Magnetic suspension bearing controller construction method based on feature dominant control

Abstract

In the field of magnetic suspension bearing control, the invention provides a magnetic suspension bearing controller construction method based on feature dominant control, and the method comprises the steps: constructing a magnetic suspension bearing mathematical model; mathematical models of the displacement sensor and the power amplifier are constructed; carrying out kinematic mechanics analysis on the magnetic suspension bearing; a PID controller is constructed; constructing an improved PINN neural network; constructing a model prediction controller based on reinforcement learning; constructing a leading controller; factor coefficient selection and adjustment of the three control algorithms are based on a mathematical model between a stator and rotor gap and electromagnetic force in the five-degree-of-freedom hybrid magnetic suspension bearing and kinematic mechanics characteristics of a magnetic suspension rotor. The magnetic suspension bearing is stabilized and corrected by means of a feature leading controller composed of a PID controller, a PINN neural network controller and a model prediction controller based on reinforcement learning, and a more accurate and stable control effect can be achieved.

Description

Technical Field

[0001] The invention relates to the technical field of magnetic suspension bearing control, and in particular to a method for constructing a magnetic suspension bearing controller based on feature-dominant control. Background Art

[0002] With the rapid development in the fields of aerospace, transportation, machinery manufacturing, medical equipment, etc., rotating mechanical equipment is developing towards high speed, intelligence, high precision, etc., and the performance of the support unit is crucial, which directly determines the reliability of the equipment and the stability of long-term operation. Traditional mechanical bearings will inevitably produce mechanical wear, low heat dissipation efficiency, lubricating oil pollution and other problems that deteriorate the performance of mechanical bearings, and high-precision and high-stability magnetic bearing systems are increasingly used in various high-end mechanical equipment, such as high-speed rotating machinery and precision measuring equipment. The control technology of magnetic bearings is one of the key technologies to ensure the efficient operation of these systems. Although traditional control methods such as PID control perform well in many industrial applications, they have certain limitations in dealing with nonlinear systems and parameter uncertainties.

[0003] In actual industrial production, it is difficult to establish an accurate mathematical model of magnetic bearings due to the small suspension gap, nonlinearity, and severe coupling of magnetic bearing systems. In addition, it is difficult to control open-loop unstable systems. Therefore, although there has been some progress in the research on magnetic suspension control in recent years, it still cannot meet the needs of large-scale engineering applications. In addition, most studies are aimed at rigid rotors or rotors that are in a stable state after crossing the order. When the rotor crosses the critical speed, the vibration amplitude and phase of the rotor will change dramatically, the unbalanced state of the rotor will change, and existing algorithms such as adaptive iterative algorithms and influence coefficient methods may fail. Model predictive control can enhance the adaptability and robustness of unbalanced vibration control algorithms. In the face of extreme working conditions and severe environmental interference, the control performance may still be reduced due to the inability of model parameters to adapt to these changes. Physical information neural network (PINN) is an emerging technology that combines traditional neural networks with physical models. By introducing physical laws as additional constraints during the training process, it can improve the prediction accuracy and generalization ability of the model. Although existing PINN applications have shown potential in some fields, their research on magnetic bearing control is still insufficient, especially in the real-time adjustment of PID control parameters when the system dynamics change rapidly. There is a lack of effective solution strategies, and the high performance and stability of the system are difficult to guarantee under various complex working conditions. Summary of the invention

[0004] In order to solve the above problems, the present invention provides a method for constructing a magnetic bearing controller based on feature-dominant control. This method realizes non-contact detection through displacement sensors and power amplifiers, and obtains the nonlinear differential equation of the magnetic bearing by combining the mechanism modeling of magnetic suspension, and then converts it into the Laplace equation. Then, the differential control model of the magnetic bearing is obtained by combining the mathematical models of the displacement sensor and the power amplifier. The rotor of the magnetic bearing is subjected to a kinematic analysis, and the motion stage is divided into three stages: starting, deceleration and fluctuation. A feature-dominant controller integrated by a PID controller, a PINN neural network controller and a model predictive controller based on reinforcement learning is constructed and trained. The magnetic bearing rotor matches a suitable dominant controller in different motion stages. The PID controller based on the PINN neural network dominates the starting stage, the model predictive control based on reinforcement learning dominates the deceleration stage, and the PID controller dominates the fluctuation stage. Different dominant control strategies are formed by online adjustment of the factor coefficients of the three control algorithms to maintain the stability of the magnetic bearing. Specifically including:

[0005] A method for constructing a magnetic bearing controller based on feature-dominant control, comprising:

[0006] According to the principle of magnetic suspension, Ampere's circuit theorem of magnetic circuit, Newton's law and the static mathematical relationship of the internal components of magnetic suspension bearing, the differential equation of magnetic suspension bearing is established;

[0007] Establishing a displacement sensor mathematical model and a power amplifier mathematical model, and converting the differential equation of the magnetic bearing into a Laplace model to obtain a magnetic bearing differential control model;

[0008] According to the static mathematical relationship of the internal components of the magnetic bearing, a kinematics analysis of the magnetic bearing from acceleration start-up, deceleration to stable operation is performed to obtain a kinematics model, which includes a magnetic bearing startup stage, a magnetic bearing deceleration stage and a magnetic bearing fluctuation stage;

[0009] Constructing an incremental PID control module according to the magnetic bearing differential control model and the kinematics model;

[0010] Based on the incremental PID control module, a PINN neural network module is constructed and trained;

[0011] Based on the magnetic bearing differential control model and the kinematic model, the Hildreth quadratic programming method is used to constrain the control input current to obtain a constrained MPC controller for carrying and transporting, wherein the MPC controller is based on the classical reinforcement learning algorithm Q-Learning to adjust the prediction time domain and control time domain of the MPC controller in real time;

[0012] Integrate the incremental PID control module, the PINN neural network module and the MPC controller into a feature-dominant controller, and select factor coefficients for the incremental PID control module, the PINN neural network module and the MPC controller respectively;

[0013] The factor coefficients of the incremental PID control module, the factor coefficients of the PINN neural network module and the factor coefficients of the MPC controller are adjusted respectively to complete the dominant control of the incremental PID control module, the PINN neural network module and the MPC controller.

[0014] Optionally, establishing the differential equation of the magnetic suspension bearing according to the magnetic suspension principle, Ampere's circuit theorem of the magnetic circuit, Newton's law and the static mathematical relationship of the internal components of the magnetic suspension bearing comprises:

[0015] The relationship between the current, force and displacement of the electromagnet is established as formula (1):

[0016]

[0017] Where F is the total attraction between the stator and rotor, μ0 is the magnetic permeability of air, k is the electromagnetic force coefficient, x is the displacement of the rotor in the magnetic bearing, N is the number of turns of the electromagnet coil, A is the cross-sectional area of ​​the stator, rotor and air gap magnetic field path, and i is the coil winding current;

[0018] The force balance method of the rotor is established as formula (2):

[0019]

[0020] Among them, F x is the sum of the electromagnetic forces generated in the x-axis direction, m is the mass of the rotor, p(t) is the external interference force, and g is the gravitational acceleration;

[0021] According to the relationship between the current, force and displacement of the electromagnet, we get F x The expression for the sum of the electromagnetic forces generated in the x-axis direction is formula (3):

[0022]

[0023] Among them, F x1 is the electromagnetic force generated by the upper electromagnet, F x2 is the electromagnetic force generated by the electromagnet below, i0 is the bias current, i x To control the current, x0 is the air gap length at the rotor equilibrium point;

[0024] Based on formula (2) and formula (3), we get formula (4):

[0025]

[0026] The Taylor expansion of the binary function is performed near the working point of the rotor and the high-order infinitesimals are neglected to obtain formula (5):

[0027] F x =k i i x +k x ; (5)

[0028] Among them, k x is the displacement stiffness of the magnetic bearing, k i is the current stiffness of the magnetic bearing,

[0029] Based on formula (4) and formula (5), the differential equation of the magnetic bearing is obtained as formula (6):

[0030]

[0031] Optionally, establishing a displacement sensor mathematical model, a power amplifier mathematical model, and converting the differential equation of the magnetic bearing into a Laplace model to obtain a magnetic bearing differential control model includes:

[0032] The differential equation of the magnetic bearing is transformed based on the Laplace model to obtain a differential control model of the magnetic bearing. The differential control model of the magnetic bearing is formula (7):

[0033]

[0034] Wherein, G(x) is the transfer function of the magnetic bearing in the x-axis direction, X(s) is the output of the magnetic bearing in the x-axis direction, I(s) is the input of the magnetic bearing in the x-axis direction, and s is the complex variable of the magnetic bearing system;

[0035] The mathematical model of the displacement sensor is formula (8):

[0036]

[0037] Among them, G f (s) is the transfer function of the displacement sensor, k s is the gain of the displacement sensor, T s is the hysteresis time constant of the displacement sensor;

[0038] The mathematical model of the power amplifier is formula (9):

[0039]

[0040] Among them, Ga (s) is the transfer function of the power amplifier, k a is the gain of the power amplifier, T a is the power amplifier hysteresis time constant.

[0041] Optionally, constructing an incremental PID control module according to the magnetic bearing differential control model and the kinematics model includes:

[0042] The control algorithm of the incremental PID control module is formula (10):

[0043]

[0044] Wherein, Δe(k)=e(k)-e(k-1), k is the sampling number, u(k) is the output value of the PID control module at the kth sampling time, e(k) is the deviation value of the input of the PID control module at the kth sampling time, e(k-1) is the deviation value of the input at the k-1th sampling time, K l is the integration coefficient, K I =K p T / T I , K D is the differential coefficient, K D =K P T D / T,K P is the proportionality coefficient, T D is the differential time, T is the sampling time, T I is the integration time.

[0045] Optionally, constructing and training a PINN neural network module based on the incremental PID control module includes:

[0046] Based on the partial differential equation in the incremental PID control module to describe the physical process, the original function T (0) The two-dimensional partial differential equation g(T) of (x, y, θ) is formula (11):

[0047] g(T):f[T (n) (x,y,θ)]+C=0; (11)

[0048] Among them, T (n) (x,y,θ) is T (0) The nth-order derivative of (x, y, θ), n = {0, 1, 2}, C is a constant, (x, y, θ) is the input parameter of the neural network, x and y are coordinates, and θ is a parameter;

[0049] The deviation modulus between g(t0) and g(T) is used as the loss function, and the gradient descent algorithm is used to adjust the weight w and bias b of the neural network so that g(t0) approaches g(T), and t(x, y, θ) approaches T. (0) (x, y, θ), g(t0) is the partial differential equation obtained after calculating the gradient of the initial neural network, and t(x, y, θ) is the final model of the neural network;

[0050] The t(x, y, θ) obtained after multiple iterations of training is the proxy model of the PINN neural network;

[0051] Among them, neurons are connected by full connection, and the output of neurons in each layer As the next layer of neurons The input of the neuron is expressed as formula (12):

[0052]

[0053] The superscript l represents the layer number of the neural network, and the subscripts i and j represent the neuron index. is the weight from the i-th neuron in the l-1th layer to the j-th neuron in the lth layer, is the bias from the i-th neuron in the l-1th layer to the j-th neuron in the lth layer, a=σ(z) is the activation function,

[0054] The last layer is the Lth layer, which is the output layer. The formula of the output fitting function is formula (15):

[0055] t(x,y,θ)=a L (x,y,θ;w,b; (15).

[0056] Optionally, when the activation function is a hyperbolic tangent function, the formula of the activation function is formula (13):

[0057]

[0058] When the activation function is a sigmoid function, the formula of the activation function is formula (14):

[0059]

[0060] Optionally, based on the magnetic bearing differential control model and the kinematic model, the Hildreth quadratic programming method is used to constrain the control input current to obtain a constrained MPC controller for carrying and transporting, wherein the MPC controller is based on the classical reinforcement learning algorithm Q-Learning to adjust the prediction time domain and control time domain of the MPC controller in real time, including:

[0061] Set the prediction time domain N p and control time domain N c ,The cost function is constructed using quadratic programming, and the cost function is constructed using quadratic programming, which is formula (16):

[0062]

[0063] l is the loss function, R is the reference output signal, To control the input weight, Δu is the change in the input, y is the output vector, and u is the input vector;

[0064] The update expression of the Q table for one round of training is formula (17):

[0065] Q π (s,a)=Q(s,a)+α[R d +ηQ π (s next,； )-Q(s,a)]; (17)

[0066] Among them, Q π (s,a) is the benefit of executing the action strategy π(s,a) in the current state s; Q(s,a) is the benefit of executing the action strategy π(s,a) in the state s before the update; α is the learning rate; R d is the immediate reward obtained by executing the action strategy π(s, a); η is the discount factor, Q π (s next,； ) is to execute the action strategy π(s, a) to reach the next state s next The total revenue of , s is the environment state, and a is the strategy selection action.

[0067] Optionally, the incremental PID control module, the PINN neural network module and the MPC controller are integrated into a feature-dominant controller, and factor coefficients are selected for the incremental PID control module, the PINN neural network module and the MPC controller, respectively, including:

[0068] The incremental PID control module, the PINN neural network module and the MPC controller respectively select factor coefficients in the range of 0 to 1, and the sum of the factors is 1.

[0069] Compared with the prior art, the above technical solution has at least the following beneficial effects:

[0070] (1) Using intelligent algorithms and experimental data, mathematical models of the magnetic bearing control current and bias current, rotor balance point air gap length and rotor displacement, displacement sensor and power amplifier, and the dynamic mechanics model of the magnetic bearing rotor are constructed. Feature-dominant control is selected. Through feature-dominant control consisting of PID control, PINN neural network control and reinforcement learning-based model predictive control, the dynamic behavior of the magnetic bearing is more accurately predicted, thereby achieving more precise control. The online adjustment of the three controller factor coefficients forms different feature-dominant control strategies, which enables the control system to predict the future state according to the motion characteristics of the rotor at different stages to adapt to complex operating conditions and environmental changes, thereby improving the overall stability and response speed of the system.

[0071] (2) Traditional PID controllers may encounter performance bottlenecks when dealing with nonlinear systems, while the use of PINN in the present invention allows the controller to better adapt to those complex nonlinear dynamic changes by learning the physical and dynamic characteristics of the system, combined with a model that can adaptively adjust parameters according to the current system state to predict the overall controller. This enables the magnetic bearing to maintain stable operation over a wider operating range.

[0072] (3) The established mathematical model and control strategy can be applied to similar magnetic bearing products and different working conditions, which can improve the application range of the equipment and its ability to cope with different working conditions and avoid the high degree of uniformity of the equipment. The kinematic mechanics analysis of the magnetic bearing rotor is carried out, and the movement of the rotor from acceleration start-up, deceleration to stable operation is modeled. The characteristics of different stages are analyzed, and the three movement stages of magnetic bearing start-up, deceleration and fluctuation are constructed. It can avoid the overshoot phenomenon of the equipment and increase the service life of the bearing. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0074] Figure 1 It is a schematic diagram of the control structure of the magnetic suspension bearing used in the present invention;

[0075] Figure 2 It is a schematic diagram of the PINN neural network structure used in the present invention;

[0076] Figure 3 It is a PINN neural network control flow chart applied by the present invention;

[0077] Figure 4Schematic diagram of the structure of the Q-MPC controller used in the present invention;

[0078] Figure 5 It is a schematic diagram of the characteristic dominant control structure applied by the present invention;

[0079] Figure 6 It is a step diagram for the specific implementation of the present invention;

[0080] Figure 7 It is a control flow chart of the present invention. DETAILED DESCRIPTION

[0081] In order to make the purpose, technical solution and advantages of the embodiment of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings of the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0082] Unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, words such as "one", "one" or "the" do not indicate a quantitative limitation, but indicate the existence of at least one. Words such as "include" or "comprise" mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connect" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect.

[0083] It should be noted that the terms "up", "down", "left", "right", "front", "back", etc. used in the present invention are only used to indicate relative position relationships. When the absolute position of the object being described changes, the relative position relationship may also change accordingly.

[0084] The method of the present invention is to construct a mathematical model of the gap between the stator and the rotor in a five-degree-of-freedom hybrid magnetic suspension bearing, the current through the electromagnet and the electromagnetic force, then construct a mathematical model of the displacement sensor and the power amplifier, collect the gap data of the magnetic bearing, perform kinematics analysis on the magnetic suspension bearing, divide the rotor motion process into acceleration, deceleration and fluctuation stages based on experimental tests and theoretical derivations according to the different motion states of the rotor during the suspension control process, study the rotor motion behavior characteristics and control method selection in each stage, select feature-dominant control, introduce PID control, PINN neural network control and model predictive control based on reinforcement learning, match a suitable dominant controller according to the characteristics of the magnetic suspension bearing rotor in different motion stages, select factor coefficients for the three controllers, and form different feature-dominant control strategies by online adjusting the factor coefficients of the three control algorithms. The feature-dominant controller is used to stabilize and correct the magnetic suspension bearing to ensure its stable operation, and finally the rotor is dynamically suspended within the allowable range of the air gap. The invention comprises the following operations: 1) constructing a mathematical model of a magnetic suspension bearing; 2) constructing a mathematical model of a displacement sensor and a power amplifier; 3) analyzing the kinematics of a magnetic suspension bearing; 4) constructing a PID controller; 5) constructing an improved PINN neural network; 6) constructing a model predictive controller based on reinforcement learning; 7) constructing a dominant controller; 8) selecting and adjusting the factor coefficients of three control algorithms; The invention is based on the mathematical model between the stator-rotor gap and the electromagnetic force in a five-degree-of-freedom hybrid magnetic suspension bearing and the kinematics characteristics of a magnetic suspension rotor, and uses a feature-dominant controller composed of a PID controller, a PINN neural network controller and a model predictive controller based on reinforcement learning to stabilize and correct the magnetic suspension bearing, thereby achieving a more accurate and stable control effect. In addition, the feature-dominant controller of the invention exhibits significant advantages over the traditional PID controller in processing complex nonlinear systems and the start-stop and variable operating conditions of the system. The invention is suitable for magnetic suspension bearing systems requiring high precision and high stability, especially in industrial applications requiring high speed and high precision. It has been verified through experiments that the controller proposed in the invention can maintain good performance under various operating conditions, effectively improving the operating efficiency and reliability of the magnetic suspension bearing.

[0085] A method for constructing a magnetic bearing controller based on feature-dominated control. Figure 1 FIG. 1 is a schematic diagram of the PINN neural network structure used in the present invention. Figure 2As shown in the figure, when solving partial differential equations, the input x, y, and θ parameters are first converted into the form of neurons to generate an initial neural network. Then, the gradient of the neural network is calculated with the help of the automatic differentiation algorithm to obtain the partial differential equation and the residual and initial boundary value residual constraints of the partial differential equation, and put them into the loss function as regular terms. Finally, the weights w and b of the neural network are adjusted using the gradient descent algorithm, and the neural network is also made to approach the original physical equation. The neural network model obtained after multiple iterative training is the PINN proxy model of the physical equation.

[0086] A method for constructing a magnetic bearing controller based on feature-dominated control. Figure 2 FIG. 1 is a schematic diagram of the control structure of the present invention applied to a magnetic bearing. Figure 1 As shown in the figure, the magnetic bearing system achieves contactless suspension of the rotor through precise control of electromagnetic force. First, the controller receives the position information of the rotor and compares it with the preset reference position to calculate the necessary adjustment signal. This signal is sent to the power amplifier to enhance its strength, thereby driving the electromagnet. The electromagnet generates corresponding magnetic forces according to the adjusted current, which accurately adjust the position of the rotor to counteract gravity and other external forces and maintain the stable suspension of the rotor. The adjusted current dynamically adjusts the strength and direction of the magnetic field by increasing or decreasing, ensuring precise control of the rotor at the desired position and the overall stability of the system. Through this closed-loop feedback mechanism, the magnetic bearing can maintain high precision and high stability under various operating conditions, completing a continuous cycle from current regulation to precise suspension.

[0087] A method for constructing a magnetic bearing controller based on feature-dominated control. Figure 3 The PINN neural network control flow chart applied in the present invention. Based on the static mathematical relationship formed by the magnetic bearing stator, rotor, electromagnet and its winding, the differential equation between the magnetic bearing control current, bias current, rotor balance point air gap length and magnetic bearing rotor displacement is established through the mechanism modeling method. The PINN neural network weights are initialized, and the genetic algorithm optimization part is entered. The network training error is used as the fitness value. The optimal weight is obtained through selection, crossover, mutation and other process optimizations and applied to the PINN neural network. According to the sampled rotor displacement and control current data, the parameter setting value of the incremental PID controller is obtained through adjustment of the PINN neural network.

[0088] The specific plan is as follows:

[0089] A method for constructing a magnetic bearing controller based on feature-dominant control is proposed. A feature-dominant controller composed of a PID controller, a PINN neural network controller and a model predictive controller based on reinforcement learning (Q-MPC) is used to match a suitable dominant controller according to different motion stages of the magnetic bearing rotor. Factor coefficients are then selected for the three controllers, and the factor coefficients of the three control algorithms are adjusted online to form different feature-dominant control strategies for the stabilization of the magnetic bearing, including:

[0090] S1. According to the principle of magnetic suspension, Ampere's circuit theorem of magnetic circuit, Newton's law and the static mathematical relationship of the internal components of the magnetic suspension bearing, the differential equation of the magnetic suspension bearing is established;

[0091] Mathematical modeling of magnetic bearings: According to the working principle of magnetic levitation, Ampere's circuit theorem and Newton's laws of magnetic circuit, and based on the static mathematical relationship of the components of the magnetic bearing, the differential equation between the control current, bias current, air gap length of the rotor balance point and the rotor displacement of the magnetic bearing is established.

[0092] This step S1 mainly includes the following principles:

[0093] Regarding the mathematical model of the magnetic bearing, there are three factors that determine the motion of the hybrid magnetic bearing: first, the displacement x of the rotor in the magnetic bearing; second, the control current i that enters the electromagnet through the power amplifier. x , and the third is the external interference force p(t) on the magnetic bearing rotor.

[0094] The relationship between the current, force and displacement of the electromagnet is established as formula (1):

[0095]

[0096] Where F is the total attraction between the stator and rotor, μ0 is the magnetic permeability of air, k is the electromagnetic force coefficient, x is the displacement of the rotor in the magnetic bearing, N is the number of turns of the electromagnet coil, A is the cross-sectional area of ​​the stator, rotor and air gap magnetic field path, and i is the coil winding current;

[0097] Accordingly, the force balance mode of the rotor is established as formula (2):

[0098]

[0099] Among them, F x is the sum of the electromagnetic forces generated in the x-axis direction, m is the mass of the rotor, p(t) is the external interference force, and g is the gravitational acceleration;

[0100] According to the relationship between the current, force and displacement of the electromagnet, we get F xThe expression for the sum of the electromagnetic forces generated in the x-axis direction is formula (3):

[0101]

[0102] Among them, F x1 is the electromagnetic force generated by the upper electromagnet, F x2 is the electromagnetic force generated by the electromagnet below, i0 is the bias current, i x To control the current, x0 is the air gap length at the rotor equilibrium point;

[0103] Since the disturbance is very small in actual work, the external disturbance force p(t) is assumed to be 0.

[0104] Based on formula (2) and formula (3), we get formula (4):

[0105]

[0106] It can be seen that the mathematical model of the magnetic bearing is a nonlinear quadratic differential equation. However, nonlinear control has not been well solved either in theory or in practice, so formula (4) is linearized. x = 0 and ignoring the higher-order infinitesimals, we get formula (5):

[0107] F x =k i i x +k x ; (5)

[0108] Among them, k x is the displacement stiffness of the magnetic bearing, k i is the current stiffness of the magnetic bearing, Although the description accuracy of formula (5) becomes worse as the displacement x moves away from the equilibrium position, practical experience has shown that the controller designed using formula (5) is still suitable in a wide range;

[0109] Based on formula (4) and formula (5), the differential equation of the magnetic bearing is obtained as formula (6):

[0110]

[0111] S2. Establishing a displacement sensor mathematical model and a power amplifier mathematical model, and converting the differential equation of the magnetic bearing into a Laplace model to obtain a magnetic bearing differential control model;

[0112] Mathematical modeling of displacement sensor and power amplifier: The displacement sensor converts the change of displacement into the change of output voltage. The power amplifier converts the voltage signal output by the controller into the excitation current signal in the electromagnet of the magnetic bearing. The nonlinear differential equation established in S1 is converted into a Laplace model, and a differential control model of the magnetic bearing is established. Considering that both the displacement sensor and the power amplifier will have a certain phase delay, their models can be expressed as a first-order inertia link and Laplace transform is performed. Finally, the models are coupled to obtain the differential control model of the magnetic bearing, which is an unstable nonlinear model.

[0113] Specifically include the following:

[0114] By Laplace transformation of formula (6), we can get the x-axis of the magnetic bearing in a single direction: (s) The differential control model of the magnetic bearing is obtained by transforming the differential equation of the magnetic bearing based on the Laplace model. The differential control model of the magnetic bearing is expressed as formula (7):

[0115]

[0116] Wherein, G(s) is the transfer function of the magnetic bearing in the x-axis direction, X(s) is the output of the magnetic bearing in the x-axis direction, I(s) is the input of the magnetic bearing in the x-axis direction, and s is the complex variable of the magnetic bearing system;

[0117] The displacement sensor converts the change of displacement into the change of output voltage. The input and output can be regarded as a linear relationship in terms of numerical value. However, there will be a certain phase delay in this link, so its model can be expressed as a first-order inertia link. The mathematical model of the displacement sensor is formula (8):

[0118]

[0119] Among them, G f (s) is the transfer function of the displacement sensor, k s is the gain of the displacement sensor, T s is the hysteresis time constant of the displacement sensor; due to the actual sensor hysteresis time constant T s It is difficult to measure, and the bandwidth of the sensor is wide, so G in formula (7) f (s) can be approximated as k s .

[0120] The power amplifier converts the voltage signal output by the controller into the excitation current signal in the electromagnet of the magnetic bearing. Because there is a certain phase delay in the power amplifier circuit, the model of this link can also be expressed as a first-order inertia link. The mathematical model of the power amplifier is formula (9):

[0121]

[0122] Among them, G a (s) is the transfer function of the power amplifier, k a is the gain of the power amplifier, T a is the hysteresis time constant of the power amplifier. Since the power amplifier has a wide bandwidth, G in formula (9) a (s) can be approximated as k a By combining the above equations, we can obtain the approximate linear mathematical model between the magnetic bearing, displacement sensor and power amplifier.

[0123] S3. According to the static mathematical relationship of the internal components of the magnetic bearing, a kinematics analysis of the magnetic bearing from acceleration start-up, deceleration to stable operation is performed to obtain a kinematics model, wherein the kinematics model includes a magnetic bearing startup stage, a magnetic bearing deceleration stage, and a magnetic bearing fluctuation stage;

[0124] Based on the static mathematical relationship of the magnetic suspension bearing established in S1, the kinematic analysis of the magnetic suspension bearing from acceleration start-up, deceleration to stable operation is carried out, and the three motion stages of magnetic suspension bearing start-up, deceleration and fluctuation are constructed. The kinematic analysis of the magnetic suspension bearing is carried out, and the controller matching controller is selected for the three operation stages of the magnetic suspension bearing. Figure 1 As shown, when the magnetic bearing is not started, the rotor is located on the lower unpowered coil. When the magnetic bearing is started, the rotor moves upward under the influence of the electromagnetic force of the upper powered coil. The present invention names this stage as the starting stage. The magnetic rotor gradually approaches the upper coil during the upward movement, resulting in a reduction in the gap with the upper powered coil. The reduction in the gap will cause the electromagnetic force on the rotor to gradually increase, which may cause it to collide with the coil and cause a failure. To avoid failure, it is necessary to ensure that the rotor speed drops to zero within the maximum gap range, and the rotor decelerates when it moves to a certain position to avoid collision. The present invention names this stage as the deceleration stage. Thereafter, the rotor continues to move up and down due to unbalanced force until it reaches dynamic balance. The present invention names this stage as the fluctuation stage.

[0125] S4, constructing an incremental PID control module according to the magnetic bearing differential control model and the kinematics model;

[0126] PID controller construction: After obtaining the differential control model of S2 and the kinematic model of S3, an incremental PID control module is constructed, and the magnetic bearing control is stabilized by using the characteristics of easy-to-implement weighted control.

[0127] The present invention adopts an incremental PID control strategy, and the control algorithm of the incremental PID control module is formula (10):

[0128]

[0129] Wherein, Δe(k)=e(k)-e(k-1), k is the sampling number, u(k) is the output value of the PID control module at the kth sampling time, e(k) is the deviation value of the input of the PID control module at the kth sampling time, e(k-1) is the deviation value of the input at the k-1th sampling time, K l is the integration coefficient, K l =K p T / T l , K D is the differential coefficient, K D =K P T D / T,K P is the proportionality coefficient, T D is the differential time, T is the sampling time, T I is the integration time. If the system is required to be stable, the root of the characteristic equation of the closed-loop system with the PID controller must be located on the left half of the s-plane.

[0130] S5. Based on the incremental PID control module, construct and train a PINN neural network module;

[0131] Improved PINN neural network controller construction: After obtaining the PID controller in step (4), construct and train the PINN neural network module, which integrates physical laws to simulate the dynamic behavior of the magnetic suspension bearing, sets the chromosome encoding method, fitness function, genetic operation and operating parameters of the genetic algorithm, and uses a hybrid optimization method combining the genetic algorithm and the PINN algorithm to train the weights of the neural network. Train the PID controller parameters and verify its performance under various working conditions, so that the magnetic suspension bearing remains stable.

[0132] Specifically include the following:

[0133] The improved PINN network is constructed. After inputting time and space data, the function is first approximated by a fully connected neural network. Then, the automatic differentiation technique is used to obtain the partial differential equation residual and initial boundary value residual constraints, which are put into the loss function as regular terms. Finally, the gradient descent method and other optimization algorithms are used to obtain the neural network connection weight parameters and the physical parameters of the partial differential equation.

[0134] The physical process is described by using multiple partial differential equations in the magnetic suspension differential controller after adding PID control. The original function T (0)The two-dimensional partial differential equation g(T) of (x, y, θ) is formula (11):

[0135] g(T):f[T (n) (x,y,θ)]+C=0; (11)

[0136] Among them, T (n) (x,y,θ) is T (0) The nth-order derivative of (x, y, θ), n = {0, 1, 2}, C is a constant, (x, y, θ) is the input parameter of the neural network, x and y are coordinates, and θ is a parameter;

[0137] like Figure 1 As shown, solve T (0) (x, y, θ), first convert the input {x, y, θ} into the form of neurons to generate the initial neural network t0(x, y, θ); use the automatic differentiation algorithm to find the gradient of t0(x, y, θ) to form the partial differential equation g(t0), and use the deviation modulus between g(t0) and g(T) as the loss function, and use the gradient descent algorithm to adjust the weight w and bias b of the neural network so that g(t0) approaches g(T), and t(x, y, θ) approaches T (0) (x, y, θ), g(t0) is the partial differential equation obtained after calculating the gradient of the initial neural network, and t(x, y, θ) is the final model of the neural network.

[0138] After multiple iterations of training, we get t(x, y, θ), which is T (0) The PINN proxy model of (x, y, θ). The deep neural network has multiple hidden layers. The input variables are normalized by the input layer and distributed to the neurons in the hidden layer. The calculation results of the output layer are gradually calculated by the activation function.

[0139] A deep neural network has multiple hidden layers. After the input variables are normalized in the input layer, they are distributed to the neurons in the hidden layer. The activation function gradually calculates the calculation results of the output layer. The neurons are connected in a fully connected way. The output of the neurons in each layer is As the next layer of neurons The input of the neuron is expressed as formula (12):

[0140]

[0141] The superscript l represents the layer number of the neural network, and the subscripts i and j represent the neuron index. is the weight from the i-th neuron in the l-1th layer to the j-th neuron in the lth layer, is the bias from the i-th neuron in the l-1th layer to the j-th neuron in the lth layer, a=σ(z) is the activation function,

[0142] When the activation function is a hyperbolic tangent function, the formula of the activation function is formula (13):

[0143]

[0144] When the activation function is a sigmoid function, the formula of the activation function is formula (14):

[0145]

[0146] Among them, z and a are the input value and output value of the neuron respectively.

[0147] The last layer is the Lth layer, which is the output layer. The formula of the output fitting function t is formula (15):

[0148] t(x,y,θ)=a L (x,y,θ;w,b; (15).

[0149] Therefore, given any input value based on formula (12), t(x, y, θ) can be quickly calculated, and the output is the three parameters to be set for the PID controller. A genetic algorithm is added on the basis of the PINN neural network, and its basic elements include chromosome encoding method, fitness function, genetic operation and operating parameters.

[0150] Since the number of initial weights of the PINN neural network is relatively large, the present invention adopts a binary encoding method that is easy to implement operations such as crossover and mutation; the fitness function is the sum of the absolute values ​​of errors at all times; the objective function is the inverse of the individual fitness; the selection operation often adopts a proportional selection operator, that is, the probability of each individual being selected is proportional to the value of its fitness function; the crossover operation uses a single-point crossover operator; the mutation operation uses a basic bit mutation operator, which refers to performing a mutation operation on a certain bit or several genes randomly set in the individual code string.

[0151] A hybrid optimization method combining genetic algorithm and PINN algorithm is used to train fuzzy neural network. and Parameters, search globally to find the chromosomes that are better after genetic optimization, that is, to obtain the approximate optimal solution of the weights, and then use the PINN algorithm to quickly and finely adjust them.

[0152] Finally, based on this neural network, it is necessary to make fine adjustments to the parameters according to the influence of key system indicators such as overshoot and stabilization time in the actual simulation curve of the stability of the magnetic levitation bearing, and test the stability, response time and accuracy of the PID controller under different operating conditions and environments to verify its performance.

[0153] S6. Based on the magnetic bearing differential control model and the kinematic model, the Hildreth quadratic programming method is used to constrain the control input current to obtain a constrained MPC controller for carrying and transporting, wherein the MPC controller is based on the classical reinforcement learning algorithm Q-Learning to adjust the prediction time domain and control time domain of the MPC controller in real time;

[0154] Construction of model predictive controller based on reinforcement learning: After obtaining the differential control model of S2 and the kinematic model of S3, the Hildreth quadratic programming method is used to optimize the control input current and obtain a constrained MPC controller. The classic reinforcement learning algorithm Q-Learning is introduced to adjust the relevant parameters of the MPC controller in real time.

[0155] A method for constructing a magnetic bearing controller based on feature-dominated control. Figure 4 The schematic diagram of the Q-MPC controller structure used in the present invention is shown in Figure 1. The basic idea of ​​MPC is to construct a loss function l, and the control input when the loss function l reaches the minimum value is the optimal input. First, set the prediction time domain N p and control time domain N c ,The cost function is constructed using quadratic programming, and the cost function is constructed using quadratic programming, which is formula (16):

[0156]

[0157] l is the loss function, R is the reference output signal, To control the input weight, Δu is the change value of the input, y is the output vector, and u is the input vector; for the quadratic programming problem, the necessary condition for judging the extreme point is the Kuhn-Tucker condition. The original dual method can be used to convert the loss function l to the minimum value into a dual problem. The present invention uses Hildreth quadratic programming to solve the dual problem.

[0158] Reinforcement learning allows the system to interact with the external environment. Each interaction will receive corresponding rewards and punishments to evaluate the interaction. The purpose is to update the function Q"(s, a) through continuous interaction. The training of reinforcement learning obeys the Markov criterion. The update expression of the Q table after one round of training is formula (17):

[0159] Q π (s,a)=Q(s,a)+α[R d +ηQπ (s next,； )-Q(s,a)]; (17)

[0160] Among them, Q π (s,a) is the benefit of executing the action strategy π(s,a) in the current state s; Q(s,a) is the benefit of executing the action strategy π(s,a) in the state s before the update; α is the learning rate; R d is the immediate reward obtained by executing the action strategy π(s, a); η is the discount factor, Q π (s next,； ) is to execute the action strategy π(s, a) to reach the next state s next The total benefit, that is, the expected future benefit, s is the environment state, and a is the strategy selection action.

[0161] The prediction time domain and control time domain of the MPC controller are optimized in real time through the Q-Learning algorithm, and a linear state observer is introduced to estimate the internal state of the system by observing the input and output of the system. After setting the learning rate and decay rate of Q-Learning, the Q-MPC controller is trained, and the stability, response time and accuracy of the Q-MPC controller are tested under different operating conditions and environments to verify its performance.

[0162] S7, integrating the incremental PID control module, the PINN neural network module and the MPC controller into a feature-dominant controller, and selecting factor coefficients for the incremental PID control module, the PINN neural network module and the MPC controller respectively;

[0163] The incremental PID control module, the PINN neural network module and the MPC controller constructed by S4, S5 and S6 are integrated into the feature-dominant controller, and then factor coefficients are selected for the three controllers, and the dominant control of each controller is completed by adjusting each factor coefficient.

[0164] A method for constructing a magnetic bearing controller based on feature-dominated control. Figure 5 This is a schematic diagram of the feature-dominant controller structure used in the present invention. The constructed PID controller, PINN neural network controller and reinforcement learning-based model predictive controller are integrated into the feature-dominant controller, and then factor coefficients are selected for the three controllers, and the dominant control of each controller is completed by adjusting each factor coefficient.

[0165] S8. Adjust the factor coefficients of the incremental PID control module, the factor coefficients of the PINN neural network module and the factor coefficients of the MPC controller respectively to complete the dominant control of the incremental PID control module, the PINN neural network module and the MPC controller.

[0166] According to the different motion stages of the magnetic bearing rotor of S3, the appropriate dominant controller is matched. The PID controller based on the PINN neural network dominates the startup stage, the model predictive control based on reinforcement learning dominates the deceleration stage, and the PID controller dominates the fluctuation stage. Different dominant control strategies are formed by online adjusting the factor coefficients of the three control algorithms.

[0167] A method for constructing a magnetic bearing controller based on feature-dominated control. Figure 6 The figure is a step diagram of the specific implementation of the present invention. Firstly, the magnetic circuit analysis and the establishment of an accurate mathematical model are carried out according to the structure of the hybrid magnetic suspension bearing.

[0168] Model predictive control based on reinforcement learning, neural network control, and PID control are selected as feature-dominant control. The points of each controller are summarized and paired with the corresponding controller according to the characteristics of each operation stage as its dominant controller. Since the startup stage is relatively simple and the prediction of this process depends on the electromagnetic mechanics principle between the displacement of the magnetic suspension bearing and the current, the PINN neural network can predict the parameters according to the physical equation. Therefore, the present invention uses a PID controller based on the PINN neural network to dominate the startup stage. The maximum spatial clearance of the rotor needs to be calculated in the deceleration stage, so the process is relatively complex and the variables increase. Model predictive control based on reinforcement learning can reduce the workload of setting control parameters. In order to make the connection between the deceleration process and the acceleration process smooth and avoid decoupling problems, the present invention uses a model predictive control based on reinforcement learning to dominate the deceleration stage. In the fluctuation stage, the rotor continues to move up and down until dynamic balance due to unbalanced force. This process is relatively simple. The present invention uses a PID controller to dominate the fluctuation stage, allowing it to converge quickly in a short time until it is stable. Build three controllers in the feature-dominant controller. Finally, the parameters corresponding to each dominant controller are obtained through empirical adjustment, and compared with those without feature-dominant control to verify the effectiveness of the dominant controller.

[0169] A method for constructing a magnetic bearing controller based on feature-dominated control. Figure 7 This is the control flow chart of the present invention. First, the displacement signal is measured, and the displacement signal is analyzed to which stage of the three motion stages it belongs to. The controller is matched for each motion stage. The PID controller based on the PINN neural network dominates the startup stage, the model predictive control based on reinforcement learning dominates the deceleration stage, and the PID controller dominates the fluctuation stage. According to engineering experience, the factor coefficients of the three control algorithms are adjusted online to form different dominant control strategies. Calculate the output value to determine whether it is stable. If it is unstable, readjust the factor coefficients and the parameters of each controller. If it is stable, stop.

[0170] The present invention uses intelligent algorithms and experimental data to construct a mathematical model between the magnetic bearing control current and bias current, the rotor balance point air gap length and the rotor displacement, the displacement sensor and the power amplifier, and the kinematics model of the magnetic bearing rotor, and selects feature-dominant control. Through feature-dominant control composed of PID control, PINN neural network control and model predictive control based on reinforcement learning, the dynamic behavior of the magnetic bearing is more accurately predicted, thereby achieving more precise control. The online adjustment of the three controller factor coefficients forms different feature-dominant control strategies, so that the control system can predict the future state according to the motion characteristics of the rotor at different stages to adapt to complex operating conditions and environmental changes, thereby improving the overall stability and response speed of the system.

[0171] Traditional PID controllers may encounter performance bottlenecks when dealing with nonlinear systems, but the use of PINN in the present invention allows the controller to better adapt to those complex nonlinear dynamic changes by learning the physical and dynamic characteristics of the system, combined with the model prediction of the overall controller that can adaptively adjust parameters according to the current system state. This enables the magnetic bearing to maintain stable operation within a wider operating range.

[0172] The established mathematical model and control strategy can be applied to similar magnetic bearing products and different working conditions, which can improve the application range of the equipment and its ability to cope with different working conditions, and avoid the high degree of uniformity of the equipment. The kinematics analysis of the magnetic bearing rotor is carried out, and the movement of the rotor from acceleration start-up, deceleration to stable operation is modeled, the characteristics of different stages are analyzed, and the three movement stages of magnetic bearing start-up, deceleration and fluctuation are constructed. It can avoid the overshoot of the equipment and increase the service life of the bearing.

[0173] The following points need to be explained:

[0174] (1) The drawings of the embodiments of the present invention only relate to the structures related to the embodiments of the present invention, and other structures may refer to the general design.

[0175] (2) For the sake of clarity, in the drawings used to describe the embodiments of the present invention, the thickness of the layers or regions is exaggerated or reduced, that is, these drawings are not drawn according to the actual scale. It is understood that when an element such as a layer, film, region or substrate is referred to as being "on" or "under" another element, the element may be "directly" "on" or "under" the other element or there may be intermediate elements.

[0176] (3) In the absence of conflict, the embodiments of the present invention and the features therein may be combined with each other to obtain new embodiments.

[0177] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. The protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for constructing a magnetic bearing controller based on feature-dominant control, characterized in that: include: According to the principle of magnetic suspension, Ampere's circuit theorem of magnetic circuit, Newton's law and the static mathematical relationship of the internal components of magnetic suspension bearing, the differential equation of magnetic suspension bearing is established; Establishing a displacement sensor mathematical model and a power amplifier mathematical model, and converting the differential equation of the magnetic bearing into a Laplace model to obtain a magnetic bearing differential control model; According to the static mathematical relationship of the internal components of the magnetic bearing, a kinematics analysis of the magnetic bearing from acceleration start-up, deceleration to stable operation is performed to obtain a kinematics model, which includes a magnetic bearing startup stage, a magnetic bearing deceleration stage and a magnetic bearing fluctuation stage; Constructing an incremental PID control module according to the magnetic bearing differential control model and the kinematics model; Based on the incremental PID control module, a PINN neural network module is constructed and trained; Based on the magnetic bearing differential control model and the kinematic model, the Hildreth quadratic programming method is used to constrain the control input current to obtain a constrained MPC controller for carrying and transporting, wherein the MPC controller is based on the classical reinforcement learning algorithm Q-Learning to adjust the prediction time domain and control time domain of the MPC controller in real time; Integrate the incremental PID control module, the PINN neural network module and the MPC controller into a feature-dominant controller, and select factor coefficients for the incremental PID control module, the PINN neural network module and the MPC controller respectively; The factor coefficients of the incremental PID control module, the factor coefficients of the PINN neural network module and the factor coefficients of the MPC controller are adjusted respectively to complete the dominant control of the incremental PID control module, the PINN neural network module and the MPC controller.

2. The method for constructing a magnetic bearing controller based on feature-dominant control according to claim 1 is characterized in that: The differential equation of the magnetic suspension bearing is established according to the magnetic suspension principle, Ampere's loop theorem of the magnetic circuit, Newton's law and the static mathematical relationship of the internal components of the magnetic suspension bearing, including: The relationship between the current, force and displacement of the electromagnet is established as formula (1): Where F is the total attraction between the stator and rotor, μ0 is the magnetic permeability of air, k is the electromagnetic force coefficient, x is the displacement of the rotor in the magnetic bearing, N is the number of turns of the electromagnet coil, A is the cross-sectional area of ​​the stator, rotor and air gap magnetic field path, and i is the coil winding current; The force balance method of the rotor is established as formula (2): Among them, F x is the sum of the electromagnetic forces generated in the x-axis direction, m is the mass of the rotor, p(t) is the external interference force, and g is the gravitational acceleration; According to the relationship between the current, force and displacement of the electromagnet, we get F x The expression for the sum of the electromagnetic forces generated in the x-axis direction is formula (3): Among them, F x1 is the electromagnetic force generated by the upper electromagnet, F x2 is the electromagnetic force generated by the electromagnet below, i0 is the bias current, i x To control the current, x0 is the air gap length at the rotor equilibrium point; Based on formula (2) and formula (3), we get formula (4): The Taylor expansion of the binary function is performed near the working point of the rotor and the high-order infinitesimals are neglected to obtain formula (5): F x =k i i x +k x ; (5) Among them, k x is the displacement stiffness of the magnetic bearing, k i is the current stiffness of the magnetic bearing, Based on formula (4) and formula (5), the differential equation of the magnetic bearing is obtained as formula (6):

3. The method for constructing a magnetic bearing controller based on feature-dominant control according to claim 2 is characterized in that: The method of establishing a displacement sensor mathematical model, a power amplifier mathematical model, and converting the differential equation of the magnetic bearing into a Laplace model to obtain a magnetic bearing differential control model includes: The differential equation of the magnetic bearing is transformed based on the Laplace model to obtain a differential control model of the magnetic bearing. The differential control model of the magnetic bearing is formula (7): Wherein, G(s) is the transfer function of the magnetic bearing in the x-axis direction, X(s) is the output of the magnetic bearing in the x-axis direction, I(s) is the input of the magnetic bearing in the x-axis direction, and s is the complex variable of the magnetic bearing system; The mathematical model of the displacement sensor is formula (8): Among them, G f (s) is the transfer function of the displacement sensor, k s is the gain of the displacement sensor, T s is the hysteresis time constant of the displacement sensor; The mathematical model of the power amplifier is formula (9): Among them, G a (s) is the transfer function of the power amplifier, k a is the gain of the power amplifier, T a is the power amplifier hysteresis time constant.

4. The method for constructing a magnetic bearing controller based on feature-dominant control according to claim 3 is characterized in that: The constructing of the incremental PID control module according to the magnetic bearing differential control model and the kinematics model comprises: The control algorithm of the incremental PID control module is formula (10): Wherein, Δe(k)=e(k)-e(k-1), k is the sampling number, u(k) is the output value of the PID control module at the kth sampling time, e(k) is the deviation value of the input of the PID control module at the kth sampling time, e(k-1) is the deviation value of the input at the k-1th sampling time, K l is the integration coefficient, K I =K p T / T I , K D is the differential coefficient, K D =K P T D / T,K P is the proportionality coefficient, T D is the differential time, T is the sampling time, T I is the integration time.

5. The method for constructing a magnetic bearing controller based on feature-dominant control according to claim 4 is characterized in that: The step of constructing and training a PINN neural network module based on the incremental PID control module includes: Based on the partial differential equation in the incremental PID control module to describe the physical process, the original function T (0) The two-dimensional partial differential equation g(T) of (x, y, θ) is formula (11): g(T):f[T (n) (x,y,θ)]+C=0; (11) Among them, T (n) (x,y,θ) is T (0) The nth-order derivative of (x, y, θ), n = {0, 1, 2}, C is a constant, (x, y, θ) is the input parameter of the neural network, x and y are coordinates, and θ is a parameter; The deviation modulus between g(t0) and g(T) is used as the loss function, and the gradient descent algorithm is used to adjust the weight w and bias b of the neural network so that g(t0) approaches g(T), and t(x, y, θ) approaches T. (0) (x, y, θ), g(t0) is the partial differential equation obtained after calculating the gradient of the initial neural network, and t(x, y, θ) is the final model of the neural network; The t(x, y, θ) obtained after multiple iterations of training is the proxy model of the PINN neural network; Among them, neurons are connected by full connection, and the output of neurons in each layer As the next layer of neurons The input of the neuron is expressed as formula (12): The superscript l represents the layer number of the neural network, and the subscripts i and j represent the neuron index. is the weight from the i-th neuron in the l-1th layer to the j-th neuron in the lth layer, is the bias from the i-th neuron in the l-1th layer to the j-th neuron in the lth layer, a=σ(z) is the activation function, The last layer is the Lth layer, which is the output layer. The formula of the output fitting function is formula (15): t(x,y,θ)=a L (x,y,θ;w,b));(15)。 6. The method for constructing a magnetic bearing controller based on feature-dominant control according to claim 5 is characterized in that: When the activation function is a hyperbolic tangent function, the formula of the activation function is formula (13): When the activation function is a sigmoid function, the formula of the activation function is formula (14):

7. The method for constructing a magnetic bearing controller based on feature-dominant control according to claim 6 is characterized in that: Based on the magnetic bearing differential control model and the kinematic model, the Hildreth quadratic programming method is used to constrain the control input current to obtain a constrained MPC controller for carrying and transporting, wherein the MPC controller is based on the classical reinforcement learning algorithm Q-Learning to adjust the prediction time domain and control time domain of the MPC controller in real time, including: Set the prediction time domain N p and control time domain N c ,The cost function is constructed using quadratic programming, and the cost function is constructed using quadratic programming, which is formula (16): l is the loss function, R is the reference output signal, To control the input weight, Δu is the change in the input, y is the output vector, and u is the input vector; The update expression of the Q table for one round of training is formula (17): Q π (s,a)=Q(s,a)+α[R d +ηQ π (s next ,;)-Q(s,a)]; (17) Among them, Q π (s,a) is the benefit of executing the action strategy π(s,a) in the current state s; Q(s,a) is the benefit of executing the action strategy π(s,a) in the state s before the update; α is the learning rate; R d is the immediate reward obtained by executing the action strategy π(s, a); η is the discount factor, Q π (s next ,;) is to execute the action strategy π(s, a) to reach the next state s next The total revenue of , s is the environment state, and a is the strategy selection action.

8. The method for constructing a magnetic bearing controller based on feature-dominant control according to claim 7, characterized in that: The incremental PID control module, the PINN neural network module and the MPC controller are integrated into a feature-dominant controller, and factor coefficients are selected for the incremental PID control module, the PINN neural network module and the MPC controller, respectively, including: The incremental PID control module, the PINN neural network module and the MPC controller respectively select factor coefficients in the range of 0 to 1, and the sum of the factors is 1.

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