A Fault-Tolerant Control Method and System for the Actuator Failure of a High-Speed Maglev Train

Abstract

This application relates to the field of high-speed maglev train control technology, and discloses a fault-tolerant control method and system for high-speed maglev train actuator failures. Specifically, the application discloses a method for modeling partial actuator failures of a maglev train single-point suspension system, introducing actuator failures and system parameter uncertainty factors, and constructing a dynamic model of the single-point suspension system under actuator failures. The state feedback control law is used to design a fault-tolerant control method and system for high-speed maglev train actuator failures. H ∞ A robust fault-tolerant controller is proposed, and the closed-loop asymptotic stability of the single-point suspension system is rigorously proved based on Schur complement theory and the bounded real lemma. Therefore, the method in this application takes actuator failures and system parameter uncertainties into account when designing the controller, improving the control performance of the controller.

Description

Technical Field

[0001] The present application relates to the technical field of high-speed maglev train control, and in particular to a fault-tolerant control method and system for high-speed maglev train actuator failure. Background Art

[0002] High-speed maglev trains are an emerging mode of transportation that utilizes electromagnetic force to achieve contactless travel between the train and the track. They offer low operating costs, a small turning radius, and flexible route selection, meeting the needs of integrated urban and suburban transportation. The suspension system is a core component of maglev trains. The levitation electromagnet, consisting of several series-connected magnetic poles, serves as the actuator of the maglev system. The suspension controller modulates the levitation force by regulating the current in the electromagnets to maintain the rated levitation gap. Operating in a strong magnetic field, the magnetic poles are susceptible to performance degradation over long periods of service (e.g., short circuits between windings, coil-to-ground shorts, short circuits in energized contacts, or increased contact resistance). Electromagnet degradation can lead to partial actuator failure (e.g., reduced effective turns, increased internal resistance), resulting in a mismatch between control system parameters, increased levitation gap fluctuations, or abnormal increases in the controller's excitation current, leading to reduced levitation control performance. In severe cases, the controller shuts off the electromagnet's excitation current, deactivating the failed electromagnet circuit. Therefore, developing fault-tolerant control strategies for partial actuator failures is of great theoretical and practical significance for the long-term service safety of maglev vehicles.

[0003] A lot of research has been done on the fault-tolerant control of actuator failures in the suspension system of maglev trains. For example: 1) Gain scheduling is combined with a method based on linear matrix inequalities to perform fault-tolerant control of sensor and actuator failures in the suspension system; 2) For a single-module suspension system of a maglev train with uncertain system parameters, a linear matrix inequality method is used to design a controller with complete fault tolerance for actuator failures. At the same time, considering the actual needs of the project, the concept of weight is introduced to modify the control law to control the change of the suspension gap under different actuator failure modes; 3) Taking the suspension module of the EMS high-speed maglev train as the research object, the passive fault-tolerant controller is designed based on the principle of synchronous stability and the stable fraction factorization method of rational functions; 4) Based on the Lyapunov-Krasovskii theorem, sufficient conditions for the robust stability of networked control systems under all possible sensor failures, packet loss and delay are derived, and then a fault-tolerant controller for networked control systems with continuous packet loss and time-varying delay is designed.

[0004] Most of the above control methods require accurate system models. However, maglev trains operate in complex environments for a long time. During operation, they are subject to time-varying external disturbances such as track unevenness and changes in the number of passengers, making it impossible to accurately obtain system parameters. This leads to a mismatch in control system parameters and greatly reduces control performance. Summary of the Invention

[0005] The present application provides a fault-tolerant control method for high-speed maglev train actuator failures to solve the problem in the prior art that time-varying external interferences such as track unevenness and changes in the number of passengers during the operation of the maglev train make it impossible to accurately obtain system parameters, resulting in control system parameter mismatch and greatly reduced control performance.

[0006] Correspondingly, the present application also provides a fault-tolerant control system for high-speed maglev train actuator failures, which is used to ensure the implementation and application of the above method.

[0007] In order to solve the above technical problems, the present application discloses a fault-tolerant control method for high-speed maglev train actuator failure, the method comprising:

[0008] Introducing actuator failure and system parameter uncertainty factors, a dynamic model of the single-point suspension system under actuator failure is constructed;

[0009] Determine the stability of single-point suspension system under actuator failure using state feedback control law H ∞ A robust fault-tolerant controller is proposed, and the closed-loop asymptotic stability of a single-point suspension system under actuator failure is proved using Schur complement theory and the bounded real lemma.

[0010] The present application also discloses a fault-tolerant control system for high-speed maglev train actuator failure, the system comprising:

[0011] The system model building module is used to introduce actuator failure and system parameter uncertainty factors to build a dynamic model of the single-point suspension system under actuator failure;

[0012] Controller building block for determining the stability of a single-point suspension system under actuator failure using a state feedback control law. H ∞ A robust fault-tolerant controller is proposed, and the closed-loop asymptotic stability of a single-point suspension system under actuator failure is proved using Schur complement theory and the bounded real lemma.

[0013] In this application, the actuator failure and system parameter uncertainty factors are introduced to model the partial actuator failure of the single-point suspension system, and the dynamic model of the single-point suspension system under actuator failure is constructed. H ∞ A robust fault-tolerant controller is proposed, and the closed-loop asymptotic stability of the single-point suspension system is rigorously proved based on Schur complement theory and the bounded real lemma. Therefore, the method in this application takes actuator failures and system parameter uncertainties into account when designing the controller, improving the control performance of the controller.

[0014] Additional aspects and advantages of the present application will be given in the following description, which will become apparent from the following description, or will be understood through practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0016] Figure 1 A flow chart of a fault-tolerant control method for high-speed maglev train actuator failures provided in an embodiment of the present application;

[0017] Figure 2 A schematic diagram of a single-point suspension system model provided in an embodiment of the present application;

[0018] Figure 3 A curve diagram of the system suspension gap change under no-fault conditions provided in an embodiment of the present application;

[0019] Figure 4 A curve diagram of system current variation under no-fault conditions provided in an embodiment of the present application;

[0020] Figure 5 A curve diagram showing the change of static suspension gap under actuator failure provided in an embodiment of the present application;

[0021] Figure 6 A curve diagram showing the change of static current under fault conditions of an actuator provided in an embodiment of the present application;

[0022] Figure 7 A simulation graph of the change in suspension gap under multiple sets of actuator fault gains provided in an embodiment of the present application;

[0023] Figure 8 A schematic diagram of a high-speed maglev train provided in an embodiment of the present application;

[0024] Figure 9 A graph showing the change in suspension clearance under a 17% failure rate of the actuator provided in an embodiment of the present application;

[0025] Figure 10 A current change curve diagram of an actuator failure with a 17% fault rate provided in an embodiment of the present application;

[0026] Figure 11 A graph showing the change in suspension clearance under a 33% failure rate of the actuator provided in an embodiment of the present application;

[0027] Figure 12 A current change curve diagram of an actuator failure with a 33% fault rate provided in an embodiment of the present application;

[0028] Figure 13This is a schematic diagram of the structure of a fault-tolerant control system for high-speed maglev train actuator failures provided in an embodiment of the present application.

[0029] Among them, 200 is the suspension system; 201 is the vehicle body, 202 is the air spring, 203 is the support arm, 204 is the guide electromagnet, 205 is the track, 206 is the track beam, 207 is the suspension electromagnet, 208 is the controller, 209 is the suspension sensor, and 210 is the long stator. DETAILED DESCRIPTION

[0030] The following describes embodiments of the present application in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present application and are not to be construed as limiting the present application.

[0031] It will be understood by those skilled in the art that, unless expressly stated otherwise, the singular forms "a", "an", "said" and "the" used herein may also include the plural forms. It should be further understood that the term "comprising" used in the specification of this application refers to the presence of features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or combinations thereof. It should be understood that when we refer to an element as being "connected" or "coupled" to another element, it may be directly connected or coupled to the other element, or there may be intermediate elements. In addition, "connected" or "coupled" as used herein may include wireless connections or wireless couplings. The term "and / or" used herein includes all or any units and all combinations of one or more associated listed items.

[0032] Those skilled in the art will understand that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art in the art to which this invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0033] In response to the technical problems existing in the prior art, the present application provides a fault-tolerant control method and system for high-speed maglev train actuator failure, aiming to solve at least one of the technical problems of the prior art.

[0034] The following specific embodiments describe in detail the technical solution of the present application and how the technical solution of the present application solves the above-mentioned technical problems. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments. The embodiments of the present application will be described below in conjunction with the accompanying drawings.

[0035] The embodiment of the present application provides a flow chart of a fault-tolerant control method for a high-speed maglev train actuator failure, as shown in FIG. Figure 1 As shown in , the method may include the following steps:

[0036] Step 101, introducing actuator failure and system parameter uncertainty factors to construct a dynamic model of the single-point suspension system under actuator failure;

[0037] Step 102: Use the state feedback control law to determine the single-point suspension system under actuator failure. H ∞ A robust fault-tolerant controller is proposed, and the closed-loop asymptotic stability of a single-point suspension system under actuator failure is proved using Schur complement theory and the bounded real lemma.

[0038] The suspension system of a high-speed maglev train is a complex multi-point coupled system. By adopting a decentralized independent suspension control strategy and the modularization of the magnet structure, the suspension system control problem can be decomposed into the control problem of a single suspension magnet through decoupling. The analysis of the dynamic model and dynamic characteristics of a single magnet suspension is general. A single-point suspension system consisting of a single suspension electromagnet and its controller and a rigid or elastic track becomes an ideal model for the design of the suspension control system of an EMS-type high-speed maglev train. The schematic diagram of the single-point suspension system model is shown in the figure below. Figure 2 As shown, the high-speed maglev train suspension system includes a car body 201, air springs 202, support arms 203, guide electromagnets 204, tracks 205, track beams 206, and suspension electromagnets 207. A single suspension electromagnet 207 and its controller 208, along with the rigid or elastic track 205, form a single-point suspension system. A suspension sensor 209 is provided on the suspension electromagnet 207, and a long stator 210 is provided on the track 205.

[0039] In the embodiment of this application, based on Figure 2 The single-point suspension system model shown in the figure is used. In addition, for the partial failure of the actuator of the single-point suspension system of the maglev train, the actuator failure and system parameter uncertainty factors are introduced to model the partial actuator failure of the single-point suspension system and construct the dynamic model of the single-point suspension system under the actuator failure. The state feedback control law and linear matrix inequality design are used. H ∞A robust fault-tolerant controller is proposed, and the closed-loop asymptotic stability of the single-point suspension system is rigorously proved based on Schur complement theory and the bounded real lemma. Therefore, the method in the embodiment of the present application takes into account actuator failures and system parameter uncertainties when designing the controller, thereby improving the control performance of the controller.

[0040] In an optional embodiment, based on Figure 2 The single-point suspension system model shown above introduces actuator failure and system parameter uncertainty factors to construct a dynamic model of the single-point suspension system under actuator failure, including:

[0041] According to Newton's second law, the mechanical equation of the suspended electromagnet in the vertical direction is:

[0042] (1)

[0043] Where: is the suspension gap between the electromagnet and the track, is the current passing through the electromagnetic coil of the suspension electromagnet, is the mass of the suspension frame, It is the external interference force, is the acceleration due to gravity, It is the electromagnetic attraction generated by the suspension electromagnet.

[0044] Assuming that the magnetic permeability of the magnetic pole is infinite and the magnetic potential is uniformly distributed over the air gap, and ignoring the effects of winding leakage flux and track beam elasticity, the inductance through the suspended electromagnet coil is:

[0045] (2)

[0046] Where: is the number of turns of the electromagnet winding; is the equivalent resistance of the magnetic circuit; A is the magnetic area of the electromagnet; is the magnetic permeability of air. Based on formula (2), the electromagnetic attraction generated by the levitation electromagnet can be expressed as:

[0047] (3)

[0048] To simplify the equation, let .

[0049] Next, the single-point suspension system is linearized at the equilibrium point. For the mechanical equation (1) in the vertical direction of the suspension electromagnet, at the equilibrium point, we have:

[0050] (4)

[0051] Where, is the external disturbance force at the equilibrium point; is the current at the equilibrium point; is the suspension gap at the equilibrium point; is the electromagnetic attraction at the equilibrium point.

[0052] Let the formula (1) = Based on equations (1), (3) and (4), the dynamic equations of the single-point suspension system under current control are obtained:

[0053] (5)

[0054] Where, is the suspension gap between the suspension electromagnet and the track, is the current passing through the electromagnetic coil of the suspension electromagnet, is the mass of the suspension frame, It is the external interference force, is the acceleration due to gravity; is the number of turns of the suspension electromagnet winding, is the equivalent resistance of the magnetic circuit, A is the magnetic area of the levitation electromagnet, is the magnetic permeability of air; is the external disturbance force at the equilibrium point; is the current at the equilibrium point; is the suspension gap at the equilibrium point; is the electromagnetic attraction at the equilibrium point;

[0055] Since there are nonlinear terms in Equation (3), it is difficult to design the controller using the linear control method commonly used in engineering. Therefore, the electromagnetic force At the balance point After linear expansion and omitting high-order terms, we get:

[0056] (6)

[0057] Take the suspension gap and the suspension electromagnet speed (downward is positive) as the state variables , current Input for the single-point suspension system, the change in suspension gap As the output, the state equation of the single-point suspension system is obtained as:

[0058] (7)

[0059] Considering the actuator's faulty component output signal deviates from the accurate value due to component aging, interference, etc., a continuous switch fault model is used to increase the virtual gain on the actuator channel. , and meet the conditions:

[0060] (8)

[0061] Based on the continuous switch fault, the actuator fault can be modeled as:

[0062] (9)

[0063] Where, It is the normal output signal of the actuator when no fault occurs; It is the output signal after considering the failure of the actuator; is the actuator failure coefficient.

[0064] Considering the uncertainty of system parameters caused by actuator failure, changes in the number of passengers during system operation, and external disturbances, the actuator failure and system parameter uncertainty are introduced into the state equation, and the dynamic model of the single-point suspension system under actuator failure is obtained:

[0065] (10)

[0066] Where, , , , , , is the system parameter uncertainty matrix, where is the identity matrix, is a known weight matrix, is the control input after considering the system actuator failure.

[0067] In an optional embodiment, a state feedback control law is used to determine the single-point suspension system under actuator failure. Robust fault-tolerant controller, and using Schur complement theory and bounded real lemma to prove the closed-loop asymptotic stability of single-point suspension system under actuator failure, including:

[0068] For the dynamic model (10) of the single-point suspension system under actuator failure, the state feedback control law is selected as:

[0069] (11)

[0070] Where, is the controller gain;

[0071] And for a given , the closed-loop transfer function from external disturbance to output satisfies:

[0072] (12)

[0073] Where, , is the identity matrix, is a complex variable defined in the domain of the Laplace transform;

[0074] Theorem 1: For the dynamic model of a single-point suspension system under actuator failure, if there exists a constant ,matrix and a symmetric positive definite matrix So that the linear matrix inequality holds:

[0075] (13)

[0076] Then for any actuator fault gain , there exists a robust fault-tolerant controller ,in , under which the dynamic model of the single-point suspension system under actuator failure has H ∞ Norm Bound ;

[0077] Theorem 1 is proved by using Schur complement theory and bounded real lemma, and it is determined that Existence of robust fault-tolerant controllers and closed-loop asymptotic stability of single-point suspension systems under actuator failures.

[0078] In an optional embodiment, Theorem 1 is proved using Schur's complement theory and the bounded real lemma to determine H ∞ The existence of robust fault-tolerant controllers and the closed-loop asymptotic stability of single-point suspension systems under actuator failures, including:

[0079] The lemmas used to prove Theorem 1 are given; the lemmas include Schur complement theory and bounded real lemma;

[0080] Based on the lemma, we can prove that there is Robust fault-tolerant controller, which makes the linear matrix inequality shown in Theorem 1 hold;

[0081] Based on the lemma, we prove that the linear matrix inequality shown in Theorem 1 can ensure that the single-point suspension system is uniformly asymptotically stable and robustly fault-tolerant under actuator failure.

[0082] Based on the lemma, we prove that the linear matrix inequality shown in Theorem 1 can ensure that the single-point suspension system under actuator failure has H ∞ Norm Bound .

[0083] In an optional embodiment, the lemma also includes Lemma 1: For a matrix of appropriate order ,and , the following equation holds:

[0084] (14)

[0085] Lemma 2 (Schur complement theory) is: For a given symmetric matrix ,in , the following three conditions are equivalent:

[0086] (1) ;

[0087] (2) ;

[0088] (3) ;

[0089] Lemma 3 (Bounded Real Lemma) is: For the following system:

[0090] (15)

[0091] Where, is the system status; is the external disturbance input; is the controlled output of the system, is a matrix of appropriate order;

[0092] The closed-loop transfer function from external disturbance to controlled output is: , let the constant , the system is asymptotically stable and satisfies The necessary and sufficient condition is that there exists a positive definite matrix Requirements:

[0093] (16)

[0094] In an alternative embodiment, based on the lemma, it is proved that there exists H ∞ The robust fault-tolerant controller, which makes the linear matrix inequality shown in Theorem 1 hold, can include:

[0095] Theorem 2: There exists H ∞ Robust Fault-Tolerant Controller This makes the linear matrix inequality (13) hold.

[0096] Proof: Let the auxiliary matrix :

[0097] (17)

[0098] Using a diagonal matrix Multiplying the auxiliary matrix (17) on the left and right respectively, we get:

[0099] (18)

[0100] From Lemma 1, we can see the first matrix inequality:

[0101] (19)

[0102] Therefore, scaling the first matrix inequality (19) yields the second matrix inequality:

[0103] (20)

[0104] Arranging the second matrix inequality (20) yields the third matrix inequality:

[0105] (twenty one)

[0106] make 、 , the linear matrix can be obtained from Schur complement theory , so the single-point suspension system has H ∞ Robust fault-tolerant controller , so that the linear matrix inequality holds true, and Theorem 2 is proved.

[0107] In an optional embodiment, based on the lemma, proving that the linear matrix inequality shown in Theorem 1 can ensure that the single-point suspension system is uniformly asymptotically stable and robustly fault-tolerant under actuator failures may include:

[0108] Theorem 3: The linear matrix inequality (13) can ensure that the single-point suspension system is uniformly asymptotically stable and robustly fault-tolerant under partial actuator failure.

[0109] Proof: Choose the Lyapunov function:

[0110] (twenty two)

[0111] The time derivative of the Lyapunov function along any trajectory of the single-point suspension system under actuator failure is:

[0112] (twenty three)

[0113] Combining the dynamic model of the single-point suspension system under actuator failure (10) and the time derivative of the Lyapunov function along any trajectory of the single-point suspension system under actuator failure (23), the dynamic model of the single-point suspension system under actuator failure (10) is substituted into formula (23) to obtain the first function:

[0114] (twenty four)

[0115] make , the first function can be organized into the second function:

[0116] (25)

[0117] When the interference is not considered, When , we can know from the linear matrix inequality (13) and Schur complement theory:

[0118] (26)

[0119] therefore, The inequality holds. According to Lyapunov's stability theorem, the single-point suspension system is uniformly asymptotically stable under actuator failure. Because the linear matrix inequality (13) takes the actuator failure into account, the single-point suspension system also has robust fault-tolerant performance under actuator failure. Theorem 3 is proved.

[0120] In an optional embodiment, based on the lemma, it is proved that the linear matrix inequality can ensure that the single-point suspension system under actuator failure has H ∞ Norm Bound , which may include:

[0121] Theorem 4: Linear matrix inequality (13) can ensure that the single-point suspension system under actuator failure has H ∞ Norm Bound .

[0122] Proof: Assume the initial state , introduce the function:

[0123] (27)

[0124] The robust stability of the single-point suspension system under actuator failure is guaranteed Boundedness and , so under zero initial conditions, for any , the following inequality holds:

[0125] (28)

[0126] The closed-loop transfer function from external disturbance to controlled output is: , let the constant , the single-point suspension system under actuator failure is asymptotically stable and satisfies The necessary and sufficient condition is that there exists a positive definite matrix Requirements:

[0127] (29)

[0128] Therefore, the bounded real lemma shows that the single-point suspension system under actuator failure has H ∞ Norm Bound , Theorem 4 is proved.

[0129] From Theorem 2-4, we can see that given the constant , for any actuator fault gain , if there exists a matrix , a symmetric positive definite matrix If the linear matrix inequality (13) holds, then the single-point suspension system is robust under the actuator failure condition. Fault-tolerant control system,Theorem 1 is proved.

[0130] In an optional embodiment, a state feedback control law is used to determine the single-point suspension system under actuator failure. After developing a robust fault-tolerant controller and proving the closed-loop asymptotic stability of a single-point suspension system under actuator failure using Schur complement theory and bounded real lemma, the method also includes:

[0131] Solve the linear matrix inequality to obtain the controller gain matrix.

[0132] In the embodiment of this application, in order to verify the effectiveness of the proposed fault-tolerant control method for high-speed maglev train actuator failure, the equations (11) and (13) determined The robust fault-tolerant controller was simulated in MATLAB for a high-speed maglev train suspension system model, and a PID controller was used for comparison. The suspension system parameters in the simulation are shown in Table 1:

[0133] Table 1 Suspension system parameters

[0134]

[0135] The chopper inside the controller is the main source of interference for maglev trains, and the instantaneous switching of the chopper will generate strong electromagnetic interference. A sine wave with an amplitude of 0.2 and a frequency of 20 rad / s is used to simulate the interference to which the suspension system is subjected in actual operation, and white noise is used to simulate the measurement noise existing in the sensor acquisition process in the actual system. Considering the failure of any actuator, according to Theorem 1, the MATLAB-LMI toolbox is used to solve the linear matrix inequality (13) to obtain the controller gain matrix:

[0136]

[0137] Next, in order to verify the proposed H ∞ The suspension control capability of the robust fault-tolerant controller will be verified by three sets of simulations: 1) static suspension under no fault; 2) static suspension under actuator fault; 3) static suspension under different actuator fault gains. H ∞ The robust fault-tolerant controller can ensure the normal and stable suspension of the maglev train in the absence of faults. The second set of simulations is to illustrate H ∞ The stable suspension of the maglev train suspension system under the action of robust fault-tolerant controller under actuator fault conditions. The last set of simulations gives the system response under different actuator gains to verify the proposed H ∞ Feasibility of robust fault-tolerant controllers under a wide range of actuator fault gains.

[0138] Simulation 1. Static suspension without fault

[0139] The static suspension performance without actuator fault is considered to verify that the two controllers can ensure the normal and stable suspension of the maglev train without fault, providing a priori basis for subsequent fault suspension simulation.

[0140] The system suspension gap change curve and current change curve under no fault are as follows: Figure 3 and Figure 4 As shown. Figure 3 and Figure 4 It can be seen that the H ∞ Both the robust fault-tolerant controller (with fault-tolerant measures) and the PID controller (without fault-tolerant measures) can achieve stable suspension within a limited time. H ∞ The time it takes for the system to reach the equilibrium point under the robust fault-tolerant controller is 0.078s, which is shorter than the time it takes for the system to reach the equilibrium point under the PID controller, which is 0.134s. H ∞ The robust fault-tolerant controller converges faster. H ∞ The robust fault-tolerant controller has a smaller current oscillation range, better steady-state suspension performance, and better robustness to external interference and measurement errors. The asymptotic stability of the system is ensured through simulation 1.

[0141] Simulation 2. Static suspension with actuator failure

[0142] Set the actuator fault gain when the actuator fails 0.5s after the system is stably suspended. δ =0.7, the simulation results are as follows Figure 5 and Figure 6 As shown. Figure 5 and Figure 6 It can be seen that when the actuator fails, H ∞ The system suspension gap change of 0.21mm under the robust fault-tolerant controller is much smaller than the suspension gap change of 1.96mm under the PID controller. H ∞ Robust fault-tolerant controllers are more robust to actuator failures. H ∞ The current increase of the system under the robust fault-tolerant controller is smaller, which can effectively solve the problem of control current surge caused by partial fault of the electromagnet coil. The fault tolerance of the system is verified by simulation 2.

[0143] Simulation 3. Static suspension under different actuator fault gains

[0144] Simulation 2 only gives the simulation results under the condition of single actuator fault gain, which cannot well explain The feasibility of robust fault-tolerant controller under a wide range of actuator fault gains. In order to better illustrate the above problem, combined with the statistical data of actuator failure in actual physical systems, the actuator fault gains are selected as δ =0.4,0.5,0.6,0.7,0.8,0.9, the simulation results are as follows Figure 7 shown.

[0145] The performance comparison of the system under different actuator fault gains is shown in Table 2. As shown in Table 2, the system can still maintain stability under multiple sets of actuator fault gains, and the steady-state error is within an acceptable range. H ∞ The robust fault-tolerant controller can achieve stable suspension of the maglev train suspension system under a wide range of actuator failures. The larger the actuator fault gain, the greater the stability deviation of the system after reaching equilibrium.

[0146] Table 2 Comparison of system performance under different actuator fault gains

[0147]

[0148] In the present application, in order to verify the H ∞ The effectiveness of the fault-tolerant control algorithm corresponding to the robust fault-tolerant controller is verified by using the developed long-stator maglev train suspension controller and a high-speed maglev train. The experimental base is located on the Tongji University high-speed maglev transportation test line. Figure 8As shown, the vehicle comprises a vehicle body 201, a track 205, and a suspension system 200, which includes a suspension controller, two suspension sensors, and a suspension electromagnet. In the experiment, one suspension electromagnet module had 12 magnetic poles, controlled by two independent suspension controllers, each controlling six poles connected in series. A suspension controller (suspension point 1) with a fault-tolerant control algorithm and a controller (suspension point 3) without a fault-tolerant control algorithm were installed on the vehicle. Data from the two suspension controllers were collected and compared. To ensure accuracy, the two suspension controllers were installed in different suspension frames and decoupled from each other. The fault-tolerant control algorithm was tested. To simulate actuator failure, two sets of experiments were conducted: 1) five poles connected in series simulated a 17% actuator failure; 2) four poles connected in series simulated a 33% actuator failure.

[0149] The experimental results of the actuator failure 17% fault are as follows Figure 9 and 10 As shown in the figure, at the suspension control point (suspension point 3) without the fault-tolerant control algorithm, an actuator failure reduced the number of effective magnetic poles, resulting in a mismatch between the actual and designed models. This prevented the suspension system from maintaining stable levitation, increased the suspension current, and caused the electromagnet to continue heating, potentially damaging the magnetic poles. However, with the fault-tolerant control algorithm, the current at suspension point 1 remained essentially the same as before the fault, with only a larger current fluctuation, which did not exceed 1A, and the gap remained stable.

[0150] The experimental results of the actuator failure 33% fault are as follows Figure 11 and Figure 12 As shown in the figure, without the fault-tolerant control algorithm, the gap at the suspension control point cannot stabilize, and the current increases to approximately 33A, worsening the situation compared to when five magnetic poles are connected in series. However, with the intervention of the proposed fault-tolerant control algorithm, the current amplitude at suspension point 1 increases slightly, averaging approximately 25A, and the fluctuation increases. The gap fluctuation increases slightly compared to when five magnetic poles are connected in series, but does not exceed ±1mm and does not affect suspension performance. Without the fault-tolerant control algorithm, the increased current amplitude can cause suspension system instability under adverse operating conditions. However, with the addition of the fault-tolerant control algorithm, the suspension control system can maintain stable suspension even in the event of an actuator failure, but the current and gap fluctuations increase.

[0151] Based on the above embodiments, the present application designs a fault-tolerant control method for high-speed maglev train actuator failures in response to partial actuator failures in the maglev train suspension system, thereby achieving stable suspension of the maglev train. In particular, the suspension gap stabilizes near the desired position within a finite time. At the same time, the influence of the inability to accurately obtain the suspension system parameters on stable suspension under complex operating environments can be suppressed. The asymptotic stability of the control system is rigorously analyzed theoretically using Schur's complement theory and the bounded real lemma, proving the stability of the suspension system at the equilibrium point under partial actuator failures. This method successfully solves the unknown / uncertain parameters and time-varying disturbances in the dynamics of the suspension system, ensuring the robustness of the control system. Finally, the effectiveness and practicality of the control scheme are verified through a series of simulations and hardware experiments. This method has the prospect of being applied to multi-point coupled suspension systems.

[0152] Based on the same principle as the method provided in the embodiment of the present application, the embodiment of the present application also provides a fault-tolerant control system for high-speed maglev train actuator failure, such as Figure 13 As shown, the system includes:

[0153] The system model building module 1301 is used to introduce actuator failure and system parameter uncertainty factors to build a dynamic model of the single-point suspension system under actuator failure;

[0154] The controller building module 1302 is used to determine the single point suspension system under actuator failure using a state feedback control law. H ∞ A robust fault-tolerant controller is proposed, and the closed-loop asymptotic stability of a single-point suspension system under actuator failure is proved using Schur complement theory and the bounded real lemma.

[0155] In the embodiment of this application, for the partial failure of the actuator of the single-point suspension system of the maglev train, the actuator failure and the uncertainty of the system parameters are introduced to model the partial failure of the actuator of the single-point suspension system and construct the dynamic model of the single-point suspension system under the failure of the actuator. The state feedback control law and linear matrix inequality design are used. H ∞ A robust fault-tolerant controller is proposed, and the closed-loop asymptotic stability of the single-point suspension system is rigorously proved based on Schur complement theory and the bounded real lemma. Therefore, in the embodiment of the present application, actuator failures and system parameter uncertainties are taken into account when designing the controller, thereby improving the control performance of the controller.

[0156] The fault-tolerant control system for high-speed maglev train actuator failure provided by the embodiment of the present application can achieve Figures 1 to 12 To avoid repetition, the various processes implemented in the method embodiment will not be described again here.

[0157] The fault-tolerant control system for high-speed maglev train actuator failure in the embodiments of the present application can execute the fault-tolerant control method for high-speed maglev train actuator failure provided in the embodiments of the present application. The implementation principles are similar. The actions performed by each module and unit in the fault-tolerant control system for high-speed maglev train actuator failure in each embodiment of the present application correspond to the steps in the fault-tolerant control method for high-speed maglev train actuator failure in each embodiment of the present application. For the detailed functional description of each module of the fault-tolerant control system for high-speed maglev train actuator failure, please refer to the description of the corresponding fault-tolerant control method for high-speed maglev train actuator failure shown in the previous text, which will not be repeated here.

[0158] The above description is merely a preferred embodiment of the present application and an illustration of the technical principles employed. Those skilled in the art should understand that the scope of the disclosure herein is not limited to technical solutions formed by specific combinations of the aforementioned technical features. It also encompasses other technical solutions formed by any combination of the aforementioned technical features or their equivalents, without departing from the aforementioned disclosure. For example, a technical solution formed by replacing the aforementioned features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A fault-tolerant control method for high-speed maglev train actuator failure, characterized in that: The method comprises: Introducing actuator failure and system parameter uncertainty factors, a dynamic model of the single-point suspension system under actuator failure is constructed; Determine the stability of single-point suspension system under actuator failure using state feedback control law H ∞ Robust fault-tolerant controller, and using Schur complement theory and bounded real lemma to prove the closed-loop asymptotic stability of single-point suspension system under actuator failure; The dynamic model of the single-point suspension system under the actuator failure is: Where, , , , , , is the system parameter uncertainty matrix, where is the identity matrix, is a known weight matrix, state quantity ; is the suspension gap between the electromagnet and the track, is the suspension gap at the equilibrium point, is the current at the equilibrium point; is the mass of the suspension frame, It is the external interference force, is the number of turns of the suspension electromagnet winding, A is the magnetic area of the levitation electromagnet, is the magnetic permeability of air, is the equivalent resistance of the magnetic circuit, To consider the control input after the system actuator fails, It is the normal output signal of the actuator when no fault occurs; It is the output signal after considering the failure of the actuator; is the actuator failure coefficient; The state feedback control law is used to determine the single point suspension system under actuator failure. H ∞ Robust fault-tolerant controller, and using Schur complement theory and bounded real lemma to prove the closed-loop asymptotic stability of single-point suspension system under actuator failure, including: For the dynamic model of the single-point suspension system under actuator failure, the state feedback control law is selected: Where, is the controller gain; And for a given , the closed-loop transfer function from external disturbance to output satisfies: Where, , is the identity matrix, is a complex variable defined in the domain of the Laplace transform; Theorem 1: For the dynamic model of a single-point suspension system under actuator failure, if there exists a constant ,matrix and a symmetric positive definite matrix So that the linear matrix inequality holds: Then for any actuator fault gain , there exists a robust fault-tolerant controller ,in , under which the dynamic model of the single-point suspension system under actuator failure has H ∞ Norm Bound ; Theorem 1 is proved by using Schur complement theory and bounded real lemma, and it is determined that H ∞ Existence of robust fault-tolerant controllers and closed-loop asymptotic stability of single-point suspension systems under actuator failures.

2. The fault-tolerant control method for high-speed maglev train actuator failure according to claim 1, characterized in that: The Schur complement theory and bounded real lemma are used to prove Theorem 1 and determine H ∞ The existence of robust fault-tolerant controllers and the closed-loop asymptotic stability of single-point suspension systems under actuator failures, including: The lemmas used to prove Theorem 1 are given; the lemmas include Schur complement theory and bounded real lemma; Based on the lemma, we can prove that H ∞ Robust fault-tolerant controller, which makes the linear matrix inequality shown in Theorem 1 hold; Based on the lemma, we prove that the linear matrix inequality shown in Theorem 1 can ensure the uniform asymptotic stability and robust fault tolerance of the single-point suspension system under actuator failure. Based on the lemma, we prove that the linear matrix inequality shown in Theorem 1 can ensure that the single-point suspension system under actuator failure has H ∞ Norm Bound .

3. The fault-tolerant control method for high-speed maglev train actuator failure according to claim 2, characterized in that: The lemma also includes Lemma 1: For a matrix of appropriate order ,and , the following inequality holds: The Schur complement theory is: for a given symmetric matrix ,in , the following three conditions are equivalent: （1） ； （2） ； （3） ； The bounded real lemma is: For the following system: Where, is the system status; is the external disturbance input; is the controlled output of the system, is a matrix of appropriate order; The closed-loop transfer function from external disturbance to controlled output is: , let the constant , the system is asymptotically stable and satisfies The necessary and sufficient condition is that there exists a positive definite matrix Requirements: 。 4. The fault-tolerant control method for high-speed maglev train actuator failure according to claim 3, characterized in that: Based on the lemma, we prove that there exists H ∞ The robust fault-tolerant controller makes the linear matrix inequality shown in Theorem 1 hold, including: Let the auxiliary matrix : Using a diagonal matrix Left-multiply and right-multiply the auxiliary matrix respectively, and we get: From Lemma 1, we can know the first matrix inequality: Therefore, scaling the second matrix yields the second matrix inequality: Rearranging the second matrix inequality yields the third matrix inequality: make 、 , according to Schur complement theory, we can get the linear matrix , so there exists H ∞ Robust Fault-Tolerant Controller , so that the linear matrix inequality holds.

5. The fault-tolerant control method for high-speed maglev train actuator failure according to claim 3, characterized in that: Based on the lemma, we prove that the linear matrix inequality shown in Theorem 1 can ensure that the single-point suspension system is uniformly asymptotically stable and robustly fault-tolerant under actuator failure, including: Choose the Lyapunov function: The time derivative of the Lyapunov function along any trajectory of the single-point suspension system under actuator failure is: Combining the dynamic model of the single-point suspension system under actuator failure and the time derivative of the Lyapunov function along any trajectory of the single-point suspension system under actuator failure, the first function is obtained: make , the first function can be organized into the second function: When the interference is not considered, When , we know from the linear matrix inequality and Schur complement theory that: therefore, The inequality holds. According to Lyapunov's stability theorem, the single-point suspension system is uniformly asymptotically stable under actuator failure. Because the linear matrix inequality takes into account the case of actuator failure, the single-point suspension system also has robust fault-tolerant performance under actuator failure.

6. The fault-tolerant control method for high-speed maglev train actuator failure according to claim 3, characterized in that: Based on the lemma, it is proved that the linear matrix inequality can ensure that the single-point suspension system under the actuator failure has zero initial conditions. H ∞ Norm Bound ,include: Assuming the initial state , introduce the function: The robust stability of the single-point suspension system under actuator failure is guaranteed Boundedness and , so under zero initial conditions, for any , the following inequality holds: The closed-loop transfer function from external disturbance to controlled output is: , let the constant , the single-point suspension system under actuator failure is asymptotically stable and satisfies The necessary and sufficient condition is that there exists a positive definite matrix Requirements: Therefore, the bounded real lemma shows that the single-point suspension system under actuator failure has H ∞ Norm Bound .

7. The fault-tolerant control method for high-speed maglev train actuator failure according to claim 1, characterized in that: The state feedback control law is used to determine the single point suspension system under actuator failure. After developing a robust fault-tolerant controller and proving the closed-loop asymptotic stability of a single-point suspension system under actuator failure using Schur complement theory and bounded real lemma, the method further includes: The linear matrix inequality is solved to obtain the controller gain matrix.

8. A fault-tolerant control system for high-speed maglev train actuator failure, characterized in that: The system comprises: The system model building module is used to introduce actuator failure and system parameter uncertainty factors to build a dynamic model of the single-point suspension system under actuator failure; Controller building block for determining the stability of a single-point suspension system under actuator failure using a state feedback control law. H ∞ Robust fault-tolerant controller, and using Schur complement theory and bounded real lemma to prove the closed-loop asymptotic stability of single-point suspension system under actuator failure; The dynamic model of the single-point suspension system under the actuator failure is: Where, , , , , , is the system parameter uncertainty matrix, where is the identity matrix, is a known weight matrix, state quantity ; is the suspension gap between the electromagnet and the track, is the suspension gap at the equilibrium point, is the current at the equilibrium point; is the mass of the suspension frame, It is the external interference force, is the number of turns of the suspension electromagnet winding, A is the magnetic area of the levitation electromagnet, is the magnetic permeability of air, is the equivalent resistance of the magnetic circuit, To consider the control input after the system actuator fails, It is the normal output signal of the actuator when no fault occurs; It is the output signal after considering the failure of the actuator; is the actuator failure coefficient; The state feedback control law is used to determine the single point suspension system under actuator failure. H ∞ Robust fault-tolerant controller, and using Schur complement theory and bounded real lemma to prove the closed-loop asymptotic stability of single-point suspension system under actuator failure, including: For the dynamic model of the single-point suspension system under actuator failure, the state feedback control law is selected: Where, is the controller gain; And for a given , the closed-loop transfer function from external disturbance to output satisfies: Where, , is the identity matrix, is a complex variable defined in the domain of the Laplace transform; Theorem 1: For the dynamic model of a single-point suspension system under actuator failure, if there exists a constant ,matrix and a symmetric positive definite matrix So that the linear matrix inequality holds: Then for any actuator fault gain , there exists a robust fault-tolerant controller ,in , under which the dynamic model of the single-point suspension system under actuator failure has H ∞ Norm Bound ; Theorem 1 is proved by using Schur complement theory and bounded real lemma, and it is determined that H ∞ Existence of robust fault-tolerant controllers and closed-loop asymptotic stability of single-point suspension systems under actuator failures.

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