A method for constructing a magnetic suspension bearing controller based on feature dominant control

Abstract

In the control field of magnetic suspension bearing, the application provides a magnetic suspension bearing controller construction method based on characteristic dominant control, which comprises the following steps: magnetic suspension bearing mathematical model construction; displacement sensor and power amplifier mathematical model construction; magnetic suspension bearing kinematics analysis; PID controller construction; improved PINN neural network construction; model predictive controller construction based on reinforcement learning; dominant controller construction; factor coefficient selection and adjustment of three control algorithms; based on the mathematical model between the gap between the stator and rotor and the electromagnetic force in the five-degree-of-freedom hybrid magnetic suspension bearing and the kinematics characteristics of the magnetic suspension rotor, the characteristic dominant controller composed of the PID controller, the PINN neural network controller and the model predictive controller based on reinforcement learning is used for stabilizing correction of the magnetic suspension bearing, so that more accurate and stable control effect can be realized.

Description

Technical Field

[0001] This invention relates to the field of magnetic levitation bearing control technology, and in particular to a method for constructing a magnetic levitation bearing controller based on feature-driven control. Background Technology

[0002] With the rapid development of aerospace, transportation, machinery manufacturing, and medical equipment, rotating machinery is evolving towards higher speeds, greater intelligence, and higher precision. The performance of the support unit is crucial, directly determining the reliability and long-term operational stability of the equipment. Traditional mechanical bearings inevitably suffer from mechanical wear, low heat dissipation efficiency, and lubricant contamination, leading to performance degradation. High-precision and highly stable magnetic levitation bearing systems are increasingly being used in various high-end mechanical equipment, such as high-speed rotating machinery and precision measuring equipment. Control technology for magnetic levitation bearings is one of the key technologies ensuring the efficient operation of these systems. While traditional control methods such as PID control perform well in many industrial applications, they have limitations in handling nonlinear systems and parameter uncertainties.

[0003] In practical industrial production, establishing accurate mathematical models for magnetic levitation bearings is difficult due to their small levitation gap, nonlinearity, and severe coupling. Furthermore, controlling open-loop unstable systems is challenging. Therefore, although research on magnetic levitation control has made progress in recent years, it still cannot meet the needs of large-scale engineering applications. In addition, most research focuses on rigid rotors or rotors that are stable after crossing a certain speed. When the rotor crosses the critical speed, the vibration amplitude and phase change drastically, altering the rotor's imbalance state. 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; however, when facing extreme operating conditions and severe environmental disturbances, control performance may still decline due to model parameters not adapting to these changes. Physical Information Neural Networks (PINNs), as an emerging technology combining traditional neural networks and physical models, can improve the model's prediction accuracy and generalization ability by introducing physical laws as additional constraints during training. Although existing PINN applications have shown potential in some areas, their research in magnetic levitation bearing control is still insufficient, especially in the real-time adjustment of PID control parameters when the system is dynamically changing rapidly. There is a lack of effective solutions, and the high performance and stability of the system under various complex operating conditions are difficult to guarantee. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a method for constructing a magnetic levitation bearing controller based on feature-dominated control. This method achieves non-contact detection through displacement sensors and power amplifiers. It combines the mechanism modeling of magnetic levitation to obtain the nonlinear differential equation of the magnetic levitation bearing, which is then converted into a Laplace equation. Next, it combines the mathematical models of the displacement sensors and power amplifiers to obtain the differential control model of the magnetic levitation bearing. The kinematics of the magnetic levitation bearing rotor are analyzed, dividing the motion phase into three stages: start-up, deceleration, and fluctuation. A feature-dominated controller integrating a PID controller, a PINN neural network controller, and a reinforcement learning-based model predictive controller is constructed and trained. Appropriate dominant controllers are matched to different motion stages of the magnetic levitation bearing rotor. The PINN neural network-based PID controller dominates the start-up stage, the reinforcement learning-based model predictive control 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 levitation bearing. Specifically, it includes:

[0005] A method for constructing a magnetic levitation bearing controller based on feature-dominated control includes:

[0006] Based on the principles of magnetic levitation, Ampere's circuital law for magnetic circuits, Newton's laws, and the static mathematical relationships of the internal components of a magnetic levitation bearing, a differential equation for the magnetic levitation bearing is established.

[0007] A mathematical model for the displacement sensor and a mathematical model for the power amplifier are established, and the differential equation of the magnetic levitation bearing is converted into a Laplace model to obtain a differential control model for the magnetic levitation bearing.

[0008] Based on the static mathematical relationships of the internal components of the magnetic levitation bearing, a kinematic analysis of the magnetic levitation bearing is performed from acceleration start-up, deceleration to stable operation, to obtain a kinematic model. The kinematic model includes the magnetic levitation bearing start-up stage, the magnetic levitation bearing deceleration stage, and the magnetic levitation bearing fluctuation stage.

[0009] Based on the differential control model of the magnetic levitation bearing and the kinematics model, an incremental PID control module is constructed.

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

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

[0012] The incremental PID control module, the PINN neural network module, and the MPC controller are integrated into a feature-dominated controller, and factor coefficients are selected 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 PINN neural network module, and the MPC controller are adjusted respectively to achieve 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 levitation bearing based on the principles of magnetic levitation, Ampere's circuital law for magnetic circuits, Newton's laws, and the static mathematical relationships of the internal components of the magnetic levitation bearing includes:

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

[0016]

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

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

[0019]

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

[0021] Based on the relationship between the current, force, and displacement of the electromagnet, F is obtained. x The expression for the sum of electromagnetic forces generated in the x-axis direction is given by formula (3):

[0022]

[0023] Among them, F x1 F is the electromagnetic force generated by the electromagnet above. x2 i 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 balance point;

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

[0025]

[0026] By performing a Taylor expansion of a bivariate function near the operating point of the rotor and neglecting higher-order infinitesimals, we obtain formula (5):

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

[0028] Where, k x For the displacement stiffness of the magnetic levitation bearing, k i For the current stiffness of the magnetic levitation bearing,

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

[0030]

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

[0032] The differential equation of the magnetic bearing is transformed based on the Laplace model to obtain the differential control model of the magnetic bearing, which is Equation (7):

[0033]

[0034] Where 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 for the displacement sensor is given by formula (8):

[0036]

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

[0038] The mathematical model of a power amplifier is given by formula (9):

[0039]

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

[0041] Optionally, the step of constructing an incremental PID control module based on the differential control model of the magnetic levitation bearing and the kinematics model includes:

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

[0043]

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

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

[0046] The physical process is described by the partial differential equation in the incremental PID control module, and the original function T (0) The two-dimensional partial differential equation g(T) of (x,y,θ) is given by 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 derivative term of (x,y,θ), where n={0,1,2}, C is a constant, (x,y,θ) is the input parameter of the neural network, where x and y are coordinates and θ is a parameter;

[0049] Using the magnitude of the deviation between g(t0) and g(T) as the loss function, the gradient descent algorithm is used to adjust the weights w and biases b of the neural network so that g(t0) approximates g(T), and t(x,y,θ) approximates T. (0) (x,y,θ), g(t0) are the partial differential equations obtained after taking the gradient of the initial neural network, and t(x,y,θ) are the final model of the neural network;

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

[0051] In this layer, neurons are connected via fully connected structures, and the output of each neuron in each layer... As the next layer of neurons The input, the expression for the forward propagation process of the neuron is formula (12):

[0052]

[0053] In this context, the superscript 'l' represents the layer number of the neural network, and the subscripts 'i' and 'j' represent the neuron indices. Let be the weights from the i-th neuron in layer (l-1) to the j-th neuron in layer l. Let be the bias from the i-th neuron in layer (l-1) to the j-th neuron in layer l, and let a = σ(z) be the activation function.

[0054] The last layer is the Lth layer, which is the output layer. The formula for the fitting function of the output 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 for the activation function is formula (13):

[0057]

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

[0059]

[0060] Optionally, based on the differential control model of the magnetic levitation bearing and the kinematic model, the Hildersee quadratic programming method is used to constrain the control input current to obtain a constrained MPC controller for transport. The MPC controller is tuned in real-time using the classical reinforcement learning algorithm Q-Learning, including the prediction time domain and control time domain:

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

[0062]

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

[0064] The update expression for the Q-table after one round of training is given by 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) represents the reward for executing action policy π(s,a) in the current state s; Q(s,a) represents the reward for executing action policy π(s,a) in the state s before the update; α is the learning rate; R d The immediate reward obtained by executing the action policy π(s, a); η is the discount factor, Q π (s next,； To execute the action policy π(s, a) to reach the next state s next The total reward is denoted by s, where s represents the environmental state and a represents the action chosen by the strategy.

[0067] Optionally, the step of integrating the incremental PID control module, the PINN neural network module, and the MPC controller into a feature-dominated controller, and selecting factor coefficients for the incremental PID control module, the PINN neural network module, and the MPC controller respectively, includes:

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

[0069] The above technical solution has at least the following advantages compared with the existing technology:

[0070] (1) Using intelligent algorithms and experimental data, mathematical models of the control current and bias current of the magnetic levitation bearing, the air gap length at the rotor balance point and the rotor displacement, the displacement sensor and the power amplifier, and the kinematic model of the magnetic levitation bearing rotor are constructed. Feature-dominated control is selected, and through feature-dominated control composed of PID control, PINN neural network control and model predictive control based on reinforcement learning, the dynamic behavior of the magnetic levitation bearing is predicted more accurately, thereby achieving more precise control. The online adjustment of the coefficients of the three controller factors forms different feature-dominated control strategies, enabling the control system to predict the future state according to the motion characteristics of the rotor at different stages, so as 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. However, the use of PINN in this invention allows the controller to better adapt to complex nonlinear dynamic changes by learning the physical and dynamic characteristics of the system. Combined with a model that can adaptively tune parameters according to the current system state, this enables the magnetic levitation 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 levitation 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 equipment being highly monolithic. A kinematic analysis of the magnetic levitation bearing rotor is performed, modeling the rotor's motion from acceleration and deceleration to stable operation, analyzing the characteristics of different stages, and constructing three motion stages for the magnetic levitation bearing: startup, deceleration, and fluctuation. This can avoid overshooting and increase the service life of the bearing. Attached Figure Description

[0073] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0074] Figure 1 This is a schematic diagram of the magnetic levitation bearing control structure used in this invention;

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

[0076] Figure 3 This is a flowchart of the PINN neural network control method used in this invention;

[0077] Figure 4This is a schematic diagram of the Q-MPC controller structure used in this invention;

[0078] Figure 5 This is a schematic diagram of the feature-dominant control structure applied in this invention;

[0079] Figure 6 This is a flowchart illustrating the specific implementation steps of the present invention;

[0080] Figure 7 This is the control flowchart of the present invention. Detailed Implementation

[0081] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0082] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms “first,” “second,” and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms “an,” “a,” or “the,” and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms “comprising,” “including,” or “including,” and similar terms mean that the element or object preceding the word encompasses the element or object listed following the word and its equivalents, without excluding other elements or objects. The terms “connected,” “linked,” or “connected,” and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect.

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

[0084] The method of this invention involves constructing a mathematical model of the gap between the stator and rotor in a five-degree-of-freedom hybrid magnetic levitation bearing, and the relationship between the current and electromagnetic force through the electromagnet. Further mathematical models of the displacement sensor and power amplifier are then constructed. Gap data of the magnetic bearing is collected, and kinematic analysis of the magnetic levitation bearing is performed. Based on different rotor motion states during levitation control, and using experimental testing and theoretical derivation, the rotor motion process is divided into acceleration, deceleration, and fluctuation stages. The characteristics of rotor motion behavior and the selection of control methods for each stage are studied. Characteristic-dominant control is selected, and PID control, PINN neural network control, and model predictive control based on reinforcement learning are introduced. Appropriate dominant controllers are matched according to the characteristics of different motion stages of the magnetic levitation bearing rotor. Factor coefficients are then selected for the three controllers, and different characteristic-dominant control strategies are formed by adjusting the factor coefficients of the three control algorithms online. The characteristic-dominant controller is used to stabilize and correct the magnetic levitation bearing to ensure its stable operation, ultimately enabling the rotor to dynamically levitate within the allowable air gap range. The invention includes the following operations: 1) mathematical model construction of the magnetic levitation bearing; 2) mathematical model construction of the displacement sensor and power amplifier; 3) kinematic analysis of the magnetic levitation bearing; 4) PID controller construction; 5) improved PINN neural network construction; 6) reinforcement learning-based model predictive controller construction; 7) dominant controller construction; 8) selection and adjustment of factor coefficients for the three control algorithms. Based on the mathematical model of the relationship between the stator-rotor gap and electromagnetic force in a five-degree-of-freedom hybrid magnetic levitation bearing and the kinematic characteristics of the magnetic levitation rotor, this invention utilizes a feature-dominant controller composed of a PID controller, a PINN neural network controller, and a reinforcement learning-based model predictive controller to stabilize and correct the magnetic levitation bearing, achieving more precise and stable control. Furthermore, the feature-dominant controller of this invention exhibits significant advantages over traditional PID controllers in handling complex nonlinear systems and in situations involving system start-up, shutdown, and variable operating conditions. This invention is suitable for magnetic levitation bearing systems requiring high precision and stability, especially in industrial applications demanding high speed and precision. Experimental verification shows that the controller proposed in this invention maintains good performance under various operating conditions, effectively improving the operating efficiency and reliability of the magnetic levitation bearing.

[0085] A method for constructing a magnetic levitation bearing controller based on feature-dominated control. Figure 1 This is a schematic diagram of the PINN neural network structure used in this invention. Figure 2As shown, when solving partial differential equations, the input x, y, and θ parameters are first converted into neurons to generate an initial neural network. Then, an automatic differentiation algorithm is used to calculate the gradient of the neural network, obtaining the partial differential equation and its residuals, along with initial-boundary value residual constraints, which are then used as regularization terms in the loss function. Finally, the gradient descent algorithm is used to adjust the weights w and b of the neural network, simultaneously making the network approximate the original physical equation. The neural network model obtained after multiple iterations of training is the PINN surrogate model for this physical equation.

[0086] A method for constructing a magnetic levitation bearing controller based on feature-dominated control. Figure 2 This is a schematic diagram illustrating the application of the present invention to the control structure of a magnetic levitation bearing. Figure 1 As shown, the magnetic levitation bearing system achieves contactless levitation of the rotor through precise control of electromagnetic force. First, the controller receives the rotor's position information and compares it with a preset reference position, calculating the necessary adjustment signal. This signal is sent to a power amplifier to amplify its strength, thereby driving the electromagnet. The electromagnet generates a corresponding magnetic force based on the adjusted current. This magnetic force precisely adjusts the rotor's position to counteract gravity and other external forces, maintaining stable levitation. The adjusted current dynamically regulates the strength and direction of the magnetic field by increasing or decreasing it, 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 levitation bearing can maintain high precision and stability under various operating conditions, completing a continuous cycle from current adjustment to precise levitation.

[0087] A method for constructing a magnetic levitation bearing controller based on feature-dominated control. Figure 3 This is a flowchart of the PINN neural network control used in this invention. Based on the static mathematical relationships of the magnetic levitation bearing stator, rotor, electromagnet, and their windings, differential equations are established through mechanistic modeling to relate the magnetic levitation bearing control current, bias current, rotor balance point air gap length, and rotor displacement. The PINN neural network weights are initialized, and the system enters the genetic algorithm optimization phase. The network training error is used as the fitness value, and the optimal weights are obtained through selection, crossover, and mutation processes and applied to the PINN neural network. Based on the sampled rotor displacement and control current data, the PINN neural network adjusts the parameters to be used by the incremental PID controller.

[0088] The specific plan is as follows:

[0089] A method for constructing a magnetic levitation bearing controller based on feature-dominated control is proposed. This method uses a feature-dominated controller composed of a PID controller, a PINN neural network controller, and a reinforcement learning-based model predictive controller (Q-MPC). Appropriate dominant controllers are matched according to different motion stages of the magnetic levitation 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-dominated control strategies applied to the stabilization of the magnetic levitation bearing. These strategies include:

[0090] S1. Based on the principle of magnetic levitation, Ampere's circuital law for magnetic circuits, Newton's laws, and the static mathematical relationships of the internal components of the magnetic levitation bearing, establish the differential equation of the magnetic levitation bearing.

[0091] Mathematical modeling of magnetic levitation bearings: Based on the working principle of magnetic levitation, and taking Ampere's circuital law and Newton's laws as the criteria, and based on the static mathematical relationships of the components of the magnetic levitation bearing, differential equations are established between the control current, bias current, air gap length at the rotor balance point, and rotor displacement of the magnetic levitation bearing.

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

[0093] Regarding the mathematical model of magnetic levitation bearings, there are three factors that determine the motion of hybrid magnetic levitation bearings: firstly, the displacement x of the rotor in the magnetic levitation bearing; secondly, the control current i that enters the electromagnet via a power amplifier. x The third is the external disturbance force p(t) experienced by the magnetic levitation bearing rotor.

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

[0095]

[0096] Where F is the total attraction between the stator and rotor, μ0 is the permeability of air, k is the electromagnetic force coefficient, x is the displacement of the rotor in the magnetic levitation bearing, N is the number of turns of the electromagnet coil, A is the cross-sectional area of ​​the magnetic field path of the stator, rotor and air gap, 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 Let t be the sum of the electromagnetic forces generated in the x-axis direction, m be the mass of the rotor, p(t) be the external disturbance force, and g be the gravitational acceleration.

[0100] Based on the relationship between the current, force, and displacement of the electromagnet, F is obtained. xThe expression for the sum of electromagnetic forces generated in the x-axis direction is given by formula (3):

[0101]

[0102] Among them, F x1 F is the electromagnetic force generated by the electromagnet above. x2 i 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 balance point;

[0103] Since the disturbance is very small in actual operation, it is assumed that the external disturbance force p(t) is 0.

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

[0105]

[0106] It can be seen that the mathematical model of the magnetic levitation bearing is a nonlinear quadratic differential equation. However, nonlinear control has not yet been well resolved, both theoretically and practically. Therefore, equation (4) is linearized. Near the operating point of the magnetic levitation bearing rotor, i.e., x = 0 and i... x By performing a Taylor expansion of the bivariate function near 0 and neglecting higher-order infinitesimals, we obtain formula (5):

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

[0108] Where, k x For the displacement stiffness of the magnetic levitation bearing, k i For the current stiffness of the magnetic levitation bearing, Although the accuracy of Equation (5) decreases as the displacement x moves further away from the equilibrium position, practical experience has shown that controllers designed using Equation (5) are still suitable over a wide range.

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

[0110]

[0111] S2. Establish mathematical models for displacement sensors and power amplifiers, and convert the differential equations of the magnetic levitation bearing into a Laplace model to obtain the differential control model of the magnetic levitation bearing.

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

[0113] Specifically, it includes the following:

[0114] Applying the Laplace transform to equation (6) yields the magnetic levitation bearing in one direction with respect to x. (s) The mathematical model is given as output and I(s) as input. Based on the Laplace model, the differential equation of the magnetic bearing is transformed to obtain the differential control model of the magnetic bearing. The differential control model of the magnetic bearing is given by formula (7):

[0115]

[0116] Where 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] A displacement sensor converts changes in displacement into changes in output voltage. Numerically, the input and output can be considered as a linear relationship. However, there is a certain phase delay in this process. Therefore, its model can be represented as a first-order inertial element. The mathematical model of the displacement sensor is Equation (8):

[0118]

[0119] Among them, G f (s) is the transfer function of the displacement sensor, k s For the gain of the displacement sensor, T s Let T be the hysteresis time constant of the displacement sensor; since the actual sensor hysteresis time constant T... s It is difficult to measure, and the sensor has a wide bandwidth, so G in equation (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 levitation bearing. Because the power amplifier circuit has a certain phase delay, the model of this link can also be represented as a first-order inertial 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 T is the gain of the power amplifier. a G is the lag time constant of the power amplifier. Since the power amplifier has a wide bandwidth, G in equation (9) is... a (s) can be approximated as k a By combining the above equations, an approximate linear mathematical model can be obtained between the magnetic levitation bearing, the displacement sensor, and the power amplifier.

[0123] S3. Based on the static mathematical relationship of the internal components of the magnetic levitation bearing, a kinematic analysis of the magnetic levitation bearing is performed from acceleration start-up, deceleration to stable operation, to obtain a kinematic model. The kinematic model includes the magnetic levitation bearing start-up stage, the magnetic levitation bearing deceleration stage, and the magnetic levitation bearing fluctuation stage.

[0124] Based on the static mathematical relationships of the magnetic levitation bearings established in S1, a kinematic analysis of the magnetic levitation bearings from acceleration to deceleration to stable operation is performed. Three motion stages—start-up, deceleration, and fluctuation—are constructed for the magnetic levitation bearings. A kinematic analysis of the magnetic levitation bearings is conducted to identify these three operational stages and select a matching controller. Regarding the kinematic analysis of the magnetic levitation bearings, such as... Figure 1 As shown, when the magnetic levitation bearing is not activated, the rotor is located on the lower, unenergized coil. When the magnetic levitation bearing is activated, the rotor moves upward under the influence of the electromagnetic force of the upper, energized coil; this invention names this stage the activation stage. As the magnetic levitation rotor moves upward, it gradually approaches the upper coil, causing the gap between the rotor and the upper energized coil to narrow. This narrowing gap leads to a gradual increase in the electromagnetic force on the rotor, potentially causing it to collide with the coil and malfunction. To avoid this malfunction, the rotor's speed must be reduced to zero within the maximum gap range. At a certain position, the rotor decelerates to avoid collision; this invention names this stage the deceleration stage. Subsequently, due to the imbalance of forces, the rotor continues to move up and down until dynamic equilibrium is reached; this invention names this stage the fluctuation stage.

[0125] S4. Based on the differential control model of the magnetic levitation bearing and the kinematics model, construct an incremental PID control module;

[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. Taking advantage of the easy implementation of weighted control, the magnetic levitation bearing control is stabilized.

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

[0128]

[0129] Where Δe(k) = e(k) - e(k-1), k is the sampling sequence number, u(k) is the output value of the PID control module at the k-th sampling time, e(k) is the input deviation value of the PID control module at the k-th sampling time, e(k-1) is the input deviation value at the (k-1)-th sampling time, and K l K is the integral coefficient. l =K p T / T l K D K is the differential coefficient. D =K P T D / T,K P T is the proportionality coefficient. D T is the differential time, and T is the sampling time. I For integral time. If system stability is required, the roots of the characteristic equation of the closed-loop system with a PID controller must lie on the left half of the s-plane.

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

[0131] Improved PINN Neural Network Controller Construction: After obtaining the PID controller from step (4), a PINN neural network module is constructed and trained. This network integrates physical laws to simulate the dynamic behavior of the magnetic levitation bearing. The chromosome encoding method, fitness function, genetic operations, and operating parameters of the genetic algorithm are set. A hybrid optimization method combining the genetic algorithm and the PINN algorithm is used to train the weights of the neural network. The PID controller parameters are trained to verify its performance under various working conditions, thereby ensuring the stability of the magnetic levitation bearing.

[0132] Specifically, it includes the following:

[0133] To improve the PINN network construction, after inputting time and space data, the function is first approximated by a fully connected neural network. Then, automatic differentiation is used to find the residuals of the partial differential equation and the initial boundary value residual constraints, which are then used as regularization terms in the loss function. Finally, optimization algorithms such as gradient descent 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 using multiple partial differential equations in the magnetic levitation differential controller after incorporating PID control. The original function T (0)The two-dimensional partial differential equation g(T) of (x,y,θ) is given by 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 derivative term of (x,y,θ), where n={0,1,2}, C is a constant, (x,y,θ) is the input parameter of the neural network, where x and y are coordinates and θ is a parameter;

[0137] like Figure 1 As shown, solve T (0) First, the input {x,y,θ} is converted into the form of neurons, generating an initial neural network t0(x,y,θ). The gradient of t0(x,y,θ) is calculated using an automatic differentiation algorithm, forming a partial differential equation g(t0). The deviation modulus between g(t0) and g(T) is used as the loss function. Gradient descent is then used to adjust the weights w and bias b of the neural network, making g(t0) approximate g(T), and t(x,y,θ) approximate T. (0) (x,y,θ) and g(t0) are the partial differential equations obtained after taking the gradient of the initial neural network, and t(x,y,θ) is the final model of the neural network.

[0138] The t(x,y,θ) obtained after multiple iterations of training is T. (0) The PINN surrogate model for (x,y,θ). Deep neural networks have multiple hidden layers. Input variables are normalized by the input layer and then distributed to neurons in the hidden layers. The output layer's computation result is obtained step-by-step by activation functions.

[0139] Deep neural networks have multiple hidden layers. Input variables are normalized by the input layer and then distributed to neurons in the hidden layers. Activation functions progressively calculate the output layer's result. Neurons are connected via fully connected layers. The output of each neuron in each layer... As the next layer of neurons The input, the expression for the forward propagation process of the neuron is formula (12):

[0140]

[0141] In this context, the superscript 'l' represents the layer number of the neural network, and the subscripts 'i' and 'j' represent the neuron indices. Let be the weights from the i-th neuron in layer (l-1) to the j-th neuron in layer l. Let be the bias from the i-th neuron in layer (l-1) to the j-th neuron in layer l, and let a = σ(z) be the activation function.

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

[0143]

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

[0145]

[0146] Where z and a are the input and output values ​​of the neuron, respectively.

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

[0148] t(x,y,θ)=a L (x,y,θ;w,b); (15).

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

[0150] Since the PINN neural network has a large number of initial weights, this invention adopts a binary encoding method that is easy to implement with operations such as crossover and mutation; the fitness function is the sum of the absolute values ​​of errors over all time steps; the objective function is the reciprocal of the individual's fitness; the selection operation often uses the 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 the single-point crossover operator; the mutation operation uses the basic bit mutation operator, which refers to performing mutation operations on one or more randomly selected bits of genes in the individual's encoding string.

[0151] Training a fuzzy neural network using a hybrid optimization method combining genetic algorithms and the PINN algorithm. and The parameters are used to search globally for chromosomes that are superior after genetic optimization, thus obtaining an approximate optimal solution for the weights, and then the PINN algorithm is used to quickly and finely adjust them.

[0152] Finally, based on this neural network, it is necessary to fine-tune the parameters according to the influence of key system indicators such as overshoot and settling time in the actual simulation curve 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 differential control model of the magnetic levitation bearing and the kinematic model, the control input current is constrained by the Hildersee quadratic programming method to obtain the constrained MPC controller for carrying and transporting, wherein the MPC controller is tuned in real time in the prediction time domain and control time domain based on the classical reinforcement learning algorithm Q-Learning.

[0154] Model Predictive Controller Construction Based on Reinforcement Learning: After obtaining the differential control model of S2 and the kinematic model of S3, the Hildersee quadratic programming method is used to optimize and constrain the control input current to obtain a constrained MPC controller. The classic reinforcement learning algorithm Q-Learning is introduced to tune the relevant parameters of the MPC controller in real time.

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

[0156]

[0157] Let l be the loss function and R be the reference output signal. To control the input weights, Δu represents the change in the input quantity, y is the output vector, and u is the input vector. For the quadratic programming problem, the necessary condition for determining the extreme point is the Kuhn-Tak condition. Using the primal-dual method, finding the minimum value of the loss function l can be transformed into a dual problem. This invention uses Hildersee quadratic programming to solve this dual problem.

[0158] Reinforcement learning allows the system to interact with the external environment. Each interaction is rewarded or penalized to evaluate the interaction. The goal is to update the function Q"(s,a) through continuous interaction. The training of reinforcement learning follows 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) represents the reward for executing action policy π(s,a) in the current state s; Q(s,a) represents the reward for executing action policy π(s,a) in the state s before the update; α is the learning rate; R d The immediate reward obtained by executing the action policy π(s, a); η is the discount factor, Q π (s next,； To execute the action policy π(s, a) to reach the next state s next The total return, i.e. the expected future return, is s, where s is the environmental state and a is the strategy action.

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

[0162] S7. 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;

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

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

[0165] S8. Adjust the factor coefficients of the incremental PID control module, the PINN neural network module, and 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] Based on the different motion stages of the magnetic levitation bearing rotor of S3, a suitable dominant controller is matched. The PID controller based on PINN neural network dominates the start-up 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 adjusting the factor coefficients of the three control algorithms online.

[0167] A method for constructing a magnetic levitation bearing controller based on feature-dominated control. Figure 6 This is a step diagram illustrating the specific implementation of the present invention. First, magnetic circuit analysis and a precise mathematical model are established based on the structure of the hybrid magnetic levitation bearing.

[0168] The design integrates reinforcement learning-based model predictive control, neural network control, and PID control as the feature-dominant control. The points of each controller are summarized and paired with the corresponding controller based on the characteristics of each operating stage, serving as its dominant controller. Since the start-up stage is relatively simple and predicting this process relies on the electromagnetic principles between the displacement and current of the magnetic levitation bearing, the PINN neural network can predict parameters based on physical equations. Therefore, this invention uses a PINN neural network-based PID controller to dominate the start-up stage. The deceleration stage requires calculating the maximum spatial clearance of the rotor, making the process relatively complex and increasing the number of variables. Reinforcement learning-based model predictive control can reduce the workload of control parameter tuning. To ensure a smooth transition between the deceleration and acceleration processes and avoid decoupling problems, this invention uses reinforcement learning-based model predictive control to dominate the deceleration stage. In the fluctuation stage, the rotor continues to move up and down due to force imbalance until dynamic equilibrium is reached. This process is relatively simple, and this invention uses a PID controller to dominate the fluctuation stage, allowing it to converge quickly within a short time until stability. Three controllers are constructed 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 levitation bearing controller based on feature-dominated control. Figure 7 This is the control flowchart of the present invention. First, the displacement signal is measured and analyzed to determine which of the three motion stages it belongs to. Controllers are matched for each motion stage. A PID controller based on a PINN neural network dominates the start-up stage, a model predictive control based on reinforcement learning dominates the deceleration stage, and the PID controller dominates the fluctuation stage. Based on engineering experience, the factor coefficients of the three control algorithms are adjusted online to form different dominant control strategies. The output value is calculated, and its stability is determined. If unstable, the factor coefficients and controller parameters are readjusted; if stable, the process stops.

[0170] This invention utilizes intelligent algorithms and experimental data to construct mathematical models of the control current and bias current of the magnetic levitation bearing, the air gap length at the rotor balance point, the rotor displacement, and the relationships between the displacement sensor and the power amplifier, as well as a kinematic model of the magnetic levitation bearing rotor. Characteristic-driven control is employed, consisting of PID control, PINN neural network control, and reinforcement learning-based model predictive control, to more accurately predict the dynamic behavior of the magnetic levitation bearing, thereby achieving more precise control. Online adjustment of the coefficients of the three controller factors forms different characteristic-driven control strategies, enabling the control system to predict future states based on the rotor's motion characteristics at different stages, adapting to complex operating conditions and environmental changes, thus improving the overall stability and response speed of the system.

[0171] Traditional PID controllers may encounter performance bottlenecks when handling nonlinear systems. However, the use of PINN in this invention, by learning the physical and dynamic characteristics of the system, allows the controller to better adapt to complex nonlinear dynamic changes. Combined with a model predictive controller that can adaptively tune parameters based on the current system state, this enables the magnetic levitation bearing to maintain stable operation over a wider operating range.

[0172] The established mathematical model and control strategy can be applied to similar magnetic levitation bearing products and different operating conditions, improving the equipment's application range and ability to cope with various conditions, thus avoiding the equipment's high degree of simplification. Kinematic analysis of the magnetic levitation bearing rotor is performed, modeling the rotor's motion from acceleration to deceleration to stable operation, analyzing the characteristics of different stages, and constructing three motion stages for the magnetic levitation bearing: startup, deceleration, and fluctuation. This can prevent overshoot and increase the bearing's service life.

[0173] The following points need to be explained:

[0174] (1) The accompanying drawings of the embodiments of the present invention only involve the structures involved in the embodiments of the present invention. Other structures can refer to the general design.

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

[0176] (3) Where there is no conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other to obtain new embodiments.

[0177] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. The scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for constructing a magnetic levitation bearing controller based on feature-dominated control, characterized in that, include: Based on the principles of magnetic levitation, Ampere's circuital law for magnetic circuits, Newton's laws, and the static mathematical relationships of the internal components of a magnetic levitation bearing, a differential equation for the magnetic levitation bearing is established. A mathematical model for the displacement sensor and a mathematical model for the power amplifier are established, and the differential equation of the magnetic levitation bearing is converted into a Laplace model to obtain a differential control model for the magnetic levitation bearing. Based on the static mathematical relationships of the internal components of the magnetic levitation bearing, a kinematic analysis of the magnetic levitation bearing is performed from acceleration start-up, deceleration to stable operation, to obtain a kinematic model. The kinematic model includes the magnetic levitation bearing start-up stage, the magnetic levitation bearing deceleration stage, and the magnetic levitation bearing fluctuation stage. Based on the differential control model of the magnetic levitation bearing and the kinematics model, an incremental PID control module is constructed. Based on the incremental PID control module, a PINN neural network module is constructed and trained; Based on the magnetic levitation bearing differential control model and the kinematics model, the Hildersee quadratic programming method is used to constrain the control input current to obtain an MPC controller with constraints. The MPC controller is tuned in real time in the prediction time domain and control time domain based on the classical reinforcement learning algorithm Q-Learning. The incremental PID control module, the PINN neural network module, and the MPC controller are integrated into a feature-dominated controller, and factor coefficients are selected 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 PINN neural network module, and the MPC controller are adjusted respectively to achieve the dominant control of the incremental PID control module, the PINN neural network module, and the MPC controller. The incremental PID control module, the PINN neural network module, and the MPC controller each select factor coefficients ranging from 0 to 1, and the sum of the factors is 1.

2. The method for constructing a magnetic levitation bearing controller based on feature-dominated control according to claim 1, characterized in that, The differential equations for a magnetic levitation bearing, established based on the principles of magnetic levitation, Ampere's circuital law for magnetic circuits, Newton's laws, and the static mathematical relationships of the internal components of the bearing, include: The relationship between the current, force, and displacement of an electromagnet is established as formula (1): ；（1） Where F is the total attraction force between the stator and rotor. Let be the magnetic permeability of air. The electromagnetic force coefficient, x Let N be the displacement of the rotor in the magnetic levitation bearing, and N be the number of turns of the electromagnet coil. A The cross-sectional area of ​​the stator, rotor, and air gap magnetic field path. i This refers to the coil winding current; The force balance mode of the rotor is established by formula (2): ；（2） in, This represents the sum of the electromagnetic forces generated along the x-axis. For the mass of the rotor, For external interference force, It is the acceleration due to gravity; Based on the relationship between the current, force, and displacement of the electromagnet, we obtain... The expression for the sum of electromagnetic forces generated in the x-axis direction is given by formula (3): ；（3） in, The electromagnetic force generated by the electromagnet above. The electromagnetic force generated by the electromagnet below. For bias current, To control the current, The air gap length at the rotor balance point; Based on formulas (2) and (3), we obtain formula (4): ；（4） By performing a Taylor expansion of the bivariate function near the operating point of the rotor and neglecting higher-order infinitesimals, we obtain formula (5): ；（5） in, For the displacement stiffness of the magnetic levitation bearing, ; For the current stiffness of the magnetic levitation bearing, ; Based on formulas (4) and (5), the differential equation of the magnetic levitation bearing is obtained as formula (6): ；（6）。 3. The method for constructing a magnetic levitation bearing controller based on feature-dominated control according to claim 2, characterized in that, The steps of establishing mathematical models for the displacement sensor and power amplifier, and converting the differential equation of the magnetic levitation bearing into a Laplace model to obtain the differential control model of the magnetic levitation bearing include: The differential equation of the magnetic bearing is transformed based on the Laplace model to obtain the differential control model of the magnetic bearing, which is Equation (7): ；（7） in, Let be the transfer function of the magnetic levitation bearing in the x-axis direction. This refers to the output of the magnetic levitation bearing in the x-axis direction. This represents the input of the magnetic levitation bearing in the x-axis direction. s For the complex variables of the magnetic levitation bearing system; The mathematical model of the displacement sensor is given by formula (8): ；（8） in, Let be the transfer function of the displacement sensor. For the gain of the displacement sensor, The hysteresis time constant of the displacement sensor; The mathematical model of the power amplifier is given by formula (9): ；（9） in, Let be the transfer function of the power amplifier. For the gain of the power amplifier, This is the hysteresis time constant of the power amplifier.

4. The method for constructing a magnetic levitation bearing controller based on feature-dominated control according to claim 3, characterized in that, The step of constructing an incremental PID control module based on the differential control model of the magnetic levitation bearing and the kinematics model includes: The control algorithm of the incremental PID control module is formula (10): ； （10） in, , k For sampling sequence number, This represents the output value of the PID control module at the k-th sampling time. For the first k The deviation value of the input to the PID control module at the next sampling time. For the first The deviation value input at the next sampling time The integral coefficient is... , These are the differential coefficients. , This is the proportionality coefficient. For differential time, Sampling time, The time for integration.

5. The method for constructing a magnetic levitation bearing controller based on feature-dominated control according to claim 4, characterized in that, The construction and training of the PINN neural network module based on the incremental PID control module includes: The physical process is described by the partial differential equations in the incremental PID control module, and the original function... Two-dimensional partial differential equations , which is formula (11): ；（11） in, for The nth derivative term, C is a constant. Here, x and y are the input parameters of the neural network, and θ is the parameter. by and The deviation modulus between the two values ​​is used as the loss function, and the weights of the neural network are adjusted using the gradient descent algorithm. and bias , make Approaching ,and, Approaching , The partial differential equation obtained after taking the gradient of the initial neural network is... This is the final model for the neural network; After multiple iterations of training A surrogate model for the PINN neural network; In this layer, neurons are connected via fully connected structures, and the output of each neuron in each layer... As the next layer of neurons The expression for the forward propagation process of the neuron is given by formula (12): ；（12） Among them, superscript l The subscript representing the layer number of the neural network. i and j Represents the neuron index. For the first The first in the layer The first neuron to the second The first in the layer The weights of each neuron, For the first The first in the layer The first neuron to the second The first in the layer Bias of each neuron For activation function, The last layer is the Lth layer, which is the output layer. The formula for the fitting function of the output is formula (15): ；（15）。 6. The method for constructing a magnetic levitation bearing controller based on feature-dominated control according to claim 5, characterized in that, When the activation function is a hyperbolic tangent function, the formula for the activation function is formula (13): ； （13） When the activation function is the sigmoid function, the formula for the activation function is formula (14): ；（14）。 7. The method for constructing a magnetic levitation bearing controller based on feature-dominated control according to claim 6, characterized in that, Based on the differential control model of the magnetic levitation bearing and the kinematics model, the Hildersee quadratic programming method is used to constrain the control input current to obtain a constrained MPC controller. The MPC controller is tuned in real-time using the classical reinforcement learning algorithm Q-Learning, and the prediction and control time domains of the MPC controller include: Set the prediction time domain and control time domain The cost function is constructed using quadratic programming, as shown in formula (16): ；（16） l Let R be the loss function, and R be the reference output signal. To control the input weights, Let y be the change in the input quantity, y be the output vector, and u be the input vector; The update expression for the Q-table after 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) represents the reward for executing action policy π(s,a) in the current state s; Q(s,a) represents the reward for executing action policy π(s,a) in the state s before the update; α is the learning rate; R d The immediate reward obtained by executing the action policy π(s, a); η is the discount factor, Q π (s next , ; To execute the action policy π(s, a) to reach the next state s next The total reward is denoted by s, where s represents the environmental state and a represents the action chosen by the strategy.

Images