A control method for a high-speed maglev train lap joint suspension system

Abstract

The application discloses a control method of a high-speed maglev train overlapping suspension system, and relates to the technical field of suspension system control. The method comprises the following steps: decoupling the overlapping suspension system based on a constructed multi-degree-of-freedom coupled dynamics model, and constructing a target extended state observer for each single-point suspension subsystem after decoupling; the target extended state observer adopts a smooth nonlinear function as a nonlinear feedback item, and estimates the system state and total disturbance in real time according to the suspension gap error; based on the non-singular terminal sliding mode control theory, a sliding mode surface containing a nonlinear power term is designed, and a finite time control law is constructed according to the sliding mode surface, the estimated value of the total disturbance and a disturbance derivative compensation item, so as to generate a composite control voltage and apply the composite control voltage to both ends of an electromagnet to control the suspension gap. The method has strong robustness, fast response speed and good engineering realizability, and significantly improves the steady-state accuracy, dynamic stability and anti-interference ability of the maglev train under high-speed running conditions.

Description

Technical Field

[0001] This invention relates to the field of suspension system control technology, and in particular to a control method for a high-speed maglev train's levitation system. Background Technology

[0002] High-speed maglev trains rely on electromagnetic force for contactless levitation and guidance, and their levitation system is a core subsystem ensuring operational stability, safety, and passenger comfort. Due to the susceptibility of trains to multiple uncertainties during high-speed operation, such as track irregularities, aerodynamic disturbances, load variations, and parameter perturbations, the levitation gap is prone to fluctuations, potentially leading to instability. Therefore, implementing highly robust and fast-response real-time control of the levitation system is crucial. In recent years, active disturbance suppression control methods based on Extended State Observers (ESOs) have received widespread attention in the field of maglev control because they can effectively estimate and compensate for internal and external disturbances. However, traditional ESO structures suffer from slow convergence speed and limited estimation accuracy, especially when facing sudden disturbances or strong nonlinear dynamics at high speeds, making it difficult to meet the dual requirements of speed and accuracy for the levitation system.

[0003] Existing maglev suspension control strategies are mostly based on asymptotic stability theory. While they can effectively maintain small suspension gap fluctuations in steady state, they exhibit significant response lag during transient processes (such as starting, braking, cornering, or encountering sudden disturbances), failing to converge the system state to the desired value within a finite time, thus limiting the train's dynamic performance under complex operating conditions. Conventional ESOs typically employ linear or fixed-gain structures, making it difficult to reconcile the trade-off between estimated speed and noise sensitivity, leading to decreased control performance under high-frequency disturbances. Furthermore, high-speed maglev train suspension systems use overlapping structures as the smallest suspension unit, and existing control strategies for high-speed maglev suspension systems are mostly based on single-point suspension structures, neglecting the coupling effects of actual overlapping structures. Therefore, there is an urgent need to construct an overlapping suspension control scheme with finite-time convergence capability, strong anti-interference ability, and computational efficiency to improve the dynamic response quality and robust stability of high-speed maglev train suspension systems under harsh operating conditions. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a control method for the levitation system of a high-speed maglev train. By constructing an improved ESO with a nonlinear gain and bandwidth adaptive mechanism, the levitation gap is ensured to converge rapidly within a finite time and various disturbances are effectively suppressed. This method combines strong robustness, fast response speed, and good engineering feasibility, significantly improving the steady-state accuracy, dynamic stability, and anti-interference capability of the maglev train under high-speed operating conditions. The specific scheme is as follows:

[0005] This application discloses a control method for a high-speed maglev train's levitation system, including:

[0006] Construct a multi-degree-of-freedom coupled dynamic model of the overlapping suspension system;

[0007] Based on the aforementioned multi-degree-of-freedom coupled dynamics model, the overlapping suspension system is decoupled to be converted into two independent single-point suspension subsystems;

[0008] For each of the single-point levitation subsystems, a target expansion state observer is constructed; wherein, the target expansion state observer uses a smooth nonlinear function as a nonlinear feedback term to estimate the system state and total disturbance in real time based on the levitation gap error;

[0009] Based on the nonsingular terminal sliding mode control theory, a sliding surface containing nonlinear power terms is designed, and a finite-time control law is constructed according to the sliding surface, the estimated value of the total disturbance, and the disturbance derivative compensation term to generate a composite control voltage and apply it to both ends of the electromagnet of the overlapping suspension system to control the suspension gap; the disturbance derivative compensation term is used to estimate and offset the rate of change of the total disturbance with time.

[0010] Optionally, the construction of the multi-degree-of-freedom coupled dynamic model of the overlapping suspension system includes:

[0011] An electromagnet model is established based on the physical structure of the electromagnet; the electromagnet model includes electromagnetic force equations and voltage equations: ;in, Electromagnetic force, For the current of the suspending electromagnet, The distance between the levitation electromagnet and the track. The permeability of free space, The number of turns of the levitation electromagnet coil. The area of ​​the magnetic poles of the suspending electromagnet, The voltage applied across the electromagnet, This is the equivalent resistance value of the electromagnet;

[0012] A dynamic model of the suspension frame is established based on the force analysis of the aforementioned overlapping suspension system; the equations of the dynamic model of the suspension frame are: ; where the subscripts l and r represent the left and right sides, For the mass of the suspending electromagnet, x This represents the displacement of the electromagnet relative to the track. g Represents gravitational acceleration. The vertical force generated by the primary suspension system. Electromagnetic force, For the weight of the support arm, This represents the displacement of the support arm relative to the track. The force generated by the secondary suspension system, For the equivalent mass of the vehicle body, This indicates the displacement of the vehicle body relative to the track. External disturbance;

[0013] The suspension dynamics model is transformed into a state-space form; the expression of the state-space form is: ;in, , , , , , , For disturbance terms; and For the stiffness and damping of the primary suspension system, For lumped parameters, , , , .

[0014] Optionally, based on the multi-degree-of-freedom coupled dynamic model, the overlapping suspension system is decoupled to convert it into two independent single-point suspension subsystems, including:

[0015] Separate the coupled and uncoupled terms in the state-space form; the state equation after separation is: ;in, , , It is a diagonal matrix, corresponding to the uncoupled terms; , , The matrix whose main diagonal elements are all zero corresponds to the coupling term.

[0016] A decoupling control matrix is ​​constructed, and the coupling terms are eliminated using the decoupling control matrix to decouple the overlapping suspension system into two independent single-point suspension subsystems; wherein, the decoupling control matrix includes K , M , S They respectively satisfy: The state equation of the decoupled single-point levitation subsystem is: , V The control input for the decoupled system. Let be the total disturbance term after decoupling, where This represents the coupling error.

[0017] Optionally, a target extended state observer is constructed for each of the single-point suspended subsystems, including:

[0018] A target expansion state observer is constructed based on the hyperbolic tangent function, and the suspension gap error is used as input to estimate the suspension gap, gap velocity and total disturbance of each single-point suspension subsystem in real time.

[0019] The expression for the target extended state observer is: ;in, , This is an estimated value for the suspension gap. This is an estimate of the gap speed. This is an estimate of the total disturbance. For matrix The first element, For matrix The first element, , , For observer gain, η The first parameter to be designed. σ This is the second parameter to be designed. e For suspension gap error, For symbolic functions, .

[0020] Optionally, the control method for the high-speed maglev train's levitation system further includes:

[0021] Based on the bandwidth method, all poles of the target extended state observer are configured to be the same target real poles to tune the observer gain; the tuning formula for the observer gain is: , , ,in, For observer bandwidth;

[0022] The first design parameter is set to an initial value that matches the inertia of the single-point levitation subsystem, and the first design parameter is adjusted based on the initial value. Specifically, if the single-point levitation subsystem needs to improve its tracking capability against rapidly changing disturbances or requires the system response speed to meet a first preset condition, the first design parameter is increased; if the composite control voltage oscillates or exceeds a preset amplitude control value, the first design parameter is decreased. The rapidly changing disturbance is a disturbance component with a disturbance frequency higher than the observer bandwidth.

[0023] The second design parameter is adjusted based on the noise level of the single-point levitation subsystem or using an adaptive strategy. Specifically, when adjusting based on the noise level, if system measurement noise exists, the second design parameter is decreased; if it is necessary to improve the convergence speed of the target expansion state observer's output, and the robustness of the target expansion state observer under disturbance conditions meets a second preset condition, the second design parameter is increased. When adjusting based on the adaptive strategy, if the levitation gap error increases, the second design parameter is increased; if the levitation gap error decreases, the second design parameter is decreased.

[0024] Optionally, the design of the sliding surface containing nonlinear power terms based on the nonsingular terminal sliding mode control theory includes:

[0025] Define the gap error between the actual value and the reference value of the suspension gap, and the speed error between the actual value and the reference value of the gap speed;

[0026] Based on the nonsingular terminal sliding mode control theory, a sliding surface containing nonlinear power terms is designed using the gap error and the velocity error.

[0027] Wherein, the gap error is , This is the actual value of the suspension gap. The reference value for the suspension gap is; the speed error is... , This is the actual value of the gap speed. This is a reference value for the gap speed; the sliding surface ,in, It is a proportionality coefficient and , Let be the coefficients of the nonlinear power term of the sliding surface, and .

[0028] Optionally, the step of constructing a finite-time control law based on the sliding surface, the estimated value of the total disturbance, and the disturbance derivative compensation term includes:

[0029] Construct a disturbance derivative compensation term; the disturbance derivative compensation term ,in, for The first derivative, The coefficient to be compensated and , s For sliding surface, This refers to gap error;

[0030] Based on the sliding surface, the estimated value of the total disturbance, and the disturbance derivative compensation term, a control voltage expression is constructed to determine the finite-time control law;

[0031] The expression for the control voltage is: , For composite control voltage, This is the proportionality coefficient. The coefficients of the nonlinear power term of the sliding surface are... For speed error, For the disturbance derivative compensation term, This is an estimate of the total disturbance. For the desired acceleration feedforward, This is the third parameter to be designed. It is a symbolic function.

[0032] Optionally, the control method for the high-speed maglev train's levitation system further includes:

[0033] When the system state of the single-point suspension subsystem reaches the sliding surface, the finite-time control law enables the tracking error of the single-point suspension subsystem to dynamically satisfy the first convergence condition, and under the first convergence condition, the finite time for the system state to converge from the initial error to the equilibrium point satisfies the second convergence condition.

[0034] Wherein, the first convergence condition is ;

[0035] The second convergence condition is , For finite convergence time, This represents the initial error.

[0036] Optionally, the control method for the high-speed maglev train's levitation system further includes:

[0037] The coefficients of the nonlinear power term of the sliding surface are fixed as preset initial values, and different proportional coefficients and the third design parameter are selected and substituted into the finite-time control law for simulation testing.

[0038] When the single-point suspension subsystem fails to meet the first performance threshold to determine that the system response speed is insufficient, the proportional coefficient is reduced.

[0039] When the single-point suspension subsystem fails to meet the second performance threshold to determine that the system is chattering, the proportional coefficient and / or the third design parameter are increased.

[0040] Optionally, the step of generating a composite control voltage and applying it to both ends of the electromagnet of the overlapping levitation system to control the levitation gap includes:

[0041] The finite-time control law is discretized using the forward Euler method, and the discretized finite-time control law is embedded into the suspension controller.

[0042] Based on the aforementioned levitation controller, it communicates with the levitation operation platform in real time via the controller local area network bus to receive sensor data collected online by the levitation operation platform;

[0043] Based on the sensor data, the discretized finite-time control law is executed by the suspension controller to output a composite control voltage and apply it to both ends of the electromagnet of the overlapping suspension system to control the suspension gap.

[0044] The beneficial effects of this application are as follows: By constructing a multi-degree-of-freedom coupled dynamic model of the overlapping suspension system, the overlapping structure is decoupled into two independent single-point subsystems, solving the problem that traditional control methods are difficult to handle structural coupling effects, enabling the controller to accurately adapt to the actual structural characteristics and improve control targeting; a target extended state observer based on a smooth nonlinear function is designed. Utilizing its global smoothness characteristics, it can not only accurately estimate the internal state and total external disturbance of the suspension system in real time, but also effectively suppress the high-frequency chattering and sensitivity to measurement noise caused by traditional nonlinear observers, providing reliable state information for subsequent high-performance control; on this basis, a finite-time control law integrating non-singular terminal sliding mode control, disturbance derivative compensation term, and the estimated value of total disturbance is constructed to form a composite control; the output of this control law acts directly on the electromagnet as a voltage, and the precise control of the suspension gap is achieved by adjusting the current. The nonlinear power term in the sliding surface ensures that the system state converges to the equilibrium point within a preset finite time, avoiding the singularity problem of traditional terminal sliding mode. The estimated value of the total disturbance is directly fed forward to compensate for the disturbance itself, while the disturbance derivative compensation term on the sliding surface compensates for the rate of change of the disturbance, forming a complementary dual compensation mechanism. The synergistic effect of these three factors enables the levitation system to achieve rapid, accurate, and stable tracking control of the suspension gap even under complex conditions such as high-speed operation, track irregularities, and aerodynamic disturbances, significantly enhancing the dynamic response quality and robust stability of the system. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0046] Figure 1 This application discloses a flowchart of a control method for a high-speed maglev train's levitation system.

[0047] Figure 2 This is a schematic diagram of the structure of a high-speed maglev train disclosed in this application;

[0048] Figure 3 This is a schematic diagram of a high-speed maglev train suspension overlap structure disclosed in this application;

[0049] Figure 4 This is a schematic diagram of the stress analysis of a connection structure disclosed in this application;

[0050] Figure 5 This is a schematic diagram comparing the tanh function curve and the fal function curve disclosed in this application;

[0051] Figure 6 This application discloses a block diagram of a closed-loop control system based on a target ESO-structured overlap structure.

[0052] Figure 7 This is a schematic diagram comparing the control effects of four algorithms under a periodic disturbance as disclosed in this application;

[0053] Figure 8 This is a schematic diagram comparing the control effects of four algorithms under a step disturbance as disclosed in this application;

[0054] Figure 9 This is a structural diagram of an electronic device disclosed in this application. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] High-speed maglev trains levitate on the track using electromagnetic force, achieving contactless operation. However, in practice, the train is susceptible to track irregularities and airflow disturbances, leading to fluctuations in the levitation gap (the distance between the train and the track), and even instability. Current control methods (such as the traditional Extended State Observer (ESO)) have two major drawbacks:

[0057] (1) Slow response: When faced with sudden disturbances, the control is delayed and cannot quickly stabilize the suspension gap;

[0058] (2) Low precision: Traditional methods ignore the coupling effect of the "overlapping structure" (adjacent electromagnets working together) of the maglev train, resulting in insufficient control precision.

[0059] To this end, this application provides a control scheme for the levitation system of a high-speed maglev train, which is guided by the high dynamic and robust control requirements of the levitation system of the high-speed maglev train, and is characterized by finite-time convergence, non-singularity and high-efficiency disturbance suppression.

[0060] It should be noted that, for any variable appearing in this application, a single dot above the variable uniformly represents the first derivative of that variable with respect to its independent variable; a double dot above the variable uniformly represents the second derivative of that variable with respect to its independent variable; the independent variable of the derivative is determined according to the specific expression.

[0061] This invention discloses a control method for a high-speed maglev train's levitation system, see [link to relevant documentation]. Figure 1 As shown, the method includes:

[0062] Step S11: Construct a multi-degree-of-freedom coupled dynamic model of the overlapping suspension system.

[0063] High-speed maglev trains are highly integrated levitation, guidance, and propulsion systems, as shown in the attached diagram. Figure 2 As shown, the basic structure mainly includes the car body, suspension frame, suspension electromagnets, guide electromagnets, braking electromagnets, linear motors, running mechanism, control system, and onboard power supply. Its suspension system adopts an overlapping structure, meaning that adjacent electromagnets share a supporting role through the suspension frame, which is fundamentally different from the suspension system structure of medium- and low-speed maglev trains.

[0064] In this embodiment, a multi-degree-of-freedom coupled dynamic model of the high-speed maglev train's lap-suspension system (lap-suspension structure) is first established. The multi-degree-of-freedom coupled dynamic model is a mathematical model constructed specifically for the lap-suspension structure of the high-speed maglev train. Its core is to simultaneously describe the dynamic behavior (degrees of freedom) of multiple independent moving components within the structure, as well as the interactions (coupling effects) between these components. The lap-suspension system consists of two parts: an electromagnet model and a suspension frame dynamic model.

[0065] (1) Electromagnet Model: The electromagnetic part is modeled, and the mapping relationship between the external voltage input and the coil current, as well as the relationship between the electromagnet current and the levitation electromagnetic force, are established while neglecting leakage flux and magnetic saturation effects. The electromagnet model includes the electromagnetic force equation and the voltage equation:

[0066] ;

[0067] in, Electromagnetic force, For the current of the suspending electromagnet, The distance between the levitation electromagnet and the track. The permeability of free space, The number of turns of the levitation electromagnet coil. The area of ​​the magnetic poles of the suspending electromagnet, The voltage applied across the electromagnet, This is the equivalent resistance value of the electromagnet.

[0068] (2) Suspension Frame Dynamics Model: Regarding the dynamics modeling, it is first necessary to clarify the motion process of the overlapping structure. (See attached diagram) Figure 3 The diagram shown illustrates the relative positions and structure of the levitation linkage system for a high-speed maglev train. It comprises basic units including electromagnets, a suspension frame, primary suspension, and secondary suspension. The force analysis of the levitation linkage system is attached. Figure 4 As shown, applying voltage to the ends of the electromagnet coil induces a current within the coil, generating an electromagnetic force that causes the levitation electromagnet to move upwards. The electromagnetic forces generated by the electromagnets on both sides of the overlapping structure are transmitted to the support arms through the primary suspension, jointly supporting the vehicle body. The vehicle load is transmitted to the suspension frame through the secondary suspension.

[0069] according to Figure 3 Based on the force analysis results, the equations for the suspension frame dynamic model are obtained as follows:

[0070] ;

[0071] In this context, the subscripts "l" and "r" represent the left and right sides, respectively. For the mass of the suspending electromagnet, x This represents the displacement of the electromagnet relative to the track. g Represents gravitational acceleration. The vertical force generated by the primary suspension system. Electromagnetic force, For the weight of the support arm, This represents the displacement of the support arm relative to the track. The force generated by the secondary suspension system, For the equivalent mass of the vehicle body, This indicates the displacement of the vehicle body relative to the track. This is an external disturbance.

[0072] The deformation of a laminated leaf spring (primary suspension) can be expressed as the difference between the relative displacement between the electromagnet and the rail and the relative displacement between the support arm and the rail; similarly, the deformation of an air spring (secondary suspension) is equal to the displacement of the vehicle body relative to the rail minus the displacement of the support arm relative to the rail. Therefore, the forces generated by these two types of springs are determined by their respective deformation amounts.

[0073] ;

[0074] in, and For the stiffness and damping of the primary suspension system, and For the stiffness and damping of the secondary suspension, , This refers to the free length of the primary suspension (left / right leaf springs) in equilibrium. This refers to the free length of the secondary suspension (air spring) in equilibrium.

[0075] Furthermore, , , , The overlapping structure model represented by the above two equations is transformed into a state-space form:

[0076] ;

[0077] in, , , , , The control input vector corresponds to the square of the voltage or current applied across the electromagnet. , The current flowing through the left and right electromagnets is [value]. , For equivalent control quantity; is a constant vector related to the system's mass and gravity, representing the system's steady-state offset, used to compensate for the balance between gravity and suspension force. m This refers to the mass of each component in an overlapping structure; The disturbance term encompasses external disturbances such as track irregularities and aerodynamic disturbances. For lumped parameters.

[0078] Step S12: Based on the multi-degree-of-freedom coupled dynamic model, the overlapping suspension system is decoupled to convert it into two independent single-point suspension subsystems.

[0079] Since current control strategies are mostly designed for single-point suspension structures and do not consider the multi-degree-of-freedom coupling characteristics of high-speed maglev overlapping structures, the control accuracy is reduced. Therefore, in this embodiment, after constructing a multi-degree-of-freedom coupled dynamic model of the overlapping suspension system, a feedforward decoupling strategy is adopted to eliminate the coupling between channels and achieve decoupling control, so that the controller can accurately adapt to the actual structural characteristics and improve the control targeting.

[0080] Specifically, by constructing an appropriate feedforward compensator, the coupling dynamics between channels are actively canceled by the system input, so that the closed-loop system approximately presents a diagonal structure in the input-output mapping. This transforms the multivariable coupled overlapping structure into two independent single-input single-output subsystems (single-point floating subsystems), which facilitates the subsequent design of the controller and improves the overall control performance.

[0081] The coupling characteristics of the suspended state depend on the matrix. A 0 and A 1The off-diagonal terms in the equation are used to rewrite the state-space form of the overlapping structure model in step S11, separating the coupled and uncoupled terms in the system. The resulting state equation is:

[0082] ;

[0083] in, , It is a diagonal matrix, whose diagonal elements are respectively equal to the matrix... A 0 and A 1 The main diagonal element, This represents the control variable matrix, which is also a diagonal matrix, where the diagonal elements are equal to the matrix's length. B The elements on the main diagonal correspond to the uncoupled terms in the state equations of the above matrix; , A matrix whose main diagonal elements are all zero. , , Similarly, a matrix whose main diagonal elements are all zero. The above matrix corresponds to the coupling terms in the state equation.

[0084] To eliminate coupling terms, a decoupling control matrix is ​​designed. K , M , S They respectively satisfy:

[0085] ;

[0086] Substituting these terms into the state equations that separate the coupled and uncoupled terms, we obtain two independent single-point levitation subsystems after decoupling, corresponding to the levitation units on the left and right sides, respectively. The dynamics of each subsystem depend only on its own state and control input, thus simplifying the multivariable control problem into two independent single-point levitation control problems, which facilitates the design of the subsequent controller.

[0087] The state equation of the decoupled single-point levitation subsystem is:

[0088] ;

[0089] V The control variables of the decoupled system include decoupling control terms. Let be the total disturbance term after decoupling, where This represents the coupling error.

[0090] Step S13: For each of the single-point levitation subsystems, construct a target expansion state observer; wherein the target expansion state observer uses a smooth nonlinear function as a nonlinear feedback term to estimate the system state and total disturbance in real time based on the levitation gap error.

[0091] Traditional extended state observers, based on non-smooth fal functions to construct nonlinear feedback, can achieve relatively fast state estimation, but suffer from problems such as origin non-differentiability, susceptibility to high-frequency chattering, complex parameter tuning, and sensitivity to noise. In this application, based on the decoupling of the overlapping suspension system, an improved extended state observer based on the smooth nonlinear function tanh is designed to achieve high-precision estimation of the system state and real-time reconstruction of unknown disturbances. Utilizing its global smoothness, differentiability, and natural saturation characteristics, it effectively suppresses chattering, reduces noise sensitivity, simplifies parameter tuning, and improves numerical stability and engineering practicality, enhancing smoothness and robustness while maintaining good estimation performance.

[0092] For each decoupled single-point levitation subsystem, the levitation gap error is considered. e As input, the levitation gap, gap velocity, and total disturbance of each single-point levitation subsystem are estimated in real time; the specific form of the improved extended state observer is as follows:

[0093] The expression for the target extended state observer is: ;

[0094] in, , For suspension gap x 1 The estimated value, gap speed x 2 The estimated value, For total disturbance x 3 The estimated value, For matrix The first element, For matrix The first element, , , For observer gain, η The first parameter to be designed. σ This is the second parameter to be designed. e For suspension gap error, For symbolic functions, .

[0095] The observer works by using the error between the measured and estimated values ​​of the suspension gap. eA smooth nonlinear function is driven to generate correction terms that are applied to the state estimation equations. Using this improved target extended state observer, high-fidelity estimates of the levitation gap, gap change rate, and total disturbance can be obtained in real time, providing accurate state information and disturbance feedforward for constructing a finite-time control law with disturbance compensation in subsequent steps.

[0096] It should be noted that the key to ESO gain tuning lies in improving its estimation accuracy and response speed for system state and total disturbance. The bandwidth method is a widely used parameter tuning strategy in engineering, which involves configuring all poles of the ESO to the same target real pole. This allows the observer dynamics to be controlled by a single parameter. Dominant. The tuning formula for the observer gain is: , , ,in, The observer bandwidth is significantly higher than the system control bandwidth to ensure that the disturbance energy can be estimated quickly.

[0097] In one specific implementation, regarding the first parameter to be designed in the tanh function... η The initial value of the parameter can be set to match the inertial compatibility of the single-point levitation subsystem, and then gradually adjusted through simulation or experiment. Specifically, if the single-point levitation subsystem needs to improve its tracking capability against rapidly changing disturbances or requires the system response speed to meet a first preset condition, the first design parameter should be increased. The rapidly changing disturbance refers to a disturbance component with a frequency higher than the observer bandwidth; that is, when the system has high-order disturbances (such as sudden changes in orbital irregularities, aerodynamic shocks, or other complex disturbances with rapid changes) or requires a fast response, the parameter should be appropriately increased. η If the composite control voltage oscillates or exceeds the preset amplitude control value (actuator saturation), then the first design parameter is reduced. In a preferred embodiment, after debugging, it is selected as... η= 1.

[0098] In another specific implementation, the second parameter to be designed σ The main adjustment process can be based on the noise level of the single-point suspended subsystem or by using an adaptive strategy. Specifically, when adjusting based on the noise level, if the system has significant noise, a smaller value is used; if it is necessary to improve the convergence speed of the target expansion state observer's output, and the robustness of the target expansion state observer under disturbance conditions meets a second preset condition, a larger value can be used; when adjusting based on the adaptive strategy, the transition process can be adjusted to... σ It changes dynamically with the magnitude of the error, that is, it increases when the error is large. σ When the error is small, it decreases. σIn a preferred embodiment, after repeated adjustments, the following was selected: σ= 3.

[0099] like Figure 5 The diagram shows a comparison between the nonlinear fal function and the tanh function in this application. It can be seen that the tanh function exhibits an approximately linear gain when the error is small, ensuring the smoothness of the estimation and effectively suppressing the influence of high-frequency measurement noise on the estimated value; when the error is large, the gain tends to saturate, avoiding estimation overshoot caused by large instantaneous errors, thus maintaining fast convergence capability while suppressing chattering and reducing noise sensitivity.

[0100] Step S14: Based on the nonsingular terminal sliding mode control theory, a sliding surface containing nonlinear power terms is designed, and a finite-time control law is constructed according to the sliding surface, the estimated value of the total disturbance, and the disturbance derivative compensation term to generate a composite control voltage and apply it to both ends of the electromagnet of the overlapping suspension system to control the suspension gap; the disturbance derivative compensation term is used to estimate and offset the rate of change of the total disturbance with time.

[0101] In this step, a finite-time control law integrating an improved target extended state observer, a disturbance derivative compensation term, and a nonsingular terminal sliding mode control (NTSMC) is designed. This composite control framework is a control strategy that ensures the system state converges within a preset time. While overcoming the singularity problem of terminal sliding mode, it achieves fast convergence within a finite time, improving the control accuracy and robustness of the levitation system. Its implementation process is as follows:

[0102] (1) NTSMC sliding surface design. The sliding surface is the core of sliding mode control. In the embodiments of this application, the special design of the sliding surface with nonlinear power terms is used to achieve finite-time convergence and avoid the singularity problem of traditional terminal sliding mode.

[0103] First, define the tracking error: taking the suspension gap and gap velocity as the core state variables, define the tracking error between the actual values ​​and the reference values. The gap error is... The speed error is ;in, This is the actual value of the suspension gap. This is a reference value for the suspension gap. This is the actual value of the gap speed. This is a reference value for the gap speed. Error is the only input for sliding surface design, directly reflecting the deviation between the suspension state and the target state.

[0104] Secondly, in order to achieve finite-time convergence and overcome the singularity problem of traditional terminal sliding mode near the equilibrium point, a non-singular terminal sliding surface containing nonlinear power terms is designed: ,in, It is a proportionality coefficient and , Let be the coefficients of the nonlinear power term of the sliding surface, and .

[0105] (2) NTSMC control law incorporating disturbance derivative compensation term: To further enhance the system's ability to suppress sudden and high-frequency disturbances, this invention introduces a disturbance derivative compensation term into the control law. The disturbance derivative compensation term is based on the sliding surface and error. structure: ,in, for The first derivative, The coefficient to be compensated and , s For sliding surface, This represents the gap error. It is evident that the disturbance derivative compensation term is specifically used to estimate the rate of change of the disturbance over time (derivative). Integrating the disturbance derivative compensation term into the subsequent control law enables "compensation to intervene in advance even when the disturbance has no significant impact," reducing the adjustment burden of the control law and avoiding suspension gap fluctuations caused by disturbances.

[0106] (3) Finite-time control law construction and fusion: By integrating the sliding surface, the estimated value of the total disturbance, and the disturbance derivative compensation term, a control voltage expression is constructed. Based on the output composite control voltage, the final control command is generated. The control voltage expression is:

[0107] ;

[0108] in, For composite control voltage, This is the proportionality coefficient. The coefficients of the nonlinear power term of the sliding surface are... For speed error, For the disturbance derivative compensation term, This is an estimate of the total disturbance. For the desired acceleration feedforward, The third parameter to be designed and , It is a symbolic function.

[0109] It should be noted that the finite-time control law achieves finite-time convergence primarily due to the introduction of nonlinear power terms into its sliding surface, which gives the system state finite-time stability on the sliding surface. Therefore, when the system state of the single-point levitation subsystem reaches the sliding surface (i.e., ...s =0), the finite-time control law enables the tracking error of the single-point levitation subsystem to dynamically satisfy the first convergence condition, and under the first convergence condition, the finite time for the system state to converge from the initial error to the equilibrium point satisfies the second convergence condition.

[0110] The first convergence condition is that the error dynamically satisfies: The second convergence condition is that the convergence time can be analytically expressed as: , For finite convergence time, This represents the initial error.

[0111] like Figure 6 The diagram shows the closed-loop control system block diagram of the overlapping suspension system obtained by combining the target extended state observer and the finite-time control law. Based on the preceding steps, the overall signal transmission and closed-loop control execution flow of this control method are clearly demonstrated. This system takes the decoupled overlapping suspension system as the controlled object. By decoupling the overlapping structure and integrating the improved ESO and NTSMC, the final composite control voltage is generated. The controller calculates the output control quantity based on the reference input and observed values, and acts inversely on the overlapping structure controlled object, forming a complete closed-loop control circuit. The arrows in the diagram clearly indicate the signal transmission path, achieving precise finite-time control of the overlapping suspension system.

[0112] In one feasible implementation, the tuning of relevant parameters for the finite-time control law includes the sliding surface coefficients. and And the coefficients to be compensated in the disturbance derivative compensation term and the third design parameter . Used to adjust the overall control gain, relatively large. This leads to a decrease in control input, resulting in a slower system response; conversely, an increase in control input will speed up the system, but may exacerbate chattering or actuator saturation. The nonlinear power structure of the sliding surface must be determined by balancing speed and stability. Used to compensate for slip surface s The symbolic term appears in finite-time control law design and is used to suppress chattering.

[0113] The specific tuning process is as follows: First, fix the coefficients of the nonlinear power term of the sliding surface. Set an initial value, and then take different scaling factors. and the third design parameter Simulation tests were conducted using the control law to observe the system response. When the single-point suspended subsystem fails to meet the first performance threshold, indicating insufficient system response speed, the control law was appropriately reduced. When a single-point levitation subsystem fails to meet the second performance threshold for determining system chattering, increase... and / or During this process, the system is gradually adjusted until it stabilizes and the chattering essentially disappears. In a preferred embodiment, after repeated adjustments, [the system is selected as...]. , , .

[0114] In another feasible implementation, the selection is based on the anti-interference requirements of the overlapping suspension system. Initially, if the system is poor at suppressing external disturbances such as track irregularities and aerodynamic disturbances, the initial value should be appropriately increased. Value; if the system oscillates due to overcompensation, appropriately reduce it. The optimal value was determined through multi-condition simulation testing. The value ensures that the disturbance derivative compensation term effectively offsets the total disturbance effect without introducing additional system oscillations.

[0115] As can be seen, this step, based on Lyapunov's finite-time stability theory, proves that the closed-loop system state can converge to the neighborhood of the equilibrium point within a preset time. Furthermore, by rationally designing the sliding mode surface parameters and ESO bandwidth, the convergence time can be further shortened and the chattering amplitude reduced. Compared to traditional asymptotic stability control strategies, this method not only accelerates the system response but also improves the instantaneous suppression capability against sudden disturbances, providing theoretical support and engineering feasibility for achieving "fast, accurate, and stable" levitation control of high-speed maglev trains in complex operating environments.

[0116] The beneficial effects of this application are as follows: By constructing a multi-degree-of-freedom coupled dynamic model of the overlapping suspension system, the overlapping structure is decoupled into two independent single-point subsystems, solving the problem that traditional control methods are difficult to handle structural coupling effects, enabling the controller to accurately adapt to the actual structural characteristics and improve control targeting; a target extended state observer based on a smooth nonlinear function is designed. Utilizing its global smoothness characteristics, it can not only accurately estimate the internal state and total external disturbance of the suspension system in real time, but also effectively suppress the high-frequency chattering and sensitivity to measurement noise caused by traditional nonlinear observers, providing reliable state information for subsequent high-performance control; on this basis, a finite-time control law integrating non-singular terminal sliding mode control, disturbance derivative compensation term, and the estimated value of total disturbance is constructed to form a composite control; the output of this control law acts directly on the electromagnet as a voltage, and the precise control of the suspension gap is achieved by adjusting the current. The nonlinear power term in the sliding surface ensures that the system state converges to the equilibrium point within a preset finite time, avoiding the singularity problem of traditional terminal sliding mode. The estimated value of the total disturbance is directly fed forward to compensate for the disturbance itself, while the disturbance derivative compensation term on the sliding surface compensates for the rate of change of the disturbance, forming a complementary dual compensation mechanism. The synergistic effect of these three factors enables the levitation system to achieve rapid, accurate, and stable tracking control of the suspension gap even under complex conditions such as high-speed operation, track irregularities, and aerodynamic disturbances, significantly enhancing the dynamic response quality and robust stability of the system.

[0117] Based on the above embodiments, this application focuses on high real-time performance and ease of maintenance. Through an integrated scheme of high-performance real-time controller + synchronous transmission + fast power drive, the finite-time control algorithm based on the improved target ESO designed in this invention is embedded into the high-speed maglev levitation controller. The controller receives real-time data such as levitation gap and current collected by sensors, updates the state and disturbance estimation in real time through the improved ESO, and outputs control commands to drive the electromagnet actuator, achieving closed-loop stable control of the levitation gap and ensuring that the system state converges to the reference value within a finite time. Specifically, it includes the following steps:

[0118] The finite-time control law is discretized using the forward Euler method, and the discretized finite-time control law is embedded into the suspension controller.

[0119] Based on the aforementioned levitation controller, it communicates with the levitation operation platform in real time via the controller local area network bus to receive sensor data collected online by the levitation operation platform;

[0120] Based on the sensor data, the discretized finite-time control law is executed by the suspension controller to output a composite control voltage and apply it to both ends of the electromagnet of the overlapping suspension system to control the suspension gap.

[0121] In this embodiment, the levitation controller and the operating platform (host computer) communicate in real time via a Controller Area Network (CAN) driver card. In this system architecture, the levitation operating platform collects various sensor data (levitation gap, acceleration, current, etc.) generated during the experiment, packages this raw or pre-processed experimental data, and transmits it at high speed to the host computer software via the CAN bus and CAN driver card. Upon receiving the data, the host computer software stores, visualizes, and performs further offline analysis and processing, providing a basis for experimental evaluation and parameter optimization. The system's control algorithm uses the forward Euler method for discretization, and the discretized control law is ported and downloaded to the DSP28335 embedded system. The DSP28335, with its high-performance floating-point arithmetic capabilities, rich peripheral interfaces, and high optimization for real-time control, can efficiently execute the control algorithm and interact with the levitation operating platform in a closed loop via the CAN driver card, exhibiting good real-time performance, reliability, and scalability, thereby achieving high-precision and stable control of the levitation system.

[0122] As can be seen, the improved ESO structure designed in this embodiment simplifies the requirements for high-order disturbance modeling, requiring only position and velocity feedback to achieve high-fidelity reconstruction of the total disturbance; the NTSMC control law avoids high-frequency chattering caused by complex sign functions, and the use of continuous approximation further reduces actuator wear. The overall algorithm has a light computational burden, clear parameter adjustment logic, and is easy to implement on embedded platforms such as DSP28335. It has good real-time performance and engineering application value, and is particularly suitable for high-speed maglev vehicle control systems with limited resources but stringent performance requirements.

[0123] To verify the control effect of the present invention, a simulation comparison experiment was conducted. Figure 7 and Figure 8 The levitation gap response curves of the proposed method (ESO-NTSMC) under periodic and step disturbances are presented, along with those of proportional-integral-derivative (PID), conventional sliding mode control, and linear quadratic regulator (LQR). Figure 7 As can be seen, under periodic perturbations, the method of this invention exhibits the smallest gap fluctuation amplitude, and the fluctuation rapidly decays to a steady state, while other comparative methods show larger fluctuation amplitudes and slower decay. Figure 8It is evident that, at the instant of a step disturbance, the maximum gap deviation of the method of this invention is significantly lower than that of other methods, and it can recover to the desired value in a short time. Simulation results fully demonstrate that, whether in the transient transition process or the suppression process of different disturbances in steady state, compared with PID control, sliding mode control, and LQR control, the ESO-NTSMC control exhibits faster levitation gap convergence speed, higher levitation tracking accuracy, and stronger robustness. It is particularly suitable for the "fast, accurate, and stable" control requirements of levitation gap for high-speed maglev trains under complex operating conditions.

[0124] Furthermore, embodiments of this application also disclose an electronic device, Figure 9 This is a structural diagram of an electronic device 20 according to an exemplary embodiment. The content of the diagram should not be construed as limiting the scope of this application.

[0125] Figure 9 This is a schematic diagram of the structure of an electronic device 20 provided in an embodiment of this application. The electronic device 20 may specifically include: at least one processor 21, at least one memory 22, a power supply 23, a communication interface 24, an input / output interface 25, and a communication bus 26. The memory 22 stores a computer program, which is loaded and executed by the processor 21 to implement the relevant steps in the control method for the high-speed maglev train's levitation system disclosed in any of the foregoing embodiments.

[0126] In this embodiment, the power supply 23 is used to provide operating voltage for each hardware device on the electronic device 20; the communication interface 24 can create a data transmission channel between the electronic device 20 and external devices, and the communication protocol it follows can be any communication protocol applicable to the technical solution of this application, and is not specifically limited here; the input / output interface 25 is used to acquire external input data or output data to the outside world, and its specific interface type can be selected according to specific application needs, and is not specifically limited here.

[0127] In addition, the memory 22, as a carrier for resource storage, can be a read-only memory, random access memory, disk, or optical disk, etc. The resources stored on it can include an operating system 221, computer programs 222, and data 223, etc. The data 223 can include various types of data. The storage method can be temporary storage or permanent storage.

[0128] The operating system 221 is used to manage and control the various hardware devices on the electronic device 20 and the computer program 222, which may be Windows Server, Netware, Unix, Linux, etc. In addition to including a computer program capable of performing the control method for the high-speed maglev train connection and levitation system disclosed in any of the foregoing embodiments, the computer program 222 may further include computer programs capable of performing other specific tasks.

[0129] Furthermore, this application also discloses a computer-readable storage medium, which includes random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disks, magnetic disks, optical disks, or any other form of storage medium known in the art. The computer program, when executed by a processor, implements the aforementioned control method for the high-speed maglev train's levitation system. Specific steps of this method can be found in the corresponding content disclosed in the foregoing embodiments, and will not be repeated here.

[0130] Furthermore, embodiments of this application also provide a computer program product, including a computer program / instruction, which, when executed by a processor, implements any of the control methods of the above-described high-speed maglev train levitation system.

[0131] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0132] The steps of the control method or algorithm for the high-speed maglev train's levitation system described in conjunction with the embodiments disclosed herein can be implemented directly using hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disks, removable disks, CD-ROMs, or any other form of storage medium known in the art.

[0133] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0134] The control method for a high-speed maglev train levitation system provided by the present invention has been described in detail above. Specific examples have been used to illustrate the principle and implementation of the present invention. The description of the above embodiments is only for helping to understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A control method for a high-speed maglev train's levitation system, characterized in that, include: Construct a multi-degree-of-freedom coupled dynamic model of the overlapping suspension system; Based on the aforementioned multi-degree-of-freedom coupled dynamics model, the overlapping suspension system is decoupled to be converted into two independent single-point suspension subsystems; For each of the single-point levitation subsystems, a target expansion state observer is constructed; wherein, the target expansion state observer uses a smooth nonlinear function as a nonlinear feedback term to estimate the system state and total disturbance in real time based on the levitation gap error; the smooth nonlinear function has global smoothness, differentiability and natural saturation characteristics, including the tanh hyperbolic tangent function; Based on the nonsingular terminal sliding mode control theory, a sliding surface containing nonlinear power terms is designed. A finite-time control law is constructed based on the sliding surface, the estimated value of the total disturbance, and the disturbance derivative compensation term to generate a composite control voltage, which is applied to both ends of the electromagnet of the overlapping suspension system to control the suspension gap. The disturbance derivative compensation term is used to estimate and cancel the rate of change of the total disturbance with time. The estimated value of the total disturbance is used for feedforward compensation of the total disturbance, forming a complementary double compensation with the disturbance derivative compensation term.

2. The control method for the high-speed maglev train's levitation system according to claim 1, characterized in that, The multi-degree-of-freedom coupled dynamic model for constructing the overlapping suspension system includes: An electromagnet model is established based on the physical structure of the electromagnet; the electromagnet model includes electromagnetic force equations and voltage equations: ;in, Electromagnetic force, For the current of the suspending electromagnet, The distance between the levitation electromagnet and the track. The permeability of free space, The number of turns of the levitation electromagnet coil. The area of ​​the magnetic poles of the suspending electromagnet, The voltage applied across the electromagnet, This is the equivalent resistance value of the electromagnet; A dynamic model of the suspension frame is established based on the force analysis of the aforementioned overlapping suspension system; the equations of the dynamic model of the suspension frame are: ; where the subscripts l and r represent the left and right sides, Let be the mass of the suspending electromagnet, x be the displacement of the electromagnet relative to the track, and g be the acceleration due to gravity. The vertical force generated by the primary suspension system. Electromagnetic force, For the weight of the support arm, This represents the displacement of the support arm relative to the track. The force generated by the secondary suspension system, For the equivalent mass of the vehicle body, This indicates the displacement of the vehicle body relative to the track. External disturbance; The suspension dynamics model is transformed into a state-space form; the expression of the state-space form is: ;in, , , , , , , For disturbance terms; and For the stiffness and damping of the primary suspension system, For lumped parameters, , , , .

3. The control method for the high-speed maglev train's levitation system according to claim 2, characterized in that, Based on the aforementioned multi-degree-of-freedom coupled dynamics model, the overlapping suspension system is decoupled to transform it into two independent single-point suspension subsystems, including: Separate the coupled and uncoupled terms in the state-space form; the state equation after separation is: ;in, , , It is a diagonal matrix, corresponding to the uncoupled terms; , , The matrix whose main diagonal elements are all zero corresponds to the coupling term. A decoupling control matrix is ​​constructed, and the coupling terms are eliminated using the decoupling control matrix to decouple the overlapping suspension system into two independent single-point suspension subsystems; wherein the decoupling control matrix includes K, M, and S, which respectively satisfy: The state equation of the decoupled single-point levitation subsystem is: V is the control variable of the decoupled system. Let be the total disturbance term after decoupling, where This represents the coupling error.

4. The control method for the high-speed maglev train's levitation system according to claim 2, characterized in that, For each of the single-point suspended subsystems, a target expansion state observer is constructed, including: A target expansion state observer is constructed based on the hyperbolic tangent function, and the suspension gap error is used as input to estimate the suspension gap, gap velocity and total disturbance of each single-point suspension subsystem in real time. The expression for the target extended state observer is: ;in, , This is an estimated value for the suspension gap. This is an estimate of the gap speed. This is an estimate of the total disturbance. For matrix The first element, For matrix The first element, , , Let η be the observer gain, η be the first parameter to be designed, σ be the second parameter to be designed, and e be the suspension gap error. For symbolic functions, .

5. The control method for the high-speed maglev train's levitation system according to claim 4, characterized in that, Also includes: Based on the bandwidth method, all poles of the target extended state observer are configured to be the same target real poles to tune the observer gain; the tuning formula for the observer gain is: , , ,in, For observer bandwidth; The first design parameter is set to an initial value that matches the inertia of the single-point levitation subsystem, and the first design parameter is adjusted based on the initial value. Specifically, if the single-point levitation subsystem needs to improve its tracking capability against rapidly changing disturbances or requires the system response speed to meet a first preset condition, the first design parameter is increased; if the composite control voltage oscillates or exceeds a preset amplitude control value, the first design parameter is decreased. The rapidly changing disturbance is a disturbance component with a disturbance frequency higher than the observer bandwidth. The second design parameter is adjusted based on the noise level of the single-point levitation subsystem or using an adaptive strategy. Specifically, when adjusting based on the noise level, if system measurement noise exists, the second design parameter is decreased; if it is necessary to improve the convergence speed of the target expansion state observer's output, and the robustness of the target expansion state observer under disturbance conditions meets a second preset condition, the second design parameter is increased. When adjusting based on the adaptive strategy, if the levitation gap error increases, the second design parameter is increased; if the levitation gap error decreases, the second design parameter is decreased.

6. The control method for the high-speed maglev train's levitation system according to claim 1, characterized in that, The sliding surface design, based on the nonsingular terminal sliding mode control theory, which includes nonlinear power terms, includes: Define the gap error between the actual value and the reference value of the suspension gap, and the speed error between the actual value and the reference value of the gap speed; Based on the nonsingular terminal sliding mode control theory, a sliding surface containing nonlinear power terms is designed using the gap error and the velocity error. Wherein, the gap error is , This is the actual value of the suspension gap. The reference value for the suspension gap is; the speed error is... , This is the actual value of the gap speed. This is a reference value for the gap speed; the sliding surface ,in, It is a proportionality coefficient and , Let be the coefficients of the nonlinear power term of the sliding surface, and .

7. The control method for the high-speed maglev train's levitation system according to claim 1, characterized in that, The construction of a finite-time control law based on the sliding surface, the estimated value of the total disturbance, and the disturbance derivative compensation term includes: Construct a disturbance derivative compensation term; the disturbance derivative compensation term ,in, for The first derivative, The coefficient to be compensated and s is the sliding surface. This refers to gap error; Based on the sliding surface, the estimated value of the total disturbance, and the disturbance derivative compensation term, a control voltage expression is constructed to determine the finite-time control law; The expression for the control voltage is: , For composite control voltage, This is the proportionality coefficient. The coefficients of the nonlinear power term of the sliding surface are... For speed error, For the disturbance derivative compensation term, This is an estimate of the total disturbance. For the desired acceleration feedforward, This is the third parameter to be designed. It is a symbolic function.

8. The control method for the high-speed maglev train's levitation system according to claim 7, characterized in that, Also includes: When the system state of the single-point suspension subsystem reaches the sliding surface, the finite-time control law enables the tracking error of the single-point suspension subsystem to dynamically satisfy the first convergence condition, and under the first convergence condition, the finite time for the system state to converge from the initial error to the equilibrium point satisfies the second convergence condition. Wherein, the first convergence condition is ; The second convergence condition is , For finite convergence time, This represents the initial error.

9. The control method for the high-speed maglev train's levitation system according to claim 7, characterized in that, Also includes: The coefficients of the nonlinear power term of the sliding surface are fixed as preset initial values, and different proportional coefficients and the third design parameter are selected and substituted into the finite-time control law for simulation testing. When the single-point suspension subsystem fails to meet the first performance threshold to determine that the system response speed is insufficient, the proportional coefficient is reduced. When the single-point suspension subsystem fails to meet the second performance threshold to determine that the system is chattering, the proportional coefficient and / or the third design parameter are increased.

10. The control method for the high-speed maglev train's levitation system according to any one of claims 1 to 9, characterized in that, The generation of a composite control voltage and its application to both ends of the electromagnet in the overlapping levitation system to control the levitation gap includes: The finite-time control law is discretized using the forward Euler method, and the discretized finite-time control law is embedded into the suspension controller. Based on the aforementioned levitation controller, it communicates with the levitation operation platform in real time via the controller local area network bus to receive sensor data collected online by the levitation operation platform; Based on the sensor data, the discretized finite-time control law is executed by the suspension controller to output a composite control voltage and apply it to both ends of the electromagnet of the overlapping suspension system to control the suspension gap.

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