A deadbeat direct current control method for six-phase permanent magnet motor based on dynamic time planning

Abstract

The application discloses a kind of six-phase permanent magnet motor deadbeat direct current control methods based on dynamic time planning: by establishing dimension reduction transformation matrix, the influence of open-circuit fault on mathematical model and voltage complex plane distribution is analyzed, further utilize fault mathematical model and dimension reduction transformation matrix, the harmonic plane current reference value under different fault types is deduced, and the general formula of deadbeat direct current control rate is constructed.On this basis, with dynamic adjustment time as optimization goal, form motor system transient process standard optimization problem.To fixed current increment, the magnetic flux complex plane is divided, according to the magnetic flux information and voltage information of each magnetic flux grid, the motion time of each forward path in dynamic programming is calculated, and time planning is carried out in backward level mode, and an optimal path with shortest time is searched out in reverse direction, which can significantly improve the dynamic performance of motor in different fault-tolerant modes, and has good algorithm execution efficiency.

Description

Technical Field

[0001] This invention belongs to the field of multiphase motor drive control, and in particular relates to a deadbeat direct current control method for a six-phase permanent magnet motor based on dynamic time programming. Background Technology

[0002] Compared to ordinary three-phase motors, six-phase permanent magnet motors have smaller torque ripple, higher control freedom, and stronger fault tolerance, and have received widespread attention and application in the transportation industry, including electric vehicles, multi-electric / all-electric aircraft, and electric ship propulsion.

[0003] After a phase loss fault occurs in a six-phase motor, a wide range of residual degrees of freedom remain. Simultaneously, the post-fault operating efficiency and torque output capability must be considered, essentially forming a multi-degree-of-freedom, complex-constrained optimization problem. The fault-tolerant implementation of predictive control in this problem requires further research. Currently, based on different fault modeling methods, predictive control techniques for six-phase permanent magnet motors after open-circuit faults can be divided into normal transformation array strategies and dimension-reduced transformation array strategies. However, both strategies focus primarily on steady-state operating indicators after an open-circuit fault, namely the loss level and torque range of the six-phase permanent magnet motor system, with less attention paid to dynamic adjustment indicators such as torque settling time. However, after an open-circuit fault, the voltage and current relationships of the motor system undergo reshaping, the voltage complex plane is distorted, and the complex constraints of various physical quantities after the fault further complicate the dynamic performance optimization problem of a six-phase permanent magnet motor after an open-circuit fault, making it a real-time multi-objective optimization problem where obtaining an optimal analytical solution is difficult.

[0004] To address these problems in traditional methods, this invention proposes a deadbeat-free direct current control method for a six-phase permanent magnet motor based on dynamic time programming. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention provides a deadbeat direct current control method for a six-phase permanent magnet motor based on dynamic time programming. This method constructs a general formula for deadbeat direct current control and achieves high dynamic adjustment capability of the six-phase permanent magnet motor after an open-circuit fault through a dynamic time programming algorithm.

[0006] The technical solution adopted in this invention is a deadbeat-free direct current control method for a six-phase permanent magnet motor based on dynamic time programming. This article uses an open-circuit fault in the W phase of the motor as an example to illustrate the technical solution of this invention, the specific content of which is as follows:

[0007] Step 1): When an open-circuit fault occurs in the motor, any matrix that satisfies the pairwise orthogonality of the α-β-z1-z2-z3 axes can be used as the dimension-reduction transformation matrix after a single-phase open-circuit fault. Here, α-β represents the fundamental subspace, z1 represents the harmonic subspace, and z2-z3 represents the zero-order subspace. The dimension-reduction transformation matrix T can then be derived. 5s / 2s :

[0008]

[0009] When establishing a fault mathematical model in the rotating coordinate system of the motor, it is only necessary to perform a rotation transformation on the α-β subspace involved in the electromechanical energy conversion, using the rotation transformation matrix T. 2s / 2r for:

[0010]

[0011] In the formula O 3×3 Let θ be a third-order identity matrix. e This is the rotor position angle.

[0012] Final transformation matrix T 5s / 2r for:

[0013]

[0014] The current rotation transformation process in the dq subplane is as follows:

[0015]

[0016] In the formula, dq is derived from the α-β subspace through coordinate rotation transformation. Due to an open-circuit fault in phase W, the phase W current i W =0. i A i B i C i U i V i represents the phase current of the remaining five-phase winding when phase W is open. d i q i z1 i z2 i z3 This represents the current along the d, q, z1, z2, and z3 axes in the motor's rotating coordinate system. Similarly, the voltage vector and flux linkage vector in the dq subplane can also be derived from the above rotational transformation.

[0017] When an open-circuit fault occurs in the motor, the inverter bridge arm connected to the lost-phase winding cannot function properly, resulting in distortion of the voltage vector complex plane. The expression for voltage complex plane distortion is:

[0018]

[0019] In the formula, u α u β u z1 These are the projections of the voltage vector onto the α, β, and z1 axes, respectively, U dc S is the DC bus voltage. p,A S p,B S p,C S p,U S p,V The switch states of the five phases of the inverter are represented by "1" and "0", which respectively represent the upper bridge arm and the lower bridge arm of the inverter being on.

[0020] Step 2): The general formula for deadbeat direct current control can be obtained by discretizing the flux linkage formula and voltage formula in the rotating coordinate system. The specific expression is as follows:

[0021]

[0022] Where A=L qq T s / (L dd L qq - L dq L qd ), B= -L dq T s / (L dd L qq - L dq L qd ),

[0023] C= -R s i d,k +R s L dq i d,k / L qq +ω e φ d,k L dq / L qq +ω e φ q,k D= -L dd T s / (L dd L qq - L dq L qd ),

[0024] E= -L qd T s / (L dd L qq - L dq L qd ), F = -R s iq,k +R s L qd i d,k / L dd +ω e φ q,k L qd / L dd +ω e φ d,k .

[0025] In the formula, we can let Δi d,k+1 =i d,ref -i d,k , Δi q,k+1 =i q,ref -i q,k To determine the (k+1)Tth digit that satisfies the control requirements s Stator voltage u at time d,k and u q,k Where k and k+1 represent the kT-th digits respectively. s (k+1)T s At discrete time T s For discrete control period, u d,k u q,k u d,k+1 u q,k+1 Let i represent the projections of the stator voltage onto the d and q axes at times k and k+1, respectively. d,ref and i q,ref These represent the d-axis and q-axis current reference values, respectively, i d,k and i q,k φ represents the projection of the stator current on the d and q axes at time k, respectively. d,k φ q,k R represents the projections of the stator flux linkage onto the d and q axes at time k, respectively. s ω represents the stator resistance of the motor. e L is the electric angular velocity of the motor. dd L qq L represents the d-axis and q-axis equivalent inductances after an open-circuit fault, respectively. dq L qd Let i represent the coupling inductance between the d and q axes, respectively. Let the motor use i... d In the control mode where =0, i d,ref = 0, i q,ref This can be provided by the speed loop controller.

[0026] For harmonic subspaces, it is only necessary to satisfy:

[0027]

[0028] In the formula u z1,k Let i be the projection of the voltage vector in the harmonic subspace onto the z1 axis.z1,ref L is the reference value for harmonic plane current. z1 This is the stator leakage inductance impedance.

[0029] The reference values ​​of the harmonic plane current of the motor under different fault-tolerant modes are obtained by solving the optimal solution using the following formula, the specific expression of which is as follows:

[0030]

[0031] In the formula, h={A, B, …, U, V, …} represents the residual phase number; J L and J T This represents the optimization objective function under different fault-tolerant modes, namely, loss mode and torque mode; a h and b h These represent the compensation coefficients of the residual phase current in the α-β coordinate system, respectively; I m This indicates the amplitude of the phase current during healthy operation.

[0032] Step 3): The transient constraints that the motor must satisfy under fault operation are as follows:

[0033] Maximum voltage amplitude constraint:

[0034]

[0035] In the formula, V max V represents the maximum output phase voltage amplitude of a six-phase inverter. n-fault This represents the magnitude of the basic voltage vector of the α-β subplane after a fault.

[0036] Magnetic flux equal amplitude constraint:

[0037]

[0038] During the transient operation of the motor, the optimal time trajectory t adj The single-objective optimization problem can be expressed as:

[0039]

[0040] The flux linkage complex plane is divided by taking a fixed current increment, and the flux linkage value and the voltage value at the vertex of each flux linkage grid are calculated using the dq axis voltage and flux linkage formula.

[0041] Step 4): Starting from the beginning of the optimal time trajectory and ending at the end, the magnetic flux complex plane is divided using a fixed current increment. Based on the flux linkage and voltage values ​​from Step 3), the motion time of each forward path is calculated, as shown in the following expression:

[0042]

[0043] In the above formula, u d ( - m)=|u - u d,m |,u q ( - n)=|u - u q,n |,Δφ d ( - m)=φ - φ d,m , Δφ q ( - n)= φ - φ q,n Among them, m, n These represent the preceding and following mesh numbers for the d-axis and q-axis components, respectively, with values ​​of 1, 2, 3, ... . u d,m They represent in The d-axis voltage component at point m, φ φ d,m They represent in The d-axis flux linkage component at point m, u u q,n They represent in The q-axis voltage component at point n, φ φ q,n They represent in The q-axis flux linkage component at position n.

[0044] Step 5: Swap the start and end points of the optimal time trajectory, reverse the search for the optimal path with the shortest time, and take the first-level grid voltage of the optimal path as the (k+1)T-th grid voltage. s The output voltage is determined at time (k+1)T. s At time (k+2), steps 3 and 4 are executed again to calculate the (k+2)T-th time. s The optimal output voltage at any given time is determined, and this process is repeated continuously to achieve a complete dynamic time planning algorithm.

[0045] Compared with existing technical solutions, the beneficial effects of the technical solution of this invention are:

[0046] This invention derives and establishes a dimension-reduction transformation matrix, further derives a mathematical model of motor faults, and analyzes the distribution of voltage vectors in the complex plane. Based on this, a universal control law for deadbeat-free direct current control of a six-phase permanent magnet synchronous motor is constructed, and a multivariate optimization problem for the dynamic performance of a six-phase permanent magnet synchronous motor under open-circuit faults is established and solved using dynamic time programming techniques. Based on this, the optimal time trajectory of the six-phase permanent magnet synchronous motor under open-circuit faults is obtained, thereby improving the dynamic adjustment capability of the motor after a fault. Attached Figure Description

[0047] Figure 1 This is the control principle diagram of the present invention;

[0048] Figure 2 This is the control flowchart of the present invention;

[0049] Figure 3 These are experimental waveforms of the traditional deadbeat algorithm under motor fault operation.

[0050] Figure 4 These are experimental waveforms of the algorithm of this invention under motor fault operation. Detailed Implementation

[0051] The following describes in detail, with reference to examples and accompanying drawings, a deadbeat-free direct current control method for a six-phase permanent magnet motor based on dynamic time programming, and uses an open-circuit fault in phase W of the motor as an example to illustrate the technical solution of the present invention.

[0052] The principle diagram of the method of the present invention is as follows: Figure 1 As shown, it includes the following steps:

[0053] Step 1: When an open-circuit fault occurs in the motor windings, the dimension-reduced transformation matrix under an open-circuit fault in a six-phase motor is derived based on the principle of space vector decoupling. The dimension-reduced transformation matrix is ​​then used to establish a fault mathematical model. Based on the switching states of the remaining phase inverters after the fault, the voltage complex plane distortion under a six-phase motor fault is analyzed, as detailed below:

[0054] When a W-phase open-circuit fault occurs in the motor, the W-phase current i W =0. The voltage equations and flux linkage equations for the remaining five-phase windings in the natural coordinate system are:

[0055]

[0056] In the formula, U 5s For voltage matrix, U 5s =[U A U B U C U U U V ]T ;R 5s Let R be the resistance matrix. 5s =R s O 5×5 O 5×5 It is a fifth-order identity matrix; I 5s Let I be the current matrix. 5s =[I A I B I C I U I V ] T ;where φ 5s Let φ be the flux linkage matrix. 5s =[φ A φ B φ C φ U φ V ] T ;φ f λ represents the flux linkage amplitude generated by the permanent magnets of the motor in each phase winding; 5s This is the flux linkage coefficient matrix.

[0057] According to the principle of space vector decoupling, any matrix satisfying pairwise orthogonality of the α-β-z1-z2-z3 axes can be used as the dimension reduction transformation matrix after a single-phase open-circuit fault. Here, α-β represents the fundamental subspace, z1 represents the harmonic subspace, and z2-z3 represents the zero-order subspace, specifically expressed as T. 5s / 2s =[α-β-z1-z2-z3] T Among them, α, β, z1, z2, and z3 must be mutually orthogonal. The connection methods of z2 and z3 are related to the neutral point connection of the motor, and are respectively: z2=[1 1 1 0 0] T z3=[0 0 0 1 1] T Thus, the dimension reduction transformation matrix T is obtained. 5s / 2s :

[0058]

[0059] Similar to the case of a healthy motor, only a rotational transformation of the α-β subspace involved in the electromechanical energy conversion is required, with the rotational transformation matrix T... 2s / 2r for:

[0060]

[0061] In the formula, θ e O is the rotor position angle. 3×3 It is a third-order identity matrix.

[0062] T 5s / 2s Left multiply T 2s / 2rThe final rotation transformation matrix T is obtained. 5s / 2r :

[0063]

[0064] After decoupling the fault mathematical model in the natural coordinate system through the above rotation transformation, the equations for the dq subplane voltage and flux linkage are obtained as follows:

[0065]

[0066] In the formula, R s Let ω be the stator resistance of the motor, p represent the differential operator, and ω be the differential operator. e Let θ be the electric angular velocity of the motor. e U is the rotor position angle of the motor. d u q u z1 φ is the projection component of the stator voltage on the dq-z1 axis. d φ q φ z1 Let i be the projection component of the stator flux linkage on the dq-z1 axis. d i q i z1 L represents the projected component of the stator current on the dq-z1 axis. W (θ e The stator inductance matrix after an open-circuit fault is expressed as follows:

[0067]

[0068] In the formula I 3s Let L be the current matrix. z1 L0 represents the leakage inductance of the stator winding, L2 represents the average value of the main self-inductance, and L2 represents the amplitude of the second harmonic of the main self-inductance.

[0069] When an open-circuit fault occurs in the motor, the inverter bridge arm connected to the lost-phase winding cannot function properly, resulting in distortion of the voltage vector complex plane. This voltage complex plane distortion can be derived from the following formula:

[0070]

[0071] In the formula, u α u β u z1 These are the projections of the voltage vector onto the α, β, and z1 axes, respectively, U dc S is the DC bus voltage. p,A S p,B S p,C S p,U S p,VThe switch states of the five phases of the inverter are represented by "1" and "0", which respectively represent the upper bridge arm and the lower bridge arm of the inverter being on.

[0072] Step 2): Based on the principle of constant magnetomotive force, the optimization objectives are to minimize stator copper loss and maximize output torque after phase loss, i.e., loss mode and torque mode. Considering the current constraint relationship during phase loss operation, the harmonic plane reference values ​​for the loss mode and torque mode are further derived based on the dimension-reduced transformation matrix after phase loss, using the following optimization function:

[0073]

[0074] In the formula, h={A, B, …, U, V, …} represents the residual phase number; J L and J T Let a represent the optimization objective function under loss mode and torque mode, respectively; h and b h These represent the compensation coefficients of the residual phase current in the α-β coordinate system, respectively; I m The phase current amplitude represents the phase current amplitude during healthy operation. The harmonic plane reference values ​​obtained from the solution are shown in Table 1.

[0075] Table 1. Current reference values ​​under different fault-tolerant modes

[0076]

[0077] By establishing a current prediction model after a fault, a general formula for deadbeat direct current control is constructed, and combined with...

[0078] Equation (8) in step 1) expresses the inductance matrix as the following general formula:

[0079]

[0080] In the formula, L dd L qq L represents the d-axis and q-axis equivalent inductances after an open-circuit fault, respectively; dq L qd These represent the coupled inductance between the d and q axes, respectively.

[0081] Combining the flux linkage equation (7) from step 1), the general formula for flux linkage after an open-circuit fault can be expressed as:

[0082]

[0083] In the formula, φ md and φ mq These represent the projection components of the rotor flux linkage on the d and q axes after an open-circuit fault, respectively.

[0084] According to equation (12), the derivatives of the magnetic flux linkage vectors along the d and q axes can be written as:

[0085]

[0086] Ignore θ e Changes on L dd L qq L dq and L qd The numerical effect is considered, and by discretizing equations (13)-(14), we can obtain the following equations:

[0087]

[0088] In the formula, Δφ d,k+1 =φ d,k+1 -φ d,k , Δφ q,k+1 =φ q,k+1 -φ q,k k represents the kT-th s At discrete control time T s For discrete control cycles.

[0089] Furthermore, substituting equations (15)-(16) into equation (6), we can obtain the general formula for the deadbeat direct current control rate:

[0090]

[0091] Where A=L qq T s / (L dd L qq -L dq L qd ), B = -L dq T s / (L dd L qq -L dq L qd ), C = -R s i d,k +R s L dq i d,k / L qq +ω e φ d,k L dq / L qq +ω e φ q,k D = -L dd T s / (L dd L qq -L dq L qd ), E = -Lqd T s / (L dd L qq -L dq L qd ), F = -R s i q,k +R s L qd i d,k / L dd +ω e φ q,k L qd / L dd +ω e φ d,k .

[0092] In the formula, we can let Δi d,k+1 =i d,ref -i d,k , Δi q,k+1 =i q,ref -i q,k To determine the (k+1)Tth digit that satisfies the control requirements s Stator voltage u at time d,k and u q,k Where k and k+1 represent the kT-th digits respectively. s (k+1)T s At discrete time T s For discrete control period, u d,k u q,k u d,k+1 u q,k+1 Let i represent the projections of the stator voltage onto the d and q axes at times k and k+1, respectively. d,ref and i q,ref These represent the d-axis and q-axis current reference values, respectively, i d,k and i q,k φ represents the projection of the stator current on the d and q axes at time k, respectively. d,k φ q,k R represents the projections of the stator flux linkage onto the d and q axes at time k, respectively. s ω represents the stator resistance of the motor. e L is the electric angular velocity of the motor. dd L qq L represents the d-axis and q-axis equivalent inductances after an open-circuit fault, respectively. dq L qd Let i represent the coupling inductance between the d and q axes, respectively. Let the motor use i... d In the control mode where =0, i d,ref = 0, i q,ref This can be provided by the speed loop controller.

[0093] For harmonic subspaces, the following equation only needs to be satisfied:

[0094]

[0095] In the formula u z1,k Let i be the projection of the voltage vector in the harmonic subspace onto the z1 axis. z1,ref L is the reference value for harmonic plane current. z1 This is the stator leakage inductance impedance.

[0096] Step 3): Establish the maximum voltage amplitude constraint under motor phase loss fault:

[0097]

[0098] In the formula, V max V represents the maximum output phase voltage amplitude of a six-phase inverter. n-fault This represents the magnitude of the basic voltage vector of the α-β subplane after a fault.

[0099] Magnetic flux equal amplitude constraint:

[0100]

[0101] The multi-objective optimization problem in the transient process of the motor is transformed into a problem with t. adj For this optimization problem with a single objective, the objective function is:

[0102]

[0103] After determining the objective function, the magnetic flux complex plane is subjected to a fixed current increment Δi. q =0.1A to perform meshing, with the start time of the optimal time trajectory as the starting point and the end time as the ending point. According to equations (6) to (7), the flux linkage value and voltage value of each flux linkage mesh are calculated.

[0104] Step 4): Starting from the optimal time trajectory, select three directions of travel to form a dynamic programming path. Use the endpoint of each path as the starting point for the next moment, repeating the above steps until the endpoint of the optimal time trajectory is reached. Finally, combine the flux linkage and voltage values ​​from step 3) to calculate the travel time t for each path. grid :

[0105]

[0106] In the above formula, u d ( - m)=|u - u d,m |,u q ( - n)=|u - u q,n |,Δφ d ( - m)=φ - φ d,m , Δφ q ( - n)= φ - φ q,n Among them, m, n These represent the preceding and following mesh numbers for the d-axis and q-axis components, respectively, with values ​​of 1, 2, 3, ... . u d,m They represent in The d-axis voltage component at point m, φ φ d,m They represent in The d-axis flux linkage component at point m, u u q,n They represent in The q-axis voltage component at point n, φ φ q,n They represent in The q-axis flux linkage component at position n.

[0107] Step 5): Based on the time information of all grids on the critical path obtained in Step 4), swap the start and end points of the optimal time trajectory. Starting from the start point, each step selects the smallest time grid to form the optimal path, which is equivalent to reverse searching to find a critical path with the shortest time as the optimal path. The voltage of the first-level grid of the optimal path is taken as the (k+1)T-th grid. s The output voltage is at time (k+1)T, and at time (k+1)T s At time (k+2), steps 3) and 4) are executed again to calculate the (k+2)T-th time. s The optimal output voltage at each time point is determined, and this process is repeated cyclically to achieve a complete dynamic time programming algorithm. The specific implementation process of the dynamic programming algorithm can be described by... Figure 2 express.

[0108] To verify the effectiveness of this invention, an experiment was conducted on a 5kW six-phase permanent magnet synchronous motor. The sampling period was set to 10kHz, the speed reference was set to 200r / min, and the load was 5 N·m. The motor was set to operate in copper loss mode with the W phase open circuit. The control method of this invention was compared experimentally with the traditional deadbeat direct current control method, and the experimental results are shown in the figure below. Figure 3 and Figure 4As shown in the experimental results, the addition of the time planning algorithm effectively improved the dynamic response time of the motor, proving that the present invention effectively improves the dynamic performance of the motor under fault conditions.

[0109] As described above, this invention proposes a fault-tolerant deadbeat direct current control for a six-phase permanent magnet synchronous motor, which, combined with a novel time planning algorithm, optimizes the dynamic performance of the multiphase motor under fault operation.

[0110] The above description of the function and working process of the present invention in conjunction with the accompanying drawings is only one preferred real-time example. However, the present invention is not limited to the specific function and working process described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A deadbeat-free direct current control method for a six-phase permanent magnet motor based on dynamic time programming, characterized in that, Includes the following steps: 1) When an open-circuit fault occurs in the motor, derive and establish a dimension-reduced transformation matrix, and further derive a mathematical model of the motor fault based on the dimension-reduced transformation matrix, and analyze the voltage complex plane vector distribution; 2) Based on the dimension reduction transformation matrix and fault mathematical model in step 1), the reference value of the harmonic plane current is derived, and the general formula for the deadbeat direct current control law is constructed: ; Where A=L qq T s / (L dd L qq -L dq L qd ), B = -L dq T s / (L dd L qq -L dq L qd ), C = -R s i d,k +R s L dq i d,k / L qq +ω e φ d,k L dq / L qq +ω e φ q,k D = -L dd T s / (L dd L qq -L dq L qd ), E = -L qd T s / (L dd L qq -L dq L qd ), F = -R s i q,k +R s L qd i d,k / L dd +ω e φ q,k L qd / L dd +ω e φ d,k Let Δi d,k+1 =i d,ref -i d,k , Δi q,k+1 = i q,ref -i q,k To determine the (k+1)Tth digit that satisfies the control requirements s Stator voltage u at time d,k and u q,k Where k and k+1 represent the kT-th digits respectively. s (k+1)T s At discrete time T s For discrete control period, u d,k u q,k u d,k+1 u q,k+1 Let i represent the projections of the stator voltage onto the d and q axes at times k and k+1, respectively. d,ref and i q,ref These represent the d-axis and q-axis current reference values, respectively, i d,k and i q,k φ represents the projection of the stator current on the d and q axes at time k, respectively. d,k φ q,k R represents the projections of the stator flux linkage onto the d and q axes at time k, respectively. s ω represents the stator resistance of the motor. e L is the electric angular velocity of the motor. dd L qq L represents the d-axis and q-axis equivalent inductances after an open-circuit fault, respectively. dq L qd These represent the coupling inductance between the d and q axes, respectively. 3) Establish transient constraints under motor fault operation, and transform the multi-objective optimization problem into a single-objective optimization problem of the optimal time trajectory; take the start time of the optimal time trajectory as the starting point and the end time as the ending point, use a fixed current increment to divide the flux linkage complex plane into flux linkage meshes, and calculate the flux linkage value and voltage value of each flux linkage mesh. 4) Starting from the optimal time trajectory, select three directions of movement to form a dynamic programming path. Use the end point of each path as the starting point of the next moment and continue moving in the three directions until the end point of the optimal time trajectory is reached. Finally, combine the flux linkage and voltage values ​​from step 3) to calculate the movement time of each path. 5) After the forward path reaches the end of the optimal time trajectory, swap the starting point and the ending point of the forward path; based on the movement time of all forward paths in step 4), search in reverse to find the optimal path with the shortest time, and further use the voltage value of the first-level magnetic flux grid in the optimal path as the output voltage at the next moment, and repeat steps 3) and 4).

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