A multi-objective pareto optimal based permanent magnet synchronous motor model predictive control method

Abstract

The application discloses a permanent magnet synchronous motor model prediction control method based on multi-target Pareto optimization, which comprises the following steps: measuring two-phase current, motor speed and rotor position of the permanent magnet synchronous motor, converting the two-phase current into d and q axis currents according to the rotor position, and simultaneously converting the alternative voltage vector of the inverter into d and q axis voltages; inputting the d and q axis currents, the d and q axis voltages and the motor speed into a permanent magnet synchronous motor current prediction model to predict future current state values; establishing a multi-target optimization model containing torque ripple, current total harmonic distortion, switching frequency and power loss, and obtaining a Pareto optimal solution set by using a multi-target particle swarm algorithm combined with non-dominated sorting and crowded distance calculation, obtaining an optimal weight factor, and automatically adjusting the target weight according to the motor operating state under different operating conditions; and constructing a cost function based on the optimal weight factor, and selecting the voltage vector that minimizes the cost function as the optimal control output.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of permanent magnet motor control, and more particularly to a permanent magnet synchronous motor model predictive control method based on multi-target Pareto optimization. BACKGROUND

[0002] As an advanced control strategy, model predictive control is widely used in the field of permanent magnet synchronous motor control for its ability to deal with multivariable control systems and optimize dynamic performance, maximize the dynamic response and stability of motor systems by optimizing control inputs in real time.

[0003] Traditional model predictive control usually adopts a single-target optimization strategy, mainly focusing on minimizing torque ripple or flux tracking accuracy. However, in practical applications, permanent magnet synchronous motor drive systems face multiple conflicting control objectives, including torque ripple suppression, current total harmonic distortion reduction, switching frequency optimization, and power loss minimization. These control objectives have complex coupling relationships and trade-off problems, and single-target optimization often leads to the deterioration of certain performance indicators, making it difficult to achieve overall optimal control of the system.

[0004] In addition, in the model predictive control of permanent magnet synchronous motors, the weight factor tuning problem of the cost function is the main technical challenge currently faced. Existing weight factor design methods mainly include empirical method, rating method, and trial-and-error method. The empirical method relies on the practical experience of engineers and lacks theoretical guidance, making it difficult to guarantee the optimization effect. The rating method sets the weight factor of the stator flux as the ratio of the rated electromagnetic torque to the rated stator flux amplitude, which can only achieve relative coordination of torque and flux at the rated operating condition, but the control performance significantly decreases under complex operating conditions such as variable speed and variable load. The trial-and-error method obtains the weight factor configuration through repeated online debugging, which is not only extremely tedious and time-consuming, but also difficult to obtain a global optimal solution, especially when the number of control objectives increases, the combination space of weight factors increases exponentially, and traditional methods are unable to meet the requirements.

[0005] More importantly, existing methods generally lack a deep understanding of the nature of multi-objective optimization, ignoring the Pareto optimal relationship between different control objectives. In multi-objective optimization problems, there is often no single solution that optimizes all objectives simultaneously, but a set of Pareto optimal solutions, each representing a trade-off between different objectives. The traditional weighted sum method essentially converts the multi-objective problem into a single-objective problem, which cannot fully exploit the potential of multi-objective optimization and cannot provide decision-makers with a rich selection space.

[0006] Therefore, how to overcome the difficulty in setting the conventional weight factor and the limitation of single-target optimization in the model predictive control of the permanent magnet synchronous motor so as to improve the comprehensive performance and robustness of the model predictive control is a problem to be solved by the person skilled in the art. SUMMARY

[0007] Therefore, the application provides a model predictive control method for a permanent magnet synchronous motor based on multi-target Pareto optimality to solve some of the technical problems mentioned in the background art.

[0008] To achieve the above-mentioned purpose, the application adopts the following technical solutions.

[0009] A model predictive control method for a permanent magnet synchronous motor based on multi-target Pareto optimality, comprising the following steps:

[0010] S1. Measure the two-phase current, motor speed and rotor position of the permanent magnet synchronous motor, and convert the two-phase current into d-axis and q-axis currents according to the rotor position, and convert the alternative voltage vector of the inverter into d-axis and q-axis voltages;

[0011] S2. Input the d-axis and q-axis currents, the alternative voltage vector corresponding to the d-axis and q-axis voltages, and the motor speed into the current prediction model of the permanent magnet synchronous motor to predict the future current state value;

[0012] S3. Establish a multi-target optimization model containing torque ripple, current total harmonic distortion, switching frequency and power loss, and obtain a Pareto optimal solution set by using a multi-target particle swarm algorithm combined with non-dominated sorting and crowded distance calculation, obtain the optimal weight factor, and automatically adjust the target weight according to the motor operating state under different operating conditions;

[0013] S4. Construct a cost function based on the optimal weight factor, and select the voltage vector that minimizes the cost function as the optimal control output.

[0014] Preferably, in step S1, the d-axis and q-axis currents are:

[0015]

[0016] wherein i d (k), i q (k) are the converted d-axis and q-axis currents, and θ(k) is the rotor position at time k. a (k), i b (k) are the converted d-axis and q-axis currents, and θ(k) is the rotor position at time k.

[0017] The d-axis and q-axis voltages are:

[0018]

[0019] wherein Udc is the DC bus voltage, [s a is the DC bus voltage, [s b is the DC bus voltage, [s c T is the switch state corresponding to the alternative voltage vector of the inverter, u d (k) are the d, q axis voltages converted from the alternative voltage vector at k time, respectively. q (k) are the d, q axis voltages converted from the alternative voltage vector at k time, respectively.

[0020] Preferably, in step S2, the permanent magnet synchronous motor current prediction model is:

[0021]

[0022] where i d (k+1) and i q (k+1) are the predicted current state values at future k+1 time, p is the number of motor pole pairs, T s is the control period, ψ f is the permanent magnet flux, R s is the motor resistance, ω m (k) is the motor speed at k time, L d , L q are the d, q axis inductances, respectively, i d (k), i q (k) are the d, q axis currents at k time, respectively, u d (k), u q (k) are the d, q axis voltages at k time, respectively.

[0023] Preferably, in step S3, the method for obtaining the optimal weight factor is specifically:

[0024] S31. A multi-objective optimization model is established, which includes torque ripple, current total harmonic distortion, switching frequency and power loss;

[0025] S32. The running parameters of the multi-objective particle swarm algorithm are set, and the initial particle swarm is randomly generated;

[0026] S33. For each particle's weight factor, the MPTC simulation model is run to calculate the corresponding multi-objective function value for multi-objective fitness evaluation;

[0027] S34. The non-dominated sorting is performed on the particle swarm, the particles are layered according to the dominance relationship, and the crowding distance is calculated for the solutions in the same non-dominated layer;

[0028] S35. The external archive of Pareto optimal solution set is maintained, and the non-dominated solution archive is updated. When the archive size exceeds the preset upper limit, the crowding distance is trimmed;

[0029] ​S36. Update the velocity and position of each particle according to the historical optimal position of the particle and the global optimal guiding solution selected from the external archive; repeat step S33-step S36 until the iteration termination condition is met;

[0030] S37. Select the optimal weight factor from the Pareto front by multi-criteria decision making using the technical comprehensive evaluation method.

[0031] Preferably, in step S4, the cost function constructed based on the optimal weight factor is specifically:

[0032]

[0033] wherein g is the cost function, is the reference torque, is the predicted torque at k+1 moment, is the reference stator flux linkage, is the predicted stator flux linkage at k+1 moment, is the current limiting function, λ opt is the optimal weight factor.

[0034] Preferably, in step S31, the multi-objective optimization model established including torque ripple, current total harmonic distortion, switching frequency and power loss is specifically:

[0035]

[0036]

[0037] wherein F(λ) is the multi-objective function, is the root mean square value of torque ripple, is the reference torque at k moment, is the actual torque at k moment, N is the number of sampling points, is the current total harmonic distortion rate, is the effective value of n-th harmonic current, is the effective value of fundamental current, is the average switching frequency, is the switching frequency at k moment, is the total power loss, is the switching loss, is the on-state loss, , are the turn-on and turn-off energy losses of the jth switch, is the on-state voltage drop of the jth switch, is the average current of the jth switch.

[0038] Preferably, in step S34, the dominance relationship is:

[0039] For two solutions a and b, if solution a is not inferior to solution b in all objectives and is strictly superior to solution b in at least one objective, then solution a is said to dominate solution b; all non-dominated solutions constitute a non-dominated layer, i.e. a Pareto front.

[0040] Preferably, in step S34, the crowding distance of solutions within the same non-dominated layer is:

[0041]

[0042] in, Let be the crowding distance of the i-th solution. , Let be the function values ​​of the (i+1)th solution and the (i-1)th solution after sorting, respectively, for the m-th objective. , These are the maximum and minimum values ​​of the m-th target, respectively.

[0043] Preferably, step S36, the specific method for updating the velocity and position of each particle, is as follows:

[0044] For each particle, a guided solution is selected from the external archive based on the crowding distance;

[0045] The update speed and location are as follows:

[0046]

[0047]

[0048] in, , Let be the velocity and position of the i-th particle in the (t+1)th iteration, respectively. , Let be the velocity and position of the i-th particle in the t-th iteration, respectively. For inertial weights, , As a learning factor, , It is a random number. This represents the historical best position of the i-th particle. To guide the particles, , t is the current iteration number, G max Maximum number of iterations.

[0049] Preferably, step S37 includes the following:

[0050] S371. Standardize the function values ​​of each solution in the Pareto solution set for each objective;

[0051] S372. Calculate the distance of each solution to the positive ideal solution and the distance to the negative ideal solution based on the normalized value of each solution on each target and the positive ideal value of each target and the target weight;

[0052] S373. Calculate the relative closeness of each solution, and select the solution with the largest relative closeness value as the optimal weight factor.

[0053] Compared with the prior art, the permanent magnet synchronous motor model predictive control method based on multi-objective Pareto optimality provided by the technical solution disclosed in the present application introduces the Pareto optimal theory and the multi-objective particle swarm optimization algorithm, solves the weight factor design difficulty and single-objective optimization limitation problem in the traditional permanent magnet synchronous motor model predictive control, establishes a multi-objective mathematical model of torque ripple, current total harmonic distortion, switching frequency and power loss, obtains a Pareto optimal solution set of the weight factor by using the non-dominated sorting and crowded distance maintenance strategy, integrates the multi-criteria decision of the technique for order preference by similarity to an ideal solution and the working condition adaptive mechanism, realizes the coordinated optimization of multiple control targets and the intelligent weight selection, and provides a systematic multi-objective optimization solution for the high-performance driving control of the permanent magnet synchronous motor. The present application effectively improves the current total harmonic distortion while significantly reducing the electromagnetic torque ripple, reduces the switching loss, greatly improves the multi-working condition adaptability, and significantly improves the comprehensive performance and robustness of the permanent magnet synchronous motor model predictive control. BRIEF DESCRIPTION OF DRAWINGS

[0054] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiment or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of the provided drawings.

[0055] Figure 1 A permanent magnet synchronous motor model predictive control method based on multi-objective Pareto optimality provided by the present application is shown in the figure.

[0056] Figure 2 The execution flowchart of the multi-objective particle swarm optimization algorithm provided by the present application is shown in the figure. DETAILED DESCRIPTION

[0057] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0058] The embodiment of the application discloses a permanent magnet synchronous motor model prediction control method based on multi-target Pareto optimality, like Figure 1 , comprising the following steps:

[0059] S1. Measure the two-phase current of the permanent magnet synchronous motor, the motor speed and the rotor position, and convert the two-phase current into d, q axis currents according to the rotor position, and convert the alternative voltage vector of the inverter into d, q axis voltage;

[0060] S2. Input the d, q axis currents, the alternative voltage vector corresponding to the d, q axis voltage and the motor speed into the permanent magnet synchronous motor current prediction model to predict the future current state value;

[0061] S3. Establish a multi-target optimization model containing torque ripple, current total harmonic distortion, switching frequency and power loss, and obtain a Pareto optimal solution set by using a multi-target particle swarm algorithm combined with non-dominated sorting and crowded distance calculation, obtain an optimal weight factor, and automatically adjust the target weight according to the motor operating state under different operating conditions;

[0062] S4. Based on the optimal weight factor, a cost function is constructed, and the voltage vector that minimizes the cost function is selected as the optimal control output.

[0063] In order to further implement the above technical scheme, in step S1, the d, q axis currents are:

[0064]

[0065] Wherein, i d (k), i q (k) are the converted d, q axis currents of the a, b two-phase currents i a (k), i b (k) at k moment, and θ(k) is the rotor position at k moment;

[0066] The d, q axis voltage is:

[0067]

[0068] Wherein, U dc is the DC bus voltage, [s a , s b , s c ] T is the switching state corresponding to the alternative voltage vector of the inverter, u d (k), u q (k) are the converted d, q axis voltages of the alternative voltage vector at k moment;

[0069] In the embodiment, seven groups of alternative voltage vectors of the inverter are converted into seven d, q-axis voltages u d (k) and u q (k), the seven groups of alternative voltage vectors of the inverter correspond to the switching states [s a , s b , s c ] T , respectively [0, 0, 0] T , [1, 0, 0] T , [1, 1, 0] T , [0, 1, 0] T , [0, 1, 1] T , [0, 0, 1] T , [1, 0, 1] T ; the seven groups of current state values corresponding to the subsequent predicted future current state values are.

[0070] In order to further implement the above technical solutions, in step S2, the permanent magnet synchronous motor current prediction model is:

[0071]

[0072] Wherein, i d (k+1) and i q (k+1) are the predicted future current state values at time k+1, p is the motor pole pair number, T s is the control period, ψ f is the permanent magnet flux, R s is the motor resistance, ω m (k) is the motor speed at time k, L d , L q are the d, q-axis inductances, respectively, i d (k), i q (k) are the d, q-axis currents at time k, respectively, u d (k), u q (k) are the d, q-axis voltages at time k, respectively; the motor pole pair number, the control period, the permanent magnet flux, the motor resistance, and the d, q-axis inductances are measured by the manufacturer before the permanent magnet synchronous motor is shipped.

[0073] In order to further implement the above technical solutions, as Figure 2 , in step S3, the method for obtaining the optimal weight factor is specifically:

[0074] S31. A multi-objective optimization model is established, which includes torque ripple, current total harmonic distortion, switching frequency and power loss;

[0075] S32. Set the running parameters of the multi-objective particle swarm algorithm, and randomly generate an initial particle swarm;

[0076] S33. For each particle, run the MPTC simulation model to calculate the corresponding multi-objective function value for multi-objective fitness evaluation; MPTC stands for Model Predictive Torque Control.

[0077] S34. Perform non-dominated sorting on the particle swarm, stratify the particles according to the dominance relationship, and calculate the crowding distance for solutions in the same non-dominated layer.

[0078] S35. Maintain an external archive Archive of Pareto optimal solution sets, and update the non-dominated solution archive. When the size of the archive exceeds the preset upper limit, perform pruning according to the crowding distance.

[0079] S36. Update the speed and position of each particle according to the historical optimal position of the particle and the global optimal guiding solution selected from the external archive. Repeat steps S33-S36 until the iteration termination condition is met.

[0080] In this embodiment, the iteration termination condition is that the preset maximum number of iterations G max or the Pareto front in the external archive has not been significantly improved for a continuous number of generations.

[0081] S37. Select the optimal weight factor from the Pareto front through multi-criteria decision making using the technology comprehensive evaluation method.

[0082] In this embodiment, the particle swarm size N is set to 100, the search space is [1, 50], the maximum number of iterations G max = 200, the dimension of each particle is consistent with the number of optimization objectives, and the particle position and speed are initialized as follows:

[0083]

[0084] wherein, is the initial position of the i-th particle, is the initial speed of the i-th particle, and rand() is a random number between 0 and 1.

[0085] Each particle represents a set of MPTC cost function weight factors to be optimized. The position vector of particle i is substituted into the MPTC cost function, a simulation of a preset duration and working condition is run, torque, current and other data during the simulation are collected, and four objective function values corresponding to the particle are calculated according to the multi-objective function.

[0086] To further implement the above technical solution, in step S4, the cost function constructed based on the optimal weight factor is as follows: ​

[0087]

[0088] wherein g is a cost function, is a reference torque, is a predicted torque at k+1, is a reference stator flux linkage, is a predicted stator flux linkage at k+1, is a current limiting function, λ opt is an optimal weight factor.

[0089] To further implement the above technical solution, step S31, the multi-objective optimization model established including torque ripple, current total harmonic distortion, switching frequency and power loss is specifically:

[0090]

[0091]

[0092] wherein F(λ) is a multi-objective function, λ is a weight factor, is a root mean square value of torque ripple, is a reference torque at k, is an actual torque at k, N is a sampling point number, is a current total harmonic distortion rate, is an effective value of n-th harmonic current, is an effective value of fundamental current, is an average switching frequency, is a switching frequency at k, is a total power loss, is a switching loss, is an on-state loss, , are turn-on and turn-off energy losses of the jth switch, is an on-state voltage drop of the jth switch, is an average current of the jth switch;

[0093] In the embodiment, the root mean square value of torque ripple is used for evaluation, and the target aims to minimize torque fluctuation and improve operation stability; is used for measuring the sinusoidal degree of stator current, and the target aims to reduce current harmonics, reduce harmonic loss and interference on the power grid; evaluation of the frequency of switching action of power devices, the target aims to control the switching frequency and reduce the switching loss; including switching loss and on-state loss.

[0094] To further implement the above technical scheme, in step S34, the dominance relationship is:

[0095] For two solutions a and b, if the function value of solution a on all objectives is not worse than that of solution b, i.e. and is strictly better than that of solution b on at least one objective, i.e. solution a is said to dominate solution b; all mutually non-dominated solutions constitute a non-dominated layer, i.e. a Pareto front, denotes the function value of solution a on the jth objective, denotes the function value of solution b on the jth objective.

[0096] To further implement the above technical scheme, in step S34, the crowding distance of solutions in the same non-dominated layer is:

[0097]

[0098] wherein, is the crowding distance of the ith solution, , are the function values of the (i+1)th solution and the (i-1)th solution after sorting on the mth objective respectively, , are the maximum value and the minimum value of the mth objective respectively, and a solution with a larger crowding distance means that it is sparser around, and should be preferentially retained to ensure the diversity of the solution set.

[0099] In the embodiment, step S35 is external archiving Archive:

[0100]

[0101] wherein, Population is the current population or particle group, representing a group of solutions being processed in the current iteration; Archive represents the external archive or non-dominated solution set, used to save all optimal solutions found by the algorithm so far, i.e. non-dominated solutions, and the Archive is constantly updated and optimized with the iteration of the algorithm; x is any individual taken from the union set of the current population Population and the old Archive, and y represents another solution or individual / particle for comparison, denotes the absence, denotes that solution y dominates solution x, denotes that no y can be found in the entire set to dominate x, and if the condition is met, x is a non-dominated solution; at the end of each iteration, Population and Archive are combined, and new non-dominated solutions are screened out to update Archive;

[0102] Archive update rule: add non-dominated solutions in current population to the archive, and remove old solutions dominated by new solutions from the archive; when the size of the archive exceeds the preset upper limit, according to the crowding distance, delete the solution with the smallest crowding distance first, and keep the solution with the largest crowding distance, so as to maintain the uniform distribution of the Pareto front.

[0103] In order to further implement the above technical scheme, step S36, the specific method of updating the speed and position of each particle is:

[0104] Select a guide solution for each particle from the external archive based on the crowding distance; usually use roulette or tournament method, so that the solutions in the sparsely distributed area have a higher probability of being selected;

[0105] Update the speed and position as:

[0106]

[0107]

[0108] wherein, , is the speed and position of the i th particle at the t+1 th iteration, , is the speed and position of the i th particle at the t th iteration, is the inertia weight, , is the learning factor, , is a random number, is the historical optimal position of the i th particle, is the guide particle, , , t is the current iteration number, G max is the maximum iteration number.

[0109] In practical applications, step S3 automatically adjusts the target weight according to the running state of the motor:

[0110]

[0111] wherein, is the adaptive target weight vector, corresponding to the weight of torque ripple, current total harmonic distortion THD, switching frequency and power loss respectively.

[0112] In order to further implement the above technical scheme, the specific content of step S37 includes:

[0113] S371. Standardize the function value of each solution in the Pareto solution set on each target;

[0114] S372. Calculate the distance of each solution to the positive ideal solution and the distance to the negative ideal solution based on the normalized value of each solution on each objective and the positive ideal value of each objective and the objective weight;

[0115]

[0116]

[0117] wherein, is the distance of the ith solution to the positive ideal solution, is the distance of the ith solution to the negative ideal solution, is the weight of the jth objective, is the normalized value of the ith solution on the jth objective, is the positive ideal value of the jth objective, is the negative ideal value of the jth objective;

[0118] S373. Calculate the relative closeness of each solution, and select the solution with the largest relative closeness value as the optimal weight factor;

[0119]

[0120] wherein, is the relative closeness of the ith solution.

[0121] The various embodiments in the specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0122] The above description of disclosed embodiments enables a person skilled in the art to implement or use the present application. Various modifications to the embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A model predictive control method for permanent magnet synchronous motors based on multi-objective Pareto optimality, characterized in that, Includes the following steps: S1. Measure the two-phase current, motor speed and rotor position of the permanent magnet synchronous motor, and convert the two-phase current into d-axis and q-axis currents according to the rotor position. At the same time, convert the inverter's alternative voltage vector into d-axis and q-axis voltages. S2. Input the d-axis current, q-axis voltage corresponding to the candidate voltage vector, and motor speed into the permanent magnet synchronous motor current prediction model to predict future current state values; S3. Establish a multi-objective optimization model that includes torque ripple, total harmonic distortion of current, switching frequency and power loss, and use the multi-objective particle swarm optimization algorithm combined with non-dominated sorting and congestion distance calculation to obtain the Pareto optimal solution set, obtain the optimal weight factor, and automatically adjust the target weight according to the motor operating state under different operating conditions. S4. Construct a cost function based on the optimal weighting factor, and select the voltage vector that minimizes the cost function as the optimal control output; Step S3, the method for obtaining the optimal weight factor is as follows: S31. Establish a multi-objective optimization model that includes torque ripple, total harmonic distortion of current, switching frequency and power loss; S32. Set the running parameters of the multi-objective particle swarm algorithm and randomly generate the initial particle swarm; S33. For the weight factor of each particle, run the MPTC simulation model to calculate the corresponding multi-objective function value in order to perform multi-objective fitness evaluation; S34. Perform non-dominated sorting on the particle swarm, stratify the particles according to the dominance relationship, and calculate the crowding distance for solutions within the same non-dominated layer; S35. Maintain the external archive of the Pareto optimal solution set and update the archive of non-dominated solutions. When the archive size exceeds the preset limit, prune it according to the congestion distance. S36. Update the velocity and position of each particle based on its historical best position and the globally optimal guiding solution selected from the external archive; repeat steps S33-S36 until the iteration termination condition is met. S37. Employ a comprehensive technical evaluation method to select the optimal weighting factor from the Pareto frontier through multi-criteria decision-making; In step S4, the cost function constructed based on the optimal weight factor is as follows: Where g is the cost function, For reference torque, Predict the torque at time k+1. For reference stator flux linkage, Predict the stator flux linkage at time k+1. Let λ be the current limiting function. opt This is the optimal weighting factor.

2. The model predictive control method for permanent magnet synchronous motors based on multi-objective Pareto optimality as described in claim 1, characterized in that, In step S1, the d-axis and q-axis currents are: in, i d ( k ), i q ( k () represent time k, respectively a , b Two-phase current i a ( k ), i b ( k The converted d-axis and q-axis currents θ ( k () represents the rotor position at time k; The d-axis and q-axis voltages are: in, U dc For DC bus voltage, [ s a , s b , s c ] T This refers to the switching state corresponding to the alternative voltage vector of the inverter. u d ( k ), u q ( k () are the vector transformations of the candidate voltages at time k. d , q Shaft voltage.

3. The model predictive control method for permanent magnet synchronous motors based on multi-objective Pareto optimality as described in claim 1, characterized in that, In step S2, the current prediction model for the permanent magnet synchronous motor is as follows: in, i d ( k +1) and i q ( k +1) represents the predicted current state value at time k+1 in the future. p This represents the number of pole pairs of the motor. T s To control the period, ψ f It is a permanent magnet flux linkage. R s For motor resistance, ω m ( k Let k be the motor speed at time k. L d , L q They are respectively d , q Shaft inductor, i d ( k ), i q ( k () represents the d-axis and q-axis currents at time k, respectively. u d ( k ), u q ( k () represent time k, respectively d , q Shaft voltage.

4. The model predictive control method for permanent magnet synchronous motors based on multi-objective Pareto optimality as described in claim 1, characterized in that, Step S31, the multi-objective optimization model established, which includes torque ripple, total harmonic distortion of current, switching frequency, and power loss, is as follows: Where F(λ) is a multi-objective function, This is the root mean square value of torque ripple. The reference torque at time k, Let N be the actual torque at time k, and N be the number of sampling points. The total harmonic distortion of the current. The effective value of the nth harmonic current. This is the effective value of the fundamental current. The average switching frequency, Let k be the switching frequency at time k. For total power loss, For switching losses, For on-state loss, , These represent the energy losses for turning on and off the j-th switch, respectively. Let be the on-state voltage drop of the j-th switch. Let be the average current of the j-th switch.

5. The model predictive control method for permanent magnet synchronous motors based on multi-objective Pareto optimality as described in claim 1, characterized in that, In step S34, the dominance relationship is as follows: For two solutions a and b, if solution a is not inferior to solution b in all objectives and is strictly superior to solution b in at least one objective, then solution a is said to dominate solution b; all non-dominated solutions constitute a non-dominated layer, i.e. a Pareto front.

6. The model predictive control method for permanent magnet synchronous motors based on multi-objective Pareto optimality as described in claim 1, characterized in that, In step S34, the crowding distance of solutions within the same non-dominated layer is: in, Let be the crowding distance of the i-th solution. , Let be the function values ​​of the (i+1)th solution and the (i-1)th solution after sorting, respectively, for the m-th objective. , These are the maximum and minimum values ​​of the m-th target, respectively.

7. The model predictive control method for permanent magnet synchronous motors based on multi-objective Pareto optimality as described in claim 1, characterized in that, Step S36, the specific method for updating the velocity and position of each particle is as follows: For each particle, a guided solution is selected from the external archive based on the crowding distance; The update speed and location are as follows: in, , Let be the velocity and position of the i-th particle in the (t+1)th iteration, respectively. , Let be the velocity and position of the i-th particle in the t-th iteration, respectively. For inertial weights, , As a learning factor, , It is a random number. This represents the historical best position of the i-th particle. To guide the particles, , t is the current iteration number, G max Maximum number of iterations.

8. The model predictive control method for permanent magnet synchronous motors based on multi-objective Pareto optimality as described in claim 1, characterized in that, The specific content of step S37 includes: S371. Standardize the function values ​​of each solution in the Pareto solution set for each objective; S372. Based on the standardized value of each solution on each objective, as well as the positive ideal value and objective weight of each objective, calculate the distance to the positive ideal solution and the distance to the negative ideal solution for each solution; S373. Calculate the relative proximity of each solution and select the solution with the largest relative proximity value as the optimal weight factor.

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