Reluctance type spherical motor rotor position estimation method based on improved segmentation thought

Abstract

The invention discloses a reluctance type spherical motor rotor position estimation method based on an improved segmentation thought, which belongs to the technical field of reluctance type spherical motor intelligent control, and comprises the following steps: obtaining reluctance, inductance and flux linkage characteristic data of a reluctance type spherical motor by using finite elements; flux linkage characteristic data is determined to serve as an analysis and calculation tool through comparative analysis; preliminarily dividing the curve family into three sections according to the variation trend of the flux linkage curve family, and proposing a proper analytical expression for the characteristics of each section of curve; based on the principle of minimum error, an optimal segmentation point and an optimal calculation point are obtained by adopting an optimization algorithm, and the coefficient of the analytical expression is obtained by the measured flux linkage data. And substituting the flux linkage and the current which are measured in real time into a corresponding analytical expression to obtain the spin motion rotor position of the reluctance type spherical motor. The reluctance type spherical motor rotor position estimation method provided by the invention has the characteristics of simple algorithm, high precision and the like.

Description

Technical Field

[0001] The present invention relates to a method for estimating the rotor position of a reluctance spherical motor based on an improved segmentation idea, and belongs to the field of control of reluctance spherical motors. Background Art

[0002] A reluctance spherical motor is a rotary motor capable of achieving multi-degree-of-freedom motion, and can replace a motion system composed of multiple single-degree-of-freedom motors. The reluctance spherical motor has the characteristics of simple structure, light weight, small volume, fast response speed, etc., and has broad application potential in the fields of robot end, medical devices, aerospace, intelligent tracking, etc. In the motion control of the reluctance spherical motor, the rotor position needs to be obtained in real time. At present, there are various rotor position estimation methods, including the look-up table method, the intelligent method, and the analytical method. The look-up table method can be used to describe the relationship between magnetic flux linkage, current, and rotor position, but this method requires a large amount of sample data; although the intelligent method has strong robustness and self-adaptability, its training process is long and difficult to implement; the analytical method segments the magnetic flux linkage data according to the structural properties of the motor, and uses an analytical expression of an appropriate form to represent the relationship curve of the magnetic flux linkage with respect to the phase current and the rotor position, considering the non-linear characteristics of the magnetic flux linkage data, having high calculation accuracy and high efficiency. However, at present, when using the segmentation idea to perform rotor position analytical estimation on a reluctance motor, the magnetic flux curve is usually simply segmented based on the structural characteristics of the motor stator and rotor. Although the calculation process of the segmentation point is simple, the estimation accuracy is still lacking. Therefore, it is of great significance to study a rotor position analytical estimation method based on an improved segmentation idea with higher accuracy. Summary of the Invention

[0003] Object of the Invention: Aiming at the problems in the background art, the present invention provides a method for estimating the rotor position of a reluctance spherical motor based on an improved segmentation idea, which can simply and accurately estimate the rotor position.

[0004] Technical Solution: The present invention discloses a method for estimating the rotor position of a reluctance spherical motor based on an improved segmentation idea, including the following steps:

[0005] Step 1: Use finite element software to establish a simulation model of the reluctance spherical motor, and obtain complete magnetic flux linkage, reluctance, and inductance characteristic data of the reluctance spherical motor within half an electrical cycle;

[0006] Step 2: Analyze the change characteristics of the magnetic flux linkage, reluctance, and inductance characteristic curve families, and select the magnetic flux linkage characteristic curve as the analysis and calculation tool according to the principle that the low coincidence degree of the curve families is easy to distinguish;

[0007] Step 3: According to the change trend of the magnetic flux linkage curve family, initially divide the magnetic flux linkage curve into three segments, and design an analytical expression for each segment curve characteristic;

[0008] Step 4: Based on the principle of minimizing the error between the calculated flux linkage and the simulated flux linkage, an optimization algorithm is used to obtain the optimal segmentation points and calculation points;

[0009] Step 5: Measure the flux linkage data of the corresponding points by the clamping method, and the coefficients of the analytical expression are obtained by operating on the measured flux linkage data, so as to obtain a complete analytical model for rotor position estimation;

[0010] Step 6: During the motor movement, substitute the calculated flux linkage and excitation current measured in real time into the corresponding analytical expression, and the rotor position of the reluctance spherical motor's spin motion can be obtained.

[0011] Further, in the said Step 3, the flux linkage curve is initially divided into three segments, with a total of 5 position points, arranged in ascending order as β u , β 1 , β m , β 2 , β a , where β u represents the non-aligned position, that is, the position where the center line of the stator pole is aligned with the center line between the rotor poles, and β a represents the aligned position, that is, the position where the center line of the stator pole completely coincides with the center line of the rotor pole; β 1 and β 2 are two segmentation points. The first segment is concave, with a range of β u ~β 1 ; the second segment is convex, with a range of β 1 ~β 2 ; the third segment is linear, with a range of β 2 ~β a ; appropriate analytical expressions are designed according to the characteristics of each curve segment as follows:

[0012]

[0013] In the formula, ψ(β, i) represents the flux linkage value at the excitation current i and the rotor angle β; a(i)~g(i) respectively represent the coefficients of the analytical expression related to the excitation current i.

[0014] Further, based on the principle of minimizing the error between the calculated flux linkage and the simulated flux linkage, the genetic algorithm is used to obtain the optimal segmentation points β 1 , β 2 and the calculation point β m , specifically as follows:

[0015] Step 4.1: Population initialization;

[0016] The individual coding method is real number coding, and each individual is a real number string, which consists of 4 parts: the connection weight between the input layer and the hidden layer, the hidden layer threshold, the connection weight between the hidden layer and the output layer, and the output layer threshold;

[0017] Step 4.2: Fitness function. According to the individual, obtain the initial β of the analytical expression 1 , β 2 and β m , calculate the absolute value of the error between the magnetic flux linkage and the simulated magnetic flux linkage as the individual fitness value F. The calculation formula is

[0018]

[0019] In the formula, n is the number of magnetic flux linkage values; o i is the i-th calculated value of the magnetic flux linkage; y i is the i-th simulated value of the magnetic flux linkage; k is a coefficient;

[0020] Step 4.3: Operation selection. Select the roulette wheel method, that is, the selection strategy based on fitness proportion. The selection probability p of each individual i i is:

[0021] f i = k / F i (3)

[0022]

[0023] In the formula, F i is the fitness value of individual i. The smaller the fitness value, the better. Therefore, take the reciprocal of the fitness value before individual selection; k is a coefficient; N is the number of population individuals;

[0024] Step 4.4: Crossover operation. Since the individuals use real number coding, the real number crossover method is used for the crossover operation. The crossover operation of the k-th chromosome a k and the l-th chromosome a l at the j-th position is as follows:

[0025]

[0026] In the formula, b is a random number between [0, 1];

[0027] Step 4.5: Mutation operation. Select the j-th gene a of the i-th individual ij for mutation. The mutation operation method is as follows:

[0028]

[0029] In the formula, a max represents the upper bound of gene a ij ; a min represents the lower bound of gene a ij ; f(g) = r 2 (1 - g / G max ) 2 ; r2 is a random number; g is the current iteration number; G max is the maximum number of evolutions; r is a random number between [0, 1];

[0030] Step 4.6: Finally, obtain the optimal segmentation point β 1 , β 2 and the calculation point β m .

[0031] Furthermore, in step 5, the flux linkage data of the corresponding points at different excitation currents are obtained by the clamping method, and the coefficients of the analytical expression are calculated from the measured flux linkage data according to the following formula:

[0032]

[0033] In the formula, ψ u (i), ψ 1 (i), ψ m (i), ψ 2 (i) and ψ a (i) respectively represent the flux linkage values with respect to the excitation current i at the positions of β u , β 1 , β m , β 2 , β a position.

[0034] Furthermore, the rotor position of the spin motion of the reluctance spherical motor in step 6 is specifically as follows:

[0035]

[0036] Beneficial effects:

[0037] The present invention is applicable to the spin motion of the reluctance spherical motor and is also applicable to the rotary motion of the switched reluctance motor. By using finite element software to obtain the flux linkage, reluctance, and inductance characteristic data of the reluctance spherical motor, and taking the principle that the characteristic data curves corresponding to different excitation currents are easy to distinguish, the flux linkage characteristic data is determined as the analysis and calculation tool. According to the change trend of the flux linkage curve, the curve is initially divided into three segments, and appropriate analytical expressions are designed according to the characteristics of each segment curve. Based on the principle of minimizing the calculation error, an optimization algorithm is used to obtain the optimal segmentation point and the calculation point, and the coefficients of the analytical expression are obtained by operating on the measured flux linkage data. Substituting the measured and calculated flux linkage and excitation current into the corresponding analytical expression, the rotor position of the spin motion of the reluctance spherical motor can be obtained, achieving the purpose of the present invention. Compared with the traditional method, this method for estimating the rotor position of the spin motion of the reluctance spherical motor has the advantages of simple design, fast operation, high estimation accuracy, etc., and has good engineering application value. Description of the Drawings

[0038] Figure 1 is the flowchart of rotor position estimation;

[0039] Figure 2 is the characteristic curve diagram of magnetic flux linkage, reluctance, and inductance during the spin motion of a reluctance spherical motor;

[0040] Figure 3 is the segmented diagram of the magnetic flux linkage characteristic curve;

[0041] Figure 4 is the comparison diagram of the estimated angle and the measured angle of the traditional method segmented according to the motor structure;

[0042] Figure 5 is the comparison diagram of the estimated angle and the measured angle of the improved segmentation method proposed by the present invention. Detailed implementation manners

[0043] The present invention will be further specifically described below in conjunction with the accompanying drawings and examples.

[0044] The present invention discloses a rotor position estimation method based on the improved segmentation idea. Taking the spin motion of a reluctance spherical motor as an example, it includes the following steps:

[0045] Step 1: Use finite element software to establish an electromagnetic simulation model of the reluctance spherical motor, and obtain the magnetic flux linkage, reluctance, and inductance characteristic data of a single set of coils of the reluctance spherical motor within the range of excitation current I from [0:0.1:3 A] and rotor spin motion angle β from [0:1:30°].

[0046] Step 2: Analyze the change characteristics of the magnetic flux linkage, reluctance, and inductance characteristic curve families, and select the magnetic flux linkage characteristic curve as the analysis and calculation tool according to the principle that the low coincidence degree of the curve families is easy to distinguish. As Figure 2 shown, there are different degrees of overlap in the reluctance and inductance characteristic curves, which affect the estimation accuracy of the rotor position. Select the magnetic flux linkage characteristic curve as the analysis and calculation tool according to the principle that the curves are easy to distinguish.

[0047] Step 3: According to the change trend of the magnetic flux linkage curve family, preliminarily divide the magnetic flux linkage curve into three segments, and design an analytical expression for each segment curve characteristic.

[0048] As Figure 3 shown, according to the change trend of the magnetic flux linkage curve, the magnetic flux linkage curve is preliminarily divided into three segments, with a total of 5 position points, arranged from small to large as β u 、β 1 、β m 、β 2 、β a , where β u = 0°, β a = 30°. The first segment is concave, and the range is β u ~β1 ; The second segment is convex, with a range of β 1 ~β 2 ; The third segment is linear, with a range of β 2 ~β a . According to the characteristics of each curve segment, the following appropriate analytical expressions are designed

[0049]

[0050] In the formula, ψ(β, i) represents the magnetic flux value at the excitation current i and the rotor angle β; a(i) to g(i) respectively represent the coefficients of the analytical expression related to i.

[0051] Step 4: Based on the principle of minimizing the error between the calculated magnetic flux and the simulated magnetic flux, an optimization algorithm is used to obtain the optimal segmentation points and calculation points.

[0052] In this embodiment, the genetic algorithm is used to obtain the optimal segmentation points β 1 、β 2 and the calculation point β m , specifically as follows:

[0053] Step 4.1: Population initialization;

[0054] The individual coding method is real number coding. Each individual is a real number string, which consists of 4 parts: the connection weights between the input layer and the hidden layer, the hidden layer threshold, the connection weights between the hidden layer and the output layer, and the output layer threshold.

[0055] Step 4.2: Fitness function. According to the individual, the initial β 1 、β 2 and β m of the analytical expression are obtained, and the absolute value of the error between the calculated magnetic flux and the simulated magnetic flux is calculated as the individual fitness value F. The calculation formula is:

[0056]

[0057] In the formula, n is the number of magnetic flux values; o i is the i-th magnetic flux calculation value; y i is the i-th magnetic flux simulation value; k is a coefficient.

[0058] Step 4.3: Operation selection. The roulette wheel method is selected, that is, the selection strategy based on fitness proportion. The selection probability p i of each individual i is:

[0059] f i =k / F i (3)

[0060]

[0061] Where F i is the fitness value of individual i. The smaller the fitness value, the better. Therefore, the reciprocal of the fitness value is taken before individual selection; k is a coefficient; N is the number of individuals in the population.

[0062] Step 4.4: Crossover operation. Since the individuals use real number coding, the real number crossover method is adopted for the crossover operation. The crossover operation of the k-th chromosome a k and the l-th chromosome a l at the j-th position is as follows:

[0063]

[0064] Where b is a random number between [0, 1].

[0065] Step 4.5: Mutation operation. Select the j-th gene a ij of the i-th individual for mutation. The mutation operation method is as follows:

[0066]

[0067] Where a max represents the upper bound of gene a ij ; a min represents the lower bound of gene a ij ; f(g) = r 2 (1 - g / G max ) 2 ; r 2 is a random number; g is the current iteration number; G max is the maximum number of evolutions; r is a random number between [0, 1].

[0068] Step 4.6: Finally, obtain the optimal segmentation points β 1 and β 2 and the calculation point β m . The finally optimized optimal segmentation points and calculation points are: β 1 = 8°, β m = 17°, β 2 = 27°.

[0069] Step 5: Measure the flux linkage data of the corresponding positions by the clamping method. The coefficients of the analytical expression are obtained by operating on the measured flux linkage data, and then a complete rotor position estimation analytical model is obtained. The flux linkage data at five positions of β u , β 1 , β m , β 2 , β a under different excitation currents are measured by the clamping method. The coefficients of the analytical expression are obtained by operating on the measured flux linkage data according to formula (7).

[0070]

[0071] In the formula, ψ u (i), ψ 1 (i), ψ m (i), ψ 2 (i) and ψ a (i) respectively represent the flux linkage values with respect to the exciting current i at the positions of β u , β 1 , β m , β 2 , β a .

[0072] Step 6: During the operation of the motor, substitute the flux linkage and exciting current obtained by real-time measurement and calculation into the corresponding analytical expression, and the rotor position of the reluctance spherical motor during the spin motion can be obtained.

[0073]

[0074] To accurately obtain the rotor position, it is first necessary to ensure the accuracy of the exciting current and the flux linkage. To avoid cumulative errors during the calculation process, when the winding current returns to 0 each time, the initial flux linkage ψ(0) = 0, and the calculation formula of the flux linkage is as follows

[0075]

[0076] In the formula, ψ(k) represents the calculated flux linkage at the kth sampling point; u(k) represents the measured voltage at the kth sampling point; i(k) represents the measured current at the kth sampling point; r is the winding resistance; T is the sampling interval.

[0077] Figure 4 and Figure 5 represent the rotor position estimation error diagrams when the exciting current of a single group of coils is 1.5 A and 2 A, and it can be seen that Figure 5 the error shown Figure 4 is overall smaller than the error shown Figure 5 In addition, the maximum estimation error is about 2°, Figure 4 the maximum estimation error is close to 3°, indicating that the method proposed by the present invention has high accuracy.

[0078] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention without departing from the principle and spirit of the present invention.

Claims

1. A method for estimating the rotor position of a reluctance spherical motor based on an improved segmentation concept, characterized in that: The following steps are involved: Step 1: Use finite element software to establish a simulation model of a reluctance spherical motor and obtain complete magnetic flux, magnetic resistance and inductance characteristic data of the reluctance spherical motor within half an electrical cycle; Step 2: Analyze the changing characteristics of the flux linkage, magnetic resistance and inductance characteristic curve family, and select the flux linkage characteristic curve as the analysis and calculation tool based on the principle that the curve family has low overlap and is easy to distinguish; Step 3: According to the changing trend of the magnetic flux curve family, the magnetic flux curve is initially divided into three sections, and an analytical expression is designed for the characteristics of each section of the curve; Step 4: Based on the principle of minimizing the error between the calculated flux and the simulated flux, an optimization algorithm is used to obtain the best segmentation points and calculation points; Step 5: Measure the flux data of the corresponding points by the clamping method. The coefficients of the analytical expression are obtained by calculating the measured flux data, and then a complete analytical model for rotor position estimation is obtained. Step 6: During the motor movement, the magnetic flux and excitation current calculated by real-time measurement are substituted into the corresponding analytical expressions to obtain the rotor position of the reluctance spherical motor's spinning motion.

2. The method for estimating the rotor position of a reluctance spherical motor based on the improved segmentation concept according to claim 1 is characterized in that: In step 3, the flux curve is initially divided into three segments, with a total of 5 position points, which are arranged from small to large as β u , β1, β m , β2, β a , where β u represents the non-aligned position, that is, the position where the stator pole centerline is aligned with the rotor inter-pole centerline, β a Indicates the alignment position, that is, the position where the stator pole centerline and the rotor pole centerline completely overlap; β1 and β2 are two segmentation points, the first segment is concave, and the range is β u ~β1; the second section is convex, ranging from β1 to β2; the third section is linear, ranging from β2 to β a ; According to the characteristics of each curve segment, the appropriate analytical expression is designed as follows: Where ψ(β,i) represents the flux value at the excitation current i and the rotor angle β; a(i)~g(i) represent the coefficients of the analytical expression related to the excitation current i.

3. The method for estimating the rotor position of a reluctance spherical motor based on the improved segmentation concept according to claim 2 is characterized in that: Based on the principle of minimizing the error between the calculated flux and the simulated flux, a genetic algorithm is used to obtain the optimal segmentation points β1, β2 and the calculated point β m , as follows: Step 4.1: Population initialization; The individual coding method is real number coding. Each individual is a real number string, which consists of four parts: the connection weight between the input layer and the hidden layer, the hidden layer threshold, the connection weight between the hidden layer and the output layer, and the output layer threshold. Step 4.2: Fitness function, get the initial β1, β2 and β of analytical expression according to the individual m , calculate the absolute value of the error between the magnetic flux and the simulated magnetic flux as the individual fitness value F, and the calculation formula is Where n is the number of flux linkage values; i is the calculated value of the i-th magnetic flux; y i is the ith flux simulation value; k is the coefficient; Step 4.3: Operation selection, select the roulette method, that is, the selection strategy based on fitness ratio, and the selection probability p of each individual i i for: f i =k / F i (3) In the formula, F i is the fitness value of individual i. The smaller the fitness value, the better. Therefore, the inverse of the fitness value is calculated before individual selection. k is the coefficient. N is the number of individuals in the population. Step 4.4: Crossover operation. Since individuals are coded with real numbers, the crossover operation uses the real number crossover method. The kth chromosome a k and chromosome l l The crossover operation at position j is as follows: Where b is a random number between [0,1]; Step 4.5: Mutation operation, select the jth gene a of the i-th individual ij To mutate, the mutation operation method is as follows: In the formula, a max Indicates gene a ij The upper bound of min Indicates gene a ij The lower bound of f(g) = r2(1-g / G max ) 2 ; r2 is a random number; g is the current iteration number; G max is the maximum number of evolutions; r is a random number between [0,1]; Step 4.6: Finally, the best segmentation points β1, β2 and calculation point β are obtained. m .

4. The method for estimating the rotor position of a reluctance spherical motor based on the improved segmentation concept according to claim 1, characterized in that: In step 5, the flux data of the corresponding point under different excitation currents are measured by the clamping method, and the coefficients of the analytical expression are calculated from the measured flux data according to the following formula: In the formula, ψ u (i), ψ1(i), ψ m (i), ψ2(i) and ψ a (i) represents β u , β1, β m , β2, β a The flux linkage value at the position related to the excitation current i.

5. The method for estimating the rotor position of a reluctance spherical motor based on the improved segmentation concept according to claim 4 is characterized in that: The rotor position of the reluctance spherical motor spinning motion in step 6 is specifically as follows:

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