus voltage, s i (i=b, c, d, e) is the switching state of the upper arm power devices of inverter b, c, d, e, s i =1 means open, s i =0 means off;

[0043] Step 6.2: Use the fault-tolerant reduced-order transformation matrix to transform the four-phase voltage into a two-phase stationary coordinate system.

[0044]

[0045] Thus, the voltage vectors of the fundamental wave space and the third harmonic space of the two-phase stationary coordinate system after the open circuit fault are obtained, where the basic voltage vectors u8 and u 14 , u7, u1 amplitude is 0.441U dc , basic voltage vector u 13 、u4、u2、u 11 The amplitude is 0.325U dc , the amplitude of u9 and u6 is 0.447U dc , basic voltage vector u 12 、u3 amplitude is 0.616U dc , basic voltage vector u 10 、u5 amplitude is 0.145U dc .

[0046] Further, the specific process of step 7 is:

[0047] Step 7.1, based on the principle of suppressing the third harmonic current, the above basic voltage vector is used to synthesize a virtual voltage vector so that it is zero in the third harmonic space, and then the virtual voltage vector synthesized by the above basic voltage vector in the fundamental wave space is obtained. The amplitude of these virtual voltage vectors vv1 and vv5 is 0.447U dc , the amplitude of vv2, vv4, vv6, and vv8 is 0.394U dc , the amplitude of vv3 and vv7 is 0.526U dc .

[0048] Step 7.2: In order to make the optimal voltage vector selected in each step have the same control effect, it is necessary to process the amplitudes of these virtual voltage vectors to make the synthesized virtual voltage vectors have the same amplitude.dc As the reference of the virtual voltage vector amplitude, vv1 and vv5 need to be multiplied by the coefficient k, which is 0.88; vv3 and vv7 need to be multiplied by the coefficient k, which is 0.75. The synthesized virtual voltage vector can be expressed as vv i = k(d1u i +d2u j ), i=1…8, u i Represents a basic voltage vector with the synthesized virtual voltage vector, u j represents another basic voltage vector of the synthesized virtual voltage vector, d1 and d2 represent the action coefficients of the corresponding two basic voltage vectors respectively, and k is the coefficient that makes all virtual voltage vectors have the same amplitude.

[0049] Further, in step 7, the relationship between each synthesized virtual voltage vector and the basic voltage vector is:

[0050]

[0051] Further, the specific process of step 9 is as follows:

[0052] Step 9.1, calculate the reference voltage vector angle

[0053]

[0054] Where: is the projection of the reference voltage vector on the β axis; is the projection of the reference voltage vector on the α axis; θ u is the reference voltage vector angle. Based on this, the sector where the reference voltage vector is located is determined, and the virtual voltage vector in the sector is determined to be the optimal voltage vector according to the new voltage cost function in step 5;

[0055] Step 9.2, project the reference voltage vector onto the optimal voltage vector, and calculate the optimal action time of the optimal voltage vector in a control cycle based on the geometric method.

[0056]

[0057] Where: t opt is the optimal voltage vector action time; θ i is the optimal voltage vector angle; θ u is the reference voltage vector angle; |u ref | is the reference voltage vector amplitude; |u opt | is the optimal voltage vector amplitude; T s To control the cycle.

[0058] The present invention has the following beneficial effects:

[0059] 1) The present invention converts the current cost function into a voltage cost function equivalently, avoiding the process of indirectly selecting the voltage vector according to the iteration of the current cost function, adopts the current method based on zero-beat to obtain the reference voltage vector, and accurately establishes the relationship between the reference voltage vector and the reference current. It can not only obtain the accuracy of current control, but also make the torque control effect through the voltage vector more direct and simpler, and greatly reduce the amount of calculation.

[0060] 2) The present invention processes the amplitude of the virtual voltage vector after the fault to be equal, and then divides each sector into equal parts. Then, a new voltage cost function is combined to directly obtain the virtual voltage vector corresponding to the sector where the reference voltage vector is located, which is the optimal voltage vector. This not only saves the process of determining the minimum distance between the reference voltage vector and the adjacent virtual vector, but also avoids the repeated iterative calculation process, and obtains the optimal voltage vector more concisely and intuitively, greatly reducing the amount of calculation.

[0061] 3) The present invention calculates the optimal voltage vector duty cycle by geometric method, which simplifies the traditional model prediction duty cycle calculation method based on the derivation of the current cost function, makes the control more precise, and greatly reduces the amount of calculation.

[0062] 4) The use of deadbeat-based model predictive fault-tolerant control not only eliminates the iterative process of the cost function, but also has better dynamic performance; in addition, the use of duty cycle control improves the steady-state performance.

[0063] 5) The present invention incorporates the fault-tolerant control strategy into the beat-free model predictive control of the present invention, which not only effectively suppresses the torque pulsation caused by the open-circuit fault, but also achieves the excellent steady-state and dynamic performance of the motor under the open-circuit fault condition with minimal calculation compared with the traditional model predictive control. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 The block diagram of the deadbeat model-based predictive fault-tolerant control for the five-phase PMSM;

[0065] Figure 2 It is the open circuit basic voltage vector distribution of phase A;

[0066] Figure 3 Synthesize virtual voltage vector distribution and sector division for phase A open circuit;

[0067] Figure 4 It is the five-phase PMSM reference voltage vector projection and geometric method schematic diagram;

[0068] Figure 5 This is the FFT waveform of the B-phase current under the five-phase PMSM fault tolerance condition;

[0069] Figure 6The torque and speed waveforms of the five-phase PMSM when it switches from normal operation to fault tolerance;

[0070] Figure 7 It is the torque step waveform under the fault-tolerant state of the five-phase PMSM;

[0071] Figure 8 It is the speed step waveform of the five-phase PMSM in the fault-tolerant state. DETAILED DESCRIPTION

[0072] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings.

[0073] The control block diagram designed by the present invention is as follows Figure 1 As shown in the figure, the present invention is composed of a double closed-loop system consisting of a deadbeat model predictive control current inner loop and a PI control speed outer loop. First, the given speed and the actual speed collected by the photoelectric encoder are subtracted to obtain the speed error, and the speed error is input into the speed loop PI controller. After PI adjustment, the q-axis reference current i is output. q ref .

[0074] The non-fault phase current i after the A phase open circuit fault is obtained by collecting the current sensor B 、i C 、i D 、i E According to the principle that the magnetic motive force remains unchanged before and after the fault, the fault-tolerant reduced-order transformation matrix based on the principle of minimum copper loss after phase A is open can be derived:

[0075]

[0076] Where: α = 0.4π. The acquired current is transformed into the dq coordinate system using the transformation matrix and the Park transformation matrix. Therefore, the mathematical equation of the five-phase PMSM under fault condition can be expressed as

[0077]

[0078] Where: u d 、u q 、i d 、i q are the voltage and current in the dq coordinate system; R is the stator resistance; L is the inductance; ω is the electrical angular velocity; is the permanent magnet flux. The voltage equation is discretized using the previous Euler method, and the current value at time k+1 is

[0079]

[0080] Due to the delay of digital control, considering one step of delay, the current at time k+2 is

[0081]

[0082] According to the deadbeat idea, the reference current is assigned to the current at time k+2, that is, i ref =i k+2 , and substituting it into equation (4), the reference current is

[0083]

[0084] The cost function of the traditional model predictive current control can generally be designed as

[0085]

[0086] Substituting equations (4) and (5) into equation (6), we can obtain

[0087]

[0088] Using the Park inverse transformation matrix to transform the voltage in the dq coordinate system in equation (7) into the two-phase stationary coordinate system, the voltage cost function can be derived as follows:

[0089]

[0090] The voltage at time k+1 is derived from equation (5) as equation (9), which is transformed into a two-phase stationary coordinate system using the Park inverse transformation matrix and used as the reference voltage in equation (8).

[0091]

[0092] Furthermore, when phase A is open, the non-fault phase voltage corresponding to different switching states of the power devices in the five-phase PMSM inverter can be expressed as

[0093]

[0094] Where: U dc is the DC bus voltage, s i(i＝b、c、d、e) Indicates the switching state of the power devices in the four bridge arms b, c, d, and e in the inverter, s i =1 means the power device is turned on, s i = 0 means the device is turned off. The four-phase voltage is transformed to the two-phase stationary coordinate system through the fault-tolerant reduced-order transformation matrix to obtain

[0095]

[0096] The voltage vector distributions of fundamental wave space and harmonic wave space corresponding to different switching states are obtained from formula (11), as follows: Figure 2 As shown. Among them, in the fundamental wave space, u8, u 14, u7, u1 amplitude is 0.441U dc ;u 13 、u4、u2、u 11 The amplitude is 0.325U dc ; The amplitude of u9 and u6 is 0.447U dc ;u 12 、u3 amplitude is 0.616U dc ;u 10 、u5 amplitude is 0.145U dc .

[0097] Depend on Figure 2 It can be seen that after the motor fails, the voltage vector is unevenly distributed and there is a voltage vector in the harmonic space. Based on the principle of suppressing the third harmonic current to zero, the above basic voltage vector is used to synthesize the virtual voltage vector to make it zero in the third harmonic space, and then the virtual voltage vector synthesized in the fundamental space is obtained. In the fundamental space, the amplitude of vv1 and vv5 is 0.447U dc ; The amplitude of vv2, vv4, vv6, and vv8 is 0.394U dc ; The amplitude of vv3 and vv7 is 0.526U dc In order to make the optimal voltage vector selected in each step have the same control effect, the amplitudes of these virtual voltage vectors need to be processed equally so that the synthesized virtual voltage vectors have the same amplitude. dc As the reference of the virtual voltage vector amplitude, vv1 and vv5 need to be multiplied by a coefficient of 0.88; vv3 and vv7 need to be multiplied by a coefficient of 0.75. The synthesis method of the virtual voltage vector and the action time of each basic voltage vector are shown in Table 1. The distribution of the virtual voltage vector is shown in Figure 3 shown.

[0098] Table 1 Synthesized virtual voltage vector

[0099]

[0100]

[0101] The synthesized virtual voltage vector in Table 1 can be expressed as vv i = k(d1u i+ d2u j ), where i=1...8, u i represents a basic voltage vector, u j represents another basic voltage vector, d1 and d2 represent the corresponding basic voltage vector action coefficients respectively, and k is the coefficient that makes all virtual voltage vectors have the same amplitude.

[0102] The current cost function is converted into a voltage cost function, and the original current cost function iteration process is equivalently converted into a process of calculating the distance between the reference voltage vector and the virtual voltage vector. Therefore, the virtual voltage vector closest to the reference voltage vector is the optimal voltage vector u opt .

[0103] Since the virtual voltage vector synthesized after the fault is unevenly distributed in space, the sector surrounded by adjacent voltage vectors is not a uniform sector. In order to directly determine the optimal vector corresponding to the sector where the reference voltage vector is located, the vertex bisector of the adjacent virtual voltage vector is used as the boundary of the new sector. The advantage of dividing the sector in this way is that the virtual voltage vector closest to the reference voltage vector can be directly obtained without multiple calculations. The sector division diagram is shown in Figure 3.

[0104] Take the reference voltage vector in sector 1 as an example (the area surrounded by vv1 and vv2), assuming that the distance between the reference voltage vector and the optimal voltage vector is r, as Figure 4 As shown. If sector division is not performed, then the distance between the reference voltage vector and the two adjacent virtual voltage vectors needs to be calculated. The distance between the reference voltage vector and vv1 is r1, and the distance between the reference voltage vector and vv2 is r2. Obviously, r1<r2, so r=r1. However, by dividing the sectors (with the dotted line as the sector boundary), as long as the reference voltage vector falls in sector I, the optimal voltage vector vv1 can be immediately obtained.

[0105] In order to improve the steady-state performance of the control system and reduce the torque ripple and current harmonic content, the duty cycle control is introduced by projecting the reference voltage vector to the optimal voltage vector, such as Figure 4 As shown. Based on the geometric method, the optimal voltage vector duty cycle can be calculated

[0106]

[0107] Where: θ u Represents the angle of the reference voltage vector, θ i Represents the angle of the optimal voltage vector, T s To control the cycle.

[0108] The selected basic voltage vector and action time are input into the PWM module to generate a PWM waveform, control the on and off of the power devices in the inverter, and realize the fault-tolerant control of the five-phase PMSM.

[0109] The current harmonic analysis, torque and speed waveforms of the motor in steady state are as follows: Figure 5 and 6As shown in the figure, it can be seen that the torque pulsation after the fault occurs is similar to that during normal operation, and the speed is stable at 300rpm; the harmonic content of the B-phase current in the steady state after the fault is 0.78%. It proves that the invented fault-tolerant control algorithm has good steady-state performance under the condition of motor open circuit fault. In the fault-tolerant condition, the load and speed step waveforms are as follows Figure 7 and 8 As shown. It can be seen that when the load steps from 5Nm to 10Nm, the torque tracking is timely and accurate; when the speed steps from 200rpm to 300rpm, there is no obvious overshoot in the feedback speed. The above dynamic simulation fully proves that after the algorithm of the present invention is used for the open-circuit fault PMSM, the motor still has excellent dynamic performance.

[0110] In summary, the present invention reconstructs the voltage vector after the fault to form a virtual voltage vector with equal amplitude, and then divides each sector into equal parts. The reference voltage vector is obtained by current calculation based on the idea of ​​no-beat, and the reference voltage vector is projected onto the optimal voltage vector of the sector, so as to directly obtain the minimum distance between the reference voltage vector and the virtual voltage vector, eliminating the process of iterating the current cost function. The amount of calculation is greatly reduced, and the duty cycle is calculated by the geometric method, which simplifies the traditional finite set model prediction duty cycle calculation method. By analyzing the simulation results, it can be seen that the proposed algorithm reduces the torque pulsation and current harmonic content of the motor after the fault, and maintains the dynamic performance of the model predictive control, which can ensure the stable operation of the motor under fault conditions.

[0111] It should be understood that the above embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent modifications of the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

Claims

1. A five-phase permanent magnet synchronous motor PMSM model predictive fault-tolerant control method based on zero-beat, characterized in that: The steps include: Step 1: The actual speed of the five-phase PMSM detected is used as the feedback speed n of the motor and the given speed n of the motor. ref The motor speed error is obtained by subtracting n, and the q-axis current of the motor is obtained through the PI controller, and this current is used as the q-axis reference current. At the same time, i d =0 control, d-axis reference current Step 2: Based on the principle of minimum copper loss, reconstruct the fault-tolerant reduced-order transformation matrix of the five-phase PMSM in the case of an open-circuit fault in phase A. Where: α = 0.4π; Step 3: Use the fault-tolerant reduced-order transformation matrix to transform the remaining non-fault phase current i collected by the current sensor into B 、i C 、i D 、i E The current i transformed into the fundamental wave space and harmonic wave space of the two-phase stationary coordinate system α 、i β 、i y , and then the current in the dq coordinate system is obtained by Park transformation Step 4: Establish and discretize the voltage equation of the five-phase PMSM with a single-phase open circuit fault in the dq coordinate system to obtain the current value at time k+1 On this basis, the discrete voltage equation is iterated once to obtain the current value at time k+2 Where: R is the stator resistance; L is the stator inductance; ω is the electrical angle; is the permanent magnet flux; T s To control the cycle; is the current at time k+1; is the current at time k+2; is the voltage at time k+1; Step 5: Set the reference current on the dq coordinate system and Assign to and Derivation of reference voltage based on deadbeat idea and Then use the Park inverse transformation matrix to transform it to the two-phase stationary coordinate system to obtain the reference voltage on the two-phase stationary coordinate system and The new voltage cost function is designed in the two-phase stationary coordinate system: Where: is the reference voltage, is the voltage in the stationary coordinate system at time k+1; Step 6, using a fault-tolerant reduced-order transformation matrix to transform the non-fault phase voltages corresponding to different switching states of the power devices in the PMSM inverter to a two-phase stationary coordinate system, and obtain voltage vector distribution diagrams in the fundamental wave space and the harmonic wave space after the open circuit fault; Step 7: To suppress the third harmonic current i y =0 is the principle to synthesize the voltage vectors in the harmonic space of the two-phase stationary coordinate system to zero, and then obtain the synthetic virtual voltage vector in the fundamental wave space of the two-phase stationary coordinate system, and take the virtual voltage vector with the shortest amplitude as the base value, perform equal amplitude processing on the virtual voltage vector, and obtain the processed virtual voltage vector vv i = k(d1u i+ d2u j ), i=1…8, u i is a basic voltage vector synthesized with the virtual voltage vector, u j is another basic voltage vector synthesized with the virtual voltage vector, d1 and d2 are the action coefficients of the two corresponding basic voltage vectors, and k is the coefficient that makes all virtual voltage vectors have the same amplitude; Step 8: divide the equal-amplitude virtual voltage vector into sectors in the fundamental wave space. The area enclosed by two adjacent virtual voltage vectors is an isosceles triangle. The vertex bisector of the isosceles triangle is used as the dividing line of each sector. Each isosceles triangle is divided into sectors in equal parts. Each virtual voltage vector falls on the center line of each sector. Step 9, according to the reference voltage on the two-phase stationary coordinate system obtained in step 5, calculate the sector where the reference voltage vectors corresponding to the two reference voltages are located, and then according to the voltage cost function in step 5, it can be determined that the virtual voltage vector in the sector where the reference voltage vector is located is the optimal voltage vector to be optimized, and the optimal voltage vector is projected onto the reference voltage vector, and then the optimal action time t of the optimal voltage vector in each control cycle is obtained by the geometric method. opt ; Step 10: Convert the selected optimal voltage vector and optimal action time into basic voltage vectors and action time of each basic voltage vector. Where: t1 is the action time of the first basic voltage vector; t2 is the action time of the second basic voltage vector; t opt is the optimal voltage vector action time; d1 is the first basic voltage proportion in the virtual vector; d2 is the second basic voltage proportion in the virtual voltage vector; k is the new virtual voltage amplitude proportional coefficient, T s To control the cycle; The selected basic voltage vector and action time are input into the PWM module to generate a PWM waveform, control the on and off of the power devices in the inverter, and realize the fault-tolerant control of the five-phase PMSM.

2. The method according to claim 1, characterized in that The mathematical model of the five-phase PMSM with a single-phase open-circuit fault in step 4 in the dq coordinate system is discretized by the previous Euler method to obtain Thus, the current value at time k+2 is obtained by iteration 3. The method according to claim 1, characterized in that: The specific process of step 5 is as follows: Step 5.1, based on the idea of ​​zero beat, the reference current and and in step 4 and The reference voltage in the dq coordinate system is derived as Furthermore, the reference current and It can be expressed as Step 5.2, design the traditional current cost function as Step 5.3, add the current at time k+2 in step 4 and the current at time k+2 in step 5.

1. and Substituting the expression into the current cost function, the equivalent voltage cost function is obtained: Step 5.4, use the Park inverse transformation matrix to transform the voltage in the dq coordinate system in the equivalent voltage cost function into the two-phase stationary coordinate system, thereby obtaining a new voltage cost function.

4. The method according to claim 1, characterized in that The specific process of step 6 is as follows: Step 6.1, when phase A is open, the voltage of each non-fault phase corresponding to the switching state of the upper bridge arm power device in the five-phase PMSM inverter can be expressed as Where: U dc is the bus voltage, s i (i=b, c, d, e) is the switching state of the upper arm power devices of inverter b, c, d, e, s i =1 means open, s i =0 means off; Step 6.2: Use the fault-tolerant reduced-order transformation matrix to transform the four-phase voltage into a two-phase stationary coordinate system. Thus, the voltage vectors of the fundamental wave space and the third harmonic space of the two-phase stationary coordinate system after the open circuit fault are obtained, where the basic voltage vectors u8 and u 14 , u7, u1 amplitude is 0.441U dc , basic voltage vector u 13 、u4、u2、u 11 The amplitude is 0.325U dc , the amplitude of u9 and u6 is 0.447U dc , basic voltage vector u 12 、u3 amplitude is 0.616U dc , basic voltage vector u 10 、u5 amplitude is 0.145U dc .

5. The method according to claim 1, characterized in that The specific process of step 7 is as follows: Step 7.1, based on the principle of suppressing the third harmonic current, the above basic voltage vector is used to synthesize a virtual voltage vector so that it is zero in the third harmonic space, and then the virtual voltage vector synthesized by the above basic voltage vector in the fundamental wave space is obtained. The amplitude of these virtual voltage vectors vv1 and vv5 is 0.447U dc , the amplitude of vv2, vv4, vv6, and vv8 is 0.394U dc , the amplitude of vv3 and vv7 is 0.526U dc ; Step 7.2: In order to make the optimal voltage vector selected in each step have the same control effect, it is necessary to process the amplitudes of these virtual voltage vectors to make the synthesized virtual voltage vectors have the same amplitude, with 0.394U dc As the reference of the virtual voltage vector amplitude, vv1 and vv5 need to be multiplied by the coefficient k, k is 0.88; vv3 and vv7 need to be multiplied by the coefficient k, k is 0.

75. The synthesized virtual voltage vector can be expressed as vv i = k(d1u i+ d2u j ), i=1…8, u i Represents a basic voltage vector with the synthesized virtual voltage vector, u j represents another basic voltage vector of the synthesized virtual voltage vector, d1 and d2 represent the action coefficients of the corresponding two basic voltage vectors respectively, and k is the coefficient that makes all virtual voltage vectors have the same amplitude.

6. The method according to claim 1, characterized in that In step 7, the relationship between each synthesized virtual voltage vector and the basic voltage vector is:

7. The method according to claim 1, characterized in that The specific process of step 9 is as follows: Step 9.1, calculate the reference voltage vector angle Where: is the projection of the reference voltage vector on the β axis; is the projection of the reference voltage vector on the α axis; θ u is the reference voltage vector angle; Based on this, the sector where the reference voltage vector is located is determined, and the virtual voltage vector in the sector is determined to be the optimal voltage vector according to the new voltage cost function in step 5; Step 9.2, project the reference voltage vector onto the optimal voltage vector, and calculate the optimal action time of the optimal voltage vector in a control cycle based on the geometric method. Where: t opt is the optimal voltage vector action time; θ i is the optimal voltage vector angle; θ u is the reference voltage vector angle; |u ref is the reference voltage vector amplitude; |u opt | is the optimal voltage vector amplitude; T s To control the cycle.

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