A maglev train levitation control method, device, and storage medium

Abstract

The present invention relates to a maglev train levitation control method, device and storage medium. The method obtains the basic unevenness form of the target track beam, constructs a track unevenness model, and calculates the disturbance generated by the track unevenness by using the track unevenness model; constructs a nominal model of the maglev train levitation system; superimposes the disturbance and the nominal model of the maglev train levitation system to obtain the actual model of the maglev train levitation system; obtains the actual value of the current levitation air gap, and calculates the levitation air gap error; determines whether the levitation air gap error is 0. If so, the current output current magnitude is maintained, and a new actual value of the levitation air gap is obtained. Otherwise, the optimal current magnitude is output by using the tube model-based predictive control method to adjust the air gap, and a new actual value of the levitation air gap is obtained. Compared with the prior art, the present invention has the advantages of fully considering the influence of track unevenness on the maglev train levitation system using a model predictive controller, thereby enhancing the robustness of the levitation system, etc.

Description

Technical Field

[0001] The present invention relates to the field of rail transit, and in particular, to a maglev train levitation control method, device, and storage medium. Background Art

[0002] With the continuous development of urbanization and the increasing traffic demand, maglev trains, as an efficient, environmentally friendly, and fast means of transportation, have gradually attracted attention. Different from traditional rail trains, maglev trains achieve contactless levitation operation through maglev technology, thus avoiding friction and wear, and improving the running speed and safety.

[0003] The levitation system of maglev trains is crucial for ensuring the stable, efficient, and safe operation of trains. During the actual operation process, maglev trains face various disturbances, among which the influence of track irregularities on the levitation system is the most direct and significant. Model predictive control, as a control method that can actively handle constraints, is gradually being applied to the maglev train levitation control system. However, existing model predictive levitation control methods are all designed based on ideal working conditions and ignore the disturbances caused by track irregularities. For example, Chinese Patent CN115473464A discloses a maglev yaw motor control method based on neural network model predictive control. This method includes, while yawing, the rotor converter adopting a fuzzy neural network model predictive control strategy to control the current of the rotor, so that the rotor of the maglev yaw motor remains at the levitation equilibrium point throughout the yawing process, and can achieve coordinated control of the stator and rotor. However, in fact, this method may cause the state of the levitation system to exceed the constraints, thereby triggering the failure of the controller and ultimately leading to the instability of the maglev train levitation system. Therefore, how to improve the robustness of the maglev train levitation system on the premise of considering track irregularities has become a problem to be solved in this field. Summary of the Invention

[0004] The purpose of the present invention is to overcome the above-mentioned defect of the existing technology that ignores the disturbance to the maglev train levitation system caused by track irregularities, and to provide a maglev train levitation control method, device, and storage medium to enhance the robustness of the levitation system.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] According to the first aspect of the present invention, there is provided a maglev train levitation control method, including the following steps:

[0007] S1, obtaining the basic irregularity form of the target track beam, constructing a track irregularity model, and using the track irregularity model to calculate the disturbance generated by track irregularities;

[0008] S2. Based on Newton's laws of motion and Maxwell's equations, construct a nominal model of the maglev train levitation system;

[0009] S3. Based on the perturbation and the nominal model of the maglev train levitation system, superimpose to obtain an actual model of the maglev train levitation system;

[0010] S4. Obtain the actual value of the current levitation air gap, calculate the levitation air gap error, and obtain the magnitude of the current output at present;

[0011] S5. Determine whether the levitation air gap error is 0. If so, execute step S6; otherwise, execute step S7;

[0012] S6. Keep the magnitude of the current output at present and return to step S4;

[0013] S7. Based on the track irregularity model, the nominal model of the maglev train levitation system, and the actual model of the maglev train levitation system, use the method of model predictive control based on the tube model to output the optimal current magnitude, adjust the air gap, and return to step S4.

[0014] As a preferred technical solution, for the method of model predictive control based on the tube model, the specific implementation process includes:

[0015] Based on the perturbation, contract the constraints of the actual model;

[0016] Based on the nominal model and the contracted constraints, optimize the preset objective function to obtain the optimal output of the nominal model;

[0017] Based on the optimal output of the nominal model, use feedback control to obtain the optimal current magnitude of the output of the actual model.

[0018] As a preferred technical solution, the expression of the track irregularity model is:

[0019]

[0020] In the formula, α i is the weight coefficient, y i represents the basic irregularity form of the track beam, s is the longitudinal abscissa of the track beam, and i = 1, 2, 3, 4.

[0021] As a preferred technical solution, the values of the weight coefficient include:

[0022] α i = 0, 1 (i = 1, 2, 3, 4)

[0023] The expression of the basic irregularity form includes:

[0024]

[0025]

[0026] In the formula, s is the longitudinal abscissa of the track beam, s period is the period when the basic irregularity form appears, L is the measured length of the track beam, a 1 , a 2 , b 1 , b 2 are the amplitudes of each basic irregularity measured in advance.

[0027] As a preferred technical solution, the calculation formula of the perturbation is:

[0028] w = y[(k + 1)s 0 - y[ks 0 , k = 0, 1, 2, ……

[0029] In the formula, s 0 is the sampling distance, and y[ks 0 is the sequence of track irregularity points generated by sampling.

[0030] As a preferred technical solution, the expression of the nominal model of the maglev train suspension system is:

[0031]

[0032] Among them,

[0033]

[0034] In the formula, represents the nominal model of the maglev train suspension system, is the state of the nominal model of the maglev train suspension system, △x g represents the suspension gap error, represents the first derivative of the suspension gap error, is the output of the nominal model of the maglev train suspension system, m is the mass of the maglev train car body, k e is the electromagnetic constant, x g0 is the reference value of the suspension gap, i c is the actual value of the electromagnetic coil current, i c0 is the reference value of the electromagnetic coil current.

[0035] As a preferred technical solution, the calculation formula of the suspension gap error is:

[0036] △x g = x g - x g0

[0037] In the formula, △x gis the suspension air gap error, x g is the actual value of the suspension air gap, x g0 is the reference value of the suspension air gap.

[0038] As a preferred technical solution, the expression of the actual model of the maglev train suspension system is:

[0039]

[0040] where

[0041]

[0042]

[0043] In the formula, Σ represents the actual model of the maglev train suspension system, x is the state of the actual model of the maglev train suspension system, u is the output of the actual model of the maglev train suspension system, w is the disturbance generated by track irregularities,

[0044] The constraints of the actual model of the maglev train suspension system are:

[0045] x ∈ X = {x|x lb ≤ x ≤ x ub}

[0046] u ∈ U = {u|u lb ≤ u ≤ u ub}

[0047] In the formula, x lb represents the difference between the actual minimum value and the reference value of the suspension air gap, x ub represents the difference between the actual maximum value and the reference value of the suspension air gap, X is the set of states of the actual model of the maglev train suspension system, u lb represents the difference between the actual minimum output current of the coil and the reference value, u ub represents the difference between the actual maximum output current of the coil and the reference value, U is the set of outputs of the actual model of the maglev train suspension system.

[0048] According to the second aspect of the present invention, there is provided a maglev train suspension control device, including a memory, a processor, and a program stored in the memory, and the processor implements the method when executing the program.

[0049] According to the third aspect of the present invention, there is provided a storage medium, on which a program is stored, and the method is implemented when the program is executed.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] 1. The present invention takes into account the influence of track irregularities on the suspension system, models the track irregularities, calculates the corresponding disturbances using the track irregularity model, and obtains the actual model of the maglev train suspension system by superimposing the disturbances and the nominal model of the maglev train suspension system. It can fully consider the influence of the disturbances brought by track irregularities on the suspension system. On this basis, the method of predictive control based on the tube model is used to control the output of the optimal current magnitude and adjust the air gap, which can effectively improve the accuracy of model prediction. Compared with the traditional model predictive control method that ignores external disturbances, this method can effectively enhance the robustness of the suspension system;

[0052] 2. The control method for the maglev train suspension system provided by the present invention has strong scenario adaptability and is generally applicable to high-, medium-, and low-speed maglev trains. Brief Description of the Drawings

[0053] Figure 1 is a schematic flow chart of the method provided by the present invention;

[0054] Figure 2 is a schematic diagram of the track beam in the embodiment of the present invention;

[0055] Figure 3 is the actual state predicted by the suspension system controller at a certain moment in the embodiment of the present invention;

[0056] Figure 4 is the air gap error under the actual operation of the maglev train in the embodiment of the present invention. Detailed Embodiment

[0057] The present invention will be described in detail below with reference to the drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and the detailed implementation manners and specific operation processes are given, but the protection scope of the present invention is not limited to the following embodiments.

[0058] Embodiment

[0059] As Figure 1 shown, this embodiment provides a maglev train suspension control method based on tube model predictive control (tube-MPC), which specifically includes the following steps:

[0060] Step S1, obtain the basic irregularity form of the target track beam, construct the track irregularity model of the track beam, and calculate the disturbances generated by the track irregularities using the track irregularity model.

[0061] As Figure 2 shown, in this embodiment, the longitudinal direction of the target track beam is taken as the s-axis and the vertical direction is taken as the y-axis for construction.

[0062] The expression of the track irregularity model is:

[0063]

[0064] In the formula, α i (i = 1, 2, 3, 4) is the weight coefficient, and y i (i = 1, 2, 3, 4) represents the basic irregularity form of the track beam, and s is the longitudinal abscissa of the track beam.

[0065] Among them, the weight coefficient α i (i = 1, 2, 3, 4) takes values including:

[0066] α i = 0, 1 (i = 1, 2, 3, 4) (2)

[0067] The 4 basic irregularity forms y i (i = 1, 2, 3, 4) of the track beam have expressions including:

[0068]

[0069] In the formula, s period is the period when the basic irregularity form appears, L is the length of the track beam, and a 1 , a 2 , b 1 , b 2 are the amplitudes of each basic irregularity. L, a 1 , a 2 , b 1 , b 2 are all obtained through actual measurement.

[0070] The calculation formula for the disturbance w caused by track irregularity is:

[0071] w = y[(k + 1)s 0 - y[ks 0 , k = 0, 1, 2,... (7)

[0072] Among them,

[0073] s 0 = v * t 0 (8)

[0074] In the formula, s 0 is the sampling distance, v is the running speed of the maglev train, t 0 is the sensor sampling time, and y[ks 0 is the track irregularity point sequence generated by sampling. The parameter v is measured by the maglev train speed sensor, and t 0 is a preset value in advance.

[0075] Step S2: Based on Newton's laws of motion and Maxwell's equations, and through linearization, construct the nominal model of the maglev train suspension system

[0076] The calculation of the nominal model of the maglev train suspension system includes:

[0077]

[0078] Among them,

[0079]

[0080] In the formula, is the state of the nominal model of the maglev train suspension system, and △x g represents the suspension air gap error, represents the first derivative of the suspension air gap error, is the output of the nominal model of the maglev train suspension system, m is the mass of the maglev train car body set in advance, and k e is the electromagnetic constant, x g0 is the reference value of the suspension air gap, and i c0 is the reference value of the electromagnetic coil current.

[0081] Among them, the calculation formula of the suspension air gap error △x g is:

[0082] △x g = x g - x g0 (13)

[0083] In the formula, x g is the actual value of the suspension air gap. The actual value of the suspension air gap x g is obtained through the sensors on the train.

[0084] The calculation of the output of the nominal model of the maglev train suspension system

[0085]

[0086] In the formula, i c is the actual value of the electromagnetic coil current. The actual value of the electromagnetic coil current i c is obtained through the current sensors on the train.

[0087] Step S3: Based on the disturbance w and the nominal model of the maglev train suspension system superimpose to obtain the actual model Σ of the maglev train suspension system.

[0088] The calculation of the actual model Σ of the maglev train suspension system includes:

[0089]

[0090] Among them,

[0091]

[0092] In the formula, Σ represents the actual model of the maglev train suspension system, is the state of the actual model of the maglev train suspension system, u = i c - i c0 is the output of the actual model of the maglev train suspension system, and w is the disturbance generated by the track irregularity.

[0093] The calculation of the constraints of the actual model Σ of the maglev train suspension system includes:

[0094] x ∈ X = {x|x lb ≤ x ≤ x ub} (16)

[0095] u ∈ U = {u|u lb ≤ u ≤ u ub} (17)

[0096] In the formula, x lb is the lower bound of the state of the actual model of the system, that is, the difference between the actual minimum value of the suspension air gap and the reference value, and x ub is the upper bound of the state of the actual model of the system, that is, the difference between the actual maximum value of the suspension air gap and the reference value. X is the set of states of the actual model of the maglev train suspension system, and u lb is the lower bound of the output of the actual model of the system, that is, the difference between the actual minimum value of the coil output current and the reference value, and u ub is the upper bound of the output of the actual model of the system, that is, the difference between the actual maximum value of the coil output current and the reference value. U is the set of outputs of the actual model of the maglev train suspension system.

[0097] Step S4, obtain the current actual value of the suspension air gap, calculate the suspension air gap error △x g = x g - x g0 , and obtain the magnitude of the current output.

[0098] Among them, the output current is obtained through the current sensor on the train, and the actual value of the suspension air gap x g is obtained through the sensor on the train, and the reference value of the suspension air gap x g0 is also a known quantity that can be obtained in advance.

[0099] Step S5, the suspension system controller determines whether the suspension air gap error is 0. If so, execute Step S6; otherwise, execute Step S7;

[0100] Step S6, the suspension system controller maintains the current output current magnitude and returns to Step S4;

[0101] Step S7, the suspension system controller, based on the track unevenness model y(s) (used to obtain the disturbance w), the nominal model of the maglev train suspension system and the actual model Σ of the maglev train suspension system, uses the tube model predictive control method to output the optimal current magnitude, adjust the air gap, and return to Step S4.

[0102] Among them, the principle and specific implementation process of the tube model predictive control method include:

[0103] a. Based on the disturbance, contract the constraints of the actual model;

[0104] b. Optimize the preset objective function based on the nominal model and the contracted constraints to obtain the optimal output of the nominal model;

[0105] c. Based on the optimal output of the nominal model, use the feedback control law to calculate the optimal output current of the actual model from the optimal output of the nominal model.

[0106] Among them, the calculation of constraint contraction includes:

[0107]

[0108] In the formula, is the Minkowski subtraction, and Φ is the positive robust invariant set;

[0109] The calculation of the preset objective function includes:

[0110]

[0111] In the formula, Np is the prediction horizon, P, Q, and R are weight matrices, is the predicted nominal state, is the predicted terminal state, is the predicted nominal input. The parameters Np, P, Q, and R are all preset values in advance.

[0112] The calculation of the feedback control law includes:

[0113]

[0114] In the formula, is the optimal output of the nominal model, u * (k) is the optimal output of the actual model, represents the system optimal gain matrix. The parameter is the solution obtained by the controller optimizing the cost function J.

[0115] To verify the effectiveness of the maglev train suspension control method proposed in this embodiment, next, the response of the maglev train suspension system under the same uneven track and different speed levels, that is, different disturbance magnitudes, will be tested. Specifically, this embodiment will use the proposed maglev train suspension control method based on tube model predictive control to simulate the suspension system and check whether the state of the suspension system exceeds the constraints.

[0116] In the Matlab environment, the proposed maglev train suspension control method based on tube model predictive control is used for simulation, and the speed of the maglev train v = 500 km / h and the sensor sampling time t 0 = 0.01 s are set. Through disturbance calculation, the maximum disturbance corresponding to this working condition is 0.85 mm.

[0117] Figure 3 shows the actual state predicted by the suspension system controller at a certain moment. The state refers to the suspension air gap error and the first derivative of the suspension air gap error of the suspension system. The horizontal axis in the figure represents the aforementioned suspension air gap error, and the vertical axis represents the aforementioned first derivative of the suspension air gap error. The blue hollow points represent the predicted actual state of the system, the green solid points represent the predicted nominal state of the system, and the dark shaded part represents the system actual state constraint (X c ), and the light shaded part represents the contracted system nominal state constraint This figure can directly reflect that under the action of disturbance, the maglev train suspension control method based on tube model predictive control ensures that the predicted actual state of the system never exceeds the system actual state constraint by actively contracting the constraint, effectively improving the system robustness.

[0118] Figure 4 shows the air gap error during the actual operation of the maglev train. The horizontal axis in the figure represents the aforementioned sampling times, and the vertical axis represents the aforementioned suspension air gap error. The blue line represents the air gap error during the actual operation of the maglev train, and the red line represents the upper and lower bounds of the air gap error constraint. This figure can directly reflect that under the action of disturbance, the maglev train suspension control method based on tube model predictive control can ensure that the maglev train actually operates stably under the specified air gap constraint, effectively improving the system robustness.

[0119] From the above analysis of the simulation results, it can be seen that this method ensures that the state of the suspension system does not exceed the actual system constraints under the action of track unevenness disturbances of different magnitudes, effectively improving the robustness of the suspension system

[0120] Furthermore, this embodiment provides a maglev train suspension control device based on tube model predictive control, which includes a memory, a processor, and a program stored in the memory. When the processor executes the program, the foregoing method is implemented. The device processor includes a central processing unit (CPU), which can execute various appropriate actions and processes according to computer program instructions stored in a read-only memory (ROM) or computer program instructions loaded from a storage unit into a random access memory (RAM). In the RAM, various programs and data required for device operation can also be stored. The CPU, ROM, and RAM are connected to each other via a bus. An input / output (I / O) interface is also connected to the bus. Multiple components in the device are connected to the I / O interface, including: an input unit, such as a keyboard, a mouse, etc.; an output unit, such as various types of displays, speakers, etc.; a storage unit, such as a disk, an optical disc, etc.; and a communication unit, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit allows the device to exchange information / data with other devices through a computer network such as the Internet and / or various telecommunication networks. The processing unit executes each of the methods and processes described above, such as steps S1 to S7 in the foregoing embodiment. For example, in some embodiments, steps S1 to S7 can be implemented as a computer software program, which is tangibly contained in a machine-readable medium, such as a storage unit. In some embodiments, part or all of the computer program can be loaded and / or installed onto the device via the ROM and / or the communication unit. When the computer program is loaded into the RAM and executed by the CPU, one or more of steps S1 to S7 described above can be executed. Alternatively, in other embodiments, the CPU can be configured to execute method S1 to S7 in any other appropriate manner (e.g., by means of firmware). The functions described above can be at least partially executed by one or more hardware logic components. For example, without limitation, exemplary types of hardware logic components that can be used include: field programmable gate arrays (FPGA), application specific integrated circuits (ASIC), application specific standard products (ASSP), system on a chip (SOC), complex programmable logic devices (CPLD), and so on.

[0121] Further, this embodiment also provides a storage medium, on which a program is stored, and when the program is executed, the foregoing method is implemented. The program code for implementing the method of the present invention can be written in any combination of one or more programming languages. These program codes can be provided to a processor or a controller of a general-purpose computer, a special-purpose computer, or other programmable data processing devices, so that when the program codes are executed by the processor or the controller, the functions / operations specified in the flowchart and / or block diagram are implemented. The program codes can be executed entirely on the machine, partially on the machine, executed partially on the machine as an independent software package and partially on a remote machine, or executed entirely on a remote machine or server. In the context of the present invention, a computer-readable medium can be a tangible medium that can contain or store a program for use by or in connection with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium can include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media would include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disc read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0122] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field based on the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the prior art should fall within the protection scope determined by the claims.

Claims

1. A method for controlling the suspension of a maglev train, characterized in that: The following steps are involved: S1, obtaining the basic irregularity form of the target track beam, constructing a track irregularity model, and using the track irregularity model to calculate the disturbance caused by the track irregularity; S2, construct the nominal model of the maglev train suspension system based on Newton’s laws of motion and Maxwell’s equations; S3, based on the disturbance and the nominal model of the maglev train suspension system, superimposing to obtain an actual model of the maglev train suspension system; S4, obtaining the current actual value of the suspension air gap, calculating the suspension air gap error, and obtaining the current output current; S5, determining whether the suspension air gap error is 0, if so, executing step S6, otherwise executing step S7; S6, maintain the current output current and return to step S4; S7, based on the track irregularity model, the nominal model of the maglev train suspension system and the actual model of the maglev train suspension system, output the optimal current size using a tube model-based predictive control method, adjust the air gap, and return to step S4; For the method based on tube model predictive control, the specific execution process includes: Based on the disturbance, shrinking the constraints of the actual model; Optimizing a preset objective function based on the nominal model and the shrunk constraints to obtain an optimal output of the nominal model; Based on the optimal output of the nominal model, using feedback control to obtain the optimal current magnitude output by the actual model; The expression of the track irregularity model is: In the formula, α i is the weight coefficient, y i It represents the basic irregularity form of the track beam, s is the longitudinal abscissa of the track beam, and i=1,2,3,4; The values ​​of the weight coefficient include: α i ＝0,1(i＝1,2,3,4) In the formula, when the track irregularity model is not Appear When the i-th basic irregularity form is i =0; when the track is not smooth Appear When the i-th basic irregularity form is i =1; The expressions of the basic irregular forms include: In the formula, s period is the period of occurrence of basic irregularities, L is the measured length of the track beam, a1, a2, b1, b2 are the amplitudes of basic irregularities measured in advance; The calculation of the objective function includes: In the formula, Np is the prediction step size, P, Q, R are weight matrices, To predict the nominal state, To predict the terminal state, Nominal input for forecasting.

2. The maglev train suspension control method according to claim 1, characterized in that: The calculation formula of the disturbance is: w=y[(k+1)s0]-y[ks0],k=0,1,2,…… Where s0 is the sampling distance, and y[ks0] is the track irregularity point sequence generated by sampling.

3. The maglev train suspension control method according to claim 1, characterized in that: The expression of the nominal model of the maglev train suspension system is: in, In the formula, represents the nominal model of the maglev train suspension system, is the state of the nominal model of the maglev train suspension system, △x g represents the suspension air gap error, represents the first-order derivative of the suspension air gap error, is the output of the nominal model of the maglev train suspension system, m is the mass of the maglev train body, k e is the electromagnetic constant, x g0 is the reference value of the suspension air gap, i c is the actual value of the electromagnetic coil current, i c0 is the reference value of the electromagnetic coil current.

4. The maglev train suspension control method according to claim 1, characterized in that: The calculation formula of the suspension air gap error is: △x g =x g -x g0 In the formula, △x g is the suspension air gap error, x g is the actual value of the suspension air gap, x g0 is the reference value of the suspension air gap.

5. The maglev train suspension control method according to claim 1, characterized in that: The expression of the actual model of the maglev train suspension system is: in, Where Σ represents the actual model of the maglev train suspension system, x is the state of the actual model of the maglev train suspension system, u is the output of the actual model of the maglev train suspension system, and w is the disturbance caused by track unevenness. The constraints of the actual model of the maglev train suspension system are: x∈X={x|x lb ≤x≤x ub } u∈U={u|u lb Oh, oh. ub } In the formula, x lb Indicates the difference between the actual minimum value of the suspension air gap and the reference value, x ub represents the difference between the actual maximum value of the suspension air gap and the test value, X is the actual model state set of the maglev train suspension system, u lb Indicates the difference between the minimum value of the actual coil output current and the reference value, u ub It represents the difference between the maximum value of the actual coil output current and the reference value, and U is the actual model output set of the maglev train suspension system.

6. A maglev train suspension control device, comprising a memory, a processor, and a program stored in the memory, characterized in that: When the processor executes the program, the method according to any one of claims 1 to 5 is implemented.

7. A storage medium having a program stored thereon, characterized in that: When the program is executed, the method according to any one of claims 1 to 5 is implemented.

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