CN110323989A - Permanent magnet synchronous motor method for identification of rotational inertia based on population - Google Patents

Abstract

The invention discloses a method for identifying the moment of inertia of a permanent magnet synchronous motor based on particle swarms. The present invention proposes a method for identifying the moment of inertia of a permanent magnet synchronous motor based on particle swarms, including: in the problem of identifying the moment of inertia of PMSM, the rotor dynamics equation involved is: Where T _e is the electromagnetic torque, T _l is the load torque, J is the moment of inertia, ω is the angular velocity, B is the viscous friction coefficient, and C is the Coulomb friction coefficient. The electromagnetic torque can be estimated according to formula (3‑6), expressed as The key to identifying moment of inertia J by PSO algorithm is to establish evaluation function (fitness function) and optimize it. In order to evaluate the pros and cons of particles, the evaluation function of the i-th particle is selected as the following quadratic form The beneficial effect of the present invention is that the identification accuracy of the moment of inertia is greatly improved by using the particle swarm algorithm.

Description

Moment of inertia identification method for permanent magnet synchronous motor based on particle swarm

technical field

The invention relates to the field of permanent magnet synchronous motors, in particular to a method for identifying the moment of inertia of permanent magnet synchronous motors based on particle swarms.

Background technique

The existing on-line parameter identification methods for permanent magnet synchronous motors (PMSM) mainly include least squares method and model reference adaptive algorithm.

The traditional technology has the following technical problems:

The least squares method continuously collects new data through the designed model, and uses a recursive algorithm to continuously update the identification results until the sum of the squares of the errors is minimized to achieve the purpose of accurate identification. The above two identification algorithms are difficult to achieve high-precision rapid identification, and there are certain limitations when used.

Contents of the invention

The technical problem to be solved by the present invention is to provide a particle swarm-based permanent magnet synchronous motor moment of inertia identification method, using the particle swarm algorithm to realize the moment of inertia identification algorithm, which has the advantages of high precision, fast convergence and no need for coding.

In order to solve the above-mentioned technical problems, the present invention provides a method for identifying the moment of inertia of a permanent magnet synchronous motor based on particle swarms, including: in the problem of identifying the moment of inertia of PMSM, the rotor dynamics equation involved is:

Where T _e is the electromagnetic torque, T _l is the load torque, J is the moment of inertia, ω is the angular velocity, B is the viscous friction coefficient, and C is the Coulomb friction coefficient. According to the formula (3-6), the electromagnetic torque can be estimated, expressed as

The key to identifying moment of inertia J by PSO algorithm is to establish evaluation function (fitness function) and optimize it. In order to evaluate the pros and cons of particles, the evaluation function of the i-th particle is selected as the following quadratic form

In one of the embodiments, the basic steps of the particle swarm optimization algorithm are as follows, and the corresponding flow chart is shown in Figure 1:

(1) Set the size of the particle population, and randomly initialize a group of particles within a certain range, including the position and velocity of the particles;

(2) Evaluate the fitness of all particles according to the selected objective function;

(3) Updating of the individual optimal value P _best . For all particles in the population, compare its fitness value with its own optimal value achieved in the previous generation search process, if it is better than the optimal value P _best , then take the current fitness value as the individual optimal value P _best ;

(4) The update of the global optimal value G _best . For all particles in the population, compare its fitness value with the optimal value of all particles in the entire particle swarm in the search process of previous generations. If it is better than the optimal value G _best , take the current fitness value as the global optimal value. Good value G _best ;

(5) According to the formula, the specific speed and position can be obtained;

(6) Determine whether the number of iterations meets the standard of the experiment, if so, end the iteration, and output the optimal solution G _best ; otherwise, go back to step (2) and continue to start a new round of iterative optimization.

In one of the embodiments, by analyzing the information of individuals in the group, information sharing is realized on this basis, and finally the analysis and calculation of data can be realized during the movement of the whole group, and finally the most Excellent solution. The initial population of particle swarm optimization is a group of random solutions, the position of particle i in N-dimensional space is expressed as X _i =(x _i1 , _xi2 ,...,x _iN ), and the flight speed is expressed as V _i =(v _i1 ,v _i2 ,...,v _iN ). Each particle has an fitness value determined by the objective function. In the _iterative process, the particle can track two "extreme values" to realize its own update and optimization. The optimal value reached by itself in the process; the global extremum G _best is the optimal value reached by all particles in the entire particle swarm during the previous generation search process.

Particles use the following formulas to update velocity information and position information.

Among them, i=1,2,...,N, d=1,2,...,D, N and D respectively represent the size of the particle swarm and the dimension of the search space; Indicates the velocity of the i-th particle on the d-dimension; v _d,max is the maximum velocity of the particle in the range space; Indicates the position of the i-th particle in the d dimension; Indicates the historical best of the i-th particle; Indicates the optimal value of the t-th iteration group; c ₁ and c ₂ are called learning factors or acceleration coefficients; r ₁ and r ₂ are random numbers between [0,1] generated by random functions.

Formula (3-1) mainly updates the velocity of particles through three parts: the first part It is an individual memory item, which is used to describe the influence of the size and direction of the last iteration speed, and has the function of balancing the global and partial search capabilities of the particle; the second part is a typical individual cognitive item, which is the best point from the current point to the particle itself. A vector of points, representing a vector, the direction is mainly the optimal position in the system, the action of the particle has been tested by itself; the third part is a group cognition item, which also represents a vector, and the direction is that the particle itself points to the global optimal position, which means the cooperation and information sharing among particles. Particles react to motion based on their own experience and the optimal experience of other particles.

Introduce the inertia factor w to make its value positive. Update formula (3-1) to (3-4),

Among them, the larger the w value is, the stronger the global search ability is, and the weaker the local search ability is; the smaller the w value is, the weaker the global search ability is, and the stronger the local search ability is.

In one of the embodiments, the selection weight decreasing method is used, that is, the inertia weight becomes smaller as the number of iterations increases.

w(t)＝w _max -(w _max -w _min )/N _max (3-5)

Where N _max is the maximum number of iterations.

A computer device includes a memory, a processor, and a computer program stored in the memory and operable on the processor, and the processor implements the steps of any one of the methods when executing the program.

A computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the steps of any one of the methods described above are realized.

A processor, the processor is used to run a program, wherein the program executes any one of the methods when running.

Beneficial effects of the present invention:

Using the particle swarm algorithm greatly improves the identification accuracy of the moment of inertia. According to the simulation research, the commonly used least squares method and model reference adaptive method have an error of 1% to 5%, while the error of particle swarm algorithm identification is within 0.1%. When considering the moment of inertia, a more accurate model of the motor is used. For this, a rotordynamic model with viscous and Coulomb friction is used. The use of particle swarm algorithm to realize rotation variable identification has the advantage of being suitable for models with nonlinear characteristics such as Coulomb friction, and secondly, the size of the number of particle swarms can be used to adjust the identification accuracy and speed, and can be extended to parallel computing and distributed The way of processing (for example, under the framework of the Industrial Internet of Things, the iterative calculation of a large number of particles is processed in the cloud).

Description of drawings

FIG. 1 is a flow chart of the method for identifying the moment of inertia of a permanent magnet synchronous motor based on particle swarms in the present invention.

Fig. 2 is a schematic diagram of a specific embodiment of the method for identifying the moment of inertia of a permanent magnet synchronous motor based on particle swarms in the present invention.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and implement it, but the examples given are not intended to limit the present invention.

Particle Swarm Optimization (PSO) algorithm is an intelligent algorithm method for solving optimization problems. Through the analysis of the information of the individuals in the group, information sharing is realized on this basis, and finally the analysis and calculation of the data can be realized during the movement of the whole group, and finally the optimal solution can be obtained. The initial population of particle swarm optimization is a group of random solutions, the position of particle i in N-dimensional space is expressed as X _i =(x _i1 , _xi2 ,...,x _iN ), and the flight speed is expressed as V _i =(v _i1 ,v _i2 ,...,v _iN ). Each particle has an fitness value determined by the objective function. In the _iterative process, the particle can track two "extreme values" to realize its own update and optimization. The optimal value reached by itself in the process; the global extremum G _best is the optimal value reached by all particles in the entire particle swarm during the previous generation search process.

Particles use the following formulas to update velocity information and position information.

Among them, i=1,2,...,N, d=1,2,...,D, N and D respectively represent the size of the particle swarm and the dimension of the search space; Indicates the velocity of the i-th particle on the d-dimension; v _d,max is the maximum velocity of the particle in the range space; Indicates the position of the i-th particle in the d dimension; Indicates the historical best of the i-th particle; Indicates the optimal value of the t-th iteration group; c ₁ and c ₂ are called learning factors or acceleration coefficients; r ₁ and r ₂ are random numbers between [0,1] generated by random functions.

Formula (3-1) mainly updates the velocity of particles through three parts: the first part It is an individual memory item, which is used to describe the influence of the size and direction of the last iteration speed, and has the function of balancing the global and partial search capabilities of the particle; the second part is a typical individual cognitive item, which is the best point from the current point to the particle itself. A vector of points, representing a vector, the direction is mainly the optimal position in the system, the action of the particle has been tested by itself; the third part is a group cognition item, which also represents a vector, and the direction is that the particle itself points to the global optimal position, which means the cooperation and information sharing among particles. Particles react to motion based on their own experience and the optimal experience of other particles.

Introduce the inertia factor w to make its value positive. Update formula (3-1) to (3-4),

Among them, the larger the w value is, the stronger the global search ability is, and the weaker the local search ability is; the smaller the w value is, the weaker the global search ability is, and the stronger the local search ability is. Whether the performance of particle swarm optimization algorithm is good or not depends very much on the selection of inertia weight. In order to avoid long convergence time and falling into local optimum, many scholars have studied the selection of inertia weights. The more popular method is to choose the weight decreasing method, that is, as the number of iterations increases, the inertia weight becomes smaller.

w(t)＝w _max -(w _max -w _min )/N _max (3-5)

Where N _max is the maximum number of iterations.

In the problem of PMSM moment of inertia identification, the rotordynamic equations involved are:

Where T _e is the electromagnetic torque, T _l is the load torque, J is the moment of inertia, ω is the angular velocity, B is the viscous friction coefficient, and C is the Coulomb friction coefficient. According to the formula (3-6), the electromagnetic torque can be estimated, expressed as

The key to identifying moment of inertia J by PSO algorithm is to establish evaluation function (fitness function) and optimize it. In order to evaluate the pros and cons of particles, the evaluation function of the i-th particle is selected as the following quadratic form

When the value corresponding to the above evaluation function is smaller, the predicted electromagnetic torque is closer to the real electrical torque, which also means that the identified moment of inertia is closer to the true value.

The basic steps of the particle swarm algorithm are as follows, and the corresponding flow chart is shown in Figure 1:

(1) Set the size of the particle population, and randomly initialize a group of particles within a certain range, including the position and velocity of the particles;

(2) Evaluate the fitness of all particles according to the selected objective function;

(3) Updating of the individual optimal value P _best . For all particles in the population, compare its fitness value with its own optimal value achieved in the previous generation search process, if it is better than the optimal value P _best , then take the current fitness value as the individual optimal value P _best ;

(4) The update of the global optimal value G _best . For all particles in the population, compare its fitness value with the optimal value of all particles in the entire particle swarm in the search process of previous generations. If it is better than the optimal value G _best , take the current fitness value as the global optimal value. Good value G _best ;

(5) According to the formula, the specific speed and position can be obtained;

(6) Determine whether the number of iterations meets the standard of the experiment, if so, end the iteration, and output the optimal solution G _best ; otherwise, go back to step (2) and continue to start a new round of iterative optimization.

Referring to Figure 2, set a 4500RPM permanent magnet synchronous motor with a moment of inertia of 0.0003617kg.m^2 and a rated voltage of 300VDC. Using the PSO algorithm for identification, it converges at the 30th iteration, the identification result is 0.00036163kg.m^2, and the error rate is 0.019%.

The above-mentioned embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention shall be determined by the claims.

Claims (7)

1. A permanent magnet synchronous motor moment of inertia identification method based on particle swarm, it is characterized in that, comprises: in the problem of PMSM moment of inertia identification, the rotor dynamics equation involved is: Where T _e is the electromagnetic torque, T _l is the load torque, J is the moment of inertia, ω is the angular velocity, B is the viscous friction coefficient, and C is the Coulomb friction coefficient. According to the formula (3-6), the electromagnetic torque can be estimated, expressed as The key to identifying moment of inertia J by particle swarm algorithm is to establish evaluation function and optimize it. In order to evaluate the pros and cons of particles, the evaluation function of the i-th particle is selected as the following quadratic form 2. The method for identifying the moment of inertia of a permanent magnet synchronous motor based on particle swarm as claimed in claim 1, wherein the basic steps of the particle swarm algorithm are as follows, and the corresponding flow chart is shown in Figure 3-1: (1) Set the size of the particle population, and randomly initialize a group of particles within a certain range, including the position and velocity of the particles; (2) Evaluate the fitness of all particles according to the selected objective function; (3) Updating of the individual optimal value P _best . For all particles in the population, compare its fitness value with its own optimal value achieved in the previous generation search process, if it is better than the optimal value P _best , then take the current fitness value as the individual optimal value P _best ; (4) The update of the global optimal value G _best . For all particles in the population, compare its fitness value with the optimal value of all particles in the entire particle swarm in the search process of previous generations. If it is better than the optimal value G _best , take the current fitness value as the global optimal value. Good value G _best ; (5) According to the formula, the specific speed and position can be obtained; (6) Determine whether the number of iterations meets the standard of the experiment, if so, end the iteration, and output the optimal solution G _best ; otherwise, go back to step (2) and continue to start a new round of iterative optimization. 3. The method for identifying the moment of inertia of permanent magnet synchronous motor based on particle swarm as claimed in claim 1, characterized in that, by analyzing the information of the individuals in the group, the sharing of information is realized on this basis, and finally the entire In the process of group movement, the analysis and calculation of data can be realized, and finally the optimal solution can be obtained. The initial population of particle swarm optimization is a group of random solutions, the position of particle i in N-dimensional space is expressed as X _i =(x _i1 , _xi2 ,...,x _iN ), and the flight speed is expressed as V _i =(v _i1 ,v _i2 ,...,v _iN ). Each particle has an fitness value determined by the objective function. In the _iterative process, the particle can track two "extreme values" to realize its own update and optimization. The optimal value reached by itself in the process; the global extremum G _best is the optimal value reached by all particles in the entire particle swarm during the previous generation search process. Particles use the following formulas to update velocity information and position information. Among them, i=1,2,...,N, d=1,2,...,D, N and D respectively represent the size of the particle swarm and the dimension of the search space; Indicates the velocity of the i-th particle on the d-dimension; v _d,max is the maximum velocity of the particle in the range space; Indicates the position of the i-th particle in the d dimension; Indicates the historical best of the i-th particle; Indicates the optimal value of the t-th iteration group; c ₁ and c ₂ are called learning factors or acceleration coefficients; r ₁ and r ₂ are random numbers between [0,1] generated by random functions. Formula (3-1) mainly updates the velocity of particles through three parts: the first part It is an individual memory item, which is used to describe the influence of the size and direction of the last iteration speed, and has the function of balancing the global and partial search capabilities of the particle; the second part is a typical individual cognitive item, which is the best point from the current point to the particle itself. A vector of points, representing a vector, the direction is mainly the optimal position in the system, the action of the particle has been tested by itself; the third part is a group cognition item, which also represents a vector, and the direction is that the particle itself points to the global optimal position, which means the cooperation and information sharing among particles. Particles react to motion based on their own experience and the optimal experience of other particles. Introduce the inertia factor w to make its value positive. Update formula (3-1) to (3-4), Among them, the larger the w value is, the stronger the global search ability is, and the weaker the local search ability is; the smaller the w value is, the weaker the global search ability is, and the stronger the local search ability is. 4. The method for identifying the moment of inertia of permanent magnet synchronous motor based on particle swarm as claimed in claim 1, characterized in that, the selection weight decrement method is used, that is, as the number of iterations increases, the inertia weight is originally smaller. ω(t)＝ω _max -(ω _max -ω _min )/N _max (3-5) Where N _max is the maximum number of iterations. 5. A computer device, comprising a memory, a processor, and a computer program stored on the memory and operable on the processor, characterized in that, when the processor executes the program, any one of claims 1 to 4 is realized The steps of the method. 6. A computer-readable storage medium, on which a computer program is stored, characterized in that, when the program is executed by a processor, the steps of the method according to any one of claims 1 to 4 are realized. 7. A processor, wherein the processor is used to run a program, wherein the method according to any one of claims 1 to 4 is executed when the program runs.