Switched reluctance motor sensorless control method based on flux linkage nonlinear modeling

Abstract

The invention discloses a flux linkage nonlinear modeling-based sensorless control method for a switched reluctance motor, and belongs to the technical field of motor control, and the method comprises the following steps: applying an ICOA to nonlinear sensorless modeling, i.e., combining a radial basis function neural network RBFNN with an improved subwolf optimization algorithm ICOA, so as to obtain a simple and compact RBFNN model. The ICOA is applied to non-linear sensorless modeling to obtain a simple and compact RBFNN model, the relationship among magnetic flux, current and rotor position is more accurate through online training, accurate commutation is realized by adopting a rotor position estimation strategy, and no matter which control mode is in, the control mode is more accurate. The current speed waveform obtained by the ICOA-RBFNN is not greatly different from the waveform obtained by the traditional FEA, the sensorless control using the ICOA-RBFNN is suitable for accurately estimating the rotating speed and the rotor position under various working conditions, the tracking error meets the requirement within a certain range, the adaptability is good, and the dynamic response capability is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of motor control, and in particular relates to a sensorless control method for a switched reluctance motor based on nonlinear modeling of flux linkage. Background Art

[0002] The increasing popularity of new energy vehicles has increased the demand for high-efficiency motor technology. In recent years, switched reluctance motors have been widely used due to their basic structure, large starting torque, flexible control and good fault tolerance. Although permanent magnet synchronous motors (PMSM) currently dominate the market with excellent performance characteristics, they face major challenges, including rising material costs and the risk of high-temperature demagnetization associated with permanent magnet materials. In contrast, SRM can achieve a wide range of speed regulation and maintain high torque output at low speeds, which makes it have great application value in electric vehicles, aerospace, industrial drives and other fields.

[0003] Finite element analysis (FEA) is often used for nonlinear modeling of switched reluctance motors. The flux linkage established by FEA can ensure high-precision phase current and rotor position, but its large amount of calculation and long simulation time cannot meet the needs of real-time control.

[0004] Similarly, analytical modeling methods are widely used. They have fast calculation speed and are suitable for embedding control algorithms. The flux data of five special positions are obtained by the torque balance method, and the fourth-order Fourier polynomials and Kriging models are used for fitting to establish more accurate flux and torque models, realizing model predictive torque control. A magnetic equivalent circuit model, which serves as a method framework, simplifies the calculation of flux and electromagnetic torque in the studied system. A method based on magnetic resistance grid is used instead of finite element method. In order to solve the problem of low accuracy of magnetic equivalent circuit modeling, coupled hybrid modeling is used to evaluate the electromagnetic analysis of SRM. The initial position of the rotor is determined by numerical analysis. In order to reduce the influence of numerical residuals and current sampling noise on self-sensing estimation, a third-order phase-locked loop PLL combined with acceleration dynamics is developed. However, the analytical method is not accurate enough.

[0005] Support vector machine (SVM) trains part of the sample data to obtain the entire nonlinear data, but the calculation takes a long time. In order to ensure the precise control of the planar SRM, sparse least squares support vector machine (LSSVM) is applied. In addition, in order to improve the regression accuracy, the hyperparameters of LSSVM can be optimized. In order to solve the problems of noisy data and outliers, a least squares support vector regression machine (MCC-LSSVR) based on the maximum entropy criterion is proposed to obtain a robust estimate of the data in the presence of outliers. Piecewise functions are used for magnetic flux fitting, which reduces the complexity. However, this method limits its applicability in scenarios requiring high accuracy.

[0006] In addition, neural networks are also used for SRM nonlinear modeling. In order to solve the nonlinear fitting challenges associated with three-dimensional data, an improved multidimensional Taylor network architecture is proposed. This architecture is combined with the error back propagation algorithm. The Levenberg-Marquardt-based back propagation algorithm is used to train the magnetic flux data. The network model is improved according to the number of inner-layer neurons, and a pre-processing enhanced back propagation neural network BPNN is introduced to construct a comprehensive three-dimensional mapping of the rotor position, thereby achieving effective sensorless control.

[0007] Traditional SRM systems usually use mechanical position sensors to obtain rotor position signals, which are then processed through mathematical transformations and control algorithms to achieve accurate position estimation. However, this sensor-based approach not only increases the complexity of the structure, but also damages the reliability and environmental robustness of the system. Therefore, sensorless control technology has attracted widespread research attention. At present, the position sensorless control of switched reluctance motors mainly includes two categories. The low-speed sensorless methods mainly include pulse injection method and inductance method, and the high-speed methods are mainly divided into flux method and observer method.

[0008] In order to estimate the rotor position information and effectively suppress noise, a regional phase-locked loop is designed, and a no-load inductance model with a wide speed range is proposed to ensure the effectiveness of rotor position estimation under heavy load conditions. The speed threshold and switching function are designed to reduce the energy loss during speed switching. In order to reduce the influence of flux error, a nonlinear state observer is designed to ensure the estimation accuracy of the position signal. The model predictive control is combined with sensorless control, and the computational burden is reduced by improving sector division. The rotor position estimation is obtained by the flux comparison method and applied to light electric vehicles. A speed adaptive bandpass observer based on orthogonal flux estimation is proposed to reduce nonlinearity, and the rotor position is estimated by a three-term PLL. The sliding mode observer SMO is used to estimate the rotor speed and position, and robust performance is demonstrated in the presence of system uncertainties. The SMO is integrated with the inductance function and successfully applied to the drive control in submersible pump applications. In order to ensure the speed control of SRM with uncertain loads, the high-order sliding mode observer HOSMO is combined with the reference model to obtain the rotor position, thereby compensating for interference and improving system response.

[0009] Traditional finite element analysis methods are computationally intensive and time-consuming, and traditional COA is prone to local optimization problems.

[0010] Based on this, the present invention designs a sensorless control method for a switched reluctance motor based on nonlinear modeling of flux linkage to solve the above problems. Summary of the Invention

[0011] The purpose of the present invention is to propose a sensorless control method for a switched reluctance motor based on nonlinear modeling of flux linkage in order to solve the problems that the traditional finite element analysis method has large computational complexity and long time consumption, and the traditional COA is prone to local optimization problems.

[0012] In order to achieve the above object, the present invention adopts the following technical solutions:

[0013] A sensorless control method for a switched reluctance motor based on nonlinear modeling of flux linkage includes the following contents:

[0014] ICOA is applied to nonlinear sensorless modeling, that is, the radial basis function neural network (RBFNN) is combined with the improved coyote optimization algorithm (ICOA) to obtain a simple and compact RBFNN model.

[0015] RBFNN has a fast convergence speed and strong approximation ability. ICOA can dynamically adjust the parameters and structure of RBFNN, reduce modeling errors by adaptively adjusting the number of hidden layer nodes, complete online training, and make the relationship between magnetic flux, current, and rotor position more accurate;

[0016] The rotor position estimation strategy is used to achieve precise commutation to ensure the stable operation of the entire closed-loop system.

[0017] As a further description of the above technical solution:

[0018] The sensorless control based on the RBFNN includes a radial basis function neural network RBFNN and RBFNN model accuracy evaluation, with MSE and R as the basis for RBFNN modeling and training, and Emax as a standard for testing model accuracy.

[0019] As a further description of the above technical solution:

[0020] The radial basis function neural network (RBFNN) architecture consists of three main components: input layer, hidden layer, and output layer. Magnetic flux and current values ​​are used as input variables, while rotor position is used as the target output for training purposes. Each processing unit in the network is represented as a node with the following connection properties:

[0021] Nodes within the same layer remain unconnected, while inter-layer connections between adjacent layers are established through weighted links. Therefore, RBFNN neural networks usually have three forms:

[0022]

[0023] However, these functions are radially symmetric, and the most commonly used function is the Gaussian function. Therefore, the hidden layer of the neural network uses the Gaussian kernel function as the activation function. When the number of input vectors is large, the complexity of the RBFNN network operation does not increase, and there are derivatives of arbitrary order:

[0024]

[0025] Where x k is the kth input vector, c kj is the center point of the jth basis function, b j is a freely selectable parameter that determines the width of the basis function around the center point, ||·|| is the Euclidean norm, and the Gaussian is a radially symmetric function that decays rapidly to zero as |xc| increases, so for a given input X∈R n , only a small number of processing units whose centers are close to x are activated;

[0026] The voltage and current information of the SRM during operation is collected by current and voltage sensors, and the relationship between magnetic flux, current and rotor position is established to complete sensorless control. The input of the constructed neural network is magnetic flux and phase current, and the tracking value is the rotor position. The actual tracking value obtained by the neural network is the rotor position after training. The input variables need to be quantized for amplitude processing. The output equation of the network is given by the following formula:

[0027]

[0028] Where H is the total number of hidden layer nodes, ω k is the connection weight between the output space and the kth hidden layer node;

[0029] In the design of neural network architecture, the number of neurons in the hidden layer can significantly affect model performance and requires careful optimization before finalizing the network structure. Expanding the depth of the network usually increases the training duration, while increasing the width of a single layer increases the complexity of the model. Conversely, an insufficient number of neurons may lead to underfitting and reduce prediction accuracy. Therefore, it is crucial to achieve an optimal balance between preventing overtraining and maintaining sufficient model expressiveness.

[0030] In RBFNN, key parameters include basis function center vectors, width parameters, and linear layer weights, which need to be accurately determined. Therefore, the main challenge of RBFNN-based system identification is to accurately estimate these unknown parameters. Therefore, the recognition performance index of the neural network can be defined as follows:

[0031]

[0032] As a further description of the above technical solution:

[0033] In the accuracy evaluation of the RBFNN model, in order to more comprehensively evaluate the prediction accuracy of the rotor position of the RBFNN model, the mean square error (MSE), linear regression correlation coefficient (R), and maximum angular error (Emax) are used as evaluation indicators of the model performance. These indicators quantitatively analyze the accuracy of the model from the perspectives of numerical deviation, linear correlation, and directional error, providing a multi-dimensional reference for model optimization and verification.

[0034] As a further description of the above technical solution:

[0035] The MSE represents the basic performance indicator of regression analysis, which quantifies the mean square error between the predicted value and the actual value. The model performance is evaluated by calculating the square error between the predicted value and the actual value of each sample and taking the average value. The smaller the MSE value, the better the prediction effect of the model.

[0036]

[0037] Where N1 is the number of training samples, Y(i) and are the actual and estimated values, respectively.

[0038] As a further description of the above technical solution:

[0039] The linear regression correlation coefficient R quantifies the strength and direction of the linear dependence between two continuous variables, indicating the degree of linear correlation between the predicted value and the true value, and can be expressed as:

[0040]

[0041] Where, and are the averages of the actual and estimated values, respectively. The value of R ranges from -1 to 1. When the value is close to -1 and 1, the linear relationship between the predicted and actual values ​​is stronger, which indicates that the accuracy of the network model is higher.

[0042] As a further description of the above technical solution:

[0043] The maximum angle error Emax is a geometric evaluation metric used to evaluate the deviation between the predicted angle and the true angle. By using the maximum angle error as an evaluation indicator, the performance of the model in prediction can be more intuitively understood, providing an important reference for optimizing the model. It can be defined as:

[0044] Emax(θ p (i)-θ a (i))max

[0045] where θ p (i) and θ a(i) are the predicted angle and the actual angle, respectively. The difference between the predicted and actual angles can be used to intuitively obtain the maximum error of the model in estimating the rotor position. This is also an important reference for evaluating the accuracy of the model. A smaller maximum error indicates that the model has higher prediction accuracy and stability, while a larger value may reflect the prediction limitations of the model under specific conditions.

[0046] As a further description of the above technical solution:

[0047] The improved coyote optimization algorithm ICOA includes the coyote optimization algorithm COA, the introduction of the improved COA and the position estimation algorithm. The COA is a meta-heuristic optimization algorithm based on swarm intelligence, which is inspired by the hunting behavior of coyotes. By simulating the cooperation and competition process of coyotes in a group, COA can achieve global search and local optimization in complex optimization problems. COA mainly models the coyote population from four aspects: birth, growth, death and migration. First, some parameters need to be defined, N p 、N c and D are the number of packs, the number of wolves without packs, and the dimension of the search space, respectively. Any random wolf in the coyote is an individual and can be defined as:

[0048]

[0049] Where, Denote any individual coyote in group p at time t in the jth dimension, and the entire wolf pack can be represented as:

[0050]

[0051] Some of the wolf pack's adaptability is manifested in:

[0052]

[0053] The probability of a coyote being driven out of its original group is defined as:

[0054]

[0055] As the leader of the pack, the alpha wolf is less adaptable to the environment than other coyotes. The leader wolf and cultural trends in the wolf pack can be described as:

[0056]

[0057] Where, and When N c The median of the j-dimensional variable for all coyotes in the entire p group when taking different values ​​at the tth time;

[0058] Coyotes go through a natural life cycle of birth and death, and to simulate genetic influences, the emergence of newborn coyotes is marked It is characterized by a convergence of parental social status and environmental factors:

[0059]

[0060] where m1 and m2 are random individual coyotes in the p wolf pack, j1 and j2 are arbitrary two-dimensional representations of the problem to be solved, and R j and rand j The range is between 0 and 1;

[0061] As the race is renewed, new coyotes are born, and new individuals are produced in the wolf pack. These new individuals will be influenced by the wolf pack and the cultural production flow, as follows:

[0062]

[0063] Where cr1 and cr2 are random coyotes belonging to the current population range, and the updated individuals in the population are expressed as:

[0064]

[0065] Where r1 and r2 are real numbers generated with uniform probability, ranging from 0 to 1;

[0066] As wolves are born and die, the wolf pack is constantly renewed, so coyotes with better abilities need to be selected:

[0067]

[0068] As a further description of the above technical solution:

[0069] In the improved COA, the nonlinear mapping relationship between magnetic flux, current and position angle is trained, and ICOA is used for parameter optimization to reduce modeling errors. The final training modeling results are as follows: Since COA is prone to produce local optimal solutions, local optimality means that individuals in the coyote population gradually converge during the iteration process, resulting in insufficient exploration of the search space. To solve this problem, first, the wolf pack update formula needs to be improved. The improved formula is as follows:

[0070]

[0071] Among them, k and ω k are the number of iterations and the state ratio of the coyote, respectively. Whether the number of iterations is too small or too large, the death of young wolves or old wolves needs to reduce the impact on the population, then ω k Can be defined as:

[0072]

[0073] Based on ω k Definition: When k is very small, ω k ≈1 or ω k >1, when k increases, ω k On the contrary, it will decrease, which reduces the number of useless iterations. Next, before introducing a new coyote individual, two operators need to be defined:

[0074]

[0075] Where, and is a random coyote in group p, based on which the two parameters can be expressed as follows:

[0076]

[0077] in, and The ratio is a better way to compare the levels of coyote introductions and the current cultural trends of wolves:

[0078] After the wolf pack update, new coyote individuals were obtained:

[0079]

[0080] Where r1, r2, r3 and r4 are all randomly generated numbers between 0 and 1;

[0081] From the above formula, we can see that after the new operator is introduced, according to the introduced coyote The corresponding wolf pack update formula is different if Small and weak, it has little impact on the wolf pack, on the contrary, when When it is strong enough, it will be beneficial to the wolf pack system. Therefore, in this way, the local optimal phenomenon in the iterative process can be effectively reduced.

[0082] As a further description of the above technical solution:

[0083] In the position estimation algorithm, in order to achieve accurate prediction of the SRM sensorless rotor position and rotor speed, the flux current rotor position should be established first. However, this method also requires accurate determination of the position of the shutdown angle to achieve the normal operation of the entire system. As the motor current continues to increase, the magnetic flux value will also increase. At this time, θ must be determined. off The position and θ offThe magnetic flux information at the position is used to ensure the normal operation of the entire system. The commutation signal is obtained by comparing and analyzing the initial and final positions of the magnetic flux and current. If the magnetic flux value is less than the set position and no match is found through the real-time lookup table, it continues. On the contrary, if the magnetic flux value exceeds the set position, commutation is performed. The commutation position is recorded based on the emitted pulse signal, and the motor speed is finally estimated by recording the time interval between these pulse signals. However, absolute equality cannot be guaranteed in actual operation, so it is necessary to establish a threshold interval value σ, σ = 0.01, through the real-time flux equation Calculate the real-time magnetic flux, where U m 、i m 、R m are the phase voltage, phase current and resistance respectively, and the optimized magnetic flux model is obtained by the proposed modeling method;

[0084] Based on the traditional control method, although the switched reluctance motor control system can operate at any given opening angle, to obtain accurate speed information, it is necessary to obtain accurate rotor position. The rotor speed can be determined by the closing angle. At the same time, the distance between any two closing angles can be expressed as:

[0085]

[0086] Where k is the number of phases of the SRM. In this paper, k = 1, 2, 3, 4, 5, 6, N r is the number of rotor poles;

[0087] If the difference between two adjacent closing angles of the SRM is obtained, the number of steps of the interval angle can be calculated by programming, and then the interval time ΔT is calculated, and finally the estimated rotor speed ω is calculated by the ratio of the interval rotor angle difference to the interval time. est , the estimated rotor speed can be used as the feedback speed of the SRD system to achieve normal operation of the system. The speed calculation can be expressed as:

[0088]

[0089] However, in the actual implementation of the simulation model, external uncertain interference can cause voltage and current fluctuations, resulting in measurement errors. To address the adverse effects of these interferences on rotor speed prediction, filtering the simulation output and experimental data curves is crucial to ensure the stable operation of the entire flux closed-loop system. The rotor information at any position can be estimated using the following formula:

[0090] θ est (j+1)=θ off (j)+∫ω est dt

[0091] During SRM operation, each time the rotor reaches θ off Position, θ off The position is determined by the preset value. When it is judged that the output condition is met, the system will output the accurate rotor position, which is equivalent to providing a reset signal judgment to avoid the rotor accumulation error caused by multiple integrations.

[0092] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0093] In the present invention, ICOA is applied to nonlinear sensorless modeling to obtain a simple and compact RBFNN model. Through online training, the relationship between magnetic flux, current and rotor position is more accurate, and a rotor position estimation strategy is adopted to achieve precise commutation. Regardless of the control mode, the current speed waveform obtained by ICOA-RBFNN is not much different from the waveform obtained by traditional FEA. Sensorless control using ICOA-RBFNN is suitable for accurately estimating speed and rotor position under various operating conditions. The tracking error meets the requirements within a certain range, has good adaptability, and improves dynamic response capability. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 A topological diagram of a switched reluctance motor sensorless control method based on nonlinear modeling of flux linkage proposed in the present invention, based on an RBF neural network;

[0095] Figure 2 This is a schematic diagram of RBFNN modeling based on improved COA for a sensorless control method for a switched reluctance motor based on flux nonlinear modeling proposed in the present invention;

[0096] Figure 3 This is a logic block diagram of a sensorless control method for a switched reluctance motor based on nonlinear modeling of flux linkage proposed in the present invention for determining the turn-off angle;

[0097] Figure 4 This is the overall control block diagram of the RBFNN based on ICOA for the sensorless control method of the switched reluctance motor based on flux nonlinear modeling proposed in the present invention;

[0098] Figure 5 Schematic diagram of an experimental setup for a sensorless control method for a switched reluctance motor based on nonlinear modeling of flux linkage proposed in the present invention;

[0099] Figure 6 A schematic diagram of the current waveform in CCC mode of a sensorless control method for a switched reluctance motor based on nonlinear modeling of flux linkage proposed in the present invention;

[0100] Figure 7Schematic diagram of experimental results at 1000 rpm for a sensorless control method for a switched reluctance motor based on flux nonlinear modeling proposed in the present invention;

[0101] Figure 8 A schematic diagram of the current waveform in APC mode of a sensorless control method for a switched reluctance motor based on nonlinear modeling of flux linkage proposed in the present invention;

[0102] Figure 9 This is a schematic diagram of experimental results at 3000 rpm for a sensorless control method for a switched reluctance motor based on flux nonlinear modeling proposed in the present invention;

[0103] Figure 10 Schematic diagram of speed waveform and speed error in different control modes of the sensorless control method for switched reluctance motor based on flux nonlinear modeling proposed by the present invention;

[0104] Figure 11 Schematic diagram of speed waveform and speed error in different control modes under dynamic speed conditions according to the sensorless control method for switched reluctance motor based on flux nonlinear modeling proposed by the present invention;

[0105] Figure 12 Schematic diagram of experimental results of speed step length under the CCC sensorless control method for switched reluctance motor based on flux nonlinear modeling proposed in the present invention;

[0106] Figure 13 This is a schematic diagram of experimental results of speed step length under the APC sensorless control method for switched reluctance motor based on flux nonlinear modeling proposed in the present invention;

[0107] Figure 14 Schematic diagram of speed waveform and speed error in different control modes under dynamic torque conditions according to the sensorless control method for switched reluctance motor based on flux nonlinear modeling proposed by the present invention;

[0108] Figure 15 Schematic diagram of experimental results of torque step under CCC, a sensorless control method for switched reluctance motor based on flux nonlinear modeling proposed in the present invention;

[0109] Figure 16 This is a schematic diagram of the experimental results of torque step under the APC sensorless control method for the switched reluctance motor based on flux nonlinear modeling proposed in the present invention. DETAILED DESCRIPTION

[0110] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0111] Example 1

[0112] like Figure 1-7 As shown in FIG, a sensorless control method for a switched reluctance motor based on nonlinear modeling of flux linkage includes the following contents:

[0113] ICOA is applied to nonlinear sensorless modeling, that is, the radial basis function neural network (RBFNN) is combined with the improved coyote optimization algorithm (ICOA) to obtain a simple and compact RBFNN model.

[0114] RBFNN has a fast convergence speed and strong approximation ability. ICOA can dynamically adjust the parameters and structure of RBFNN, reduce modeling errors by adaptively adjusting the number of hidden layer nodes, complete online training, and make the relationship between magnetic flux, current, and rotor position more accurate;

[0115] The rotor position estimation strategy is used to achieve precise commutation to ensure the stable operation of the entire closed-loop system.

[0116] Specifically, the sensorless control based on the RBFNN includes a radial basis function neural network RBFNN and RBFNN model accuracy evaluation, with MSE and R as the basis for RBFNN modeling and training, and Emax as a standard for testing model accuracy.

[0117] Specifically, the radial basis function neural network (RBFNN) architecture includes three main components: an input layer, a hidden layer, and an output layer. Magnetic flux and current values ​​are used as input variables, while rotor position is used as the target output for training purposes. Each processing unit in the network is represented as a node with the following connection properties:

[0118] Nodes within the same layer remain unconnected, while inter-layer connections between adjacent layers are established through weighted links. Therefore, RBFNN neural networks usually have three forms:

[0119]

[0120] However, these functions are radially symmetric, and the most commonly used function is the Gaussian function. Therefore, the hidden layer of the neural network uses the Gaussian kernel function as the activation function. When the number of input vectors is large, the complexity of the RBFNN network operation does not increase, and there are derivatives of arbitrary order:

[0121]

[0122] Where x k is the kth input vector, c kj is the center point of the jth basis function, b j is a freely selectable parameter that determines the width of the basis function around the center point, ||·|| is the Euclidean norm, and the Gaussian is a radially symmetric function that decays rapidly to zero as |xc| increases, so for a given input X∈R n , only a small number of processing units whose centers are close to x are activated;

[0123] The voltage and current information of the SRM during operation is collected by current and voltage sensors, and the relationship between magnetic flux, current and rotor position is established to complete sensorless control. The input of the constructed neural network is magnetic flux and phase current, and the tracking value is the rotor position. The actual tracking obtained by the neural network is the rotor position after training. The input variables need to be quantized for amplitude processing. The output equation of the network is given by the following formula

[0124]

[0125] Where H is the total number of hidden layer nodes, ω k is the connection weight between the output space and the kth hidden layer node;

[0126] In the design of neural network architecture, the number of neurons in the hidden layer can significantly affect model performance and requires careful optimization before finalizing the network structure. Expanding the depth of the network usually increases the training duration, while increasing the width of a single layer increases the complexity of the model. Conversely, an insufficient number of neurons may lead to underfitting and reduce prediction accuracy. Therefore, it is crucial to achieve an optimal balance between preventing overtraining and maintaining sufficient model expressiveness.

[0127] In RBFNN, key parameters include basis function center vectors, width parameters, and linear layer weights, which need to be accurately determined. Therefore, the main challenge of RBFNN-based system identification is to accurately estimate these unknown parameters. Therefore, the recognition performance index of the neural network can be defined as follows:

[0128]

[0129] Specifically, in the accuracy evaluation of the RBFNN model, in order to more comprehensively evaluate the prediction accuracy of the rotor position of the RBFNN model, the mean square error MSE, linear regression correlation coefficient R and maximum angular error Emax are used as evaluation indicators of the model performance. These indicators quantitatively analyze the accuracy of the model from the perspectives of numerical deviation, linear correlation and directional error, providing a multi-dimensional reference for model optimization and verification.

[0130] Specifically, the MSE represents the basic performance indicator of regression analysis, which quantifies the mean square error between the predicted value and the actual value. The model performance is evaluated by calculating the square error between the predicted value and the actual value of each sample and taking the average value. The smaller the MSE value, the better the prediction effect of the model.

[0131]

[0132] Where N1 is the number of training samples, Y(i) and are the actual and estimated values, respectively.

[0133] Specifically, the linear regression correlation coefficient R quantifies the strength and direction of the linear dependence between two continuous variables, indicating the degree of linear correlation between the predicted value and the true value, and can be expressed as:

[0134]

[0135] Where, and are the averages of the actual and estimated values, respectively. The value of R ranges from -1 to 1. When the value is close to -1 and 1, the linear relationship between the predicted and actual values ​​is stronger, which indicates that the accuracy of the network model is higher.

[0136] Specifically, the maximum angle error Emax is a geometric evaluation metric used to evaluate the deviation between the predicted angle and the true angle. By using the maximum angle error as an evaluation indicator, the performance of the model in prediction can be more intuitively understood, providing an important reference for optimizing the model. It can be defined as:

[0137] Emax(θ p (i)-θ a (i))max

[0138] where θ p (i) and θ a (i) are the predicted angle and the actual angle, respectively. The difference between the predicted and actual angles can be used to intuitively obtain the maximum error of the model in estimating the rotor position. This is also an important reference for evaluating the accuracy of the model. A smaller maximum error indicates that the model has higher prediction accuracy and stability, while a larger value may reflect the prediction limitations of the model under specific conditions.

[0139] Specifically, the improved coyote optimization algorithm ICOA includes the coyote optimization algorithm COA, the introduction of the improved COA and the position estimation algorithm. The COA is a meta-heuristic optimization algorithm based on swarm intelligence, which is inspired by the hunting behavior of coyotes. By simulating the cooperation and competition process of coyotes in a group, COA can achieve global search and local optimization in complex optimization problems. COA mainly models the coyote population from four aspects: birth, growth, death and migration. First, some parameters need to be defined, N p 、N c and D are the number of packs, the number of wolves without packs, and the dimension of the search space, respectively. Any random wolf in the coyote is an individual and can be defined as:

[0140]

[0141] Where, Denote any individual coyote in group p at time t in the jth dimension, and the entire wolf pack can be represented as:

[0142]

[0143] Some of the wolf pack's adaptability is manifested in:

[0144]

[0145] The probability of a coyote being driven out of its original group is defined as:

[0146]

[0147] As the leader of the pack, the alpha wolf is less adaptable to the environment than other coyotes. The leader wolf and cultural trends in the wolf pack can be described as:

[0148]

[0149] Where, and When N c The median of the j-dimensional variable for all coyotes in the entire p group when taking different values ​​at the tth time;

[0150] Coyotes go through a natural life cycle of birth and death, and to simulate genetic influences, the emergence of newborn coyotes is marked It is characterized by a convergence of parental social status and environmental factors:

[0151]

[0152] where m1 and m2 are random individual coyotes in the p wolf pack, j1 and j2 are arbitrary two-dimensional representations of the problem to be solved, and Rj and rand j The range is between 0 and 1;

[0153] As the race is renewed, new coyotes are born, and new individuals are produced in the wolf pack. These new individuals will be influenced by the wolf pack and the cultural production flow, as follows:

[0154]

[0155] Where cr1 and cr2 are random coyotes belonging to the current population range, and the updated individuals in the population are expressed as:

[0156]

[0157] Where r1 and r2 are real numbers generated with uniform probability, ranging from 0 to 1;

[0158] As wolves are born and die, the wolf pack is constantly renewed, so it is necessary to select for coyotes with better abilities:

[0159]

[0160] Specifically, in the improved COA, the nonlinear mapping relationship between magnetic flux, current and position angle is trained, and ICOA is used for parameter optimization to reduce modeling errors. The final training modeling result is that COA is prone to the problem of producing local optimal solutions. Local optimality means that individuals in the coyote population gradually converge during the iteration process, resulting in insufficient exploration of the search space. In order to solve this problem, first, the wolf pack update formula needs to be improved. The improved formula is as follows:

[0161]

[0162] Among them, k and ω k are the number of iterations and the state ratio of the coyote, respectively. Whether the number of iterations is too small or too large, the death of young wolves or old wolves needs to reduce the impact on the population, then ω k Can be defined as:

[0163]

[0164] Based on ω k Definition: When k is very small, ω k ≈1 or ω k >1, when k increases, ω k On the contrary, it will decrease, which reduces the number of useless iterations. Next, before introducing a new coyote individual, two operators need to be defined:

[0165]

[0166] Where, and is a random coyote in group p, based on which the two parameters can be expressed as follows:

[0167]

[0168] in, and The ratio is a better way to compare the levels of coyote introductions and the current cultural trends of wolves:

[0169] After the wolf pack update, new coyote individuals were obtained:

[0170]

[0171] Where r1, r2, r3 and r4 are all randomly generated numbers between 0 and 1;

[0172] From the above formula, we can see that after the new operator is introduced, according to the introduced coyote The corresponding wolf pack update formula is different if Small and weak, it has little impact on the wolf pack, on the contrary, when When it is strong enough, it will be beneficial to the wolf pack system. Therefore, in this way, the local optimal phenomenon in the iterative process can be effectively reduced.

[0173] Specifically, in the position estimation algorithm, in order to achieve accurate prediction of the SRM sensorless rotor position and rotor speed, the flux current rotor position However, this method also requires accurate determination of the position of the shutdown angle to achieve the normal operation of the entire system. As the motor current continues to increase, the magnetic flux value will also increase. At this time, θ must be determined. off The position and θ off The magnetic flux information at the position is used to ensure the normal operation of the entire system. The commutation signal is obtained by comparing and analyzing the initial and final positions of the magnetic flux and current. If the magnetic flux value is less than the set position and no match is found through the real-time lookup table, it continues. On the contrary, if the magnetic flux value exceeds the set position, commutation is performed. The commutation position is recorded based on the emitted pulse signal, and the motor speed is finally estimated by recording the time interval between these pulse signals. However, absolute equality cannot be guaranteed in actual operation, so it is necessary to establish a threshold interval value σ, σ = 0.01, through the real-time flux equation Calculate the real-time magnetic flux, where U m 、i m 、R mare the phase voltage, phase current and resistance respectively, and the optimized magnetic flux model is obtained by the proposed modeling method;

[0174] Based on the traditional control method, although the switched reluctance motor control system can operate at any given opening angle, to obtain accurate speed information, it is necessary to obtain accurate rotor position. The rotor speed can be determined by the closing angle. At the same time, the distance between any two closing angles can be expressed as:

[0175]

[0176] Where k is the number of phases of the SRM. In this paper, k = 1, 2, 3, 4, 5, 6, N r is the number of rotor poles;

[0177] If the difference between two adjacent closing angles of the SRM is obtained, the number of steps of the interval angle can be calculated by programming, and then the interval time ΔT is calculated, and finally the estimated rotor speed ω is calculated by the ratio of the interval rotor angle difference to the interval time. est , the estimated rotor speed can be used as the feedback speed of the SRD system to achieve normal operation of the system. The speed calculation can be expressed as:

[0178]

[0179] However, in the actual implementation of the simulation model, external uncertain interference can cause voltage and current fluctuations, resulting in measurement errors. To address the adverse effects of these interferences on rotor speed prediction, filtering the simulation output and experimental data curves is crucial to ensure the stable operation of the entire flux closed-loop system. The rotor information at any position can be estimated using the following formula:

[0180] θ est (j+1)=θ off (j)+∫ω est dt

[0181] During SRM operation, each time the rotor reaches θ off Position, θ off The position is determined by the preset value. When it is judged that the output condition is met, the system will output the accurate rotor position, which is equivalent to providing a reset signal judgment to avoid the rotor accumulation error caused by multiple integrations.

[0182] Example 2

[0183] Experimental Platform

[0184] like Figure 5As shown in Figure 2, the proposed sensorless algorithm is verified by a six-phase 12 / 10 SRM experimental device. The experimental device mainly includes a six-phase SRM, torque and speed sensors, a power converter, an FZ25J magnetic powder brake, a dSPACE loaded with a DS1401 board, a CPLD signal modulation board, a DC power supply, an oscilloscope, and a PC. The experimental prototype SRM is connected to the torque-speed sensor through a coupler, the hysteresis brake is used to provide the load torque, and the actual rotor position detected by the ATS675LSE Hall position sensor is only used as a comparison verification group instead of a feedback signal. The remaining parameters of the prototype are shown in Table I:

[0185] Table I

[0186] Key parameters and dimensions of SRM

[0187]

[0188] Experimental results under two speed conditions

[0189] In order to verify the proposed method, appropriate parameters should be selected. Therefore, through continuous optimization and debugging, good parameters for sensorless nonlinear modeling were obtained. In the experiment, the results of modeling using ICOA-RBFNN were compared with finite element analysis. Figure 6 and Figure 7 The fitting results at two different rotation speeds are shown respectively;

[0190] The experimental conditions at low speed are as follows: the stable speed is set to 1000rpm, the load torque is set to 4Nm, Figure 6 The current waveform and local magnification of the motor in steady state under CCC mode are shown. Figure 7 (a) shows the estimated result of the position signal at low speed. Figure 7 (b) shows the position error. The maximum estimated error of the rotor is 2.62°;

[0191] The experimental conditions at high speed are as follows: the stable speed is set to 3000rpm, the load torque is set to 4Nm, Figure 8 The current waveform and local magnification of the motor in steady state under APC mode are shown. Figure 9 (a) shows the estimation result of the rotor position signal at high speed, Figure 9 (b) shows the position error. The maximum estimated error of the rotor is 2.74°. Figure 6 and Figure 8 It can be seen that the modeling results based on ICOA-RBFNN are in good agreement with the finite element analysis data, and the modeling results based on ICOA-CBFNN are in good agreement with the measurement results, with high modeling accuracy. Figure 7 and Figure 9It can be seen that the estimated position can track the actual position well, and the position estimation performance is good;

[0192] Figure 10 The verification of motor speed tracking performance under RBFNN based on ICOA is given. Figure 10 (a) and (b) show the estimated and actual speeds of the motor at steady speeds of 1000 rpm and 3000 rpm, the speed interval magnification diagram, and the speed tracking error, respectively. The maximum speed tracking errors are 19 rpm and 28 rpm, respectively, indicating that the proposed sensorless control has a good effect under constant working conditions, and the estimation accuracy of position and speed has been verified.

[0193] Experimental results under variable operating conditions

[0194] The speed disturbance and load disturbance experiments of the motor were carried out to further verify the accuracy of the RBFNN rotor position estimation based on ICOA. Figure 11 The speed mutation experiment of the motor is shown when the load torque is 4Nm. Figure 11 (a) shows the waveforms of the estimated and actual speeds of the SRM when it is running steadily at 1000 rpm and a load torque of 4 Nm. At 0.2 seconds, the speed of the motor increases to 1100 rpm and increases to 1300 rpm after stabilization. Figure 11 (b) shows the waveforms of the estimated and actual speeds of the motor when it is running steadily at 3000 rpm and a load torque of 4 Nm. At 0.2 seconds, the speed drops to 2900 rpm and then drops to 2700 rpm after stabilization. According to the speed tracking error at the two speeds, the speed fluctuates slightly during the speed step, and the speed tracking error is small.

[0195] Figure 12 and Figure 13 The rotor position estimation and position error during motor speed switching are shown respectively. The results show that when speed steps are taken, the estimated angle can track the actual angle well, with the maximum angle error within 3°.

[0196] Figure 14 shows the experimental results of the motor's speed when a torque step is applied, Figure 14 (a) shows the waveforms of the estimated speed and the actual speed when the load torque of the motor increases from 4 Nm to 6 Nm when the motor is running steadily at a given speed of 1000 rpm. Figure 14 (b) shows the waveforms of the estimated speed and the actual speed when the SRM is running stably at a given speed of 3000 rpm and the load torque of the motor is reduced from 4 Nm to 3 Nm. The speed tracking error results show that when the torque changes, the estimated speed fluctuates slightly. When it is stable, the estimated speed can better match the actual speed, and the speed tracking error is small;

[0197] Figure 15 and 16 are the position errors of the rotor position estimation and the motor torque step, respectively. The results show that when the torque step occurs, the estimated angle can track the actual angle well, and the maximum angle error is within 2.9°. The comparison between the estimated angle and the actual angle shows that the accuracy of the rotor position signal estimation meets the requirements within a certain range, which indicates that the RBFNN has good dynamic response capability after online training.

[0198] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A sensorless control method for a switched reluctance motor based on nonlinear modeling of flux linkage, characterized in that: Includes the following: ICOA is applied to nonlinear sensorless modeling, that is, the radial basis function neural network (RBFNN) is combined with the improved coyote optimization algorithm (ICOA) to obtain a simple and compact RBFNN model. RBFNN has a fast convergence speed and strong approximation ability. ICOA can dynamically adjust the parameters and structure of RBFNN, reduce modeling errors by adaptively adjusting the number of hidden layer nodes, complete online training, and make the relationship between magnetic flux, current, and rotor position more accurate; The rotor position estimation strategy is used to achieve precise commutation to ensure the stable operation of the entire closed-loop system.

2. The sensorless control method for a switched reluctance motor based on flux nonlinear modeling according to claim 1, characterized in that: The sensorless control based on the RBFNN includes a radial basis function neural network RBFNN and RBFNN model accuracy evaluation, with MSE and R as the basis for RBFNN modeling and training, and Emax as a standard for testing model accuracy.

3. The sensorless control method for a switched reluctance motor based on flux nonlinear modeling according to claim 2, characterized in that: The radial basis function neural network (RBFNN) architecture consists of three main components: input layer, hidden layer, and output layer. Magnetic flux and current values ​​are used as input variables, while rotor position is used as the target output for training purposes. Each processing unit in the network is represented as a node with the following connection properties: Nodes within the same layer remain unconnected, while inter-layer connections between adjacent layers are established through weighted links. Therefore, RBFNN neural networks usually have three forms: However, these functions are radially symmetric, and the most commonly used function is the Gaussian function. Therefore, the hidden layer of the neural network uses the Gaussian kernel function as the activation function. When the number of input vectors is large, the complexity of the RBFNN network operation does not increase, and there are derivatives of arbitrary order: Where x k is the kth input vector, c kj is the center point of the jth basis function, b j is a freely selectable parameter that determines the width of the basis function around the center point, ||·|| is the Euclidean norm, and the Gaussian is a radially symmetric function that decays rapidly to zero as |xc| increases, so for a given input X∈R n , only a small number of processing units whose centers are close to x are activated; The voltage and current information of the SRM during operation is collected by current and voltage sensors, and the relationship between magnetic flux, current and rotor position is established to complete sensorless control. The input of the constructed neural network is magnetic flux and phase current, and the tracking value is the rotor position. The actual tracking value obtained by the neural network is the rotor position after training. The input variables need to be quantized for amplitude processing. The output equation of the network is given by the following formula: Where H is the total number of hidden layer nodes, ω k is the connection weight between the output space and the kth hidden layer node; In the design of neural network architecture, the number of neurons in the hidden layer can significantly affect model performance and requires careful optimization before finalizing the network structure. Expanding the depth of the network usually increases the training duration, while increasing the width of a single layer increases the complexity of the model. Conversely, an insufficient number of neurons may lead to underfitting and reduce prediction accuracy. Therefore, it is crucial to achieve an optimal balance between preventing overtraining and maintaining sufficient model expressiveness. In RBFNN, key parameters include basis function center vectors, width parameters, and linear layer weights, which need to be accurately determined. Therefore, the main challenge of RBFNN-based system identification is to accurately estimate these unknown parameters. Therefore, the recognition performance index of the neural network can be defined as follows:

4. The sensorless control method for a switched reluctance motor based on flux nonlinear modeling according to claim 3, characterized in that: In the accuracy evaluation of the RBFNN model, in order to more comprehensively evaluate the prediction accuracy of the rotor position of the RBFNN model, the mean square error (MSE), linear regression correlation coefficient (R), and maximum angular error (Emax) are used as evaluation indicators of the model performance. These indicators quantitatively analyze the accuracy of the model from the perspectives of numerical deviation, linear correlation, and directional error, providing a multi-dimensional reference for model optimization and verification.

5. The sensorless control method for a switched reluctance motor based on flux nonlinear modeling according to claim 4, characterized in that: The MSE represents the basic performance indicator of regression analysis, which quantifies the mean square error between the predicted value and the actual value. The model performance is evaluated by calculating the square error between the predicted value and the actual value of each sample and taking the average value. The smaller the MSE value, the better the prediction effect of the model. Where N1 is the number of training samples, Y(i) and are the actual and estimated values, respectively.

6. The sensorless control method for a switched reluctance motor based on flux nonlinear modeling according to claim 5, characterized in that: The linear regression correlation coefficient R quantifies the strength and direction of the linear dependence between two continuous variables, indicating the degree of linear correlation between the predicted value and the true value, and can be expressed as: Where, and are the averages of the actual and estimated values, respectively. The value of R ranges from -1 to 1. When the value is close to -1 and 1, the linear relationship between the predicted and actual values ​​is stronger, which indicates that the accuracy of the network model is higher.

7. The sensorless control method for a switched reluctance motor based on flux nonlinear modeling according to claim 6, characterized in that: The maximum angle error Emax is a geometric evaluation metric used to evaluate the deviation between the predicted angle and the true angle. By using the maximum angle error as an evaluation indicator, the performance of the model in prediction can be more intuitively understood, providing an important reference for optimizing the model. It can be defined as: Emax(θ p (i)-θ a (i)) max where θ p (i) and θ a (i) are the predicted angle and the actual angle, respectively. The difference between the predicted and actual angles can be used to intuitively obtain the maximum error of the model in estimating the rotor position. This is also an important reference for evaluating the accuracy of the model. A smaller maximum error indicates that the model has higher prediction accuracy and stability, while a larger value may reflect the prediction limitations of the model under specific conditions.

8. The sensorless control method for a switched reluctance motor based on flux nonlinear modeling according to claim 1, characterized in that: The improved coyote optimization algorithm ICOA includes the coyote optimization algorithm COA, the introduction of the improved COA and the position estimation algorithm. The COA is a meta-heuristic optimization algorithm based on swarm intelligence, which is inspired by the hunting behavior of coyotes. By simulating the cooperation and competition process of coyotes in a group, COA can achieve global search and local optimization in complex optimization problems. COA mainly models the coyote population from four aspects: birth, growth, death and migration. First, some parameters need to be defined, N p 、N c and D are the number of packs, the number of wolves without packs, and the dimension of the search space, respectively. Any random wolf in the coyote is an individual and can be defined as: Where, Denote any individual coyote in group p at time t in the jth dimension, and the entire wolf pack can be represented as: Some of the wolf pack's adaptability is manifested in: The probability of a coyote being driven out of its original group is defined as: As the leader of the pack, the alpha wolf is less adaptable to the environment than other coyotes. The leader wolf and cultural trends in the wolf pack can be described as: Where, and When N c The median of the j-dimensional variable for all coyotes in the entire p group when taking different values ​​at the tth time; Coyotes go through a natural life cycle of birth and death, and to simulate genetic influences, the emergence of newborn coyotes is marked It is characterized by a convergence of parental social status and environmental factors: where m1 and m2 are random individual coyotes in the p wolf pack, j1 and j2 are arbitrary two-dimensional representations of the problem to be solved, and R j and rand j The range is between 0 and 1; As the race is renewed, new coyotes are born, and new individuals are produced in the wolf pack. These new individuals will be influenced by the wolf pack and the cultural production flow, as follows: Where cr1 and cr2 are random coyotes belonging to the current population range, and the updated individuals in the population are expressed as: Where r1 and r2 are real numbers generated with uniform probability, ranging from 0 to 1; As wolves are born and die, the wolf pack is constantly renewed, so it is necessary to select for coyotes with better abilities:

9. The sensorless control method for a switched reluctance motor based on flux nonlinear modeling according to claim 8, characterized in that: In the improved COA, the nonlinear mapping relationship between magnetic flux, current and position angle is trained, and ICOA is used for parameter optimization to reduce modeling errors. The final training modeling results are as follows: Since COA is prone to produce local optimal solutions, local optimality means that individuals in the coyote population gradually converge during the iteration process, resulting in insufficient exploration of the search space. To solve this problem, first, the wolf pack update formula needs to be improved. The improved formula is as follows: Among them, k and ω k are the number of iterations and the state ratio of the coyote, respectively. Whether the number of iterations is too small or too large, the death of young wolves or old wolves needs to reduce the impact on the population, then ω k Can be defined as: Based on ω k Definition: When k is very small, ω k ≈1 or ω k >1, when k increases, ω k On the contrary, it will decrease, which reduces the number of useless iterations. Next, before introducing a new coyote individual, two operators need to be defined: Where, and is a random coyote in group p, based on which the two parameters can be expressed as follows: in, and The ratio is a better way to compare the levels of coyote introductions and the current cultural trends of wolves: After the wolf pack update, new coyote individuals were obtained: Where r1, r2, r3 and r4 are all randomly generated numbers between 0 and 1; From the above formula, we can see that after the new operator is introduced, according to the introduced coyote The corresponding wolf pack update formula is different if Small and weak, it has little impact on the wolf pack, on the contrary, when When it is strong enough, it will be beneficial to the wolf pack system. Therefore, in this way, the local optimal phenomenon in the iterative process can be effectively reduced.

10. The sensorless control method for a switched reluctance motor based on flux nonlinear modeling according to claim 9, characterized in that: In the position estimation algorithm, in order to achieve accurate prediction of the SRM sensorless rotor position and rotor speed, the flux current rotor position should be established first. However, this method also requires accurate determination of the position of the shutdown angle to achieve the normal operation of the entire system. As the motor current continues to increase, the magnetic flux value will also increase. At this time, θ must be determined. off The position and θ off The magnetic flux information at the position is used to ensure the normal operation of the entire system. The commutation signal is obtained by comparing and analyzing the initial and final positions of the magnetic flux and current. If the magnetic flux value is less than the set position and no match is found through the real-time lookup table, it continues. On the contrary, if the magnetic flux value exceeds the set position, commutation is performed. The commutation position is recorded based on the emitted pulse signal, and the motor speed is finally estimated by recording the time interval between these pulse signals. However, absolute equality cannot be guaranteed in actual operation, so it is necessary to establish a threshold interval value σ, σ = 0.01, through the real-time flux equation Calculate the real-time magnetic flux, where U m 、i m 、R m are the phase voltage, phase current and resistance respectively, and the optimized magnetic flux model is obtained by the proposed modeling method; Based on the traditional control method, although the switched reluctance motor control system can operate at any given opening angle, to obtain accurate speed information, it is necessary to obtain accurate rotor position. The rotor speed can be determined by the closing angle. At the same time, the distance between any two closing angles can be expressed as: Where k is the number of phases of the SRM. In this paper, k = 1, 2, 3, 4, 5, 6, N r is the number of rotor poles; If the difference between two adjacent closing angles of the SRM is obtained, the number of steps of the interval angle can be calculated by programming, and then the interval time ΔT is calculated, and finally the estimated rotor speed ω is calculated by the ratio of the interval rotor angle difference to the interval time. est , the estimated rotor speed can be used as the feedback speed of the SRD system to achieve normal operation of the system. The speed calculation can be expressed as: However, in the actual implementation of the simulation model, external uncertain interference can cause voltage and current fluctuations, resulting in measurement errors. To address the adverse effects of these interferences on rotor speed prediction, filtering the simulation output and experimental data curves is crucial to ensure the stable operation of the entire flux closed-loop system. The rotor information at any position can be estimated using the following formula: θ est (j+1)=θ off (j)+∫ω est dt During SRM operation, each time the rotor reaches θ off Position, θ off The position is determined by the preset value. When it is judged that the output condition is met, the system will output the accurate rotor position, which is equivalent to providing a reset signal judgment to avoid the rotor accumulation error caused by multiple integrations.

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