A multi-point cross-coupling levitation control method of a sliding mode driven RBF network

Abstract

This invention belongs to the field of magnetic levitation control technology and proposes a multi-point cross-coupled levitation control method using a sliding mode driven RBF network. This method first constructs a sliding surface and radial basis function neural network based on the levitation gap error of a single-point electromagnet, deriving a sliding mode driven RBF neural network control method for the single-point electromagnet. Independent sliding mode driven RBF neural network control is then implemented at each of the four electromagnets. Based on the errors between points in the four-point suspension frame, dual cross-coupling terms for gap and speed are designed, and the error terms are superimposed on the control input, ultimately forming a sliding surface driven RBF controller combining cross-coupling control. This method improves the tracking performance of the target gap and the synchronization performance between various suspension points, achieving stable levitation of the suspension frame. Verification shows that this method still has significant control effects even under operating conditions with track irregularities and malfunctions.

Description

Technical Field

[0001] This invention belongs to the field of magnetic levitation control technology and relates to a multi-point cross-coupling levitation control method using a sliding mode driven RBF network. Background Technology

[0002] Compared to traditional wheel-rail transportation, maglev trains do not rely on wheel-rail contact. Instead, they levitate using electromagnetic attraction or repulsion, with traction power provided by linear motors. This avoids the frictional resistance inherent in traditional rail transportation, where wheel-rail contact is essential. Maglev trains utilize electromagnetic force for levitation, guidance, and traction. Maglev transportation offers advantages such as low noise, strong track adaptability, good traction and braking performance, low maintenance workload, and long lifespan. Currently, the most commonly used type is the Electromaglev Train System (EMS). Active control of the levitation system is crucial for ensuring the smoothness and safety of maglev train operation. Since the reference levitation gap during maglev train operation is approximately 10 millimeters, factors such as coupling between levitation points and track irregularities can degrade the dynamic performance of the vehicle, placing high demands on the vertical control system of the maglev train.

[0003] The levitation system of maglev trains exhibits strong nonlinearity and open-loop instability, making levitation control algorithms a hot research topic. Many researchers have proposed and improved various control systems for single-point levitation. Compared to single-point levitation systems, the EMS-type suspension system is characterized by multivariable models, open-loop instability, multi-electromagnet coupling, and diverse and unknown operational disturbances, all of which directly degrade the overall dynamic performance of the vehicle. For multi-point levitation control, the common approach is to control each levitation point individually, designing control laws based on the characteristics of the single-point levitation system. However, this independent control method does not consider the coupling disturbances between levitation points, nor does it adequately address the impact of structural deviations and dynamic force interferences on the interaction forces between levitation points. Furthermore, controlling each levitation point individually prevents access to information about the others, hindering coordinated control and compromising levitation accuracy. Therefore, reducing coupling disturbances between levitation points and improving the anti-interference capability of the levitation system in a strongly coupled multi-levitation system presents a critical technical challenge.

[0004] Some research has already begun on multi-point suspension systems. Li Qinan et al. (Li Qinan, Xu Dehong. Air gap cross-coupling control of a four-electromagnet-supported steel plate magnetic levitation system [J]. Proceedings of the CSEE, 2010, 30(33): 129-134) based on the steel plate dynamic model and introduced air gap cross-coupling control to improve the dynamic air gap synchronization performance. This control method is mainly based on traditional cross-coupling control, lacks online adaptive adjustment capability, and does not pay attention to the control effect and stability under actuator failure conditions. Xu Junqi et al. (Xu Junqi, Lin Guobin, Chen Chen, et al. Multi-point suspension modeling and control of maglev vehicles under load disturbance [J]. Journal of Tongji University (Natural Science Edition), 2020, 48(09): 1353-1363) proposed a cross-coupling control algorithm based on a multi-point suspension model to compensate for the output error of the system. This method only controls the electromagnets on one side of the suspension frame through PID control, and does not control the four-point suspension system of the entire suspension frame. It does not pay attention to the control effect and stability under actuator failure conditions. For example, Chinese patent application CN116774588 A discloses a dual cross-coupling adaptive backstepping control method for the suspension frame of an EMS-type maglev train. This method includes establishing a single-electromagnetic-iron suspension system model in a four-electromagnetic-iron suspension frame and determining the system state variables; setting an extended state observer to perform independent LESO-backstepping control at each of the four electromagnets; and setting a cross-coupling controller to apply cross-coupling control at any three points, superimposing an error term into the control input. This scheme solves the problem of suppressing various external disturbances and internal coupling disturbances in the vertical direction of the EMS-type maglev train suspension frame in the prior art, thereby improving the overall stability of the vehicle and the synchronization performance of each point on the suspension frame. However, this scheme still has certain limitations, such as not verifying it for key operating conditions like actuator failure. Summary of the Invention

[0005] This invention proposes a multi-point cross-coupling suspension control method using a sliding mode driven RBF network. This method improves the tracking performance of the target gap and the synchronization performance between various suspension points, achieving stable suspension of the suspension frame. Verification shows that this method still has significant control effects when dealing with operation conditions with uneven tracks and malfunctions.

[0006] The technical solution of this invention is implemented as follows:

[0007] A multi-point cross-coupled suspension control method for sliding mode driven RBF networks includes the following steps:

[0008] S1. Establish a four-electromagnetic suspension system model. For a single-point electromagnet, construct a sliding mode surface based on the suspension gap error. Use the sliding mode surface as the input of a radial basis function neural network (RBF) and use the Adam optimizer to perform online adaptive updates of the weights of the RBF to construct a single-point sliding mode-RBF controller. Perform independent sliding mode-driven RBF neural network control at each of the four electromagnets.

[0009] S2. Apply cross-coupling control at any three floating points, and superimpose gap-velocity dual cross-coupling terms on the output of the single-point sliding mode-RBF controller to generate the final control voltage.

[0010] Preferably, in step S1, the sliding surface S 1. As follows: ;

[0011] In the formula, c The scaling factor represents the error term; e Indicates tracking error;

[0012] The tracking error is as follows: ;

[0013] In the formula, y ref The suspension gap at the equilibrium point;

[0014] y 1 represents the levitation gap between the single electromagnet and the track;

[0015] x 1 represents the change in the suspension gap near the equilibrium point, i.e., the displacement error;

[0016] x 2 represents the rate of change of displacement error.

[0017] Preferably, the input layer of the radial basis function neural network is used to receive the constructed sliding surface, wherein the nonlinear activation function used for the hidden layer... h j as follows:

[0018]

[0019] In the formula: a j For the first j The center of the Gaussian function of each neuron; d j For the hidden layer j The width of the Gaussian function of each neuron.

[0020] Preferably, the radial basis function neural network adopts a 1-5-1 neural network structure, wherein the first layer is the input layer, which is used to receive the constructed sliding surface, and the second layer is the hidden layer.

[0021] The Adam optimizer aims to minimize the loss function E, which is:

[0022]

[0023] The gradient estimate of the loss function with respect to the weights of the radial basis function neural network is the gradient value grad, where the gradient value... grad The calculation formula is:

[0024] ;

[0025] In the formula, Δ i bi The change in current output by a radial basis function neural network.

[0026] Preferably, when using the Adam optimizer to adaptively update the weights of the radial basis function neural network online, the first moment... L t The calculation formula is: ;

[0027] Second moment v t The calculation formula is: ;

[0028] In the formula, L t-1 The first moment of the previous moment; v t-1 The second moment of the previous moment; β 1 is the attenuation factor for the first moment; β 2 is the attenuation factor of the second moment.

[0029] Preferably, for the first t Deviation correction of the first moment in the next iteration L 1 is:

[0030] ;

[0031] For the first t Deviation correction of the second moment in the next iteration v 1 is:

[0032] .

[0033] Preferably, for the first j Weights w j The update formula is:

[0034] ;

[0035] In the formula, Before the iteration, Indicates the result after iteration; α is the learning rate of the radial basis function neural network; ε For smoothing terms;

[0036] Preferably, the Δ i bi The calculation formula is as follows:

[0037] ;

[0038] In the formula, w 1. w 2. w 3. w 4. w 5 represents the weights. w j middle j =1, 2, 3, 4, 5;

[0039] h 1. h 2. h 3. h 4. h 5 represent nonlinear activation functions. h j middle j =1, 2, 3, 4, 5;

[0040] Finally, combining the control of the sign function at the output, the final control law is obtained as follows:

[0041] ;

[0042] In the formula sign ( s 1) is a symbolic function. η 2 represents the gain term of the sign function, Δ i ai This refers to the change in current output of the single-point sliding mode-RBF controller after incorporating the sign function.

[0043] Preferably, the calculation of the gap-velocity dual cross-coupling term includes: calculating the gap synchronization error and the gap change speed synchronization error of any three suspension points, merging them to obtain the total synchronization error, and obtaining the corresponding gap-velocity dual cross-coupling term after the total synchronization error is passed through the feedback gain in the cross-coupling controller.

[0044] Preferably, the step of calculating the gap synchronization error of any three suspension points is as follows:

[0045] The single-point gap synchronization error is as follows: ;

[0046] Choosing any three gaps as control targets, the corresponding synchronization errors are:

[0047] , .

[0048] Preferably, the synchronization error of the gap change rate d vi The calculation is as follows: .

[0049] Preferably, the total synchronization error is:

[0050] The total synchronization error, after passing through the feedback gain in the cross-coupled controller, yields the gap-velocity dual cross-coupling term. k s d s ;

[0051] in, k s This represents the gain of the cross-coupled controller.

[0052] Preferably, the final control voltage is calculated as follows:

[0053]

[0054] in, k s For the cross-coupled controller gain;

[0055] This represents the equivalent perturbation of each electromagnet in a four-electromagnet system.

[0056] u si Indicates the first i The voltage applied by the electromagnet controls the input;

[0057] This represents the change in current obtained from the current control law of each of the four electromagnets.

[0058] This indicates the relative levitation gap y at the corresponding positions of the four electromagnets to the target gap. ref The deviation value;

[0059] This represents the total synchronization error at any three of the four electromagnets.

[0060] R This indicates the resistance of the electromagnet coil;

[0061] L This represents the equivalent inductance of an electromagnet when it is in its equilibrium position.

[0062] k i This represents the change in electromagnetic force when the current changes by a unit amount.

[0063] The beneficial effects of the present invention using the above technical solution are as follows:

[0064] This invention proposes a sliding surface-driven RBF control method with dual cross-coupling of clearance and velocity. First, based on the suspension clearance error of a single-point suspension system, a sliding surface and radial basis function neural network are constructed to derive a control method for a single electromagnet, and the stability of this control method is proven. Simultaneously, based on the errors between the points in a four-point suspension frame, dual cross-coupling terms of clearance and velocity are designed as compensation inputs to the controller input, ultimately forming a sliding surface-driven RBF controller combining cross-coupling control. The proposed method improves the interference caused by coupling between suspension points during the suspension process, enhances the synchronization performance of the suspension clearance between points, and achieves stable suspension of the suspension frame. Experimental results verify the effectiveness of the proposed method. Attached Figure Description

[0065] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0066] Figure 1 This is a schematic diagram of the four-point suspension frame structure of the present invention.

[0067] Figure 2 This is a block diagram of the open-loop suspension system of the present invention.

[0068] Figure 3 This is a structural diagram of the single-point electromagnet levitation system of the present invention.

[0069] Figure 4 This diagram illustrates the interference force settings for the inherent low-frequency periodic disturbances during the operation of a maglev vehicle under simulated operating conditions.

[0070] Figure 5 The simulation comparison results of various control methods under the working conditions are shown below.

[0071] Figure 6 The simulation comparison results of various control methods under operating condition 2 are presented.

[0072] Figure 7 The simulation comparison results of various control methods under three operating conditions are presented.

[0073] Figure 8The diagram shows the gap response results of suspension point 2 under the operating conditions of working condition 3 and SMS-RBF-CCC control.

[0074] Figure 9 The diagram shows the gap response results of the suspension point 2 under the operating conditions of condition 3 and under SMS-RBF-CCC control without using the sign function.

[0075] Figure 10 The diagram shows the gap response results of suspension point 2 under the operating conditions of working condition 3 and the backstepping with LESO method in the existing patent CN 116774588 A.

[0076] In the figure, a represents the gap response diagram of suspension point 1, b represents the gap response diagram of suspension point 2, c represents the gap response diagram of suspension point 3, and d represents the gap response diagram of suspension point 4. Detailed Implementation

[0077] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0078] This invention provides a multi-point cross-coupled suspension control method for sliding mode driven RBF networks, comprising the following steps:

[0079] A four-electromagnet suspension system model was established. For a single-point electromagnet, a sliding surface was constructed based on the suspension gap error. The sliding surface was used as the input of a radial basis function neural network, and the Adam optimizer was used to adaptively update the weights to construct a single-point sliding mode-RBF controller.

[0080] Based on the single-point sliding mode-RBF controller, gap synchronization error and speed synchronization error are introduced to construct a gap-speed dual cross-coupling term. Cross-coupling feedback compensation is applied only to any three of the four suspension points to generate a cross-coupling control law. The cross-coupling control law is superimposed on the output of the single-point sliding mode-RBF controller at the corresponding suspension point to form a sliding mode driven RBF neural network cross-coupling controller (SMS-RBF-CCC), realizing the coordinated control of the suspension system.

[0081] Specifically as follows:

[0082] 1. Model Construction of a Four-Electromagnet Suspension System

[0083] The maglev suspension system is equipped with four levitation electromagnets and a gap sensor. The levitation electromagnets provide electromagnetic force to balance the weight of the suspension system, while the gap sensor provides the levitation gap input to the controller for levitation control. A schematic diagram of the four-point suspension system of the EMS maglev train is shown below. Figure 1 As shown, Figure 1 In f i The electromagnetic force provided to the electromagnet, and simultaneously defined y i Δ is the levitation gap between the electromagnet and the track. y i and Δ f i These are the suspension gaps y i and electromagnetic force f i The change in quantity near the equilibrium point.

[0084] Because the motion of the four electromagnets on the suspension frame is coupled, the motion state of the suspension frame is decomposed into vertical ( z (axis translation), rolling () x (axis rotation), pitch () y From the three modes of rotation (axis rotation), the transformation matrix from electromagnetic force to vertical acceleration can be obtained, that is, the dynamic model is shown in equation (1):

[0085] (1)

[0086] in, (2)

[0087] In the formula: m For the mass of the suspension frame, m 1 represents the rolling equivalent mass. m 2 represents the pitch equivalent mass. A This is the force-acceleration transformation matrix.

[0088] Before building the model, we first make the following assumptions:

[0089] (1) Since the current in the electromagnet coil is small in actual operation and simulation, the magnetic saturation phenomenon is almost non-existent, so the magnetic saturation phenomenon is ignored here.

[0090] (2) Since the temperature rise of the electromagnet has little effect on the resistance during actual operation and is equipped with an efficient cooling system, the influence of the temperature rise during operation is ignored here. The eddy current dragging phenomenon that occurs under special circumstances is mainly reflected in the interference of the levitation force, so it is regarded as an external interference.

[0091] (3) For the convenience of subsequent analysis, the leakage inductance of the electromagnetic coil is ignored, and it is assumed that the permeability of the ferromagnetic material in the electromagnet circuit is infinite.

[0092] The electromagnetic force of a single electromagnet is:

[0093] (3)

[0094] In the formula:

[0095] μ 0 represents the permeability of air;

[0096] N This refers to the number of turns in the coil, i.e., the number of turns in the electromagnet winding.

[0097] A s This is the effective area of ​​the electromagnet, i.e., the area of ​​the electromagnet's magnetic poles;

[0098] i ref This refers to the coil current at the equilibrium point.

[0099] y ref The suspension gap at the equilibrium point is the point of equilibrium.

[0100] Δ i i This represents the change in current near the equilibrium point;

[0101] Δ y i For suspension gap y i The change in quantity near the equilibrium point.

[0102] Linearizing the above equation at the equilibrium point, we obtain the change in electromagnetic force as follows:

[0103] (4)

[0104] In the above formula k y This represents the change in electromagnetic force per unit length of gap change. k i Δ represents the change in electromagnetic force when the current changes by a unit amount. f i Electromagnetic force f i The change near the equilibrium point, where:

[0105] (5)

[0106] (6)

[0107] The voltage across the electromagnet coil can be expressed as:

[0108] (7)

[0109] In the formula:

[0110] i i The current passing through the electromagnet;

[0111] R This is the resistance of the electromagnet coil, i.e., the resistance of the electromagnet winding.

[0112] The total magnetic flux; where, ;

[0113] Equivalent inductance of an electromagnet in its equilibrium position ;

[0114] Therefore, the change in coil voltage is:

[0115] (8)

[0116] The sliding mode-RBF controller itself outputs the change, therefore Δ u i = u mi , ;

[0117] In summary, the open-loop transmission suspension system structure diagram is as follows: Figure 2 As shown:

[0118] The system control input is u mi ,Right now Figure 2 In u m1 , u m2 , u m3 , u m4 , respectively represent the voltage control inputs applied to the electromagnets at suspension points 1, 2, 3, and 4, i.e., the voltage control inputs. i =1, 2, 3, 4, output is Δ y i The magnetic levitation suspension is a 4-input 4-output coupled system.

[0119] 2. Construct a single-point sliding mode-RBF controller

[0120] 2.1 Construction of Sliding Surface Driven RBF Neural Network Controller

[0121] The suspension frame is a multi-input, multi-output, and multi-parameter system with a certain degree of coupling. To achieve suspension control, separate suspension controllers need to be designed for each of the four suspension points, allowing independent control of each point to ensure balance. The schematic diagram of the single-iron suspension system is shown below. Figure 3 As shown.

[0122] Taking the electromagnet at levitation point 1 as an example, that is, the first... i When = 1, the relationship between the single-point levitation electromagnet and its equilibrium position is as follows:

[0123] (9)

[0124] In the formula: f d This refers to the impact of various disturbances on the system.

[0125] make , , x 1 is defined as a system state variable. x 1 represents the change in the suspension gap near the equilibrium point, i.e., the displacement error;

[0126] x 2 represents the rate of change of the displacement error, and is defined as the second state variable of the system, i.e.:

[0127] (10)

[0128] The target trajectory that needs to be tracked in the suspension gap is y ref The tracking error is:

[0129] (11)

[0130] Combination Figure 1 The single-point suspension system design of the sliding surface S 1 is

[0131] (12)

[0132] c The scaling factor representing the error term. c =2.

[0133] Based on the aforementioned designed sliding surface, online learning is performed using a radial basis function neural network for suspension control, thus enabling the sliding surface to... S The input layer is considered as the neural network input to drive the neural network, employing a 1-5-1 neural network structure. The first layer is the input layer, used to receive the constructed sliding surface, and the second layer is the hidden layer, used for the nonlinear activation function of the hidden layers. hj As shown below:

[0134] (13)

[0135] In the formula: a j For the first j The center of the Gaussian function of each neuron; d j For the hidden layer j The width of the Gaussian function of each neuron. d j =0.75.

[0136] The Gaussian function node centers of the RBF neural network are [-3, -1.5, 0, 1.5, 3].

[0137] The Adam optimizer aims to minimize the loss function E, since the control objective of this system is to make the sliding surface... S When 1 is zero, the loss function is:

[0138] (14)

[0139] The gradient estimate of the loss function with respect to the weights of the radial basis function neural network is the gradient value grad, which guides the direction and magnitude of weight updates. grad The calculation formula is:

[0140] (15)

[0141] Δ i bi This represents the change in current output by the radial basis function neural network.

[0142] The Adam (Adaptive Moment Estimation) optimizer is used to adjust the weights during network weight updates. The Adam optimizer is a method that combines momentum and adaptive learning rate. It adaptively adjusts each parameter by calculating the first and second moments of the gradient. Compared to the fixed learning rate in gradient descent, the Adam optimizer allows each parameter to have an independent adaptive learning rate.

[0143] When performing weight update iterations, it is necessary to adjust the first moment. L t Second moment v t Correction for deviation of first moment L Correction for deviations of the first and second moments v 1. Perform calculations. First-order moment. L tand second moment v t The calculation formula is as follows:

[0144] (16)

[0145] (17)

[0146] In the formula, L t-1 The first moment of the previous moment; v t-1 The second moment of the previous moment; β 1 is the attenuation factor for the first moment; β 2 is the attenuation factor for the second moment;

[0147] Weight w 1. w 2. w 3. w 4. w 5. Initialization is random, with the first and second moments initially set to 0.

[0148] For the first t Deviation correction of the first moment in the next iteration L 1 is:

[0149] (18)

[0150] For the first t Deviation correction of the second moment in the next iteration v 1 is:

[0151] (19)

[0152] For the first j Weights w j The update formula is:

[0153] (20)

[0154] In the formula, Before the iteration, Indicates the result after iteration; α is the learning rate of the radial basis function neural network; ε For smoothing terms;

[0155] Δ i bi for:

[0156] (twenty one)

[0157] In the formula,w 1. w 2. w 3. w 4. w 5 represents the weights. w j middle j =1, 2, 3, 4, 5; h 1. h 2. h 3. h 4. h 5 represent nonlinear activation functions. h j middle j =1, 2, 3, 4, 5 。

[0158] To enhance the robustness of the control system and ensure that the state trajectory converges to the sliding surface within a finite time, the final control law is obtained by combining the control of the sign function at the final output:

[0159] (twenty two)

[0160] In the formula sign ( s 1) is a symbolic function. η 2 represents the gain term of the sign function. η 2=3; Δ i ai This refers to the change in current output of the single-point sliding mode-RBF controller after incorporating the sign function.

[0161] (twenty three)

[0162] The voltage control rate of the electromagnet at suspension point 1 is:

[0163] (twenty four)

[0164] For an electromagnet at any levitation point, i.e. the first... i The voltage control rate of the electromagnet is:

[0165] (25)

[0166] The learning rate of the neural network is set according to the debugging settings. α The attenuation factor of the first moment is 0.6. β 1 is 0.9, the attenuation factor of the second moment. β 2 is 0.999. A smoothing option is set to prevent division by zero errors during the update process. ε It is 0.00000008.

[0167] 2.2 Proof of Lyapunov Stability of Controller

[0168] Design a Lyapunov function. v for:

[0169] (26)

[0170] There is an ideal weight It can satisfy the following formula:

[0171] (27)

[0172] From equations (12), (22), and (27), we can obtain:

[0173] (28)

[0174] in For weighted error, Let be the radial basis functions in an RBF neural network, where the sliding surface is the sliding surface. S 1 is used as input.

[0175] From equations (26) and (28), the derivative of the Lyapunov function can be obtained as follows:

[0176] (29)

[0177] Arrangement of equation (29) yields:

[0178] (30)

[0179] exist , , ,in This is the upper limit of the weighting error. This is the upper bound of the RBF basis functions. D It is the upper limit of external disturbances. c 3 represents the coefficients related to the Adam optimizer, where... .

[0180] Based on the above conditions, the following formula can be derived:

[0181] (31)

[0182] make We can conclude that:

[0183] (32)

[0184] when A <0, that is When it exists Make Stability has been proven.

[0185] 3. Establishment of synchronization error

[0186] To achieve better synchronization performance for each suspension point, the target for gap synchronization control of each suspension point is selected as follows:

[0187] (33)

[0188] In the formula y refi ( i =1, 2, 3, 4) are the expected gap values ​​for each suspension point.

[0189] Based on the above gap synchronization control objective, the synchronization objective can be further optimized as follows:

[0190] (34)

[0191] Based on the above formula, a target for gap synchronization error can be set. c =0:

[0192] (35)

[0193] When the expected values ​​of all gaps are the same, that is y ref = y ref The control objective can be simplified to y 1= y 2= y 3= y 4. At this time, let The gap synchronization error can be converted into:

[0194] (36)

[0195] Since the suspension frame deformation is very small compared to the suspension displacement caused by track irregularities and external force changes, it can be ignored. The suspension frame is statically indeterminate, constituting a 3-DOF system in the vertical direction. For the 4 gaps that need to be controlled, synchronous control of the gaps can be achieved by cross-coupling control at any three points. That is, the suspension frame is a 4-output, 3-control target system. Selecting gaps 1, 2, and 3 as control targets, the corresponding synchronization error is:

[0196] (37)

[0197] (38)

[0198] 4. Cross-coupling control

[0199] When only individual suspension control is performed on each suspension point, the mutual influence between the suspension points is not considered. Therefore, a gap cross-coupling term needs to be introduced into the four-point suspension system. Furthermore, to compensate for the reduced system damping and increased gap overshoot caused by a single gap coupling term, a gap change rate cross-coupling term is introduced. (Gap change rate synchronization error) d vi and gap synchronization error d xi The relationship is:

[0200] (39)

[0201] The total synchronization error is:

[0202] (40)

[0203] The total synchronization error, after passing through the feedback gain in the cross-coupled controller, yields the corresponding coupling term, which is then superimposed onto the sliding mode driven RBF neural network controller of the single electromagnet to form the cross-coupled backstepping control. u s ,Right now:

[0204] u si = u mi + k s d si (41)

[0205] In the formula: k s For the cross-coupled controller gain, k s =5000.

[0206] The final control strategy is as follows: independent sliding mode driven RBF neural network control is performed at four points, and cross-coupling control is applied at points 1, 2, and 3. An error term is superimposed on the control input to represent the disturbance caused by the actual external force and unknown factors, as shown in equation (38). i The control input applied to the electromagnet is as follows:

[0207] (42)

[0208] In the formula: k s For the cross-coupled controller gain;

[0209] This represents the equivalent perturbation of each electromagnet in a four-electromagnet system.

[0210] u si Indicates the first i The voltage applied by the electromagnet controls the input;

[0211] This represents the change in current obtained from the current control law of each of the four electromagnets.

[0212] This indicates the relative levitation gap y at the corresponding positions of the four electromagnets to the target gap. ref The deviation value;

[0213] This represents the total synchronization error at any three of the four electromagnets.

[0214] R This indicates the resistance of the electromagnet coil;

[0215] L This represents the equivalent inductance of an electromagnet when it is in its equilibrium position.

[0216] k i This represents the change in electromagnetic force when the current changes by a unit amount.

[0217] The verification example performs simulation verification under different operating conditions.

[0218] 1. Specific data of the suspension system

[0219] The parameter values ​​of the maglev train levitation system are shown in Table 1.

[0220] Table 1 Parameters of the Suspension System

[0221]

[0222] The equivalent mass of the suspension frame is determined by its dimensions and moment of inertia, and the calculation method is as follows:

[0223] (43)

[0224] In the formula: l 1. l 2 represents the distance from the center of the magnetic attraction on one side to the center of gravity of the vehicle body.

[0225] The equivalent mass of the suspension system in the rolling mode was calculated. m 1 = 941.482 kg, equivalent mass in pitch mode m 2 = 220 kg.

[0226] 2. Simulation of multiple working conditions

[0227] In actual maglev train operation, various external disturbances arise due to external factors. Considering these, simulations were conducted under four different operating conditions to verify the feasibility and effectiveness of the maglev train's levitation control method under these conditions. Simultaneously, the effectiveness of the proposed sliding mode driven RBF network multi-point cross-coupled levitation control method (SMS-RBF-CCC) was compared with that of PD, LADRC, and Backstepping control methods. The controller parameters remained consistent across all four operating conditions, as detailed below:

[0228] PD control method parameters: k p =8000, k d =5000; where, k p For proportional gain, k d This is the derivative gain term, i.e., the proportional and differential gain in linear state error feedback;

[0229] LADRC control method parameters: k p =8000, k d =5000, r 0=30, h 0 = 2 × 10 -5 , w 0 = 1500 h =2×10 -5 , b =17.894, d =0.05, x a1 =1.248, x a2 =0.4; where, k p For proportional gain, k d This is the derivative gain term, i.e., the proportional and differential gain in linear state error feedback; r 0 and h 0 is the control parameter for the fhan function. r 0 indicates the fastness factor, which determines the convergence speed of the fastest synthesis function; h 0 indicates the precision factor. w 0 represents the bandwidth, i.e., the observer bandwidth or the bandwidth of the extended state observer, which is the core tuning parameter of LADRC; h The sampling step size, b Compensation factor, d For linear interval thresholds, x a1The power exponent of the displacement error fal function is... x a2 The power exponent of the velocity error fal function;

[0230] Backstepping control method parameters: k 1 = 220 k 2 = 110; where, k 1, k 2 represents the gain term in the subsystem, namely the gain of the virtual control law and the final control law in the backstepping method design, which is used to stabilize the state variables of the subsystem step by step.

[0231] The specific operating conditions are as follows:

[0232] (1) Condition 1: Apply periodic irregular disturbance force to each position to simulate the inherent low-frequency periodic disturbance in the operation of the maglev vehicle, the magnitude of which is shown in equation (43):

[0233] (44)

[0234] The interference force settings for simulating the inherent low-frequency periodic disturbances in the operation of maglev vehicles are as follows: Figure 4 As shown.

[0235] (2) Working condition 2: The vertical unevenness values ​​on the left and right sides of the running route of the suspended magnet are fitted by the unevenness spectrum to simulate the track unevenness caused by track surface roughness, misalignment of adjacent track sections, construction tolerance, pier height difference, support settlement, etc. during construction.

[0236] The maglev train is scheduled to run at a speed of 600 km / h. Under the conditions of (1) and (2), a delay of 0.012s is applied to the disturbance between the electromagnets at positions 1 and 2, and 3 and 4 of the suspension frame.

[0237] (3) Working condition 3: In the second working condition, the simulation time is extended to 20s. At the 10th second, a fault of half reduction of electromagnet coil is added at floating point 1 and floating point 2.

[0238] Referring to gap-velocity state feedback (PD) control without cross-coupling, LADRC control, backstepping control, and the multi-point cross-coupling suspension control method (SMS-RBF-CCC) of the sliding mode driven RBF network of this invention, the effect of the control method proposed in this invention is observed by comparing various control methods, and the gain of the cross-coupling controller in the controller is also discussed. k s =5000, in the sliding surface c =2, learning rate α=0.6, Gaussian function node centers in RBF neural network are [-3, -1.5, 0, 1.5, 3], and the width of Gaussian function is...d j =0.75, η 2=3.

[0239] (4) Under the operating conditions of working condition three, whether the symbolic function is used in the SMS-RBF-CCC method of the present invention and the backstepping with LESO method disclosed in the existing patent CN 116774588 A are compared.

[0240] 3. Experimental Results

[0241] 3.1 Results of Working Condition 1:

[0242] Table 2 Clearance parameters for each control method under operating condition 1 (Suspension point 1) (Unit: mm)

[0243]

[0244] Table 3 Clearance parameters for each control method under operating condition 1, suspension point 2 (unit: mm)

[0245]

[0246] Table 4. Clearance parameters for each control method under operating condition 1, suspension point 3 (unit: mm)

[0247]

[0248] Table 5. Clearance parameters for each control method under operating condition 1, suspension point 4 (unit: mm)

[0249]

[0250] The vertical displacement changes of the four suspension points of the suspension frame under working condition 1 are as follows: Figure 5 As shown, under the first operating condition, the control algorithm proposed in this invention has a smaller control amplitude and a more stable overall gap change compared to other comparative algorithms. Table 2-5 shows a horizontal comparison using various control indicators of the suspension point as representatives. According to the analysis of various indicators, it can be concluded that the average absolute deviation, standard deviation, and peak-to-peak value of the suspension gap under the SMS-RBF-CCC control algorithm are all superior to the PD, LADRC, and Backstepping control algorithms. The simulation experiment of this set of operating conditions proves the superior performance of the controller in dealing with low-frequency periodic interference.

[0251] 3.2 Results of Working Condition Two:

[0252] Table 6 Clearance parameters for each control method at suspension point 1 under operating condition 2 (unit: mm)

[0253]

[0254] Table 7 Clearance parameters for each control method at suspension point 2 under operating condition 2 (unit: mm)

[0255]

[0256] Table 8 Clearance parameters for each control method at suspension point 3 under operating condition 2 (unit: mm)

[0257]

[0258] Table 9 Clearance parameters for each control method at suspension point 4 under operating condition 2 (unit: mm)

[0259]

[0260] Figure 6 To illustrate the vertical displacement changes of the four suspension points of the suspension frame under various control methods in the second operating condition, the SMS-RBF-CCC control algorithm outperforms the PD, LADRC, and Backstepping algorithms in terms of both suspension gap stability and variation amplitude during the suspension process. A horizontal comparison of the algorithms is conducted using various control indicators at suspension point two as representatives, as shown in Tables 6-9. Based on the suspension indicators and overall suspension effect, it can be concluded that the SMS-RBF-CCC control algorithm outperforms the PD, LADRC, and Backstepping control methods in terms of the average absolute deviation, standard deviation, and peak-to-peak value of the suspension gap. Simulation experiments under this operating condition demonstrate that the controller still exhibits significant control effectiveness in dealing with the inherent high randomness and frequency of track irregularities during actual operation.

[0261] 3.3 Results for Working Condition 3:

[0262] The suspension index at each point under operating condition 3 is calculated and evaluated based on the operating condition of failure occurring 10 seconds later.

[0263] Table 10 Clearance parameters for each control method at suspension point 1 under operating condition 3 (unit: mm)

[0264]

[0265] Table 11 Clearance parameters for each control method at suspension point 2 under operating condition 3 (unit: mm)

[0266]

[0267] Table 12 Clearance parameters for each control method at suspension point 3 under operating condition 3 (unit: mm)

[0268]

[0269] Table 13 Clearance parameters for each control method at suspension point 4 under operating condition 3 (unit: mm)

[0270]

[0271] Figure 7 In the third operating condition, each control method corresponds to the vertical displacement changes of the four suspension points of the suspension frame. The operation for the first 10 seconds is the same as in operating condition two. At the 10th second, a fault occurs where half of the electromagnet coils at suspension points one and two fail, simulating a single-sided electromagnet fault. After the fault occurs, the suspension gap on the faulty side fluctuates to some extent under the control of each algorithm, while the side without fault is less affected than the other side. Figure 8 The magnified images at 10 seconds in Suspension Point 1 and Suspension Point 2 show that the suspension gap fluctuation caused by the electromagnet failure is greater under the control algorithms of PD, LADRC, and Backstepping than under the SMS-RBF-CCC control algorithm. The control performance indicators after 10 seconds are shown in Table 10-13. Comparison of various suspension indicators after the failure shows that the SMS-RBF-CCC control algorithm outperforms PD, LADRC, and Backstepping in terms of the average absolute deviation, standard deviation, and peak-to-peak value of the suspension gap. The simulation experiments under this set of conditions demonstrate that the controller still has significant control effectiveness in operating conditions with track irregularities and failures.

[0272] 3.4 Under operating conditions of Condition 3, the use of a sign function in the SMS-RBF-CCC method proposed in this invention is compared with the backstepping with LESO method in existing patent CN 116774588 A. The suspension gap response at suspension point 2 is used as the comparison point during the comparison process. The specific operating results are shown below:

[0273] Table 14 Clearance parameters of various control methods after the failure of suspension point 2 under operating condition 3 (unit: mm)

[0274]

[0275] pass Figure 8-10 A comparison of various control methods reveals that, in the initial stage without a fault, the method proposed in this patent exhibits slightly greater fluctuations than the Backstepping with LESO method due to the need for online learning during the initial levitation phase. The presence of the sign function results in better overall levitation performance in the initial stage compared to when no sign function is used. However, after a fault occurs within 10 seconds, the method... Figures 8 to 10Comparing the control effects of each method, the control method proposed in this patent is more robust than the other two control methods when the maglev system fails. Table 14 shows the gap index of each control method after the suspension system fails after 10 seconds of operation. As can be seen from Table 14, the SMS-RBF-CCC control method using the sign function is superior to the backstepping with LESO method in the fault condition in terms of the average absolute deviation, standard deviation, and peak-to-peak value.

[0276] As can be seen from the simulation results above, the control strategy proposed in this paper has certain advantages in terms of tracking performance of target gaps and synchronization performance between various suspension points in a multi-point suspension system.

[0277] This invention proposes a sliding surface drive RBF control method with dual cross-coupling of clearance and speed for EMS maglev trains. First, a sliding surface and radial basis function neural network are constructed based on the suspension clearance error of a single-point electromagnet to derive the control method for the single-point electromagnet. Based on the error between each point in the four-point suspension frame, dual cross-coupling terms of clearance and speed are designed as compensation inputs to the controller input, ultimately forming a sliding surface drive RBF controller that combines cross-coupling control. The control method proposed in this invention improves the interference caused by the coupling between suspension points during the suspension process, enhances the synchronization performance of the suspension clearance between each point, and achieves stable suspension of the suspension frame.

[0278] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-point cross-coupled suspension control method for sliding mode driven RBF networks, characterized in that, Includes the following steps: S1. Establish a four-electromagnetic-magnetic suspension system model. For a single-point electromagnet, construct a sliding mode surface based on the suspension gap error. Use the sliding mode surface as the input of the RBF network, and use the Adam optimizer to adaptively update the weights of the RBF network online, constructing a single-point sliding mode-RBF controller. Perform independent sliding mode drive RBF network control at each of the four electromagnets; wherein, the change in current Δi output by the RBF network is... bi The Δi bi The calculation formula is as follows: ； In the formula, w1, w2, w3, w4, and w5 represent the weights w, respectively. j In the given information, j = 1, 2, 3, 4, 5; h1, h2, h3, h4, and h5 represent the nonlinear activation functions h1, h2, h3, h4, and h5, respectively. j In the given information, j = 1, 2, 3, 4, 5; Finally, combining the control of the sign function at the output, the final control law is obtained as follows: ； In the formula, sign(s1) is the sign function, η2 is the gain term of the sign function, and Δi ai S1 represents the change in current output of the single-point sliding mode-RBF controller after incorporating the sign function; where S1 represents the sliding surface. S2. Apply cross-coupling control at any three floating points, and superimpose gap-speed dual cross-coupling terms on the output of the single-point sliding mode-RBF controller to generate the final control voltage; The calculation of the gap-velocity dual cross-coupling term includes: Choosing any three gaps as control targets, the corresponding synchronization errors are: ， ； The synchronization error of the gap change rate d vi The calculation is as follows: ； The total synchronization error is: ; The total synchronization error, after passing through the feedback gain in the cross-coupled controller, yields the gap-velocity dual cross-coupling term k. s d s ; Where, k s This refers to the feedback gain in the cross-coupled controller. The final control voltage is calculated as follows: ； in, This represents the equivalent perturbation of each electromagnet in a four-electromagnet system. u si This represents the voltage control input applied to the i-th electromagnet; This represents the change in current obtained from the current control law of each of the four electromagnets. This indicates the relative levitation gap y at the corresponding positions of the four electromagnets to the target gap. ref The deviation value; This represents the total synchronization error at any three of the four electromagnets. R represents the resistance of the electromagnet coil; L represents the equivalent inductance of the electromagnet when it is in equilibrium; k i This represents the change in electromagnetic force when the current changes by a unit amount.

2. The multi-point cross-coupling suspension control method for a sliding mode driven RBF network according to claim 1, characterized in that, In step S1, the sliding surface S1 is as follows: ; In the formula, c represents the scaling factor of the error term; e represents the tracking error; The tracking error is as follows: ; In the formula, y ref The suspension gap at the equilibrium point; y1 represents the levitation gap between the single electromagnet and the track; x1 represents the change in the suspension gap near the equilibrium point, i.e., the displacement error; x2 represents the rate of change of displacement error.

3. The multi-point cross-coupling suspension control method for a sliding mode driven RBF network according to claim 2, characterized in that, The input layer of the RBF network is used to receive the constructed sliding surface, wherein the nonlinear activation function h for the hidden layer is used. j as follows: ； In the formula: ɑ j d is the center of the Gaussian function of the j-th neuron; j The width of the Gaussian function of the j-th neuron in the hidden layer; The Adam optimizer aims to minimize the loss function E, which is: ； The gradient estimate of the loss function with respect to the weights of the RBF network is the gradient value grad, which is calculated using the following formula: ； In the formula, Δi bi This represents the change in current output by the RBF network.

4. The multi-point cross-coupling suspension control method for a sliding mode driven RBF network according to claim 3, characterized in that, When the Adam optimizer is used to adaptively update the weights of the RBF network online, the first moment L t The calculation formula is ； Second moment v t The calculation formula is ; In the formula, L t-1 v is the first moment from the previous moment; t-1 β1 is the second moment of the previous moment; β2 is the decay factor of the first moment; β3 is the decay factor of the second moment.

5. The multi-point cross-coupling suspension control method for a sliding mode driven RBF network according to claim 4, characterized in that, When the Adam optimizer is used to adaptively update the weights of the RBF network online, the bias correction L1 of the first moment at the t-th iteration is: ； The deviation correction v1 for the second moment at the t-th iteration is: 。 6. The multi-point cross-coupling suspension control method for a sliding mode driven RBF network according to claim 5, characterized in that, When using the Adam optimizer to perform online adaptive updates of the weights of the RBF network, for the j-th weight w j The update formula is: ； In the formula, This represents the weights before the iteration. ε represents the weights after iteration; α is the learning rate of the RBF network; ε is the smoothing term.

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