A differential evolution calculation method and device for driving current of a cubic permanent magnet spherical motor

Abstract

The application discloses a differential evolution calculation method and device for driving current of a cubic permanent magnet spherical motor, and the method comprises the following steps: establishing an inverse torque model of the cubic permanent magnet spherical motor based on electromagnetic principles and a differential evolution algorithm; determining a specific implementation strategy of the differential evolution algorithm applied to driving current calculation of the spherical motor; obtaining a current base vector and one or more pairs of random current vectors for a target current vector by randomly sampling an initial population of current vectors, and obtaining a mutated current vector; realizing a cross operation between the mutated current vector and the target current vector in at least one dimension; limiting current values of coils corresponding to each latitude of the cross current vector according to a current output capability of a spherical motor driver; and obtaining a current vector population of the next generation through torque fitness function calculation and greedy selection; and setting an algorithm iteration termination condition. The application solves the problem of fast and stable calculation of driving current of the cubic permanent magnet spherical motor.

Description

Technical Field

[0001] This invention relates to the field of spherical motor control technology, specifically to a differential evolution calculation method and apparatus for the drive current of a cubic permanent magnet spherical motor. The method and apparatus can establish an inverse torque model of the cubic permanent magnet spherical motor through a differential evolution algorithm and quickly and stably calculate its drive current. Background Technology

[0002] Permanent magnet spherical motors (PMSMs) have broad potential applications in fields such as robot joints and satellite attitude control. Calculating their drive current is one of the key technical challenges in achieving closed-loop control of PMSMs. Over the past three decades, scholars both domestically and internationally have proposed a series of methods for calculating the drive current of PMSMs. These methods mainly include those using pseudo-inverse matrices, data-driven methods, intelligent optimization algorithms, and open-loop stepper control. Among these, the method using intelligent optimization algorithms is particularly convenient and reliable for calculating the drive current of non-circularly symmetric PMSMs, and has attracted widespread attention from scholars both at home and abroad.

[0003] The cubic permanent magnet spherical motor is a non-circularly symmetrical permanent magnet spherical motor. To achieve its closed-loop control, the differential evolution algorithm is used to calculate its drive current. Compared with intelligent optimization algorithms such as genetic algorithms, this method for calculating the drive current of spherical motors has advantages such as simple algorithm structure, faster convergence speed, and more stable operation. This invention solves the problem of fast and stable calculation of the drive current of cubic permanent magnet spherical motors. Summary of the Invention

[0004] This invention provides a method and apparatus for differential evolution calculation of the driving current of a cubic permanent magnet spherical motor, which solves the problem of fast and stable calculation of the driving current of a cubic permanent magnet spherical motor.

[0005] According to one aspect of this application, a differential evolution calculation method for the drive current of a cubic permanent magnet spherical motor is provided, comprising: creating an analytical model of the cubic permanent magnet spherical motor; generating a torque map of the spherical motor based on the analytical model; and further establishing an inverse torque model of the cubic permanent magnet spherical motor using a differential evolution algorithm; determining the specific implementation strategy, mutation factor, crossover probability, population size, maximum number of iterations, and algorithm termination condition of the differential evolution algorithm applied to the calculation of the drive current of the cubic permanent magnet spherical motor; performing initialization operations of the differential evolution algorithm; randomly sampling the initial population of the current vector of the drive current of the spherical motor; obtaining a current basis vector and one or more pairs of random current vectors for the target current vector; and generating a mutated current vector based on this. The algorithm employs random numbers and crossover probability comparison to perform crossover operations in at least one dimension between the mutated current vector and the target current vector, generating a new crossover current vector. The upper and lower limits of the coil current value corresponding to each dimension of the crossover current vector are limited according to the range of the driving current output capability of the cubic permanent magnet spherical motor driver. Fitness values ​​are calculated for all crossover current vectors based on the fitness function. Through greedy selection, crossover current vectors with fitness values ​​closer to 1 are allowed to enter the next generation of current vector population. A termination condition is set: when the fitness value of the optimal current vector reaches the specified fitness threshold range or the number of iterations of the differential evolution algorithm reaches its maximum value, the evolutionary algorithm stops searching; otherwise, the evolutionary algorithm repeats the mutation, crossover, and greedy selection operations of the target current vector.

[0006] Optionally, the rotor topology of the cubic permanent magnet spherical motor is a single-layer Halbach array composed of a certain number of cubic permanent magnets. The stator magnetic poles are arranged symmetrically in two layers along the equator. The analytical model is an electromagnetic torque analytical model of the cubic permanent magnet spherical motor based on electromagnetic theory. The torque map is a torque distribution map obtained by traversing the entire rotor air gap with a unit current-excited coil in n-degree increments along the azimuth and polar angle directions. Then, an inverse torque model of the cubic permanent magnet spherical motor using a differential evolution algorithm is established.

[0007] Optionally, the inverse torque model of the cubic permanent magnet spherical motor using the differential evolution algorithm is to determine the desired torque through the motor closed-loop control algorithm, and then use the differential evolution algorithm based on the superposition theorem to optimize the torque Map on the basis of the known desired torque, and inversely calculate the optimal drive current vector of all coils of the spherical motor.

[0008] Optionally, the specific implementation strategy of the differential evolution algorithm is to form a vector of all coil driving currents and initialize it as an initial population of current vectors, use the expected torque and the torque calculated based on the torque Map of the current vector to form the expected fitness function, perform the initialization operation of the differential evolution algorithm, and determine parameters such as mutation factor, crossover probability, and population size by adjusting parameters.

[0009] Optionally, the variant current vector is generated by multiplying the difference between one or more pairs of random current vectors by a variation factor, and then summing them with the current basis vector as a reference.

[0010] Optionally, the cross operation of at least one dimension refers to swapping the driving current value of at least one coil in the target current vector with the driving current value of the coil corresponding to the variable current vector in that dimension.

[0011] Optionally, the range of the drive current output capability refers to the absolute value of the coil current corresponding to each dimension of the current vector not exceeding the maximum current value that the current source circuit of the spherical motor driver can output, and the absolute value of the current value of each dimension of the cross current vector used to calculate the fitness value of the differential evolution algorithm not exceeding the maximum current value.

[0012] Optionally, the fitness value is calculated by combining the torque calculated based on the cross current vector after the limit with the desired torque to form a fitness function of type 1. The closer the fitness value is to 1, the more likely the current vector is to become the optimal value.

[0013] Optionally, the fitness threshold range refers to the range in which the calculated value of the Wang-1 type fitness function corresponding to the optimal cross current vector should be greater than a certain threshold and less than or equal to 1, and the number of iterations refers to the maximum number of iterations for the differential evolution algorithm to optimize the search for the drive current of the cubic permanent magnet spherical motor.

[0014] According to another aspect of this application, a cubic permanent magnet spherical motor drive current differential evolution calculation device is also provided, characterized in that it comprises:

[0015] The module includes a control module, a computing module, a storage module, and a ball motor driver module.

[0016] Furthermore, the control module is used to obtain the real-time desired torque required for the closed-loop control of the cubic permanent magnet spherical motor;

[0017] Furthermore, the calculation module is used to deploy a differential evolution algorithm model for calculating the drive current of the cubic permanent magnet spherical motor, and to optimize the calculation of the optimal current vector corresponding to the desired torque in real time.

[0018] Furthermore, the storage module is used to store algorithm variables such as the desired torque and the optimal current vector and to provide an interface for the cubic permanent magnet spherical motor drive controller to receive current vector commands.

[0019] Furthermore, the spherical motor driver module is used to receive the current vector command of the cubic permanent magnet spherical motor and output the drive current to control the spherical motor to move as desired.

[0020] The present invention has the following advantages:

[0021] This invention provides a differential evolution calculation method and apparatus for the drive current of a cubic permanent magnet spherical motor. This method can establish a torque map of the cubic permanent magnet spherical motor and obtain a real-time and stable inverse torque model. Further, a differential evolution algorithm is used to optimize the calculation of the desired torque, ultimately obtaining the current vector command to drive the cubic permanent magnet spherical motor to move as desired. Compared with existing technologies, the differential evolution algorithm used in this invention has higher stability, stronger search capability, and faster convergence speed. Therefore, this invention can effectively improve the calculation speed and stability of the drive current of a cubic permanent magnet spherical motor, supporting real-time closed-loop control of the cubic permanent magnet spherical motor. Attached Figure Description

[0022] Figure 1 A flowchart of a method for differential evolution calculation of drive current of a cubic permanent magnet spherical motor according to an embodiment of this application is shown;

[0023] Figure 2 An example diagram of a closed-loop control of a cubic permanent magnet spherical motor generating desired torque according to an embodiment of this application is shown;

[0024] Figure 3 A diagram of a cubic permanent magnet spherical motor drive current differential evolution calculation device according to an embodiment of this application is shown. Detailed Implementation

[0025] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0026] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present application.

[0027] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of this application described herein.

[0028] As mentioned in the background, existing real-time pseudo-inverse matrix calculation methods for the drive current of permanent magnet spherical motors cannot be used for calculating the drive current of non-circularly symmetric permanent magnet spherical motors. Cubic permanent magnet spherical motors are a type of non-circularly symmetric permanent magnet spherical motor. Calculating their drive current using a differential evolution algorithm has advantages over motor drive current calculation methods using intelligent optimization algorithms such as genetic algorithms, including simpler algorithm structure, faster convergence speed, and greater stability. This invention solves the problem of fast and stable calculation of the drive current of cubic permanent magnet spherical motors. In a typical embodiment of this application, a differential evolution calculation method and apparatus for the drive current of a cubic permanent magnet spherical motor are provided by employing a differential evolution algorithm.

[0029] This application provides a method for differential evolution calculation of the driving current of a cubic permanent magnet spherical motor. Figure 1 This is a flowchart of a method for differential evolution calculation of drive current of a cubic permanent magnet spherical motor according to an embodiment of this application, as shown below. Figure 1 As shown. The method includes the following steps:

[0030] Step S102: Create an analytical model of the cubic permanent magnet spherical motor, generate a torque map of the spherical motor based on the analytical model, and further establish an inverse torque model of the cubic permanent magnet spherical motor using the differential evolution algorithm.

[0031] Step S104: Determine the specific implementation strategy of the differential evolution algorithm applied to the calculation of the drive current of the cubic permanent magnet spherical motor, including the mutation factor, crossover probability, population size, maximum number of iterations and algorithm termination condition, and perform the initialization operation of the differential evolution algorithm;

[0032] Step S106: Randomly sample the initial population of the current vector of the spherical motor drive current, obtain the current basis vector and one or more pairs of random current vectors for the target current vector, and generate a mutated current vector based on this.

[0033] Step S108: Use random numbers and crossover probability comparison to perform crossover operation on at least one dimension between the mutated current vector and the target current vector to generate a new crossover current vector.

[0034] Step S110: Limit the upper and lower limits of the coil current value corresponding to each dimension of the cross current vector according to the range of the driving current output capability of the cubic permanent magnet spherical motor driver. Calculate the fitness value of all cross current vectors according to the fitness function. Greedily select the cross current vectors with fitness values ​​closer to 1 to enter the next generation of current vector population.

[0035] Step S112: Set the termination condition. When the fitness value of the optimal current vector reaches the specified fitness threshold range or the number of iterations of the differential evolution algorithm reaches the maximum value, the evolution algorithm stops searching. Otherwise, the evolution algorithm repeats the mutation, crossover, and greedy selection operations of the target current vector.

[0036] Through the above steps, based on the differential evolution algorithm, the present invention employs a differential evolution algorithm to calculate the drive current of the cubic permanent magnet spherical motor. Compared with intelligent optimization algorithms such as genetic algorithms, the algorithm structure is simpler, the convergence speed is faster, and the algorithm is more stable. Therefore, the present invention effectively solves the problem of fast and stable calculation of the drive current of the cubic permanent magnet spherical motor.

[0037] Example 1:

[0038] In this embodiment, the rotor topology of the cubic permanent magnet spherical motor is a single-layer Halbach array composed of a certain number of cubic permanent magnets. The stator poles are arranged symmetrically in two layers along the equator using multiple coils. The analytical model is an analytical model of the electromagnetic torque of the cubic permanent magnet spherical motor based on electromagnetic theory. For the cubic permanent magnet spherical motor, the electromagnetic torque analytical model can be established using the spherical harmonic function method or the equivalent current method. Assuming the rotor is stationary, the coils excited by a unit current traverse the entire rotor sphere at a certain step angle θ along the air gap azimuth and pole angle directions, and the torque at each step point is calculated and stored as T. x T y and T z Three torque maps are used, where x, y, and z represent the three degrees of freedom of the spherical motor. The inverse torque model of the cubic permanent magnet spherical motor is the desired torque T determined by the superposition theorem and the closed-loop control algorithm of the cubic permanent magnet spherical motor. d =[T dx ,T dy ,T dz ], where T dx T dy and T dz For the desired torque T d The components of the spherical motor in its three degrees of freedom. Using a differential evolution algorithm, the torque Map is optimized based on the known desired torque, and then the optimal drive current vector I of all coils of the spherical motor is calculated inversely.c In the differential evolution algorithm optimization calculation, a current vector I is known. k I can be calculated using two-dimensional interpolation methods such as bilinear interpolation. k The corresponding torque T k =[T kx ,T ky ,T kz ], where k represents the k-th target current vector, T kx T ky and T kz The actual torque T corresponding to the k-th target current vector k The components of the spherical motor in its three degrees of freedom. Let T... k and desired torque T d Substituting the values ​​into the type 1 fitness function, the optimal driving current vector I is finally obtained. c . Figure 2 This is an example diagram of a closed-loop control of a cubic permanent magnet spherical motor generating desired torque according to an embodiment of this application, as shown below. Figure 2 As shown, where x d x1 is the desired position, x1 is the actual rotor position, e1 is the deviation of the actual position from the desired position, and I is the actual rotor position. c This is the optimal driving current vector, which is also the command current vector. In this embodiment, the differential evolution algorithm is specifically implemented by constructing a vector from all coil driving currents and initializing it as the initial population of current vectors. The desired torque is used to construct the fitness function (I1). c ),

[0039]

[0040] Initialize the parameters of the differential evolution algorithm, create an initial current vector population for the differential evolution algorithm based on the current output capability range of the cubic permanent magnet spherical motor driver (assuming there are p initial current vectors), and calculate the initial fitness value of each individual. Adjust the parameters of the algorithm such as mutation factor, crossover probability, and population size by methods such as Taguchi method or full factorial experiment.

[0041] In this embodiment of the application, the variable current vector is denoted as I. m Where the subscript m represents the mutated current vector corresponding to the m-th target current vector (m = 1, 2, 3…p), u (u is an odd number) current vectors are randomly sampled from the current vector population. Taking u = 5 as an example, the sampled current vectors are denoted as I1…I5, with I1 as the current basis vector and the mutation factor denoted as F. Then the mutated current vector corresponding to the m-th target current vector is:

[0042] I m=I1+F(I2-I3)+F(I4-I5) In this embodiment of the application, for the mutated current vector and the target current vector in the current vector population, the crossover probability λ is compared with the crossover probability λ in turn according to the dimension. When the random number between 0 and 1 is less than the crossover probability λ, the coil current value corresponding to the mutated current vector in the current dimension is crossed with the coil current value corresponding to the target current vector. If no random number less than the crossover probability λ is generated in any dimension, the algorithm randomly generates a positive number w not greater than the dimension of the current vector, and then crosses the current value of the w-th dimension of the mutated current vector with the current value of the w-th dimension of the target current vector, ensuring that the crossover operation of at least one dimension of the current vector can be realized.

[0043] In this embodiment, the range of the drive current output capability refers to the fact that the absolute value of the coil current corresponding to each dimension of the current vector cannot exceed the maximum current value I that the spherical motor driver current source circuit can output. max For the j-th dimension of the m-th target current vector, when the corresponding cross current vector |I m (j)|>I max When the current exceeds the limit, a new current value is randomly generated for the j-th dimension current to replace the over-amplitude current, that is:

[0044] I m (j)=-I max +2I max ×rand()

[0045] Where m = 1, 2, 3…p, and rand() is a random number between 0 and 1.

[0046] In this embodiment, the fitness value is the calculated value of the fitness function of type 1, which is composed of the torque calculated based on the cross-current vector after the limit and the desired torque. c It is still defined as: Or other equivalent functional forms, the closer the calculated fitness value of the current vector is to 1, the more likely it is to become the optimal current vector.

[0047] In this embodiment, the fitness threshold range refers to the range where the calculated value of the Wang-1 type fitness function corresponding to the optimal cross-current vector should be greater than a certain fitness threshold δ and less than or equal to 1. That is, the fitness threshold range is (δ, 1]. For example, in this embodiment, δ = 0.99 can be defined. The number of iterations refers to the maximum number of iterations for the differential evolution algorithm to optimize the search for the cubic permanent magnet spherical motor drive current calculation. It can generally be defined as maxIteration = 200.

[0048] Example 2:

[0049] In this embodiment of the application, the cubic permanent magnet spherical motor drive current differential evolution calculation device includes: a control module, a calculation module, a storage module, and a spherical motor driver module.

[0050] In this embodiment of the application, the control module is used to obtain the real-time expected torque required for the closed-loop control of the cubic permanent magnet spherical motor;

[0051] In this embodiment of the application, the calculation module is used to deploy the differential evolution algorithm model for calculating the drive current of the cubic permanent magnet spherical motor, and to optimize the calculation of the optimal current vector corresponding to the desired torque in real time.

[0052] In this embodiment of the application, the storage module is used to store algorithm variables such as desired torque and optimal current vector and to provide an interface for the spherical motor driver to receive current vector commands;

[0053] In this embodiment of the application, the spherical motor driver module is used to receive the current vector command of the cubic permanent magnet spherical motor and output the drive current to control the spherical motor to move as desired.

[0054] Figure 3 This is a diagram of the cubic permanent magnet spherical motor drive current differential evolution calculation device according to an embodiment of the present invention, as shown below. Figure 3 As shown.

[0055] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for driving current of a spherical motor of a cubic permanent magnet, characterized by, The aforementioned method for differential evolution calculation of the driving current of a cubic permanent magnet spherical motor includes the following steps: Step S1: Create an analytical model of the cubic permanent magnet spherical motor, generate a torque map of the spherical motor based on the analytical model, and further establish an inverse torque model of the cubic permanent magnet spherical motor using the differential evolution algorithm. Step S2: Determine the specific implementation strategy of the differential evolution algorithm applied to the calculation of the drive current of the cubic permanent magnet spherical motor, including the mutation factor, crossover probability, population size, maximum number of iterations and algorithm termination condition, and perform the initialization operation of the differential evolution algorithm; Step S3: Randomly sample the initial population of the current vector of the spherical motor drive current, obtain the current basis vector and one or more pairs of random current vectors for the target current vector, and generate the mutated current vector based on this. Step S4: Use random numbers and crossover probability comparison to perform crossover operation on at least one dimension between the mutated current vector and the target current vector to generate a new crossover current vector; Step S5: Limit the upper and lower limits of the coil current value corresponding to each dimension of the cross current vector according to the range of the driving current output capability of the cubic permanent magnet spherical motor driver. Calculate the fitness value of all cross current vectors according to the fitness function. Greedily select the cross current vectors with fitness values ​​closer to 1 to enter the next generation of current vector population. Step S6: Set the termination condition. When the fitness value of the optimal current vector reaches the specified fitness threshold range or the number of iterations of the differential evolution algorithm reaches the maximum value, the evolution algorithm stops searching. Otherwise, the evolution algorithm repeats the mutation, crossover, and greedy selection operations of the target current vector. In step S2, the specific implementation strategy of the differential evolution algorithm is to form a vector of all coil driving currents and initialize it as an initial population of current vectors. The expected torque and the torque calculated based on the torque Map of the current vector are used to form a type 1 fitness function. The initialization operation of the differential evolution algorithm is executed, and the mutation factor, crossover probability, and population size parameters are determined by parameter tuning.

2. A differential evolution method for driving current of a spherical motor with cubic permanent magnet according to claim 1, wherein, In step S1, the rotor topology of the cubic permanent magnet spherical motor is a single-layer Halbach array composed of a certain number of cubic permanent magnets. The stator magnetic poles are arranged in a double-layer symmetrical arrangement along the equator using multiple coils. The analytical model is an electromagnetic torque analytical model of the cubic permanent magnet spherical motor based on electromagnetic theory. The torque map is a torque distribution map obtained by traversing the entire rotor air gap with a unit current-excited coil in n-degree increments along the azimuth and polar angle directions. Then, an inverse torque model of the cubic permanent magnet spherical motor using the differential evolution algorithm is established.

3. A differential evolution method for driving current of a spherical motor with cubic permanent magnet according to claim 2, wherein, The inverse torque model of the cubic permanent magnet spherical motor using the differential evolution algorithm is to determine the desired torque through the motor closed-loop control algorithm, and then use the differential evolution algorithm to optimize the torque Map based on the known desired torque according to the superposition theorem, thereby inversely calculating the optimal drive current vector of all coils of the spherical motor.

4. The method for differential evolution calculation of drive current of a cubic permanent magnet spherical motor according to claim 1, characterized in that, In step S3, the variant current vector multiplies the difference between one or more pairs of random current vectors by a variation factor, and then sums them based on the current basis vector to generate the variant current vector corresponding to the target current vector.

5. The method for differential evolution calculation of drive current of a cubic permanent magnet spherical motor according to claim 1, characterized in that, In step S4, the cross operation of at least one dimension refers to swapping the driving current value of at least one coil in the target current vector with the driving current value of the coil corresponding to the variable current vector in that dimension.

6. The method for differential evolution calculation of drive current of a cubic permanent magnet spherical motor according to claim 1, characterized in that, In step S5, the range of the drive current output capability refers to the absolute value of the coil current corresponding to each dimension of the current vector not exceeding the maximum current value that the spherical motor driver current source circuit can output, and the absolute value of the current value of each dimension of the cross current vector used to calculate the fitness value of the differential evolution algorithm not exceeding the maximum current value.

7. The method for differential evolution calculation of drive current of a cubic permanent magnet spherical motor according to claim 6, characterized in that, The fitness value is calculated by combining the torque calculated from the cross current vector after the limit with the desired torque as the fitness function of type 1. The closer the fitness value is to 1, the more likely the current vector is to become the optimal value.

8. The method for differential evolution calculation of drive current of a cubic permanent magnet spherical motor according to claim 1, characterized in that, In step S6, the fitness threshold range refers to the range in which the calculated value of the Wang-1 type fitness function corresponding to the optimal cross current vector should be greater than a certain threshold and less than or equal to 1. The number of iterations refers to the maximum number of iterations for the differential evolution algorithm to optimize the search for the drive current of the cubic permanent magnet spherical motor.

9. A differential evolution calculation device for a cubic permanent magnet spherical motor drive current, characterized in that, include: A control module, a computing module, a storage module, and a spherical motor driver module are used to implement the method and steps of any one of claims 1 to 8; The control module is used to acquire the real-time desired torque required for the closed-loop control of the cubic permanent magnet spherical motor; the calculation module is used to deploy a differential evolution algorithm model for calculating the drive current of the cubic permanent magnet spherical motor, and to optimize the current vector corresponding to the desired torque in real time; the storage module is used to store algorithm variables such as the desired torque and the optimal current vector and to provide an interface for the spherical motor driver to receive current vector commands; the spherical motor driver module is used to receive the current vector commands of the cubic permanent magnet spherical motor and output the drive current to control the spherical motor to move as desired.

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