Track coupling vibration control method, device and equipment and readable storage medium

Abstract

The invention discloses a train rail coupling vibration control method, device and equipment and a readable storage medium, and is applied to the technical field of intelligent control, and the method comprises the steps: obtaining a nonlinear model considering a vibration mode of a rail based on a high-speed maglev train structure of a lap joint structure, a rail vibration equation and an electromagnet kinetic equation; determining motion characteristics of the nonlinear model to obtain a motion state space equation; determining a reference model corresponding to the nonlinear model, and determining a control law when the difference between the motion state space equation and the reference model is minimum; and determining target vibration control parameters by using a control law by taking the nonlinear model as a control object reference model as an ideal target. According to the method, the nonlinear model considering the vibration mode of the track is obtained through the high-speed maglev train structure based on the lap joint structure, the corresponding reference model and control law are designed, and due to the fact that the vibration mode of the lap joint structure is considered in the nonlinear model, the suppression effect on coupling vibration of the high-speed maglev train track is better.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent control, in particular to a vehicle-track coupling vibration control method, device, equipment and readable storage medium. BACKGROUND

[0002] The most common and widely used control method in engineering is PID (Proportional Integral Derivative) control, which has the disadvantage of single information source, and only uses gap data collected by a suspension gap sensor to complete vibration suppression, which has many negative effects: more sensitive to noise. The high-frequency noise in the sensor signal will be significantly amplified through the differential element of the PID, forcing the controller to use low-pass filtering or decimation processing, thereby introducing phase lag and signal distortion, and weakening the dynamic performance of vibration suppression.

[0003] It can be seen that how to improve the suppression effect of high-speed maglev vehicle-track coupling vibration is a technical problem that needs to be solved by those skilled in the art. SUMMARY

[0004] Therefore, the purpose of the present application is to provide a vehicle-track coupling vibration control method, device, equipment and readable storage medium, which solves the technical problem of poor vibration control effect in the prior art.

[0005] To solve the above technical problems, the present application provides a vehicle-track coupling vibration control method, comprising:

[0006] A nonlinear model considering the vibration mode of the track is obtained based on the structure of the high-speed maglev train, the track vibration equation and the electromagnet dynamics equation;

[0007] Based on the equilibrium point position change characteristics and the model parameter time-varying characteristics, the motion characteristics of the nonlinear model are determined to obtain a motion state space equation;

[0008] A reference model corresponding to the nonlinear model is determined, and a control law is determined to minimize the difference between the motion state space equation and the reference model;

[0009] The nonlinear model is taken as a control object, and the reference model is taken as an ideal target. The control law is used to determine the target vibration control parameters corresponding to the nonlinear model, so as to control the vehicle-track coupling vibration of the high-speed maglev train based on the target vibration control parameters.

[0010] Optionally, the motion state space equation is ; wherein, represents the motion characteristics, is a state variable of the nonlinear model, input of the two-sided electromagnet; denotes a model matrix of the nonlinear model linearized based on the equilibrium point position variation characteristic, denotes a model matrix variation caused by equilibrium point position variation and model parameter time variation; denotes an input matrix of the nonlinear model linearized based on the equilibrium point position variation characteristic at a preset distance point of the preset equilibrium point, denotes an input matrix variation caused by equilibrium point position variation and model parameter time variation.

[0011] Optionally, a reference model corresponding to the nonlinear model is determined, and a control law that minimizes the difference between the motion state space equation and the reference model is determined, including:

[0012] the reference model corresponding to the nonlinear model is determined as ; wherein, is a state variable of the reference model, is a control input of the reference model, which is a reference input based on the nonlinear model; denotes a model matrix of the reference model, denotes an input matrix of the reference model;

[0013] the control law is designed so that the difference between the motion state space equation and the reference model under the action of the control law is minimized; wherein, , are state feedback gain and feedforward gain, respectively.

[0014] Optionally, after the reference model corresponding to the nonlinear model is determined, and the control law that minimizes the difference between the motion state space equation and the reference model is determined, the method further includes:

[0015] the control law is substituted into the motion state space equation, and the difference between the motion state space equation and the reference model is obtained to obtain a first error equation;

[0016] an external disturbance parameter is determined, and a motion state space equation containing an external disturbance is determined based on the external disturbance parameter, and a second error equation containing an external disturbance is determined;

[0017] an error of the second error equation at a steady state is determined to obtain a third error equation;

[0018] the reference model is adjusted based on the third error equation and a hysteresis relationship between current and voltage to obtain an adjusted reference model;

[0019] Correspondingly, the nonlinear model is taken as a control object, the reference model is taken as an ideal target, and the target vibration control parameter corresponding to the nonlinear model is determined by using the control law, and the target vibration control parameter comprises:

[0020] The nonlinear model is taken as a control object, the adjusted reference model is taken as an ideal target, and the target vibration control parameter corresponding to the nonlinear model is determined by using the control law.

[0021] Optionally, after obtaining the nonlinear model considering the vibration mode of the track based on the structure of the high-speed maglev train with a lap joint structure, a track vibration equation and an electromagnet dynamics equation, the method further comprises:

[0022] The nonlinear model, the reference model and the control law are simplified based on the logic of keeping the absolute displacement of the electromagnet unchanged, to obtain a simplified nonlinear model, a simplified reference model and a simplified control law;

[0023] Correspondingly, the nonlinear model is taken as a control object, the reference model is taken as an ideal target, and the target vibration control parameter corresponding to the nonlinear model is determined by using the control law, and the target vibration control parameter comprises:

[0024] The simplified nonlinear model is taken as a control object, the simplified reference model is taken as an ideal target, and the target vibration control parameter corresponding to the simplified nonlinear model is determined by using the simplified control law.

[0025] Optionally, after the nonlinear model, the reference model and the control law are simplified based on the logic of keeping the absolute displacement of the electromagnet unchanged, to obtain a simplified nonlinear model, a simplified reference model and a simplified control law, the method further comprises:

[0026] The total disturbance parameter suffered by the high-speed maglev train with a lap joint structure is determined, and a disturbance-containing and simplified nonlinear model, a disturbance-containing and simplified reference model and a disturbance-containing and simplified control law are determined based on the total disturbance parameter.

[0027] Optionally, the total disturbance parameter suffered by the high-speed maglev train with a lap joint structure is determined, and a disturbance-containing and simplified nonlinear model, a disturbance-containing and simplified reference model and a disturbance-containing and simplified control law are determined based on the total disturbance parameter, and the method comprises:

[0028] The disturbance-containing and simplified nonlinear model under the simplified control law is determined based on the total disturbance parameter and the simplified nonlinear model;

[0029] The extended state corresponding to the disturbance-containing and simplified nonlinear model is determined, to obtain an extended, disturbance-containing and simplified nonlinear model;

[0030] determining a linear extended state observer corresponding to the extended and disturbance-containing and simplified nonlinear model;

[0031] determining an observation error equation based on the linear extended state observer and the extended and disturbance-containing and simplified nonlinear model;

[0032] performing disturbance estimation based on the total disturbance parameter, to obtain an estimated disturbance;

[0033] obtaining a final control law based on the estimated disturbance and the simplified control law;

[0034] determining a reference model corresponding to the extended and disturbance-containing and simplified nonlinear model, to obtain a final reference model;

[0035] Correspondingly, taking the nonlinear model as a control object and the reference model as an ideal target, the target vibration control parameter corresponding to the nonlinear model is determined by using the control law, including:

[0036] taking the extended and disturbance-containing and simplified nonlinear model as a control object and the final reference model as an ideal target, and determining the target vibration control parameter by using the final control law.

[0037] The embodiment of the present application also provides a vehicle-track coupling vibration control device, including:

[0038] a nonlinear model determination module, configured to obtain a nonlinear model considering a vibration mode of a track based on a high-speed maglev train structure of a lap joint structure, a track vibration equation and an electromagnet dynamics equation;

[0039] a motion state space equation determination module, configured to determine a motion characteristic of the nonlinear model based on a balance point position change feature and a model parameter time-varying feature, to obtain a motion state space equation;

[0040] a control law determination module, configured to determine a reference model corresponding to the nonlinear model, and determine a control law making a difference between the motion state space equation and the reference model minimum;

[0041] a target diagnostic control parameter determination module, configured to take the nonlinear model as a control object and the reference model as an ideal target, and determine a target vibration control parameter corresponding to the nonlinear model by using the control law, so as to perform vehicle-track coupling vibration control on the high-speed maglev train based on the target vibration control parameter.

[0042] The embodiment of the present application also provides a vehicle-track coupling vibration control device, including:

[0043] a memory, configured to store a computer program;

[0044] a processor configured to execute the computer program to implement the steps of the vehicle-track coupled vibration control method.

[0045] The embodiment of the present application also provides a readable storage medium, wherein the readable storage medium stores a computer program, and the computer program is executed by a processor to implement the steps of the vehicle-track coupled vibration control method.

[0046] To solve the above technical problems, the embodiment of the present application provides a vehicle-track coupled vibration control method, which comprises the following steps: obtaining a nonlinear model considering the vibration mode of a track based on a high-speed maglev train structure of a lap joint structure, a track vibration equation and an electromagnet dynamics equation; determining the motion characteristics of the nonlinear model based on the position change characteristics of a balance point and the time-varying characteristics of model parameters to obtain a motion state space equation; determining a reference model corresponding to the nonlinear model and determining a control law for minimizing the difference between the motion state space equation and the reference model; taking the nonlinear model as a control object and the reference model as an ideal target, and determining target vibration control parameters corresponding to the nonlinear model by using the control law, so as to control the vehicle-track coupled vibration of the high-speed maglev train based on the target vibration control parameters.

[0047] As can be seen from the above technical solution, the embodiment of the present application has the following beneficial effects: compared with the current vibration suppression which is completed only by collecting gap data by a suspension gap sensor, the nonlinear model considering the vibration mode of the track is obtained based on the high-speed maglev train structure of the lap joint structure, the track vibration equation and the electromagnet dynamics equation, so that the corresponding reference model and the control law are designed, and the suspension control is more accurate due to the consideration of the vibration mode of the lap joint structure in the nonlinear model, so that the suppression effect of the high-speed maglev vehicle-track coupled vibration is better.

[0048] The embodiment of the present application also provides a vehicle-track coupled vibration control device, equipment and readable storage medium. BRIEF DESCRIPTION OF DRAWINGS

[0049] In order to more clearly illustrate the embodiments of the present application, the drawings needed in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0050] Figure 1 A flowchart of a vehicle-track coupled vibration control method provided by the embodiment of the present application is shown in the figure.

[0051] Figure 2 A schematic diagram of a high-speed maglev train lap joint structure provided by the embodiment of the present application is shown in the figure.

[0052] Figure 3A vibration suppression block diagram of a high-speed maglev train lap joint structure-track coupling system based on MRAC-ADRC is provided for the embodiment of the present application.

[0053] Figure 4 An electromagnetic iron displacement change curve under four control methods considering high-order modalities is provided for the embodiment of the present application.

[0054] Figure 5 An electromagnetic iron acceleration change curve under four control methods considering high-order modalities is provided for the embodiment of the present application.

[0055] Figure 6 An electromagnetic iron suspension current change curve under four control methods considering high-order modalities is provided for the embodiment of the present application.

[0056] Figure 7 A structural frame schematic diagram of a vehicle-track coupling vibration control device is provided for the embodiment of the present application.

[0057] Figure 8 A structural frame schematic diagram of a vehicle-track coupling vibration control device is provided for the embodiment of the present application. DETAILED DESCRIPTION

[0058] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0059] The terms “include” and “have” and any variations thereof in the specification and above drawings of the present application are intended to cover the inclusions without the exclusions. For example, a process, method, system, product or device including a series of steps or units is not limited to the listed steps or units, but can include steps or units not listed.

[0060] In order for those skilled in the art to better understand the present application, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0061] Next, a flowchart of a vehicle-track coupling vibration control method provided by the embodiment of the present application is described in detail. Figure 1 A flowchart of a vehicle-track coupling vibration control method provided for the embodiment of the present application, which can include:

[0062] S101, a nonlinear model considering the vibration modalities of the track is obtained based on the high-speed maglev train structure of the lap joint structure, the track vibration equation and the electromagnetic iron dynamics equation.

[0063] The electronic device in this embodiment can be a computer, a mobile phone, etc. The high-speed maglev train structure of the lap joint structure in this embodiment refers to a segmented lap joint beam structure (such as a cantilever beam lap joint) of a high-speed maglev track, rather than a continuous whole track. Such a structure will cause a local stiffness mutation of the track at the connection, which will cause track vibration when the train passes, and further transmit the vibration to the vehicle body through the electromagnet, forming a "vehicle-track coupled vibration". The track vibration equation in this embodiment describes the dynamic behavior of the track under the action of electromagnetic force, train load and its own elasticity, which is usually established based on the elastic beam theory (such as the Euler-Bernoulli beam equation); the electromagnet dynamics equation in this embodiment describes the dynamic relationship between the electromagnetic force, current, voltage and air gap (suspension gap). The vibration mode of the track considered in this embodiment refers to the i-th order vibration mode of the track, which explicitly introduces the specific order vibration form (such as the first order bending, the second order torsion, etc.) inherent in the track structure when modeling, so as to more accurately describe the dynamic response of the track under the excitation of electromagnetic force. When designing the nonlinear model in this embodiment, the design is mainly based on the simply supported beam basic model, the torque balance equation, the Newtonian mechanics equation, the modal analysis, the beam vibration equation, the electromagnetic force equation, the voltage equation space, and the lap joint structure of the high-speed maglev train structure is considered in this process. For easy understanding, please refer to Figure 2 , Figure 2 A schematic view of a high-speed maglev train lap joint structure provided by an embodiment of the present application, Figure 2 and the meanings of the letters in the text are shown in Table 1, which is a letter meaning table provided by an embodiment of the present application.

[0064] Table 1. A letter meaning table

[0065]

[0066]

[0067]

[0068]

[0069] The nonlinear model in this embodiment is as formula (1), (1)

[0070] wherein, represents the second derivative of the track displacement of the j-th order system at time t; represents the j-th order track damping ratio; represents the j-th order track modal frequency; represents the first derivative of the track displacement of the j-th order system at time t; represents the orbit displacement of the j-th order system at time t; parameters, parameters, . represents the second-order derivative of the left electromagnet displacement; represents the second-order derivative of the right electromagnet displacement; represents the second-order derivative of the boom system displacement; represents the first-order derivative of the left electromagnet displacement; represents the first-order derivative of the boom system displacement; represents the current of the left electromagnet; represents the voltage of the left electromagnet; represents the voltage of the right electromagnet; represents the resistance of the electromagnet; represents the first-order derivative of the current of the left electromagnet; represents the constant vacuum permeability; represents the first-order derivative of the left levitation gap; represents the current of the right electromagnet; represents the first-order derivative of the current of the right electromagnet; represents the first-order derivative of the right levitation gap; the naming principle of the symbols is that the subscript r represents the right side, and the subscript l represents the left side; the superscript one dot represents the first-order derivative, and the superscript two dots represents the second-order derivative.

[0071] In S102, the motion characteristics of the nonlinear model are determined based on the equilibrium point position variation characteristics and the model parameter time variation characteristics, and a motion state space equation is obtained.

[0072] In the suspension control of the high-speed maglev train in this embodiment, the equilibrium point position variation characteristics refer to the dynamic deviation (such as 6-12 mm fluctuation) of the actual levitation gap (such as the nominal value of 8 mm) between the electromagnet and the track due to external disturbance or system nonlinearity when the train is running. In the high-speed maglev track coupling vibration control, the model parameter time variation characteristics refer to the real-time variation of the key parameters describing the dynamic characteristics of the system with the running conditions, which causes the mathematical model to be unable to be accurately expressed by fixed constants. It should be noted that the motion state space equation is:

[0073] (2);

[0074] wherein, represents the motion characteristics, is a state variable of the nonlinear model, is an input of the electromagnet on both sides, is the track displacement, is the differential of the track displacement, is the displacement of the left electromagnet of the lap joint structure, ​Differential of the displacement of the left electromagnet of the lap joint structure, Differential of the displacement of the right electromagnet of the lap joint structure, Differential of the displacement of the right electromagnet of the lap joint structure. U is a control input, which is a control voltage or current; represents a model matrix obtained after linearization of the nonlinear model based on the position variation characteristics of the equilibrium point (linearized near the preset equilibrium point), represents a change in the model matrix caused by the position variation of the equilibrium point and the time variation of the model parameters (variation of the equilibrium point and the model parameters); represents an input matrix obtained after linearization of the nonlinear model based on the position variation characteristics of the equilibrium point at a preset distance point (near the preset equilibrium point) of the preset equilibrium point, represents a change in the input matrix caused by the position variation of the equilibrium point and the time variation of the model parameters (variation of the equilibrium point and the model parameters). In this embodiment, the motion state space equation is designed based on modern control theory. This embodiment gives the formula (2) for determining the motion characteristics. In this embodiment, a specific motion state space equation is given, which improves the accuracy of the determination of the motion state space equation.

[0075] S103, determining a reference model corresponding to the nonlinear model, and determining a control law that minimizes the difference between the motion state space equation and the reference model.

[0076] In this embodiment, when the reference model corresponding to the nonlinear model is determined, the reference model is mainly designed based on the motion characteristics of the nonlinear model. This embodiment designs a control law to make the motion state space equation of the nonlinear model approach the reference model under the action of the control law, that is, to minimize the difference between the motion state space equation and the reference model. It should be noted that the correct reference model should satisfy: ① the relative order of the reference model > the relative order of the controlled object; ② the reference model should be a minimum phase system (zero point in the left half plane). The basic idea of MRAC is to first express the reference model, and then determine the control parameters in the subsequent derivation.

[0077] It should be further noted that based on any of the above embodiments, the above determination of the reference model corresponding to the nonlinear model and the determination of the control law that minimizes the difference between the motion state space equation and the reference model can include:

[0078] S1031, determining that the reference model corresponding to the nonlinear model is ; wherein, is a state variable of the reference model, is a control input of the reference model, which is a reference input based on the nonlinear model. The reference input is the input item of the reference model, or the control input of the reference system; a model matrix representing the reference model, an input matrix representing the reference model. Respectively represent the target position of the two-sided electromagnet (i.e. control target).

[0079] is the reference model. represents the real number field. The embodiment gives the reference model formula:

[0080] (3);

[0081] S1032, design control law so that the motion state space equation is minimized under the action of the control law and the reference model; wherein, , respectively are the state feedback gain and feedforward gain.

[0082] The embodiment that the motion state space equation is minimized under the action of the control law and the reference model means approximation. The embodiment designs the control law shown in formula so that the motion state space equation approximates the reference model under the action of the control law:

[0083] (4);

[0084] wherein, , respectively are the state feedback gain and feedforward gain.

[0085] The embodiment gives the specific method of the control law, which improves the accuracy of determining the control law.

[0086] It needs to be further explained that after determining the reference model corresponding to the nonlinear model and determining the control law that minimizes the difference between the motion state space equation and the reference model, it can further include:

[0087] Step 1: Substitute the control law into the motion state space equation, and subtract the reference model to obtain a first error equation;

[0088] The embodiment can make , Substitute (4) into (2) and subtract (3) to obtain the error equation of the motion state space equation and the reference model:

[0089] ;

[0090] The embodiment can design the feedback gain adjustment rate and the feedforward gain adjustment rate of the MRAC as:

[0091] ;

[0092] wherein, is a positive definite matrix, represents feedback coefficient and feedforward coefficient adjusting gain, E represents error, P represents positive definite symmetric matrix, is the product when designing control rate. By adjusting these two parameters in control to keep stable, find the required FK value, so that the control is stable state, always get the value of FK, prove that the above method based on MRAC suspension control design is effective (designing motion state space equation and reference model).

[0093] Step 2: determine the external disturbance parameter, and determine the motion state space equation containing external disturbance based on the external disturbance parameter, determine the second error equation containing external disturbance;

[0094] Further consider external disturbance in this embodiment, obtain the motion state space equation containing external disturbance:

[0095] ;

[0096] wherein , is unknown external disturbance (i.e. external disturbance).

[0097] Step 3: determine the error of the second error equation at steady state, obtain the third error equation;

[0098] The error equation based on external disturbance in this embodiment is:

[0099] ;

[0100] Expand as:

[0101] ;

[0102] wherein, represents the error of F, F is feedforward gain, represents the error of K; and respectively represent the expected damping of the track system and the lapping structure system; represents the matrix, represents four elements of the matrix ; and respectively represent the error of feedback gain and feedforward gain and ideal value. e1-e6 is the difference of A-Am corresponding variable, such as e1=x1-xm1 (in formula 5); , For bandwidth. When formula At steady state, there is: At this time, the third error equation of the system can be written as:

[0103]

[0104] Step 4: Adjust the reference model based on the third error equation and the hysteresis relationship between current and voltage to obtain an adjusted reference model;

[0105] The reference model set by this embodiment ultimately ignores the hysteresis relationship between current and voltage:

[0106]

[0107] Wherein, And Respectively represent the desired bandwidth of the track system and the clamped structure system, And Respectively represent the desired damping of the track system and the clamped structure system.

[0108] Correspondingly, taking the nonlinear model as the control object and the reference model as the ideal target, the target vibration control parameter corresponding to the nonlinear model is determined by using the control law, which can include:

[0109] Step 5: Taking the nonlinear model as the control object and the adjusted reference model as the ideal target, the target vibration control parameter corresponding to the nonlinear model is determined by using the control law.

[0110] After adjusting the reference model, this embodiment needs to change the ideal target to the adjusted reference model. This embodiment designs the reference model by considering external disturbance. The essence is to dynamically reconstruct the "ideal target" of the control system into an achievable "anti-interference trajectory", so as to improve the vibration suppression effect.

[0111] S104, taking the nonlinear model as the control object and the reference model as the ideal target, the target vibration control parameter corresponding to the nonlinear model is determined by using the control law, and the high-speed maglev train is controlled based on the target vibration control parameter. Coupling vibration of train and track.

[0112] This embodiment uses the MRAC control method (nonlinear model) to act on the controlled object, and obtains the control law by deducing the condition for satisfying the stability of the closed-loop system.

[0113] It should be further pointed out that after obtaining the nonlinear model considering the vibration mode of the track based on the structure of the high-speed maglev train based on the clamped structure, the track vibration equation and the electromagnetic dynamics equation according to any of the above embodiments, the nonlinear model can also include:​​

[0114] S1011, the nonlinear model, the reference model and the control law are simplified based on the logic of keeping the absolute displacement of the electromagnet unchanged, to obtain the simplified nonlinear model, the simplified reference model and the simplified control law;

[0115] This embodiment is mainly to simplify the control method designed based on MRAC (Model Reference Adaptive Control, i.e. the reference model and the control law designed based on the nonlinear model above are controlled, or the adjusted reference model and the control law designed are also controlled). The MRAC control method needs to use all state variables of the system, which will introduce a lot of noise in actual engineering. If the state observer is designed to obtain the state variable, it will be difficult to realize due to the time-varying of system parameters. Therefore, although the MRAC control method can effectively realize adaptive control under ideal conditions, its performance may be limited when facing complex external disturbances and state variable acquisition problems. Therefore, the MRAC control is simplified. For the problem of vehicle-track coupling vibration suppression, the main problem to be solved is the vibration of the electromagnet (the control cost required to change the motion characteristics of the track is too large), that is, when the track vibrates due to electromagnetic force, the control system of the electromagnet does not respond to this vibration, and the absolute displacement of the electromagnet remains unchanged. This embodiment simplifies the MRAC control method according to this, ignores the motion process of the track system, and sets the control target to keep the dynamic characteristics of the left and right electromagnets consistent with the reference system. The principle of reducing order (simplifying) of the nonlinear model is to consider that it is difficult to change the inherent characteristics of the track by adjusting the electromagnetic force. The controlled object is reduced in order, and of course the control law is reduced in order. The reference model is naturally reduced in order.

[0116] Let , the nonlinear model is simplified as:

[0117] ;

[0118] wherein, , ,

[0119] , represents the change of the parameter in the matrix.

[0120] wherein, represents the input of the left electromagnet of the lap joint structure, is the input of the left electromagnet of the lap joint structure; z

[0121] is the displacement, i is the current, and C is a constant; for the simplified nonlinear model design the MRAC control law, and the simplified (reduced order) reference model is:

[0122] ;

[0123] Similarly to step S2, the reduced MRAC control law is derived as:

[0124] ;

[0125] wherein, is the simplified nonlinear model of the controlled system and the error of the reference system . By solving a positive definite matrix ( ).

[0126] Correspondingly, taking the nonlinear model as the control object and the reference model as the ideal target, the control law is used to determine the target vibration control parameters corresponding to the nonlinear model, including:

[0127] S1012, taking the simplified nonlinear model as the control object and the simplified reference model as the ideal target, the simplified control law is used to determine the target vibration control parameters corresponding to the simplified nonlinear model.

[0128] In this embodiment, the adaptability of the model can be improved through simplification (reduction). It can be understood that in actual engineering, it is difficult to obtain relatively accurate track displacement and track displacement differential state variables. After reduction, these two state variables are not needed.

[0129] It should be further explained that, based on the above embodiment, after simplifying the nonlinear model, the reference model and the control law based on the logic of keeping the absolute displacement of the electromagnet unchanged to obtain the simplified nonlinear model, the simplified reference model and the simplified control law, the total disturbance parameter received by the high-speed maglev train of the lap joint structure can be determined, and the disturbance-containing and simplified nonlinear model, the disturbance-containing and simplified reference model and the disturbance-containing and simplified control law can be determined based on the total disturbance parameter. In this embodiment, the disturbance-containing and simplified models are designed, which improves the accuracy of the suppression control.

[0130] It should be further explained that, based on the above embodiment, the total disturbance parameter received by the high-speed maglev train of the lap joint structure is determined, and the disturbance-containing and simplified nonlinear model, the disturbance-containing and simplified reference model and the disturbance-containing and simplified control law are determined based on the total disturbance parameter. It can include:

[0131] S1: based on the total disturbance parameter and the simplified nonlinear model, the disturbance-containing and simplified nonlinear model under the simplified control law is determined;

[0132] The ADRC method is introduced on the basis of the simplified MRAC to obtain the MRAC-ADRC suspension control method. The specific process is as follows:

[0133] The controlled system under the MRAC control law (simplified nonlinear model) which can be written as:

[0134] ;

[0135] In the formula, . , The error between the actual value and the ideal value of the system response in the adaptive gain adjustment process is represented by e. is expressed as , is the total disturbance parameter. It can be understood that the disturbance can be divided into external disturbance and internal disturbance of the model, and this part of the disturbance is the total disturbance, which contains two parts,

[0136] S2: Determine the extended state corresponding to the simplified nonlinear model containing disturbance to obtain the extended and simplified nonlinear model containing disturbance;

[0137] Let , , and write e as the extended state:

[0138] (16); the extended state in this embodiment is adjusted by feeding back the error between the output of the system and the output estimated by the observer. This error feedback mechanism adjusts the dynamics of the estimator through a gain matrix. When the error tends to zero, the extended state is ultimately equal to the more real state of the system. The extended state logic of the extended observer is based on the feedback and correction of the state estimation error, and the real state of the system is more accurately estimated by introducing an additional state (extended state), and the convergence and stability of the error are ensured through the feedback mechanism.

[0139] S3: Determine the linear extended state observer corresponding to the extended and simplified nonlinear model containing disturbance;

[0140] In order to further improve the anti-disturbance ability of the system, a linear extended state observer (LESO) is designed for the above formula:

[0141] ;

[0142] In the formula, is the state variable of the LESO, is a matrix​ The elements are the formulas. Estimation of state variables in the middle. This is the gain for LESO.

[0143] S4: Determine the observation error equations using the linear extended state observer and the extended, perturbated, and simplified nonlinear model;

[0144] Will and Subtraction yields the LESO observation error equation:

[0145] ;

[0146] In the formula, .

[0147] The error of LESO observations not only converges, but the range of error convergence can also be adjusted by bandwidth.

[0148] S5: Based on the total disturbance parameters, perform disturbance estimation to obtain the estimated disturbance;

[0149] When a suitable observation bandwidth is selected, this embodiment can use ESO to observe disturbances to the overlapping structure without requiring the original system model parameters, through the LESO observer designed above. , use and Make an estimate.

[0150] S6: Based on the estimated disturbance and the simplified control law, the final control law is obtained;

[0151] This embodiment substitutes the estimated disturbance into the MRAC control law to obtain a new control law:

[0152] (19);

[0153] This leads to a block diagram of vibration suppression in the high-speed maglev train's overlap structure-track coupling system based on MRAC-ADRC, as follows: Figure 3 As shown, Figure 3 This is a block diagram of vibration suppression of a high-speed maglev train connection structure-track coupling system based on MRAC-ADRC, provided for an embodiment of the present invention.

[0154] S7: Determine the reference model corresponding to the extended, perturbated, and simplified nonlinear model to obtain the final reference model;

[0155] Pair The final reference model is set as follows:

[0156] (20);

[0157] Correspondingly, taking the nonlinear model as a control object, taking the reference model as an ideal target, and determining the target vibration control parameter of the nonlinear model by using the control law can include:

[0158] S8: taking the extended and disturbance-containing and simplified nonlinear model as a control object, taking the final reference model as an ideal target, and determining the target vibration control parameter by using the final control law.

[0159] The embodiment ensures engineering feasibility through order reduction optimization.

[0160] The vehicle-track coupled vibration control method provided in the embodiment can include: S101, obtaining a nonlinear model considering a vibration mode of a track based on a high-speed maglev train structure of a lap joint structure, a track vibration equation, and an electromagnet dynamics equation; S102, determining a motion characteristic of the nonlinear model based on a balance point position change feature and a model parameter time-varying feature, and obtaining a motion state space equation; S103, determining a reference model corresponding to the nonlinear model, and determining a control law that makes a difference between the motion state space equation and the reference model minimum; S104, taking the nonlinear model as a control object, taking the reference model as an ideal target, and determining a target vibration control parameter of the nonlinear model by using the control law, so as to perform vehicle-track coupled vibration control on the high-speed maglev train based on the target vibration control parameter. Compared with the current vibration suppression completed by gap data collected by a suspension gap sensor, the application obtains the nonlinear model considering the vibration mode of the track based on the high-speed maglev train structure of the lap joint structure, the track vibration equation, and the electromagnet dynamics equation, so as to design the corresponding reference model and the control law. Since the nonlinear model considers the vibration mode in the lap joint structure, the suspension control is more accurate, so that the suppression effect on the high-speed maglev vehicle-track coupled vibration is better.

[0161] In order to make the application more convenient to understand, the embodiment of the application provides a flow example of a vehicle-track coupled vibration control method, which can specifically include:

[0162] Step 1: obtaining a nonlinear model considering an i-th order vibration mode of a track based on a high-speed maglev train structure of a lap joint structure, a track vibration equation, and an electromagnet dynamics equation.

[0163] The nonlinear model in the embodiment is a control object. The nonlinear model reference formula (1).

[0164] Step 2: determining a motion characteristic of the nonlinear model based on a balance point position change feature and a model parameter time-varying feature, and obtaining a motion state space equation.

[0165] The motion state space equation in this embodiment refers to formula (2).

[0166] Step 3: Design a reference model corresponding to the nonlinear model based on the motion state space equation.

[0167] The reference model of this embodiment refers to formula (3).

[0168] Step 4: Determine the control law that minimizes the difference between the motion state space equation and the reference model, and obtain the initial control law.

[0169] In order to distinguish between each control law, the initial control law and the claim part in this embodiment have certain differences. The initial control law of this embodiment refers to formula (4).

[0170] Step 5: Obtain the error equation of the nonlinear model and the ideal reference model based on the initial control law, the motion state space equation, and the ideal reference model.

[0171] The error equation in this embodiment refers to formula (5).

[0172] Step 6: Determine the motion state space equation containing external disturbances based on the external disturbance parameters.

[0173] The motion state space equation containing external disturbances in this embodiment refers to formula (7).

[0174] Step 7: Determine the error equation containing external disturbances based on the external disturbance parameters.

[0175] The error equation containing external disturbances in this embodiment refers to formula (8).

[0176] Step 8: Determine the error equation containing external disturbances at steady state, and obtain the error equation containing external disturbances at steady state.

[0177] The error equation containing external disturbances at steady state in this embodiment is formula (10).

[0178] Step 9: Adjust the reference model based on the hysteresis relationship between current and voltage and the error equation containing external disturbances at steady state, and obtain the adjusted reference model.

[0179] The adjusted reference model in this embodiment refers to formula (11).

[0180] Step 10: Perform order reduction on the nonlinear model based on the logic of keeping the absolute displacement of the electromagnet unchanged, and obtain the reduced nonlinear model containing external disturbances.

[0181] The reduced nonlinear model containing external disturbances in this embodiment refers to formula (12). After establishing the nonlinear model, a linear model can be obtained by linearization at the equilibrium point. These nonlinear models can be understood as linear models.

[0182] Step 11: Design the adjusted reference model to determine the reduced order reference model corresponding to the reduced order nonlinear model.

[0183] The reduced order reference model in this embodiment, please refer to formula (13).

[0184] Step 12: Based on the reduced order nonlinear model and the reduced order reference model and the initial control law, obtain the reduced order control law.

[0185] The reduced order control law in this embodiment, please refer to formula (14).

[0186] Step 13: Determine the reduced order nonlinear model under the reduced order control law, obtain the adjusted nonlinear model.

[0187] The adjusted nonlinear model in this embodiment, please refer to formula (15).

[0188] Step 14: Determine the extended state nonlinear model corresponding to the adjusted nonlinear model.

[0189] The extended state nonlinear model in this embodiment, please refer to formula (16).

[0190] Step 15: Design the extended state nonlinear model based on the linear extended state observer, obtain the observed and extended nonlinear model.

[0191] The observed and extended nonlinear model in this embodiment, please refer to formula (17).

[0192] Step 16: Based on the observed and extended nonlinear model and the extended state nonlinear model, obtain the observation error equation.

[0193] The observation error equation in this embodiment, please refer to formula (18).

[0194] Step 17: Substitute the estimated disturbance into the reduced order control law to obtain the reduced order control law with disturbance.

[0195] The reduced order control law with disturbance in this embodiment, please refer to formula (19).

[0196] Step 18: Design the reduced order reference model to determine the extended reference model corresponding to the extended state nonlinear model.

[0197] The extended reference model in this embodiment, please refer to formula (20).

[0198] Step 19: Using the extended reference model as the control objective of the observed and extended nonlinear model, determine the target control parameters corresponding to the observed and extended nonlinear model based on the control law with disturbance and reduced order.

[0199] This invention proposes a composite strategy (MRAC-ADRC) integrating Active Disturbance Rejection Control (ADRC) and Model Reference Adaptive Control (MRAC), primarily addressing the issues of system disturbance rejection and state observation. This method achieves excellent coupled vibration suppression by using only the levitation gap, levitation current, and the differential of the gap (as can be seen from the reduced-order model equations, which used two more state variables before the reduction), achieving similar results. No similar scheme can achieve comparable performance. This method simplifies MRAC by establishing a reduced-order model through analysis of the vehicle-track coupled vibration characteristics, utilizes an adaptive control law to achieve reference model tracking to suppress vibration, and then introduces ADRC to enhance the system's disturbance rejection capability, thus solving the problems of system disturbance rejection and state observation.

[0200] The beneficial effects of the embodiments of the present invention are as follows:

[0201] (1) This design ensures that the electromagnet will not further amplify the vibration of the track, effectively suppressing coupled vibration while ensuring that the coupling system maintains good adaptability to higher flexible bridge stiffness.

[0202] (2) The control law in this embodiment is an adaptive control law, which automatically adjusts when system parameters change. This reduces the controller's dependence on coupled system parameters, thereby enhancing system robustness.

[0203] (3) It is difficult to obtain the two state variables of accurate track displacement and track displacement derivative. After order reduction, it is no longer necessary to obtain these two state variables. Taking full account of the sensor data available in the project, the feasibility of the project is ensured by order reduction optimization of MRAC.

[0204] (4) Through this design, the control system has high robustness to changes in structural parameters, which can reduce the difficulty of construction; the coupling system has better adaptability to bridges with higher flexibility, both of which can reduce construction costs.

[0205] Simulation conditions: The target suspension gap of the suspension system is set to 10 mm, i.e. Configure the bandwidth of the reference system. , The damping is 0.707, that is... .set up The matrix is ​​an identity matrix, and the gain adjustment matrix is... ESO bandwidth The relevant parameters in TD are: The simulation time is set to 20 seconds, and the simulation step is 0.001 seconds. The MRAC, LQR, PID and MRAC-ADRC methods are used for comparison experiments. The parameters of the lap joint structure model and the parameters of the PID control method are shown in Table 2, which is a related parameter table of a simulation experiment.

[0206] Table 2 Related parameter table of a simulation experiment

[0207]

[0208] Simulation experiment content: considering high-order modal vehicle-track coupling vibration suppression experiment. Considering the first and second order modes, the control performance of the four control methods is compared without considering external disturbance. The effect is shown in Figure 4 、 Figure 5 and Figure 6 , Figure 4 is a kind of electromagnetic iron displacement change curve provided by the embodiment of the application under the consideration of high-order modal four control methods; Figure 5 is a kind of electromagnetic iron acceleration change curve provided by the embodiment of the application under the consideration of high-order modal four control methods; Figure 6 is a kind of electromagnetic iron suspension current change curve provided by the embodiment of the application under the consideration of high-order modal four control methods.

[0209] Simulation result analysis: from Figure 4 It can be seen that the electromagnetic iron displacement fluctuation of the MRAC-ADRC method (the method provided by the application based on nonlinear model, reference model and control law for control and simplification) is the smallest, and the preset equilibrium point position can be reached. In tracking the reference input, the response speed of MRAC-ADRC is faster than that of MRAC method. This is because in the MRAC-ADRC method, in addition to the state feedback and feedforward through the error of the current system and the reference system, disturbance compensation is also added. The disturbance not only reflects the external disturbance suffered by the current system, but also compensates the model residual error of MRAC control in the approaching process, so as to speed up the process of approaching the reference system. Figure 5 The acceleration amplitude of the four control methods in the acceleration curve is 4.16x10-3m / s 2 , 2.41x10-3m / s 2 , 6.70x10-4m / s 2 , 2.13x10-4m / s 2 . It can be seen that the acceleration value based on the MRAC method (i.e. the method for simplification in the above) is much smaller than the method based on linear system. And MRAC-ADRC further reduces the coupling vibration on the basis of original MRAC. This also shows that MRAC-ADRC can not only speed up the response speed, but also further suppress the vehicle-track coupling vibration. Figure 6For the current curves of the four control methods, it can be seen that the equilibrium point current of the MRAC-ADRC is consistent with that of the LQR (linear quadratic regulator) method, which indicates that the addition of the ADRC eliminates the static error in the MRAC, and enables the suspension gap to reach the preset position. The simulation results show that the control method can effectively improve the adaptability of the system to the flexible track and the robustness of parameter perturbation, and the required control effort is small, and has good engineering application value.

[0210] The vehicle-track coupled vibration control device provided by the embodiment of the application is described below, and the vehicle-track coupled vibration control device described below can be correspondingly referred to the vehicle-track coupled vibration control method described above.

[0211] Figure 7 The structural framework schematic diagram of the vehicle-track coupled vibration control device provided by the embodiment of the application can include:

[0212] The nonlinear model determination module 100 is configured to obtain a nonlinear model considering the vibration mode of the track based on the high-speed maglev train structure of the lap joint structure, the track vibration equation and the electromagnet dynamics equation;

[0213] The motion state space equation determination module 200 is configured to determine the motion characteristics of the nonlinear model based on the equilibrium point position change feature and the model parameter time-varying feature, and obtain a motion state space equation;

[0214] The control law determination module 300 is configured to determine a reference model corresponding to the nonlinear model, and determine a control law that makes the motion state space equation and the reference model have the least difference;

[0215] The target diagnostic control parameter determination module 400 is configured to take the nonlinear model as a control object and the reference model as an ideal target, determine a target vibration control parameter corresponding to the nonlinear model by using the control law, and perform vehicle-track coupled vibration control on the high-speed maglev train based on the target vibration control parameter.

[0216] Further, based on the above embodiment, the motion state space equation is ; wherein, represents the motion characteristics, is a state variable of the nonlinear model, is an input of the electromagnet on both sides; represents a model matrix obtained by linearizing the nonlinear model based on the equilibrium point position change feature, represents the change of the model matrix caused by the change of the equilibrium point position and the time-varying of the model parameters; represents an input matrix of the nonlinear model based on the equilibrium point position variation characteristics after linearization at a preset distance point of a preset equilibrium point, represents an input matrix variation caused by equilibrium point position variation and model parameter time variation.

[0217] Further, based on the above-mentioned embodiments, the control law determination module 300 can comprise:

[0218] a reference model determination unit configured to determine a reference model corresponding to the nonlinear model as ; wherein, is a state variable of the reference model, is a control input of the reference model, which is a reference input based on the nonlinear model; represents a model matrix of the reference model, represents an input matrix of the reference model;

[0219] a control law determination unit configured to design a control law such that the motion state space equation is minimized under the action of the control law and the reference model; wherein, , are state feedback gain and feedforward gain, respectively.

[0220] Further, based on any of the above-mentioned embodiments, the vehicle-track coupled vibration control device can further comprise:

[0221] a first error equation determination module configured to substitute the control law into the motion state space equation and subtract the reference model to obtain a first error equation;

[0222] a second error equation determination module configured to determine an external disturbance parameter and determine a motion state space equation containing external disturbances based on the external disturbance parameter to determine a second error equation containing external disturbances;

[0223] a third error equation determination module configured to determine an error of the second error equation at a steady state to obtain a third error equation;

[0224] an adjusted reference model determination module configured to adjust the reference model based on the third error equation and a hysteresis relationship between current and voltage to obtain an adjusted reference model;

[0225] Correspondingly, the target diagnostic control parameter determination module 400 can comprise:

[0226] a first target diagnostic control parameter determination unit configured to take the nonlinear model as a control object and the adjusted reference model as an ideal target, and determine the target vibration control parameter corresponding to the nonlinear model by using the control law.

[0227] Further, based on any of the above embodiments, the vehicle-track coupled vibration control device can further include:

[0228] a simplification module configured to simplify the nonlinear model, the reference model and the control law based on a logic of keeping the absolute displacement of the electromagnet unchanged, to obtain a simplified nonlinear model, a simplified reference model and a simplified control law;

[0229] Correspondingly, the target diagnostic control parameter determination module 400 can include:

[0230] a second target diagnostic control parameter determination unit configured to take the simplified nonlinear model as a control object, the simplified reference model as an ideal target, and determine a target vibration control parameter corresponding to the simplified nonlinear model by using the simplified control law.

[0231] Further, based on any of the above embodiments, the vehicle-track coupled vibration control device can further include:

[0232] a disturbance parameter considering module configured to determine a total disturbance parameter received by the high-speed maglev train of the lap joint structure, and determine a disturbance-containing and simplified nonlinear model, a disturbance-containing and simplified reference model and a disturbance-containing and simplified control law based on the total disturbance parameter.

[0233] Further, based on the above embodiment, the disturbance parameter considering module can include:

[0234] a disturbance-containing and simplified nonlinear model determination unit configured to determine a disturbance-containing and simplified nonlinear model under the simplified control law based on the total disturbance parameter and the simplified nonlinear model;

[0235] an expanded and disturbance-containing and simplified nonlinear model determination unit configured to determine an expanded state corresponding to the disturbance-containing and simplified nonlinear model, to obtain an expanded and disturbance-containing and simplified nonlinear model;

[0236] a linear expanded state observer determination unit configured to determine a linear expanded state observer corresponding to the expanded and disturbance-containing and simplified nonlinear model;

[0237] an observation error equation determination unit configured to determine an observation error equation based on the linear expanded state observer and the expanded and disturbance-containing and simplified nonlinear model;

[0238] an estimated disturbance determination unit configured to perform disturbance estimation based on the total disturbance parameter, to obtain an estimated disturbance;

[0239] a final control law determination unit configured to determine a final control law based on the estimated disturbance and the simplified control law;

[0240] a final reference model determination unit configured to determine a reference model corresponding to the expanded and disturbance-included and simplified nonlinear model to obtain a final reference model;

[0241] Correspondingly, the target diagnostic control parameter determination module 400 can include:

[0242] a third target diagnostic control parameter determination unit configured to take the expanded and disturbance-included and simplified nonlinear model as a control object, the final reference model as an ideal target, and determine the target vibration control parameter by using the final control law.

[0243] It should be noted that the order of the modules and units in the above vehicle-track coupled vibration control device can be changed without affecting the logic.

[0244] Figure 7 The features of the corresponding embodiments can be described with reference to Figure 7 The related descriptions of the corresponding embodiments will not be repeated here.

[0245] The vehicle-track coupled vibration control device provided by the embodiments of the present application can include: a nonlinear model determination module 100 configured to obtain a nonlinear model considering the vibration mode of a track based on the structure of a high-speed maglev train with a lap joint structure, a track vibration equation, and an electromagnet dynamics equation; a motion state space equation determination module 200 configured to determine the motion characteristics of the nonlinear model based on the position change characteristics of an equilibrium point and the time-varying characteristics of model parameters to obtain a motion state space equation; a control law determination module 300 configured to determine a reference model corresponding to the nonlinear model and determine a control law that makes the difference between the motion state space equation and the reference model the smallest; and a target diagnostic control parameter determination module 400 configured to take the nonlinear model as a control object, the reference model as an ideal target, and determine a target vibration control parameter corresponding to the nonlinear model by using the control law to perform vehicle-track coupled vibration control on the high-speed maglev train based on the target vibration control parameter. Compared with the current vibration suppression that is completed only by collecting gap data by a suspension gap sensor, the present application obtains a nonlinear model considering the vibration mode of a track based on the structure of a high-speed maglev train with a lap joint structure, a track vibration equation, and an electromagnet dynamics equation, thereby designing a corresponding reference model and a control law. Since the nonlinear model considers the vibration mode in the lap joint structure, the suspension control is more accurate, and thus the suppression effect on the high-speed maglev train-track coupled vibration is better.

[0246] A vehicle-track coupled vibration control device provided by an embodiment of the present application is described below. The vehicle-track coupled vibration control device described below can correspond to the vehicle-track coupled vibration control method described above.

[0247] Figure 8 A structural framework diagram of a vehicle-track coupled vibration control device provided by an embodiment of the present application is shown in FIG. 1. As shown in FIG. 1, the vehicle-track coupled vibration control device includes a memory 60 for storing a computer program. Figure 8

[0248] A processor 61 for executing the computer program to implement the steps of the vehicle-track coupled vibration control method of the above-described embodiment.

[0249] The vehicle-track coupled vibration control device provided by the embodiment can include, but is not limited to, a smart phone, a tablet computer, a notebook computer, or a desktop computer, etc.

[0250] The processor 61 can include one or more processing cores, such as a 4-core processor, an 8-core processor, etc. The processor 61 can be implemented in at least one of a hardware form of a Digital Signal Processing (DSP), a Field-Programmable Gate Array (FPGA), and a Programmable Logic Array (PLA). The processor 61 can also include a main processor and a coprocessor. The main processor is a processor for processing data in an awake state, also known as a Central Processing Unit (CPU). The coprocessor is a low-power processor for processing data in a standby state. In some embodiments, the processor 61 can be integrated with a Graphics Processing Unit (GPU). The GPU is responsible for rendering and drawing the content required to be displayed on the display screen. In some embodiments, the processor 61 can also include an Artificial Intelligence (AI) processor. The AI processor is used to process computing operations related to machine learning.

[0251] ​The memory 60 can include one or more computer-readable storage media that can be non-transitory. The memory 60 can also include high-speed random access memory and nonvolatile, computer-readable storage media such as one or more magnetic disk storage devices, flash memory devices. In the embodiment, the memory 60 is used at least to store the following computer program 601, wherein the computer program is loaded and executed by the processor 61 and can implement the related steps of the vehicle-track coupling vibration control method disclosed in any of the foregoing embodiments. In addition, the resources stored by the memory 60 can also include an operating system 602 and data 603, etc., and the storage mode can be temporary storage or permanent storage. The operating system 602 can include Windows, Unix, Linux, etc. The data 603 can include but is not limited to data required for vehicle-track coupling vibration control, etc.

[0252] In some embodiments, the vehicle-track coupling vibration control device can further include a display screen 62, an input / output interface 63, a communication interface 64, a power supply 65, and a communication bus 66.

[0253] Those skilled in the art can understand that, Figure 8 The structure shown in the above embodiments does not constitute a limitation on the vehicle-track coupling vibration control device, and can include more or fewer components than those shown in the drawings.

[0254] It can be understood that if the vehicle-track coupling vibration control method in the above embodiments is implemented in the form of a software function unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the part that contributes to the prior art or the whole or part of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium, and performs all or part of the steps of the method of each embodiment of the present application. The foregoing storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), an electrically erasable programmable ROM, a register, a hard disk, a removable magnetic disk, a CD-ROM, a magnetic disk or an optical disk, and various media that can store program codes.

[0255] Based on this, the embodiment of the present application further provides a readable storage medium (computer-readable storage medium), and the computer-readable storage medium stores a computer program. The computer program is executed by a processor to implement the steps of the vehicle-track coupling vibration control method as described above.

[0256] The above describes in detail the rail coupling vibration control method, device, equipment and readable storage medium provided by the embodiment of the present application. Each embodiment in the specification is described in a progressive manner, and each embodiment mainly describes the difference from other embodiments. The same or similar parts of each embodiment can be understood by referring to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the related parts can be understood by referring to the method part.

[0257] Those skilled in the art can further realize that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be realized by electronic hardware, computer software or a combination of both. In order to clearly illustrate the interchangeability of hardware and software, the components and steps of each example have been described in the above description in general terms. Whether the functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

Claims

1. A method for controlling vehicle-track coupled vibration, characterized in that, include: Based on the high-speed maglev train structure with overlapping structure, the track vibration equation, and the electromagnet dynamics equation, a nonlinear model considering the track vibration modes is obtained. Based on the characteristics of the equilibrium point position change and the time-varying characteristics of the model parameters, the motion characteristics of the nonlinear model are determined, and the motion state space equation is obtained. Determine a reference model corresponding to the nonlinear model, and determine a control law that minimizes the difference between the motion state space equation and the reference model; Using the nonlinear model as the control object and the reference model as the ideal target, the target vibration control parameters corresponding to the nonlinear model are determined using the control law, so as to perform track-vehicle coupled vibration control on the high-speed maglev train based on the target vibration control parameters.

2. The vehicle-track coupled vibration control method according to claim 1, characterized in that, The motion state space equation is: ;in, Indicates motion characteristics, Let these be the state variables of the nonlinear model. This is the input for the electromagnets on both sides; This represents the model matrix obtained after linearizing the nonlinear model based on the characteristics of the equilibrium point position change. This indicates the change in the model matrix caused by changes in the equilibrium point location and time-varying model parameters; This represents the input matrix obtained by linearizing the nonlinear model at a preset distance from the preset equilibrium point based on the characteristics of the equilibrium point position change. This represents the change in the input matrix caused by the change in the position of the equilibrium point and the time-varying nature of the model parameters.

3. The vehicle-rail coupled vibration control method according to claim 1, characterized in that, Determine a reference model corresponding to the nonlinear model, and determine a control law that minimizes the difference between the motion state space equation and the reference model, including: The reference model corresponding to the nonlinear model is determined as follows: ;in, For the state variables of the reference model, As the control input for the reference model, , These represent the target positions of the electromagnets on both sides, and this input is a reference input based on the nonlinear model. The model matrix represents the reference model. This represents the input matrix of the reference model; Design control law This ensures that the difference between the motion state space equations and the reference model is minimized under the control law; wherein, , These are the state feedback gain and the feedforward gain, respectively.

4. The vehicle-track coupled vibration control method according to any one of claims 1 to 3, characterized in that, After determining the reference model corresponding to the nonlinear model and determining the control law that minimizes the difference between the motion state space equation and the reference model, the method further includes: Substituting the control law into the motion state space equation and subtracting it from the reference model, we obtain the first error equation. Determine the external disturbance parameters, and based on the external disturbance parameters, determine the motion state space equation containing the external disturbance, and determine the second error equation containing the external disturbance; By determining the error of the second error equation in steady state, the third error equation is obtained; The reference model is adjusted based on the third error equation and the hysteresis relationship between current and voltage to obtain the adjusted reference model. Accordingly, the nonlinear model is used as the controlled object, and the reference model is used as the ideal target. The target vibration control parameters corresponding to the nonlinear model are determined using the control law, including: Using the nonlinear model as the control object and the adjusted reference model as the ideal target, the target vibration control parameters corresponding to the nonlinear model are determined using the control law.

5. The vehicle-rail coupled vibration control method according to claim 1, characterized in that, After obtaining a nonlinear model considering the vibration modes of the track based on the high-speed maglev train structure, track vibration equation, and electromagnet dynamics equation, the following is also included: Based on the logic of keeping the absolute displacement of the electromagnet constant, the nonlinear model, the reference model, and the control law are simplified to obtain the simplified nonlinear model, the simplified reference model, and the simplified control law. Accordingly, the nonlinear model is used as the controlled object, and the reference model is used as the ideal target. The target vibration control parameters corresponding to the nonlinear model are determined using the control law, including: Using the simplified nonlinear model as the control object and the simplified reference model as the ideal target, the target vibration control parameters corresponding to the simplified nonlinear model are determined using the simplified control law.

6. The vehicle-track coupled vibration control method according to claim 5, characterized in that, After simplifying the nonlinear model, the reference model, and the control law based on the logic of keeping the absolute displacement of the electromagnet constant, to obtain the simplified nonlinear model, the simplified reference model, and the simplified control law, the method further includes: The total disturbance parameters of the high-speed maglev train with the overlapping structure are determined, and a simplified nonlinear model with disturbance, a simplified reference model with disturbance, and a simplified control law with disturbance are determined based on the total disturbance parameters.

7. The vehicle-track coupled vibration control method according to claim 6, characterized in that, The total disturbance parameters experienced by the high-speed maglev train with the overlapping structure are determined, and based on the total disturbance parameters, a simplified nonlinear model with disturbance, a simplified reference model with disturbance, and a simplified control law with disturbance are determined, including: Based on the total disturbance parameters and the simplified nonlinear model, a simplified nonlinear model with disturbance is determined under the simplified control law; Determine the extended state corresponding to the perturbation-induced and simplified nonlinear model to obtain the extended, perturbation-induced and simplified nonlinear model; Determine the linear extended state observer corresponding to the extended, perturbed, and simplified nonlinear mode; The observation error equation is determined using the linear extended state observer and the extended, perturbated, and simplified nonlinear model. Based on the total disturbance parameters, a disturbance estimate is performed to obtain the estimated disturbance. Based on the estimated disturbance and the simplified control law, the final control law is obtained; Determine the reference model corresponding to the extended, perturbated, and simplified nonlinear model to obtain the final reference model; Accordingly, the nonlinear model is used as the controlled object, and the reference model is used as the ideal target. The target vibration control parameters corresponding to the nonlinear model are determined using the control law, including: The extended, perturbation-inducing, and simplified nonlinear model is used as the control object, and the final reference model is used as the ideal target. The target vibration control parameters are determined using the final control law.

8. A vehicle-rail coupled vibration control device, characterized in that, include: The nonlinear model determination module is used to obtain a nonlinear model considering the vibration modes of the track based on the high-speed maglev train structure with overlapping structure, track vibration equation, and electromagnet dynamics equation. The motion state space equation determination module is used to determine the motion characteristics of the nonlinear model based on the equilibrium point position change characteristics and the time-varying characteristics of the model parameters, and obtain the motion state space equation. The control law determination module is used to determine a reference model corresponding to the nonlinear model and to determine a control law that minimizes the difference between the motion state space equation and the reference model. The target diagnostic control parameter determination module is used to take the nonlinear model as the control object and the reference model as the ideal target, and use the control law to determine the target vibration control parameters corresponding to the nonlinear model, so as to perform track-vehicle coupled vibration control on the high-speed maglev train based on the target vibration control parameters.

9. A vehicle-rail coupled vibration control device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the steps of the track-coupled vibration control method as described in any one of claims 1 to 7.

10. A readable storage medium, characterized in that, The readable storage medium stores a computer program that, when executed by a processor, implements the steps of the track-vehicle coupled vibration control method as described in any one of claims 1 to 7.

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