CN111695254A - Permanent magnet synchronous motor multi-objective optimization method based on double-response curved surface method and Taguchi method - Google Patents
Permanent magnet synchronous motor multi-objective optimization method based on double-response curved surface method and Taguchi method Download PDFInfo
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Abstract
A permanent magnet synchronous motor multi-objective optimization method based on a double-response surface method and a Taguchi method belongs to the field of permanent magnet synchronous motor optimization algorithms. The method solves the problems that the existing multi-objective optimization algorithm has large optimization calculation amount, mutual influence among parameters and incapability of realizing multi-objective optimization accurately and efficiently. The invention utilizes the response surface equation and the Taguchi method proportion combined calculation, greatly reduces the difficulty of weight fusion, saves a large amount of time, makes full use of the self-carrying function of software to provide convenience for multi-objective optimization, and provides a new thought and method for the later multi-objective optimization of the permanent magnet synchronous motor. The algorithm is flexible and can be applied to various multi-objective optimization occasions. The invention is suitable for the optimized use of the permanent magnet synchronous motor.
Description
Technical Field
The invention belongs to the field of optimization algorithms of permanent magnet synchronous motors.
Background
The permanent magnet synchronous motor has the advantages of high power factor, small heat, no transmission gear abrasion, small noise, high reliability and high efficiency while bearing large overload current, and is widely applied to various fields. Such as numerically controlled machine tools, elevator systems, new energy vehicles, etc.
Because the cogging torque and the reluctance torque of the built-in permanent magnet synchronous motor have large pulsation, mechanical vibration and noise can be generated, and the running stability and the service life of the motor are seriously influenced. However, due to the fact that the built-in permanent magnet synchronous motor is easy to obtain high average torque due to the asymmetric reactance of the alternating and direct axes, the average torque is improved by adopting multi-objective optimization of the permanent magnet motor, in the multi-objective optimization process, along with the increase of an optimization target, the search frequency is increased in an exponential order, and therefore the algorithm cannot effectively detect a huge search space within a limited time; the traditional motor optimization method mainly utilizes finite element simulation software to optimize a single target, so that the problems of large optimization calculation amount and easy neglect of mutual influence among parameters exist, and meanwhile, multi-target optimization cannot be accurately and efficiently realized.
Disclosure of Invention
The invention provides a permanent magnet synchronous motor multi-objective optimization method based on a double-response curved surface method and a Taguchi method, aiming at solving the problems that the existing multi-objective optimization algorithm is large in optimization calculation amount, mutual influence among parameters and incapable of realizing multi-objective optimization accurately and efficiently.
The invention relates to a permanent magnet synchronous motor multi-objective optimization method based on a double-response curved surface method and a Taguchi method, which comprises the following specific steps:
determining an optimization target of a permanent magnet synchronous motor, and selecting three parameters related to the optimization target from rotor optimization parameters of the permanent magnet synchronous motor as optimization variables;
step two, determining the optimal range of the optimization variables in the step one;
thirdly, constructing a response surface model by using the optimization variables, and judging the rationality of the response surface model by using an analysis and verification equation of variance, wherein when the response surface model is unreasonable; step four is executed, when the response surface model is reasonable, a response surface equation is obtained, and step five is executed;
step four, selecting three parameters from the rotor optimization parameters of the permanent magnet synchronous motor as optimization variables; returning to execute the step two; the three parameters in the step are not completely the same as the three parameters in the step one;
step five, an orthogonal test method is carried out by utilizing a Taguchi method, and the influence specific gravity value of the optimized variable on the response value is calculated; executing the step six;
step six, fusing the response surface equation and the specific gravity value obtained in the step five through a weight fusion algorithm to obtain a final optimization correction equation;
and step seven, acquiring a linear function relation between the optimization variable and the optimization target by utilizing the property that the difference between the final optimization correction equation and the estimation target function is close to zero, and acquiring the optimal function value of the optimization target of the permanent magnet synchronous motor by utilizing the optimal value range of the optimization variable determined in the step two as a constraint condition.
Further, the rotor optimization parameters of the permanent magnet synchronous motor in the step one include: the inner and outer diameters of the rotor, the silicon steel sheet material and the type of the magnetic pole on the rotor; for the permanent magnet of the built-in motor, the pole arc coefficient, the thickness of the permanent magnet, the width of the magnetic isolation bridge, the thickness of the magnetic steel and the material of the permanent magnet can be used.
Further, the method for constructing the response surface model by using the optimization variables in the third step includes constructing by using Minitap software, MATLAB software or Design-Expert software.
Further, in the step five, the specific method for obtaining the influence specific gravity value of the optimized variable on the response value by using the Taguchi orthogonal test method is as follows:
fifthly, sampling each optimized variable, obtaining N groups of sampling data for each optimized variable, and calculating the average value of the N groups of sampling data of each optimized variable under an orthogonal test; wherein n is a positive integer greater than or equal to 4;
step two, solving the average value of the performance indexes of the three optimized variables under different permanent magnet thickness level values;
fifthly, calculating the variance of each optimized variable under different permanent magnet thickness level values;
and fifthly, calculating the influence proportion of each optimization parameter on the optimization target.
Further, in the fifth step, the specific method for calculating the average value of the n groups of sampling data of each optimization variable under the orthogonal test comprises the following steps:
using the formula:
and calculating to obtain the average value of the n groups of sampling data under the orthogonal test, wherein,
is the average value of the performance indexes of an optimization variable, i represents the ith group of sampling data of a certain optimization variable, TiAnd the average value of the performance indexes of the ith group of sampling data is shown.
Further, the concrete method for solving the average value of the performance indexes of the three optimized variables under different permanent magnet thickness level values in the fifth step is as follows:
the formula is adopted:
calculating to obtain an average value of performance indexes of the thickness level value of an optimized variable permanent magnet, wherein M isTAnd the torques of the optimization factors at the thickness level of the permanent magnet are shown, and T (1), T (2), T (3) and T (4) are the torques in the 1 st, 2 nd, 3 th and 4 th orthogonal experiments at the thickness level of the permanent magnet respectively.
Further, the specific method for calculating the variance of each optimized variable under different permanent magnet thickness level values in the fifth step and the third step is as follows:
when the variance of the torque is obtained, S in the formulasRepresenting an optimization objective variance; by using
The optimization target of the ith test at the jth permanent magnet thickness level is shown, and m (S) is the average value of the optimization targets of the motor.
Further, the specific method for calculating the influence proportion of each optimization parameter on the optimization target in the fifth and fourth steps is as follows:
z represents the weight of the variance of each optimization objective to the sum of the variances of all optimization objectives.
Further, the weight fusion algorithm in the sixth step adopts a formula:
converting multi-objective optimization into a process of solving an independent variable optimal value from a known optimal variable, and converting a final optimization result into a constraint relation between optimization target value functions; wherein A represents an optimization objective function, guThe method comprises the steps of estimating a corresponding first derivative in a Taylor expansion of an objective function, wherein the estimated objective function is expressed by an equation obtained by a response surface method, and P is the number of optimized variables; u denotes the u-th optimization variable, IuIs a set of values of an optimization variable, gamma is the influence degree of the optimization variable on each performance of the permanent magnet, and w*For the optimal specific gravity, the optimal specific gravity is obtained by calculation through an orthogonal test by a Taguchi method.
Further, the estimation objective function in step seven is:
wherein, A (theta) is an estimation objective function; x is the number ofiSamples representing optimization variablesThe estimation error μ () is an error estimation sum function caused by the permanent magnet leakage flux;
is due to xiChange in value of yiThe changed scale function, yiRepresenting an estimated target value that is continuously updated with the optimization process; k is yiThe number of updates, k representing the permanent magnet thickness level value, f when k is 1kiIs as follows yiThe degree of influence, psi (f), on the specific gravity of the parameter when the thickness level of the permanent magnet is 1ki)＝yi+(1/2γ)2。
The invention utilizes the response surface equation and the Taguchi method proportion combined calculation, greatly reduces the difficulty of weight fusion, saves a large amount of time, makes full use of the self-carrying function of software to provide convenience for multi-objective optimization, and provides a new thought and method for the later multi-objective optimization of the permanent magnet synchronous motor. The algorithm is flexible and can be applied to various multi-objective optimization occasions. The optimization algorithm is applied to the optimization design of the built-in permanent magnet synchronous motor. The method not only ensures that the response surface method has higher approximate precision, but also ensures the efficiency of the Taguchi method in the optimization later period.
Drawings
FIG. 1 is a graph of a model of a response surface between an average output torque and three variables according to the present invention;
FIG. 2 is a graph of a model of a response surface between a torque ripple coefficient and a three-variable obtained by the present invention;
FIG. 3 is a graph of a model of the response surface between efficiency and three variables obtained by the present invention;
FIG. 4 is a graph comparing torque performance before and after optimization;
FIG. 5 is a comparison graph of the magnetic flux density waveforms of the radial air gap of the load before and after optimization;
FIG. 6 is a comparison graph of the radial air gap flux density harmonic analysis of the load before and after optimization.
Detailed Description
In a first embodiment, the present embodiment is described with reference to fig. 1 to 3, and the present embodiment describes a permanent magnet synchronous motor multi-objective optimization method based on a dual response surface method and Taguchi (Taguchi method), which includes the following specific steps:
determining an optimization target of a permanent magnet synchronous motor, and selecting three parameters related to the optimization target from rotor optimization parameters of the permanent magnet synchronous motor as optimization variables;
step two, determining the optimal value range of the optimized variable in the step one;
thirdly, constructing a response surface model by using the optimization variables, and judging the rationality of the response surface model by using an analysis and verification equation of variance, wherein when the response surface model is unreasonable; step four is executed, when the response surface model is reasonable, a response surface equation is obtained, and step five is executed;
step four, selecting three parameters from the rotor optimization parameters of the permanent magnet synchronous motor as optimization variables; returning to execute the step two; the three parameters in the step are not completely the same as the three parameters in the step one;
fifthly, an orthogonal test method is carried out by utilizing a Taguchi method, and the influence specific gravity value of the optimized variable on the response value is calculated; executing the step six;
step six, fusing the response surface equation and the specific gravity value obtained in the step five through a weight fusion algorithm to obtain a final optimization correction equation;
and step seven, acquiring a linear function relation between the optimization variable and the optimization target by utilizing the property that the difference between the final optimization correction equation and the estimation target function is close to zero, and acquiring the optimal function value of the optimization target of the permanent magnet synchronous motor by utilizing the optimal value range of the optimization variable determined in the step two as a constraint condition.
In the embodiment, the Ansoft Maxwell software is used for determining the optimal range of the optimization variables in the step one.
In the present invention, the corresponding loss error function is smaller as the objective function estimate is closer to the desired objective function value. But when the difference between the two is close to zero, the optimization effect is considered to be optimal, the estimation objective function is close to the final optimization objective function by updating the estimation objective function, and the final optimization objective function is solved by utilizing the characteristic. Namely, when the estimated objective function is updated to meet min (A-A (theta)), the proportion of the coefficients accounting for the sum of the total coefficients before the parameters of the response surface equation can be respectively substituted into the optimization objective equation to obtain 6 unknown equations, and the problem can be converted into a simple linear programming problem by adding the constraint condition.
Further, in this embodiment, the rotor optimization parameters of the permanent magnet synchronous motor in the first step include: the inner and outer diameters of the rotor, the silicon steel sheet material and the type of the magnetic pole on the rotor; for the permanent magnet of the built-in motor, the pole arc coefficient, the thickness of the permanent magnet, the width of the magnetic isolation bridge, the thickness of the magnetic steel and the material of the permanent magnet can be used.
Further, in this embodiment, the method for constructing a response surface model by using the optimized variables in step three includes constructing by using Minitap software, MATLAB software, or Design-Expert software.
Further, in this embodiment, the specific method for obtaining the influence specific gravity value of the optimized variable on the response value by the method of performing the orthogonal test by using the Taguchi method in the step five is as follows:
fifthly, sampling each optimized variable, obtaining N groups of sampling data for each optimized variable, and calculating the average value of the N groups of sampling data of each optimized variable under an orthogonal test; wherein n is a positive integer greater than or equal to 4;
step two, solving the average value of the performance indexes of the three optimized variables under different permanent magnet thickness level values;
fifthly, calculating the variance of each optimized variable under different permanent magnet thickness level values;
and fifthly, calculating the influence proportion of each optimization parameter on the optimization target.
Further, in this embodiment, the specific method for calculating the average value of the n groups of sampling data of each optimized variable in the step five i under the orthogonal test is as follows:
using the formula:
and calculating to obtain the average value of the n groups of sampling data under the orthogonal test, wherein,
is the average value of the performance indexes of an optimization variable, i represents the ith group of sampling data of a certain optimization variable, TiAnd the average value of the performance indexes of the ith group of sampling data is shown.
Further, in this embodiment, the specific method for calculating the average value of the performance indexes of the three optimized variables under different permanent magnet thickness level values in the fifth and second steps is as follows:
the formula is adopted:
calculating to obtain an average value of performance indexes of the thickness level value of an optimized variable permanent magnet, wherein M isTAnd the torques of the optimization factors at the thickness level of the permanent magnet are shown, and T (1), T (2), T (3) and T (4) are the torques in the 1 st, 2 nd, 3 th and 4 th orthogonal experiments at the thickness level of the permanent magnet respectively.
Further, in this embodiment, the specific method for calculating the variance of each optimized variable under different permanent magnet thickness level values in step five and step three is as follows:
when the variance of the torque is obtained, S in the formulasRepresenting an optimization objective variance; by using
The optimization target of the ith test at the jth permanent magnet thickness level is shown, and m (S) is the average value of the optimization targets of the motor.
Further, in this embodiment, the specific method for calculating the influence specific gravity of each optimization parameter on the optimization target in the fifth and fourth steps is as follows:
z represents the weight of the variance of each optimization objective to the sum of the variances of all optimization objectives.
Further, in this embodiment, the weight fusion algorithm in step six adopts a formula:
converting multi-objective optimization into a process of solving an independent variable optimal value from a known optimal variable, and converting a final optimization result into a constraint relation between optimization target value functions; wherein A represents an optimization objective function, guThe method comprises the steps of estimating a corresponding first derivative in a Taylor expansion of an objective function, wherein the estimated objective function is expressed by an equation obtained by a response surface method, and P is the number of optimized variables; u denotes the u-th optimization variable, IuIs a set of values of an optimization variable, gamma is the influence degree of the optimization variable on each performance of the permanent magnet, and w*For the optimal specific gravity, the optimal specific gravity is obtained by calculation through an orthogonal test by a Taguchi method.
Further, in this embodiment, the estimation objective function in step seven is:
wherein, A (theta) is an estimation objective function; x is the number ofiA sample representing an optimization variable, the estimation error μ () being an error estimation sum function caused by permanent magnet leakage;
is due to xiChange in value of yiThe changed scale function, yiRepresenting an estimated target value that is continuously updated with the optimization process; k is yiThe number of updates, k representing the permanent magnet thickness level value, f when k is 1kiIs as follows yiThe degree of influence, psi (f), on the specific gravity of the parameter when the thickness level of the permanent magnet is 1ki)＝yi+(1/2γ)2。
Specific examples are as follows: taking a 3kW built-in permanent magnet synchronous motor as an example, an optimization design test is performed by taking the thickness of a permanent magnet, the width of a magnetic isolation bridge and a pole arc coefficient as variables and taking a torque fluctuation coefficient, an average output torque and efficiency as optimization targets, and main size parameters and main technical requirements of the motor are shown in Table 1.
TABLE 1 permanent magnet synchronous machine dimensional parameters and Main specifications
Because the aim of the invention is to improve the average output torque and reduce the torque fluctuation, the efficiency and the torque performance of the motor are analyzed only by considering the condition that the motor runs under the load working condition.
The specific implementation steps are as follows:
step 1: determining the thickness of a permanent magnet, wherein the width of a magnetic isolation bridge and a pole arc coefficient are three optimization variables, and a torque fluctuation coefficient, an average output torque and efficiency are optimization targets;
step 2: carrying out parametric analysis on the motor model by using Ansoft Maxwell to obtain an optimized variable and a parametric scanning result shown in the following table 2;
TABLE 2 optimization variables and parameterized scan results
And step 3: selecting 1, 2 and 3 as three factor levels of variables, wherein the specific values of the optimized parameters at the three factor levels are shown in the following table 3; designing 14 groups of tests according to design-expert self-contained functions and removing unreasonable test factor combinations as shown in the following table 4, establishing a response surface model and an equation, and verifying the reasonability of the equation according to variance analysis;
TABLE 3 specific values of the optimized parameters at the three-factor level
TABLE 4 results of orthogonal experiments
In the table, Thicknes is the permanent magnet thickness, Bridge magnetic isolation Bridge width, and a is the polar arc coefficient;
the response surface equation is:
equation 1:
Tav＝-1214.2+157.6D+802.8B+373.6C-88.2AB-521.0BC+427.9C2
TF＝288.6-57.0D+8.5B-388.6C+48.8DB+0.5×DC+347.2BC-3.0D2-138.4B2-181.5C2
η＝-470.8+11.6D+584.6B+8.8C+11.0AB+3.0DC+64.5BC-3.2D2-190.6B2-100.5C2
equation 2:
Tav＝40.1-0.6D-0.7B+4.2C-2.2DB-2.1BC+2.7C2
TF＝13.9+0.8D+0.2B-1.8C+1.2DB+0.02DC+1.4BC-0.7D2-0.4B2-1.2C2
η＝89.6+0.8D-2.6e×10-3B-0.4C+0.3DB+0.1DC+0.3BC-0.8D2-0.5B2-0.6C2
response value: tav: output average torque (unit N m)
TF: torque ripple factor
Eta: efficiency (%)
② independent variable: d: permanent magnet thickness (unit mm)
B: magnetic bridge width (unit mm)
C: coefficient of polar arc
Each quantity in formula 1 is an actual value; the coding values in the formula 2 are all under the thickness level factor of two permanent magnets; t ismaxMaximum torque of the motor, TminIs the minimum torque of the motor.
The response surface models obtained through the above steps are shown in fig. 2, 3 and 4, wherein the result reliability test is shown in fig. 4, and as seen from fig. 4, the response surface models have accuracy and reliability.
And 4, step 4: 14 groups of orthogonal tests are designed by using a Taguchi method, and the influence proportion of each variable on an optimization target is calculated through finite element simulation or the result of the test combination, wherein the formula is as follows:
firstly, solving the average value of all results: (the mean value is the average value of 14 sets of orthogonal tests for each optimization target, wherein T represents the output torque, for example, the mean value of the average output torque in 14 sets of orthogonal tests is calculated by the following formula, and similarly, the mean values of the torque ripple factor and the efficiency in 14 sets of orthogonal tests are calculated respectively)
The calculation results are shown in table 5 below:
TABLE 5 optimization target mean values
Solving the average value of the performance indexes under each parameter level value:
the calculation results are shown in table 6 below:
TABLE 6 mean values of the respective performance indexes at the respective parameter levels
③ calculating the variance of each parameter:
when the variance of the torque is obtained, S in the formulasRepresenting an optimization objective variance; by using
The optimization target of the ith test at the jth permanent magnet thickness level is shown, and m (S) is the average value of the optimization targets of the motor.
Influence proportion of each optimization parameter on the optimization target:
wherein: as shown in table 7, the impact of the optimization parameters on the optimization objective is weighted;
TABLE 7 influence of optimization parameters on optimization target specific gravity
And 5: combining the response surface equation with the proportion calculated by the Taguchi method through a weight fusion algorithm, wherein the process is as follows:
setting the variable parameters and the objective function as a number set, and setting an integrated number model as follows:
wherein xiA sample representing an optimization variable; k is yiNumber of updates, k represents a horizontal value, and f is 1kIs as follows yiThe degree of influence exerted on the specific gravity of the parameter at a level is added,
is due to xiChange in value of yiThe changed scale function, yiRepresenting estimated target values that are continually updated as the optimization process progresses.
A (Θ) is the estimated objective function; μ is the estimation error, here the error estimation sum function caused by the permanent magnet leakage;
w represents a weight value which is calculated by a Taguchi method; y isiIs a value assumed by experience, because continuously adding a new optimization target f in the optimization process can change the influence proportion of the optimization parameters on the optimization target, a formula four is adopted for predicting the value yiAnd updating, namely updating the target function according to a formula five:
wherein t represents the number of added optimization targets f;
y representing non-updated before adding a new optimization objective fiPredicting a value; psi (f)t) Updated value of ψ (f) after adding a new optimization target; when t is 1, ft(xi) Expressed as adding an optimization objective f, f (x)i) An updated value of (d);
indicating y that has been updated after adding a new optimization objective fiPredicted value, f (x)i) Is an optimization objective function that is continuously updated as optimization variables are added.
And performing second-order Taylor expansion on the mixed solution to obtain a formula six:
wherein λ is a constant obtained by taylor expansion of the formula five. u denotes the u-th optimization variable, IuIs a collection of optimized variable values.
wu＝f(xi),i∈Iu
Wherein P is the number of the optimized variables; giAnd hiRespectively corresponding first derivative and second derivative of Taylor formula; let wuGet the target optimal solution when w, w*The impact specific gravity of each optimization variable obtained for Taguchi (Taguchi) on the optimization objective;
converting multi-objective optimization into a process of solving an independent variable optimal value from a known optimal variable, and converting a final optimization result into a constraint relation between optimization target value functions; wherein A represents an optimization objective function, guThe method comprises the steps of estimating a corresponding first derivative in a Taylor expansion of an objective function, wherein the estimated objective function is expressed by an equation obtained by a response surface method, and P is the number of optimized variables; u denotes the u-th optimization variable, IuIs a set of values of an optimization variable, gamma is the influence degree of the optimization variable on each performance of the permanent magnet, and w*For the optimal specific gravity, the optimal specific gravity is obtained by calculation through an orthogonal test by a Taguchi method.
Step 6: as the objective function estimate is closer to the desired objective function value, the corresponding loss error function is smaller. But when the difference between the two is close to zero, the optimization effect is considered to be optimal, the estimation objective function is close to the final optimization objective function by updating the estimation objective function, and the final optimization objective function is solved by utilizing the characteristic. That is, when min (A-A (theta)) is satisfied, the proportion of the coefficients before the response surface equation parametric variables to the sum of the total coefficients can be respectively substituted into the optimization target equation, and the constraint condition obtained by adding the equation containing 6 unknowns (the unknowns are respectively three optimization variables and three optimization targets) into the parametric scanning process can convert the problem into a simple linear programming problem. Finally, the optimal solution of the three variables and the three responses of the permanent magnet synchronous motor is obtained as shown in the following table 8;
TABLE 8 optimal parameters and optimal solution for optimization objective
Inputting the optimal parameter combination of the motor, carrying out torque performance simulation, and comparing the torque performance indexes of the motor before and after optimization as shown in the attached figure 5; for the 3kW interior permanent magnet synchronous motor, when the thickness of the permanent magnet is 5.2mm, the width of the magnetic isolation bridge is 1.8mm, and the pole arc coefficient is 0.8, the average torque output is 50.81N.m, the torque fluctuation coefficient is 7.89%, the efficiency is 89.53%, and the cogging torque is 1.1227 N.m. Compared with the original motor, the torque mean value is increased from 39.39N.m to 50.81N.m, the torque fluctuation coefficient is reduced from 12.5% to 7.89%, and the efficiency is improved by 3%. Within the error range, the finite element verification result is consistent with the calculation result, which shows the reliability and accuracy of the optimized design scheme.
As can be seen from the attached drawings 5 and 6, the invention improves the fundamental wave and simultaneously weakens 3 rd harmonic, 5 th harmonic and 11 th harmonic, and because the harmonic of the radial air gap flux density is the main source of vibration and noise, the invention can effectively weaken the vibration and noise of the built-in permanent magnet synchronous motor. The practical value of the combination of the response surface method and the Taguchi on multi-objective optimization design is also shown, and a new scheme is provided for the optimization design and research of the permanent magnet synchronous motor in the future.
From the aspect of optimization algorithm, the invention greatly reduces the difficulty of weight fusion by combining the response surface equation and the Taguchi proportion calculation, saves a large amount of time, provides convenience for multi-objective optimization by fully utilizing the self-carrying function of software, and provides a new idea and method for the later multi-objective optimization of the permanent magnet synchronous motor. The verification proves that the algorithm is flexible and can be applied to various multi-objective optimization occasions. The scheme provides an optimization algorithm combining the two through a mathematical mode, and is applied to the optimization design of the built-in permanent magnet synchronous motor. The method not only ensures that the response surface method has higher approximate precision, but also ensures the efficiency of the Taguchi method in the optimization later period.
The present invention is described herein with reference to particular embodiments, but it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that features described in different dependent claims and herein may be combined in ways different from those described in the original claims. It is also to be understood that features described in connection with individual embodiments may be used in other described embodiments.
Claims (10)
1. A permanent magnet synchronous motor multi-objective optimization method based on a double-response surface method and a Taguchi method is characterized by comprising the following specific steps:
determining an optimization target of a permanent magnet synchronous motor, and selecting three parameters related to the optimization target from rotor optimization parameters of the permanent magnet synchronous motor as optimization variables;
step two, determining the optimal value range of the optimized variable in the step one;
thirdly, constructing a response surface model by using the optimization variables, and judging the rationality of the response surface model by using an analysis and verification equation of variance, wherein when the response surface model is unreasonable; step four is executed, when the response surface model is reasonable, a response surface equation is obtained, and step five is executed;
step four, selecting three parameters from the rotor optimization parameters of the permanent magnet synchronous motor as optimization variables; returning to execute the step two; the three parameters in the step are not completely the same as the three parameters in the step one;
fifthly, an orthogonal test method is carried out by utilizing a Taguchi method, and the influence specific gravity value of the optimized variable on the response value is calculated; executing the step six;
step six, fusing the response surface equation and the specific gravity value obtained in the step five through a weight fusion algorithm to obtain a final optimization correction equation;
and step seven, acquiring a linear function relation between the optimization variable and the optimization target by utilizing the property that the difference between the final optimization correction equation and the estimation target function is close to zero, and acquiring the optimal function value of the optimization target of the permanent magnet synchronous motor by utilizing the optimal value range of the optimization variable determined in the step two as a constraint condition.
2. The permanent magnet synchronous motor multi-objective optimization method based on the double-response surface method and the Taguchi method as claimed in claim 1, wherein the rotor optimization parameters of the permanent magnet synchronous motor in the step one comprise: the inner and outer diameters of the rotor, the silicon steel sheet material and the type of the magnetic pole on the rotor; for the permanent magnet of the built-in motor, the pole arc coefficient, the thickness of the permanent magnet, the width of the magnetic isolation bridge, the thickness of the magnetic steel and the material of the permanent magnet can be used.
3. The permanent magnet synchronous motor multi-objective optimization method based on the double response surface method and the Taguchi method according to claim 2, wherein the method for constructing the response surface model by using the optimization variables in the third step comprises constructing by using Minitap software, MATLAB software or Design-Expert software.
4. The permanent magnet synchronous motor multi-objective optimization method based on the double-response surface method and the Taguchi method as claimed in claim 1, wherein in the step five, the method for performing the orthogonal test by using the Taguchi method is specifically used for acquiring the influence specific gravity value of the optimization variable on the response value:
fifthly, sampling each optimized variable, obtaining N groups of sampling data for each optimized variable, and calculating the average value of the N groups of sampling data of each optimized variable under an orthogonal test; wherein n is a positive integer greater than or equal to 4;
step two, solving the average value of the performance indexes of the three optimized variables under different permanent magnet thickness level values;
fifthly, calculating the variance of each optimized variable under different permanent magnet thickness level values;
and fifthly, calculating the influence proportion of each optimization parameter on the optimization target.
5. The permanent magnet synchronous motor multi-objective optimization method based on the double-response surface method and the Taguchi method as claimed in claim 4, wherein the specific method for calculating the average value of n groups of sampling data of each optimization variable under the orthogonal test in the fifth step is as follows:
using the formula:
and calculating to obtain the average value of the n groups of sampling data under the orthogonal test, wherein,
is the average value of the performance indexes of an optimization variable, i represents the ith group of sampling data of a certain optimization variable, TiAnd the average value of the performance indexes of the ith group of sampling data is shown.
6. The permanent magnet synchronous motor multi-objective optimization method based on the double-response surface method and the Taguchi method as claimed in claim 4, wherein the concrete method for solving the performance index average value of the three optimized variables under different permanent magnet thickness levels in the fifth step and the second step is as follows:
the formula is adopted:
calculating to obtain an average value of performance indexes of the thickness level value of an optimized variable permanent magnet, wherein M isTAnd the torques of the optimization factors at the thickness level of the permanent magnet are shown, and T (1), T (2), T (3) and T (4) are the torques in the 1 st, 2 nd, 3 th and 4 th orthogonal experiments at the thickness level of the permanent magnet respectively.
7. The permanent magnet synchronous motor multi-objective optimization method based on the double-response surface method and the Taguchi method as claimed in claim 6, wherein the specific method for calculating the variance of each optimization variable under different permanent magnet thickness level values in the fifth step and the third step is as follows:
when the variance of the torque is obtained, S in the formulasRepresenting an optimization objective variance; by using
The optimization target of the ith test at the jth permanent magnet thickness level is shown, and m (S) is the average value of the optimization targets of the motor.
8. The permanent magnet synchronous motor multi-objective optimization method based on the double-response surface method and the Taguchi method as claimed in claim 7, wherein the specific method for calculating the influence proportion of each optimization parameter on the optimization objective in the fifth and fourth steps is as follows:
z represents the weight of the variance of each optimization objective to the sum of the variances of all optimization objectives.
9. The permanent magnet synchronous motor multi-objective optimization method based on the double-response surface method and the Taguchi method as claimed in claim 1, wherein the weight fusion algorithm in the sixth step adopts a formula:
converting multi-objective optimization into a process of solving an independent variable optimal value from a known optimal variable, and converting a final optimization result into a constraint relation between optimization target value functions; wherein A represents an optimization objective function, guThe method comprises the steps of estimating a corresponding first derivative in a Taylor expansion of an objective function, wherein the estimated objective function is expressed by an equation obtained by a response surface method, and P is the number of optimized variables; u denotes the u-th optimization variable, IuIs a set of values of an optimization variable, gamma is the influence degree of the optimization variable on each performance of the permanent magnet, and w*Is the optimum specific gravity.
10. The permanent magnet synchronous motor multi-objective optimization method based on the double-response surface method and the Taguchi method as claimed in claim 5, wherein the estimation objective function in the seventh step is as follows:
wherein, A (theta) is an estimation objective function; x is the number ofiA sample representing an optimization variable, the estimation error μ () being an error estimation sum function caused by permanent magnet leakage;
is due to xiChange in value of yiThe changed scale function, yiRepresenting follow-up optimizationA process-continuously updated estimated target value; k is yiThe number of updates, k representing the permanent magnet thickness level value, f when k is 1kiIs as follows yiThe degree of influence, psi (f), on the specific gravity of the parameter when the thickness level of the permanent magnet is 1ki)＝yi+(1/2γ)2。
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