WOA-Elman neural network-based sensorless control method for bearingless synchronous reluctance motor

Abstract

The invention discloses a bearingless synchronous reluctance motor sensorless control method based on a WOA-Elman neural network, and the method comprises the steps: analyzing a voltage equation, a dynamic suspension equation and a motion equation of a bearingless synchronous reluctance motor, and collecting the voltage, current, angular velocity, rotor displacement and other data of the motor; based on an Elman neural network principle, voltage and current are used as input quantities, angular velocity and rotor displacement are used as output quantities, and a sensorless neural network model of the bearingless synchronous reluctance motor is built; the whale algorithm is used for optimization to obtain an optimal neural network model, and optimal parameters are output; the angular velocity and the displacement of the bearingless synchronous reluctance motor rotor are obtained through prediction of the neural network model, and sensorless control is achieved. According to the method, additional equipment is not needed, and the angle and position information of the rotor can be quickly and accurately estimated only by extracting and processing the voltage and current signals of the motor. And two sensorless control methods of no speed and no displacement of the motor can be realized at the same time.

Description

Technical Field

[0001] The present invention relates to the technical field of bearingless motor control, and in particular to a sensorless control method for a bearingless synchronous reluctance motor based on a WOA-Elman neural network. Background Art

[0002] Compared to traditional motors, bearingless motors lack bearing support. Instead, they utilize magnetic levitation to suspend the rotor above the stator. Consequently, bearingless motors offer advantages such as zero mechanical friction, no lubrication, leak resistance, and low noise. Consequently, they have found successful applications in various fields, including biomedicine, energy, chemical engineering, and high-precision manufacturing.

[0003] However, due to its unique internal structure, the rotor of a bearingless motor inevitably undergoes radial displacement. Therefore, to ensure normal rotation of the rotor and prevent collisions between the stator and rotor, bearingless motors require the installation of speed and displacement sensors. The speed sensor, typically an optical encoder, is mounted at one end of the shaft for precise speed measurement, while the displacement sensor is installed within the stator to monitor radial displacement. However, the installation of mechanical sensors inevitably increases the cost and size of the motor, complicating the design and manufacturing process. Furthermore, in harsh operating environments such as those with high humidity, high temperature, air pollution, or dust-prone areas, the installed sensors are very susceptible to interference, resulting in their failure to function properly.

[0004] To address these issues, sensorless control technology has emerged. Currently, the most intensively researched methods include the Kalman filter, high-frequency injection, and flux observation. However, most of these methods have limitations, making it difficult to achieve both speed- and displacement-free sensorless control using the same approach. Summary of the Invention

[0005] In order to address the deficiencies in the prior art, this application proposes a sensorless control method for a bearingless synchronous reluctance motor based on a WOA-Elman neural network. By leveraging the powerful data processing and timing prediction capabilities of the Elman neural network of the whale optimization algorithm, a sensorless control method for a bearingless synchronous reluctance motor is realized. This method can simultaneously achieve speed- and displacement-free sensor control.

[0006] The technical solutions adopted in the present invention are as follows:

[0007] A sensorless control method for a bearingless synchronous reluctance motor based on a WOA-Elman neural network includes the following steps:

[0008] Step 1, constructing a mathematical model of a bearingless synchronous reluctance motor;

[0009] Step 2: Based on the mathematical model, collect the motor torque winding data under different states to form a neural network data set; and build an Elman neural network model;

[0010] Step 3: Use the whale optimization algorithm to optimize the Elman neural network and adjust the weights and thresholds of the Elman neural network;

[0011] Step 4: Based on the updated network weights and thresholds, the optimal parameters and training set are output to obtain the optimized model;

[0012] Step 5: Add the trained network model to the control system of the bearingless synchronous reluctance motor, thereby establishing a bearingless synchronous reluctance motor sensorless control system based on the improved Elman neural network based on the whale optimization algorithm, and realizing sensorless control of the bearingless synchronous reluctance motor.

[0013] Furthermore, the sensorless control of the bearingless synchronous reluctance motor includes speed sensorless control and displacement sensorless control.

[0014] Furthermore, the motor torque winding data includes voltage, current of the torque winding and the suspension winding, rotor angular velocity, and rotor displacement data.

[0015] Furthermore, the mathematical model of the bearingless synchronous reluctance motor includes a voltage equation, a torque equation, a dynamic suspension equation and a motion equation to determine the relationship between the motor angular velocity and rotor displacement and the motor voltage and current respectively.

[0016] Furthermore, the voltage equation, torque equation, and motion equation of the motor are expressed as follows:

[0017] The voltage equation for a bearingless synchronous reluctance motor is:

[0018]

[0019] Where u d and u q The torque winding is the d-axis and q-axis stator voltage components, R s is the resistance of each phase of the torque winding, i d and i q are the stator current components on the d-axis and q-axis of the torque winding, L d and L q are the d-axis and q-axis inductances of the torque winding, respectively, and ω is the angular velocity of the motor;

[0020] The torque equation of a bearingless synchronous reluctance motor is:

[0021]

[0022] Where, Te is the electromagnetic torque of the motor, P M Number of pole pairs of the torque winding;

[0023] The equation of motion for a bearingless synchronous reluctance motor is:

[0024]

[0025] Where J is the moment of inertia of the rotor, T L is the load torque of the motor.

[0026] Furthermore, the dynamic suspension equation of the motor is expressed as follows:

[0027] The length of the air gap is expressed as follows:

[0028] δ(θ)=δ0-Δδ=δ0-xcosθ-ysinθ

[0029] Where δ0 is the single-sided air gap length before eccentricity, θ is the angle between the eccentricity and the axis, and x and y are the displacement components of the rotor on the x-axis and y-axis respectively;

[0030] The dynamic suspension equation of the bearingless synchronous reluctance motor rotor is:

[0031]

[0032] Where, F x and F y Denote the controllable radial suspension force in the x-axis and y-axis directions, F sx and F sy They represent the Maxwell forces acting on the rotor in the x-axis and y-axis directions, F x0 and F y0 They represent the radial disturbance forces exerted on the rotor in the x-axis and y-axis directions, respectively, and F y0 Including the weight of the rotor mg.

[0033] Furthermore, the Elman neural network model: set the number of nodes in the input layer u(k), the number of nodes in the output layer h(k), the number of nodes in the receiving layer q c The number of nodes in the hidden layer q(k) is expressed as follows:

[0034]

[0035] Where purelin(*) is the linear transfer function of the output neuron, tanh(*) is the hyperbolic tangent function of the hidden neuron, and ω1, ω2, and ω3 are 0.7, 0.15, and 0.15, respectively.

[0036] Furthermore, the process of optimizing the Elman neural network using the whale optimization algorithm in step 3 is as follows:

[0037] S1) Initialize the parameters of the whale optimization algorithm;

[0038] S2) execute the whale hunting strategy,

[0039] S3) Use the whale optimization algorithm to continuously iterate to adjust the weights and thresholds of the Elman neural network; repeat this process until the weights and thresholds meet the specified tolerance range; at this time, terminate the loop and proceed to the next step.

[0040] Furthermore, the whale's hunting strategy consists of three stages: surrounding prey, attacking with a bubble net, and randomly searching for prey. The details of each stage are as follows:

[0041] S21) In the prey encirclement phase, the most promising individual in the existing whale group is designated as the assumed target prey location; then, the remaining individuals in the whale group adjust their positions according to the position of the determined best candidate individual; the updating process is expressed as follows:

[0042]

[0043] Where D is the distance between the whale and the prey, X is the position, X* is the position of the optimal solution currently obtained, j is the current iteration number, and A and C are adjustment coefficients, which can be expressed as follows:

[0044]

[0045] Where a is the convergence factor, which decreases linearly from 2 to 0 during the iteration process, and r1 is a random number in [0,1].

[0046] S22) Bubble net attack phase: At this time, the position and distance between the whale and the target prey are first calculated, and the whale's most likely next action is given based on this information; the mathematical expression is as follows:

[0047]

[0048] Where b is a constant that defines the shape of the logarithmic spiral, and l1 is a random number between -1 and 1;

[0049] S23) Random search for prey: Each individual in the whale group randomly searches for prey based on its own location to improve the overall search capability. This is expressed as the following equation:

[0050]

[0051] Where, X rand is a randomly selected whale position from the current population.

[0052] Furthermore, in the random prey search phase, when the condition |A|≤1 is met, the prey encirclement and bubble net attack phases are executed; when the condition |A|>1 is met, the whale will move away from the target prey and randomly select the position of an individual as a reference to update the next position. This phase is equivalent to the exploration phase.

[0053] Furthermore, the parameters of the whale optimization algorithm include the number of training iterations, minimum error, learning rate, minimum performance gradient, maximum failure count, initial population size, maximum evolutionary generations and other parameters.

[0054] Beneficial effects of the present invention:

[0055] (1) The present invention realizes a sensorless control method for a bearingless synchronous reluctance motor through the powerful data processing and timing prediction capabilities of the Elman neural network of the whale optimization algorithm, and can simultaneously realize two sensorless control methods of the motor: speedless and displacementless.

[0056] (2) The present invention does not require the addition of additional equipment. It only needs to extract and process the voltage and current signals of the motor itself to quickly and accurately estimate the angle and position information of the rotor. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 Flowchart of the sensorless control method for bearingless synchronous reluctance motor based on the improved Elman neural network based on the whale optimization algorithm;

[0058] Figure 2 It is the structural diagram of the Elman neural network;

[0059] Figure 3 Flowchart of the algorithm for whale optimization;

[0060] Figure 4 This is the sensorless control block diagram of the bearingless synchronous reluctance motor;

[0061] Figure 5 A diagram showing the actual angular velocity and predicted angular velocity of the bearingless synchronous reluctance motor provided by the present invention;

[0062] Figure 6 (a) is a diagram of the actual rotor displacement of the bearingless synchronous reluctance motor provided by the present invention;

[0063] Figure 6 (b) is a diagram showing the predicted rotor displacement of the bearingless synchronous reluctance motor provided by the present invention. DETAILED DESCRIPTION

[0064] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0065] A sensorless control method based on the improved Elman neural network using the whale optimization algorithm is implemented in the following steps:

[0066] Step 1: Analyze the voltage equation, torque equation, dynamic suspension equation, and motion equation of the bearingless synchronous reluctance motor to determine the relationship between the motor angular velocity and rotor displacement and the motor voltage and current, respectively.

[0067] Step 1-1, the motor angular velocity involves the motor's voltage equation, torque equation, and motion equation.

[0068] Among them, the voltage equation of the bearingless synchronous reluctance motor is:

[0069]

[0070] In the formula, u d and u q The torque winding is the d-axis and q-axis stator voltage components, R s is the resistance of each phase of the torque winding, i d and i q are the stator current components on the d-axis and q-axis of the torque winding, L d and L q are the d-axis and q-axis inductances of the torque winding, ω is the angular velocity of the motor, and t is time.

[0071] The torque equation of a bearingless synchronous reluctance motor is:

[0072]

[0073] Where, T e is the electromagnetic torque of the motor, P M Number of pole pairs of the torque winding.

[0074] The equation of motion for a bearingless synchronous reluctance motor is:

[0075]

[0076] Where J is the moment of inertia of the rotor, T L is the load torque of the motor.

[0077] Discretizing formula (1), we can get the following formula:

[0078]

[0079] Where, T s is the sampling period, t+1 is the time t+1, and t is the time t.

[0080] Combining equations (2) and (3) and discretizing them, we get equation (5):

[0081]

[0082] We assume that f(*) is a function related to angular velocity; then, we can rewrite Equation (5) as:

[0083] ω(t+1)=f[i d (t),i q (t),u d (t),u q (t)](6)

[0084] Therefore, when the stator current i at the current moment is known d and i q , voltage u d and u q When the angular velocity ω at the next moment is calculated, it is possible to calculate the angular velocity ω at the next moment. It should be emphasized that the present invention does not need to actually calculate these variables, but to find the relationship between these variables. For example, here, the angular velocity ω is related to the current i d 、i q , voltage u d 、u q The excellent generalization ability and ability to handle nonlinear relationships of neural networks can be used to train these variables, ultimately forming a speed sensorless module.

[0085] In steps 1-2, the displacement of the motor is related to the dynamic suspension equation of the motor.

[0086] The rotor of a bearingless synchronous reluctance motor will produce relative displacement, so the gap between the stator and the rotor will also change. The length of the air gap can be expressed by the following formula:

[0087] δ(θ)=δ0-Δδ=δ0-xcosθ-ysinθ(7)

[0088] Where δ0 is the single-sided air gap length before eccentricity, Δδ is the air gap change, θ is the angle between the eccentricity and the axis, and x and y are the displacement components of the rotor on the x-axis and y-axis, respectively.

[0089] The dynamic suspension equation of the bearingless synchronous reluctance motor rotor is:

[0090]

[0091] Where, F x and F yDenote the controllable radial suspension force in the x-axis and y-axis directions, F sx and F sy They represent the Maxwell forces acting on the rotor in the x-axis and y-axis directions, F x0 and F y0 They represent the radial disturbance forces exerted on the rotor in the x-axis and y-axis directions, respectively, and F y0 Including the weight of the rotor mg.

[0092] F x and F y It can be expressed by the following formula:

[0093]

[0094] Where M0 and M1 represent the mutual inductance of the two windings, r is the rotor radius, l is the rotor axial length, μ0 = 4π × 10 -7 is the vacuum permeability, ρ is the pole arc width parameter, K is the fundamental wave value, which is 4 / π times the full-pitch wave value, N4 and N2 are the effective turns per pole and per phase of the torque winding and suspension winding respectively. The a phase of both windings is aligned with the x-axis, and its spatial distribution follows a sine function, i x and i y are the current components on the d-axis and q-axis of the suspension winding respectively.

[0095] Here the motor pole arc width is π / 6, so ρ = π / 12. Then the above equation (5) can be changed to:

[0096]

[0097] The Maxwell force acting on the rotor can be expressed by the following equation:

[0098]

[0099] Where k is the proportional coefficient related to the motor structure, k m It represents the stiffness of the suspension force displacement, which is related to the inherent structure of the motor, air gap flux density, core length, air gap length and other parameters. Here, based on empirical estimation, k m =351N / mm.

[0100] Substituting equations (9), (10), and (11) into equation (8) and performing discretization, we can obtain the following equation:

[0101]

[0102] Assuming that g(*) is a function related to displacement, equation (12) can be rewritten as:

[0103]

[0104] Therefore, when the stator current i of the torque winding at the current moment is known d and i q , the stator current i of the suspension winding x and i y When the displacement x and y at the next moment can be calculated. It should be emphasized that the present invention does not need to actually calculate these variables, but to find the relationship between these variables. For example, here, the displacement x and y are related to the current i d 、i q 、i x 、i y The excellent generalization ability and ability to handle nonlinear relationships of neural networks can be used to train these variables, ultimately forming a displacement-free sensor module.

[0105] Step 2: Collect the voltage of the motor torque winding, the current of the torque winding and the suspension winding, the rotor angular velocity, the rotor displacement and other physical quantities under different states, and form a neural network data set with these data. Divide them into training set and test set according to the proportion, and build an Elman neural network model. Set the number of nodes in the input layer u(k), the number of nodes in the output layer h(k), and the number of nodes in the receiving layer q c The number of nodes in the hidden layer is q(k), and the number of nodes in the hidden layer is q(k). Its mathematical model can be expressed as follows:

[0106]

[0107] Where purelin(*) is the linear transfer function of the output neuron, tanh(*) is the hyperbolic tangent function of the hidden neuron, and ω1, ω2, and ω3 are 0.7, 0.15, and 0.15, respectively.

[0108] Step 3: Use the whale optimization algorithm to optimize the Elman neural network. The flow chart is as follows Figure 3 As shown, the specific process is as follows:

[0109] S1) Initialize the parameters of the whale optimization algorithm, including the number of training iterations, minimum error, learning rate, minimum performance gradient, maximum failure count, initial population size, maximum evolutionary generations, etc.

[0110] S2) Execute the whale hunting strategy, which consists of three stages: surrounding the prey, attacking with a bubble net, and randomly searching for prey. The details of each stage are as follows:

[0111] S21) Prey Surrounding Phase. The most promising individual in the existing pod is designated as the hypothetical target prey location. The remaining individuals in the pod then adjust their positions based on the location of the determined best candidate. This updating process is expressed as follows:

[0112]

[0113] Where D is the distance between the whale and the prey, X is the position, X* is the position of the optimal solution obtained so far, j is the current iteration number, and A and C are adjustment coefficients, which can be expressed as follows:

[0114]

[0115] Where a is the convergence factor, which decreases linearly from 2 to 0 during the iteration process, and r1 is a random number in [0,1].

[0116] S22) Bubble Net Attack Phase. At this point, the position and distance between the whale and the target prey are first calculated, and based on this information, the whale's most likely next move is determined. The mathematical expression for this is as follows:

[0117]

[0118] Where b is a constant that defines the shape of the logarithmic spiral, and l1 is a random number between -1 and 1.

[0119] S23) Random Prey Search Phase. Each individual in the whale group can randomly search for prey based on its own position to improve global search capabilities. In the algorithm, this is represented by the following: when the condition |A| ≤ 1 is met, the prey encirclement and bubble net attack phases are executed; when the condition |A| > 1 is met, the whale will move away from the target prey and use the position of a randomly selected individual as a reference to update the next position. This phase is equivalent to the exploration phase. This process can be expressed by the following equation:

[0120]

[0121] Where, X rand is a randomly selected whale position from the current population.

[0122] S3) Use the whale optimization algorithm to iteratively adjust the weights and thresholds of the Elman neural network. Repeat this process until the weights and thresholds meet the specified tolerance range. At this point, terminate the loop and proceed to the next step.

[0123] Step 4: Update the network weights and thresholds according to the values provided by the algorithm, output the optimal parameters and training set, and obtain the optimized model.

[0124] Step 5, such as Figure 4 As shown in the figure, the trained network model is added to the control system of the bearingless synchronous reluctance motor, thereby establishing a bearingless synchronous reluctance motor sensorless control system based on the improved Elman neural network with the whale optimization algorithm, and realizing the sensorless control of the bearingless synchronous reluctance motor.

[0125] Example 1: Speed sensorless control of a bearingless synchronous reluctance motor.

[0126] 1) Analyzing the voltage, torque, and motion equations of the bearingless synchronous reluctance motor, Equation (6) shows that the motor's angular velocity is strongly correlated with the motor's voltage and current. These physical quantities can be used as data sets for the neural network.

[0127] 2) Collect 500 sets of three-phase voltages and currents of the torque winding and suspension winding of the bearingless synchronous reluctance motor at different times, and perform Clark and Park coordinate transformation to obtain the vector u1(k)=[i d i q u d u q ] T The rotor displacement at the corresponding moment is collected to obtain the vector h1(k) = [ω]. The data is randomly divided into a training set and a test set in a ratio of 4:1. It should be noted that the sample size and the division ratio can be adjusted according to actual conditions, and different sample sizes and division ratios are also within the scope of protection of the present invention.

[0128] 3) If Figure 2 This is the block diagram of the Elman neural network. The input layer is the vector u1(k), and the output layer is the vector h1(k). A method called a "greedy algorithm" is typically used to select hidden and connecting layers. This method repeatedly tries different numbers of nodes to find the one that strikes the best balance between training error and complexity.

[0129] 4) Initialize the parameters of the whale optimization algorithm, including the number of training iterations 1000, the minimum error 10 -6 , learning rate 0.01, minimum performance gradient 10 -6 , maximum fault count 10, initial population size 30, maximum evolutionary generations 50, and other parameters. Step 3 is performed until the weights and thresholds meet the specified tolerance range, terminating the optimization process. It should be noted that the above parameters can be adjusted based on actual needs, and different setting parameters are also within the scope of protection of the present invention.

[0130] 5) Execute steps 4 to 5 to obtain the optimized training set and model, which are used as the speed sensorless control module of the bearingless synchronous reluctance motor.

[0131] 6) If Figure 4 As shown in the lower part, the present invention provides a speed sensorless control method for a bearingless synchronous reluctance motor. When the motor is actually running, the sensor collects the three-phase voltage and current signals of the torque winding, and obtains the vector [i d i q ud u q ] T , imported into the speed sensorless control module, the angular velocity ω is output, and it is used as the negative feedback control quantity of the speed outer loop to compare with the given angular velocity. The error signal obtained is input into the PI regulator to achieve closed-loop control.

[0132] In summary, the speed sensorless control of the bearing synchronous reluctance motor of the present invention can be achieved.

[0133] The present invention is further described below through specific experiments.

[0134] Analysis of experimental results: In order to verify the accuracy and feasibility of the method proposed in the present invention, a sensorless control method suitable for bearingless synchronous reluctance motors, the sensorless control method proposed in the present invention was compared with the traditional sensor control method under the same working conditions.

[0135] Figure 5 The figure shows a comparison of the angular velocity predicted by the proposed method and the angular velocity measured by the velocity sensor. It can be seen from the figure that the two waveforms of the present invention are very consistent with those of the traditional sensor control, and the error is small, which meets the requirements of the actual operation of the motor.

[0136] Example 2: Sensorless control of a bearingless synchronous reluctance motor.

[0137] 1) Analyzing the voltage equation, dynamic suspension equation, and motion equation of the bearingless synchronous reluctance motor, Equation (13) shows that the motor's rotor displacement is strongly correlated with the motor's voltage and current. These physical quantities can be used as data sets for the neural network.

[0138] 2) Collect 500 sets of three-phase currents of the torque winding and suspension winding of the bearingless synchronous reluctance motor at different times, and perform Clark and Park coordinate transformation to obtain the vector u2(k)=[i d i q i x i y ] T ; Collect the rotor displacement at the corresponding moment and obtain the vector h2(k)=[xy] T The data were randomly divided into training set and test set in a ratio of 4:1. It should be noted that the sample size and the division ratio can be adjusted according to actual conditions, and different sample sizes and division ratios also fall within the scope of protection of the present invention.

[0139] 3) If Figure 2This is the block diagram of the Elman neural network. The input layer is the vector u2(k), and the output layer is the vector h2(k). A method called a "greedy algorithm" is typically used to select hidden and connecting layers. This method repeatedly tries different numbers of nodes to find the one that strikes the best balance between training error and complexity.

[0140] 4) Initialize the parameters of the whale optimization algorithm, including the number of training iterations 1000, the minimum error 10 -6 , learning rate 0.01, minimum performance gradient 10 -6 , maximum fault count 10, initial population size 30, maximum evolutionary generations 50, and other parameters. Step 3 is performed until the weights and thresholds meet the specified tolerance range, terminating the optimization process. It should be noted that the above parameters can be adjusted based on actual needs, and different setting parameters are also within the scope of protection of the present invention.

[0141] 5) Execute steps 4 to 5 to obtain the optimized training set and model, which are used as the control module of the bearingless synchronous reluctance motor without displacement sensor.

[0142] 6) If Figure 4 As shown in the upper part, the present invention provides a control method for a bearingless synchronous reluctance motor without displacement sensor. When the motor is actually running, the sensor collects the three-phase current signals of the two sets of windings and obtains the current vector [i d i q u d u q ] T , imported into the displacement sensorless control module, and output the displacement vector [xy] T , and use this as the negative feedback control quantity of the displacement to compare with the given displacement, and the obtained error signal is input into the PID regulator to achieve closed-loop control.

[0143] In summary, the displacement sensorless control of the bearing synchronous reluctance motor of the present invention can be achieved.

[0144] The present invention is further described below through specific experiments.

[0145] Analysis of experimental results: In order to verify the accuracy and feasibility of the method proposed in the present invention, a sensorless control method suitable for bearingless synchronous reluctance motors, the sensorless control method proposed in the present invention was compared with the traditional sensor control method under the same working conditions.

[0146] Figure 6 The displacement comparison diagram of the proposed method and the displacement measured by the displacement sensor is shown in the figure. Figure 6 (a) is the displacement waveform measured by the displacement sensor. Figure 6 Figure (b) shows the rotor displacement predicted by the sensorless control method for a bearingless synchronous reluctance motor proposed in this invention. As can be seen, the waveforms from this sensorless control method closely match those from traditional sensored control, with minimal error, meeting the requirements for actual motor operation.

[0147] In summary, this invention discloses a sensorless control method for bearingless synchronous reluctance motors. This method requires no additional equipment and simply extracts and processes the motor's own voltage and current signals to quickly and accurately estimate the rotor's angle and position. Furthermore, the invention simultaneously implements both speed- and displacement-free sensorless control methods, providing a strong guarantee for the reliable operation of bearingless synchronous reluctance motors.

[0148] Throughout this specification, reference to terms such as "one example," "some examples," "illustrative examples," "example," "specific example," or "some examples" means that the specific features or characteristics described in conjunction with that example or example are included in at least one example or example of the present invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same example or example. Furthermore, the specific features or characteristics described may be combined in any suitable manner in any one or more examples or examples.

[0149] The above embodiments are intended only to illustrate the design concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. The scope of protection of the present invention is not limited to the above embodiments. Therefore, any equivalent changes or modifications made based on the principles and design concepts disclosed in the present invention are within the scope of protection of the present invention.

Claims

1. A sensorless control method for a bearingless synchronous reluctance motor based on a WOA-Elman neural network, characterized in that: The steps include: Step 1, constructing a mathematical model of a bearingless synchronous reluctance motor; Step 2: Based on the mathematical model, collect the motor torque winding data under different states to form a neural network data set; and build an Elman neural network model; Step 3: Use the whale optimization algorithm to optimize the Elman neural network and adjust the weights and thresholds of the Elman neural network; Step 4: Based on the updated network weights and thresholds, the optimal parameters and training set are output to obtain the optimized model; Step 5: Add the trained network model to the control system of the bearingless synchronous reluctance motor, thereby establishing a bearingless synchronous reluctance motor sensorless control system based on the optimized Elman neural network sensorless control method to achieve sensorless control of the bearingless synchronous reluctance motor.

2. The sensorless control method for a bearingless synchronous reluctance motor based on a WOA-Elman neural network according to claim 1, characterized in that: The sensorless control of bearingless synchronous reluctance motor includes speed sensorless control and displacement sensorless control.

3. The sensorless control method for a bearingless synchronous reluctance motor based on a WOA-Elman neural network according to claim 1, characterized in that: The motor torque winding data includes voltage, current of torque winding and suspension winding, rotor angular velocity and rotor displacement data.

4. The sensorless control method for a bearingless synchronous reluctance motor based on a WOA-Elman neural network according to claim 1, characterized in that: The mathematical model of the bearingless synchronous reluctance motor includes a voltage equation, a torque equation, a dynamic suspension equation and a motion equation to determine the relationship between the motor angular velocity and rotor displacement and the motor voltage and current respectively.

5. The sensorless control method for a bearingless synchronous reluctance motor based on a WOA-Elman neural network according to claim 4 is characterized in that: The voltage equation, torque equation, and motion equation of the motor are expressed as follows: The voltage equation for a bearingless synchronous reluctance motor is: Where u d and u q The torque winding is the d-axis and q-axis stator voltage components, R s is the resistance of each phase of the torque winding, i d and i q are the stator current components on the d-axis and q-axis of the torque winding, L d and L q are the d-axis and q-axis inductances of the torque winding, respectively, and ω is the angular velocity of the motor; The torque equation of a bearingless synchronous reluctance motor is: Where, T e is the electromagnetic torque of the motor, P M Number of pole pairs of the torque winding; The equation of motion for a bearingless synchronous reluctance motor is: Where J is the moment of inertia of the rotor, T L is the load torque of the motor.

6. The sensorless control method for a bearingless synchronous reluctance motor based on a WOA-Elman neural network according to claim 4, characterized in that: The dynamic suspension equation of the motor is expressed as follows: The length of the air gap is expressed as follows: δ(θ)=δ0-Δδ=δ0-xcosθ-ysinθ Where δ0 is the single-sided air gap length before eccentricity, θ is the angle between the eccentricity and the axis, and x and y are the displacement components of the rotor on the x-axis and y-axis respectively; The dynamic suspension equation of the bearingless synchronous reluctance motor rotor is: Where, F x and F y Denote the controllable radial suspension force in the x-axis and y-axis directions, F sx and F sy They represent the Maxwell forces acting on the rotor in the x-axis and y-axis directions, F x0 and F y0 They represent the radial disturbance forces exerted on the rotor in the x-axis and y-axis directions, respectively, and F y0 Including the weight of the rotor mg.

7. The sensorless control method for a bearingless synchronous reluctance motor based on a WOA-Elman neural network according to claim 1, characterized in that: The Elman neural network model: set the number of nodes in the input layer u(k), the number of nodes in the output layer h(k), and the number of nodes in the receiving layer q c The number of nodes in the hidden layer q(k) is expressed as follows: Where purelin(*) is the linear transfer function of the output neuron, tanh(*) is the hyperbolic tangent function of the hidden neuron, and ω1, ω2, and ω3 are 0.7, 0.15, and 0.15, respectively.

8. The sensorless control method for a bearingless synchronous reluctance motor based on a WOA-Elman neural network according to claim 1, characterized in that: The process of optimizing the Elman neural network using the whale optimization algorithm in step 3 is as follows: S1) Initialize the parameters of the whale optimization algorithm; S2) execute the whale hunting strategy, S3) Using the whale optimization algorithm to continuously iterate and adjust the weights and thresholds of the Elman neural network; repeating this process until the weights and thresholds meet the specified tolerance range; Terminate the loop at this point and proceed to the next step.

9. The sensorless control method for a bearingless synchronous reluctance motor based on a WOA-Elman neural network according to claim 8, characterized in that: The whale's hunting strategy consists of three stages: surrounding prey, attacking with a bubble net, and randomly searching for prey. The details of each stage are as follows: S21) In the prey encirclement phase, the most promising individual in the existing whale group is designated as the assumed target prey location; then, the remaining individuals in the whale group adjust their positions according to the position of the determined best candidate individual; the updating process is expressed as follows: Where D is the distance between the whale and the prey, X is the position, X* is the position of the optimal solution currently obtained, j is the current iteration number, and A and C are adjustment coefficients, which can be expressed as follows: Where a is the convergence factor, which decreases linearly from 2 to 0 during the iteration process, and r1 is a random number in [0,1]. S22) Bubble net attack phase: At this time, the position and distance between the whale and the target prey are first calculated, and the whale's most likely next action is given based on this information; the mathematical expression is as follows: Where b is a constant that defines the shape of the logarithmic spiral, and l1 is a random number between -1 and 1; S23) Random search for prey: Each individual in the whale group randomly searches for prey based on its own location to improve the overall search capability. This is expressed as the following equation: Where, X rand is a randomly selected whale position from the current population.

10. The sensorless control method for a bearingless synchronous reluctance motor based on a WOA-Elman neural network according to claim 9, characterized in that: In the random prey search phase, when the |A|≤1 condition is met, the prey encirclement and bubble net attack phase is executed; when the |A|>1 condition is met, the whale will move away from the target prey and randomly select the position of an individual as a reference to update the next position. This phase is equivalent to the exploration phase.

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