Fault-tolerant control method and system for actuator faults of high-speed maglev train

Abstract

The invention relates to the technical field of high-speed maglev train control, and discloses a fault-tolerant control method and system for actuator faults of a high-speed maglev train. The method specifically comprises the following steps: aiming at the actuator part fault of the single-point suspension system of the maglev train, introducing the actuator fault and system parameter uncertainty factors, modeling the actuator part fault of the single-point suspension system, and constructing a kinetic model of the single-point suspension system under the actuator fault. An H-infinity robust fault-tolerant controller is designed by adopting a state feedback control law, and the closed-loop asymptotic stability of the single-point suspension system is strictly proved based on a Schur complementary theory and a bounded practical lemma. Therefore, the method in the invention considers the actuator fault and the system parameter uncertainty when the controller is designed, and the control performance of the controller is improved.

Description

Technical Field

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

[0002] A high-speed maglev train is a new type of transportation vehicle that uses electromagnetic force to achieve contactless movement of the train along the track. It has low operating costs, a small turning radius, and flexible route selection, and can meet the comprehensive transportation needs of both urban and suburban areas. The suspension system is one of the core components of the maglev train. The suspension electromagnet contains several series-connected magnetic poles and is the actuator of the maglev train suspension system. The suspension controller adjusts the current in the electromagnet to change the magnitude of the suspension force and keep the suspension gap at the rated value. The magnetic poles work in a strong magnetic field environment and are prone to performance degradation (such as short circuits between windings, short circuits between the coil and the ground, short circuits of the energized joints, or increased contact resistance, etc.) after long-term service. The degradation of the electromagnet leads to partial faults of the actuator (such as a reduction in the effective number of turns and an increase in internal resistance, etc.), resulting in a mismatch with the control system parameters, increasing the fluctuation of the suspension gap or abnormally increasing the excitation current of the corresponding controller, and causing a decline in the suspension control performance. In severe cases, the excitation current of the electromagnet will be turned off by the corresponding controller, and the failed electromagnet circuit will be withdrawn from operation. Therefore, researching corresponding fault-tolerant control strategies for partial actuator faults has important theoretical and practical significance for the long-term service safety of maglev vehicles.

[0003] Regarding the fault-tolerant control of the actuator faults in the maglev train suspension system, relevant scholars have conducted a large amount of research. For example: 1) Combining gain scheduling with the method based on linear matrix inequalities to perform fault-tolerant control on the sensors and actuators in the suspension system; 2) For the single-module suspension system of a maglev train with uncertain system parameters, using the linear matrix inequality method to design a controller with complete fault tolerance for actuator failures. At the same time, considering the needs of engineering practice, the concept of weight is introduced to modify the control law to control the change of the suspension gap under different actuator fault modes; 3) Taking the suspension module of an EMS-type high-speed maglev train as the research object, using the synchronous stability principle to design a passive fault-tolerant controller based on the stable fractional factorization method of rational functions; 4) Based on the Lyapunov-Krasovskii theorem, deriving the sufficient conditions for the robust stability of the networked control system under all possible sensor faults, packet losses, and time delays, and then designing a fault-tolerant controller for the networked control system with continuous packet losses and time-varying delays.

[0004] Most of the above control methods require an accurate system model. However, the maglev train operates in a complex environment for a long time, and the time-varying external interferences such as track unevenness and changes in the number of passengers during operation make it impossible to accurately obtain the system parameters, resulting in a mismatch of the control system parameters and greatly reducing the control performance. Summary of the Invention

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

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

[0007] To solve the above technical problems, the present application discloses a fault-tolerant control method for an actuator failure of a high-speed maglev train, and the method includes: Introduce actuator failure and system parameter uncertainty factors to construct a dynamic model of a single-point levitation system with actuator failure; Use a state feedback control law to determine the H ∞ robust fault-tolerant controller of the single-point levitation system with actuator failure, and prove the closed-loop asymptotic stability of the single-point levitation system with actuator failure by using the Schur complement theory and the bounded real lemma.

[0008] The present application also discloses a fault-tolerant control system for an actuator failure of a high-speed maglev train, and the system includes: A system model construction module for introducing actuator failure and system parameter uncertainty factors to construct a dynamic model of a single-point levitation system with actuator failure; A controller construction module for using a state feedback control law to determine the H ∞ robust fault-tolerant controller of the single-point levitation system with actuator failure, and prove the closed-loop asymptotic stability of the single-point levitation system with actuator failure by using the Schur complement theory and the bounded real lemma.

[0009] In the present application, for partial actuator failures of the single-point levitation system of the maglev train, actuator failure and system parameter uncertainty factors are introduced, the partial actuator failures of the single-point levitation system are modeled, and a dynamic model of the single-point levitation system with actuator failure is constructed. A state feedback control law is used to design H ∞ a robust fault-tolerant controller, and the closed-loop asymptotic stability of the single-point levitation system is strictly proved based on the Schur complement theory and the bounded real lemma. Therefore, the method in the present application takes into account actuator failure and system parameter uncertainty when designing the controller, improving the control performance of the controller.

[0010] Additional aspects and advantages of the present application will be given in the following description part, which will become apparent from the following description or be understood through the practice of the present application. Description of the Drawings

[0011] The above and / or additional aspects and advantages of the present application will become apparent and be readily understood from the following description of embodiments in conjunction with the drawings, where: Figure 1 is a flowchart of a fault-tolerant control method for a high-speed maglev train actuator failure provided by an embodiment of the present application; Figure 2 is a schematic diagram of a single-point suspension system model provided by an embodiment of the present application; Figure 3 is a curve graph of the suspension gap change of the system without failure provided by an embodiment of the present application; Figure 4 is a curve graph of the system current change without failure provided by an embodiment of the present application; Figure 5 is a curve graph of the static suspension gap change under actuator failure provided by an embodiment of the present application; Figure 6 is a curve graph of the static current change under actuator failure provided by an embodiment of the present application; Figure 7 is a simulation curve graph of the suspension gap change under multiple groups of actuator failure gains provided by an embodiment of the present application; Figure 8 is a schematic diagram of a high-speed maglev train provided by an embodiment of the present application; Figure 9 is a curve graph of the suspension gap change under 17% actuator failure provided by an embodiment of the present application; Figure 10 is a curve graph of the current change under 17% actuator failure provided by an embodiment of the present application; Figure 11 is a curve graph of the suspension gap change under 33% actuator failure provided by an embodiment of the present application; Figure 12 is a curve graph of the current change under 33% actuator failure provided by an embodiment of the present application; Figure 13 is a schematic structural diagram of a fault-tolerant control system for a high-speed maglev train actuator failure provided by an embodiment of the present application.

[0012] Among them, 200 - suspension system; 201 - car body, 202 - air spring, 203 - support arm, 204 - guide electromagnet, 205 - track, 206 - track beam, 207 - suspension electromagnet, 208 - controller, 209 - suspension sensor, 210 - long stator. Detailed Embodiments

[0013] Embodiments of the present application will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary and are only used to explain the present application and should not be construed as a limitation of the present application.

[0014] Those skilled in the art of the present technology can understand that unless specifically stated, the singular forms "a", "an", "the" and "said" used herein may also include the plural forms. It should be further understood that the term "comprising" used in the specification of the present application means 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 say that an element is "connected" or "coupled" to another element, it can be directly connected or coupled to other elements, or there may also be intermediate elements. In addition, the "connection" or "coupling" used herein may include wireless connection or wireless coupling. The phrase "and / or" used herein includes all or any unit and all combinations of one or more related listed items.

[0015] Those skilled in the art can understand that unless otherwise defined, all terms (including technical terms and scientific terms) used herein have the same meaning as the general understanding of those of ordinary skill in the art to which the present invention belongs. It should also be understood that terms such as those defined in a general dictionary should be understood to have a meaning consistent with the meaning in the context of the prior art, and will not be interpreted with an idealized or overly formal meaning unless specifically defined as here.

[0016] For the technical problems existing in the prior art, the present application provides a fault-tolerant control method and system for high-speed maglev train actuators, aiming to solve at least one of the technical problems of the prior art. The technical solution of the present application and how the technical solution of the present application solves the above technical problems will be described in detail below with specific embodiments. These several specific embodiments below 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 with reference to the accompanying drawings.

[0017] The present application provides a flowchart of a fault-tolerant control method for high-speed maglev train actuators, as Figure 1 shown in, the method may include the following steps: Step 101, introduce actuator faults and system parameter uncertainties, and construct a dynamic model of a single-point levitation system with actuator faults; Step 102, use the state feedback control law to determine the H ∞ robust fault-tolerant controller of the single-point suspension system under actuator faults, and use the Schur complement theory and the bounded real lemma to prove the closed-loop asymptotic stability of the single-point suspension system under actuator faults.

[0018] The suspension system of the high-speed maglev train is a complex multi-point coupling system. Adopting the decentralized independent suspension control strategy and the modular idea of the magnet structure, the suspension system control problem can be decomposed into single suspension magnet control problems through decoupling. Analyzing the dynamic model and dynamic characteristics of a single magnet suspension has generality. The single-point suspension system composed 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 the EMS-type high-speed maglev train. The schematic diagram of the single-point suspension system model is as Figure 2 shown, where the suspension system of the high-speed maglev train includes a car body 201, an air spring 202, a support arm 203, a guiding electromagnet 204, a track 205, a track beam 206, and a suspension electromagnet 207. A single suspension electromagnet 207 and its controller 208 and a rigid or elastic track 205 form a single-point suspension system. A suspension sensor 209 is arranged on the suspension electromagnet 207, and a long stator 210 is arranged on the track 205.

[0019] In the embodiment of the present application, based on Figure 2 the shown single-point suspension system model, and aiming at the actuator part faults of the single-point suspension system of the maglev train, the actuator fault and system parameter uncertainty factors are introduced, the partial actuator faults of the single-point suspension system are modeled, and the dynamic model of the single-point suspension system under actuator faults is constructed. Use the state feedback control law and linear matrix inequalities to design H ∞ a robust fault-tolerant controller, and strictly prove the closed-loop asymptotic stability of the single-point suspension system based on the Schur complement theory and the bounded real lemma. Therefore, the method in the embodiment of the present application takes into account the actuator faults and system parameter uncertainties when designing the controller, and improves the control performance of the controller.

[0020] In an optional embodiment, based on Figure 2 the shown single-point suspension system model, the actuator fault and system parameter uncertainty factors are introduced, and the dynamic model of the single-point suspension system under actuator faults is constructed, including: According to Newton's second law, the mechanical equation in the vertical direction of the suspension electromagnet can be obtained as: (1) In the formula: 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, is the external disturbance force, is the acceleration due to gravity, is the electromagnetic attraction generated by the suspension electromagnet.

[0021] Assume that the magnetic permeability of the magnetic pole is infinite and the magnetic potential is uniformly distributed across the air gap. Neglecting the leakage flux of the winding and the elastic influence of the track beam, the inductance in the suspension electromagnet coil is: (2) 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 Equation (2), the electromagnetic attraction generated by the suspension electromagnet can be expressed as: (3) To simplify the equation, let .

[0022] Next, linearize the single-point suspension system at the equilibrium point. For the mechanical equation (1) of the suspension electromagnet in the vertical direction, at the equilibrium point, we have: (4) 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.

[0023] Let Substitute in Equation (1) = , Based on Equations (1), (3) and (4), the dynamic equations of the single-point suspension system under current control are obtained: (5) 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, is the external disturbance 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 suspension 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 balance point; is the electromagnetic suction force at the balance point; Due to the existence of non - linear terms in Equation (3), it is difficult to design a controller using the commonly used linear control methods in engineering. Therefore, the electromagnetic force at the balance point is linearly expanded, and after omitting the high - order terms, we get: (6) Taking the suspension gap and the speed of the suspension electromagnet (downward is positive) as state variables , the current as the input of the single - point suspension system, and the change in the suspension gap as the output, the state equation of the single - point suspension system is obtained as: (7) Considering that the actuator may fail due to component aging, interference, etc., and the output signal of the faulty component deviates from the accurate value. A continuous - type switch fault model is adopted, and a virtual gain is added to the actuator channel, and it satisfies the condition: (8) Based on the continuous - type switch fault, the actuator fault can be modeled as: (9) In the formula, is the normal output signal of the actuator when no fault occurs; is the output signal considering the actuator failure; is the actuator fault coefficient.

[0024] Considering the actuator fault and the system parameter uncertainties caused by the change in the number of passengers and external disturbances during system operation, the actuator fault and system parameter uncertainty factors are introduced into the state equation to obtain the dynamic model of the single - point suspension system under actuator fault: (10) In the formula, , , , , , is the system parameter uncertainty matrix, where is the identity matrix, is the known weight matrix, is the control input considering the actuator fault of the system.

[0025] In an alternative embodiment, a state - feedback control law is adopted to determine the A robust fault-tolerant controller is proposed, and the closed-loop asymptotic stability of the single-point suspension system under actuator faults is proved by using the Schur complement theory and the bounded real lemma, including: For the dynamic model (10) of the single-point suspension system under actuator faults, the state feedback control law is selected as: (11) where is the controller gain; and for a given , the closed-loop transfer function from the external disturbance to the output satisfies: (12) where , is the identity matrix, is the complex variable defined in the Laplace transform domain; Theorem 1 is given: For the dynamic model of the single-point suspension system under actuator faults, if there exist constants , matrix and symmetric positive definite matrix such that the linear matrix inequality holds: (13) then for any actuator fault gain , there exists a robust fault-tolerant controller , where , and under its action, the dynamic model of the single-point suspension system under actuator faults has H ∞ norm bound ; The proof of Theorem 1 is carried out by using the Schur complement theory and the bounded real lemma to determine the existence of the robust fault-tolerant controller and the closed-loop asymptotic stability of the single-point suspension system under actuator faults.

[0026] In an alternative embodiment, the proof of Theorem 1 is carried out by using the Schur complement theory and the bounded real lemma to determine H ∞ the existence of the robust fault-tolerant controller and the closed-loop asymptotic stability of the single-point suspension system under actuator faults, including: Lemmas for proving Theorem 1 are given; the lemmas include the Schur complement theory and the bounded real lemma; Based on the lemmas, it is proved that there exists a robust fault-tolerant controller such that the linear matrix inequality shown in Theorem 1 holds; Based on the lemmas, it is proved 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 faults; Based on the lemma, it is proved that the linear matrix inequality shown in Theorem 1 can ensure that the single-point suspension system under actuator faults has H ∞ a norm bound . In an alternative embodiment, the lemma further includes Lemma 1: For matrices of appropriate orders , and , the following equation holds: (14) Lemma 2 (Schur complement theory) is as follows: For a given symmetric matrix , where , the following three conditions are equivalent: (1) ; (2) ; (3) ; Lemma 3 (bounded real lemma) is as follows: For the following system: (15) where is the system state; is the external disturbance input; is the system controlled output, is a matrix of appropriate order; The closed-loop transfer function from the external disturbance to the controlled output is: Let the constant , the necessary and sufficient condition for the system to be asymptotically stable and satisfy is that there exists a positive definite matrix satisfying the condition: . (16) In an alternative embodiment, based on the lemma, it is proved that there exists H ∞ a robust fault-tolerant controller such that the linear matrix inequality shown in Theorem 1 holds, which may include: Theorem 2: There exists H ∞ a robust fault-tolerant controller such that the linear matrix inequality (13) holds.

[0027] Proof: Let the auxiliary matrix be: (17) Multiply the left and right sides of the auxiliary matrix (17) by the diagonal matrix respectively, and we get: (18) According to Lemma 1, the first matrix inequality is as follows: (19) Therefore, by scaling the first matrix inequality (19), the second matrix inequality is obtained: (20) By arranging the second matrix inequality (20), the third matrix inequality can be obtained: (21) Let and . According to the Schur complement theory, the linear matrix is obtained. Therefore, there exists a H ∞ robust fault-tolerant controller for the single-point suspension system under actuator faults, such that the linear matrix inequality holds, and Theorem 2 is proved.

[0028] In an alternative embodiment, based on the lemma, it can be proved 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 faults, which may include: Theorem 3: The linear matrix inequality (13) can ensure the uniform asymptotic stability and robust fault tolerance of the single-point suspension system under partial actuator faults.

[0029] Proof: Select the Lyapunov function: (22) The time derivative of the Lyapunov function along any trajectory of the single-point suspension system under actuator faults is: (23) Combining the dynamic model (10) of the single-point suspension system under actuator faults and the time derivative (23) of the Lyapunov function along any trajectory of the single-point suspension system under actuator faults, that is, substituting the dynamic model (10) of the single-point suspension system under actuator faults into Equation (23), the first function is obtained: (24) Let . The first function can be arranged into the second function: (25) When the disturbance is not considered, that is, , according to the linear matrix inequality (13) and the Schur complement theory, it can be known that: (26) Therefore, The inequality holds. According to Lyapunov stability theorem, it can be known that the single-point suspension system is uniformly asymptotically stable under actuator faults. Since the linear matrix inequality (13) takes into account the case of actuator failures, the single-point suspension system under actuator faults also has robust fault-tolerant performance, and Theorem 3 is proved.

[0030] In an alternative embodiment, based on the lemma, it is proved that the linear matrix inequality can ensure that the single-point suspension system under actuator faults has H ∞ norm bound , which can include: Theorem 4: The linear matrix inequality (13) can ensure that the single-point suspension system under actuator faults has H ∞ norm bound .

[0031] Proof: Assume the initial state , and introduce the function: (27) Since the robust stability of the single-point suspension system under actuator faults guarantees boundedness and , therefore, under zero initial conditions, for any , the following inequality holds: (28) The closed-loop transfer function from the external disturbance to the controlled output is: . Let the constant , the necessary and sufficient condition for the single-point suspension system under actuator faults to be asymptotically stable and satisfy is that there exists a positive definite matrix satisfying the condition: (29) Therefore, according to the bounded real lemma, the single-point suspension system under actuator faults has H ∞ norm bound , and Theorem 4 is proved.

[0032] From Theorems 2 - 4, it can be known that for a given constant , for any actuator fault gain , if there exist matrices , symmetric positive definite matrix such that the linear matrix inequality (13) holds, then the single-point suspension system under the disturbed actuator faults is a robust fault-tolerant control system, and Theorem 1 is proved.

[0033] In an optional embodiment, a state feedback control law is adopted to determine the robust fault-tolerant controller of the single-point suspension system under actuator faults. After proving the closed-loop asymptotic stability of the single-point suspension system under actuator faults by using the Schur complement theory and the bounded real lemma, the method further includes: Solving the linear matrix inequality to obtain the controller gain matrix.

[0034] In the embodiment of the present application, in order to verify the effectiveness of the proposed fault-tolerant control method for the actuator faults of the high-speed maglev train, the robust fault-tolerant controller determined by Equations (11) and (13) is simulated for the suspension system model of the high-speed maglev train in MATLAB, and a PID controller is selected for comparison. The parameters of the suspension system in the simulation are shown in Table 1: Table 1 Parameters of the suspension system

[0035] The chopper inside the controller is the main interference source of the maglev train. A strong electromagnetic interference will be generated at the moment of the chopping switch. Therefore, in the simulation a sine wave with an amplitude of 0.2 and a frequency of 20 rad / s is used to simulate the interference received by the suspension system during actual operation, and white noise is used to simulate the measurement noise existing in the sensor acquisition process of the actual system. Considering any actuator failure situation, according to Theorem 1, the linear matrix inequality (13) is solved by using the MATLAB-LMI toolbox to obtain the controller gain matrix:

[0036] Next, in order to verify the suspension control ability of the proposed H ∞ robust fault-tolerant controller, three groups of simulations will be carried out: 1) static suspension without faults; 2) static suspension under actuator faults; 3) static suspension under different actuator fault gains. The first group of simulations is to verify the H ∞ robust fault-tolerant controller can ensure the normal and stable suspension of the maglev train without faults. The second group of simulations is to illustrate the H ∞ stable suspension of the maglev train suspension system under actuator fault conditions under the action of the robust fault-tolerant controller. The last group of simulations gives the system responses under different actuator gains to test the H ∞ feasibility of the proposed robust fault-tolerant controller under a wide range of actuator fault gains.

[0037] Simulation 1. Static suspension without faults Consider the static suspension performance without actuator faults to verify that the two controllers can ensure the normal and stable suspension of the maglev train without faults, providing a prior basis for subsequent fault suspension simulations.

[0038] The curves of the suspension gap change and current change of the system without faults are respectively as Figure 3 and Figure 4 shown. From Figure 3 and Figure 4 it can be seen that the proposed H ∞ robust fault-tolerant controller (adopting fault-tolerant measures) and the PID controller (a method without adopting fault-tolerant measures) can both achieve stable suspension within a finite time. H ∞ The time for the system to reach the equilibrium point under the action of the robust fault-tolerant controller, 0.078 s, is less than the time for the system to reach the equilibrium point under the action of the PID controller, 0.134 s. H ∞ The robust fault-tolerant controller has a faster convergence speed. H ∞ The current vibration range of the robust fault-tolerant controller is smaller, the steady-state suspension performance is better, and it has better robustness to external disturbances and measurement errors. The asymptotic stability of the system is ensured through Simulation 1.

[0039] Simulation 2. Static suspension under actuator faults Set that when the system is stably suspended, the actuator fails at 0.5 s, and the actuator fault gain δ = 0.7. The simulation results are respectively as Figure 5 and Figure 6 shown. From Figure 5 and Figure 6 it can be seen that when the actuator fails, H ∞ the change in the suspension gap of the system under the robust fault-tolerant controller is 0.21 mm, which is much smaller than the change in the suspension gap of 1.96 mm under the PID controller. H ∞ The robust fault-tolerant controller has better robustness to actuator faults. And H ∞ the current increase of the system under the robust fault-tolerant controller is smaller, which can well solve the problem of the sudden increase in the control current caused by partial faults in the electromagnet coil. The fault tolerance of the system is verified through Simulation 2. Simulation 3. Static suspension under different actuator fault gains Only the simulation results under a single actuator fault gain are given in Simulation 2, which cannot well illustrate the feasibility of the robust fault-tolerant controller under a wide range of actuator fault gains. To better illustrate the above problems, combined with the actuator failure statistical data in the actual physical system, the actuator fault gains are respectively selected asδ = 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, the obtained simulation results are as follows Figure 7 shown

[0040] The comparison of system performance under different actuator fault gains is shown in Table 2. It can be seen from Table 2 that the system can still maintain stability under multiple groups of actuator fault gains, and the steady-state error is within an acceptable range. This shows that the proposed H ∞ robust fault-tolerant controller can achieve stable suspension of the maglev train suspension system under large-scale actuator failures. Moreover, the greater the actuator fault gain, the greater the stable deviation after the system reaches equilibrium

[0041] Table 2 Comparison of system performance under different actuator fault gains

[0042] In the embodiments of this application, in order to verify the effectiveness of the fault-tolerant control algorithm corresponding to the proposed H ∞ robust fault-tolerant controller, around the application of the developed long-stator maglev train suspension controller, verification is carried out using a high-speed maglev train. The experimental base is located on the high-speed maglev transportation test line of Tongji University. The schematic diagram of the high-speed maglev train is as follows Figure 8 shown, including a vehicle body 201, a track 205, and a set of suspension system 200. The suspension system 200 includes a suspension controller, two suspension sensors, and a suspension electromagnet. In the experiment, a total of 12 poles in one suspension electromagnet module are controlled by two independent suspension controllers, and each suspension controller controls 6 series-connected poles. A suspension controller containing a fault-tolerant control algorithm (suspension point 1) and a suspension controller without a fault-tolerant control algorithm (suspension point 3) are installed on the vehicle, and the data of the two suspension controllers are collected and compared. For the accuracy of the comparison test, the two suspension controllers are installed in different suspension frames and are decoupled from each other. The fault-tolerant control algorithm is tested. In order to simulate the situation of actuator failures, two groups of experiments are carried out: 1) Connect 5 series-connected poles to simulate the fault situation of 17% actuator failure; 2) Connect 4 series-connected poles to simulate the fault state of 33% actuator failure

[0043] The experimental results of 17% actuator failure are as follows Figure 9 and 10As shown in the figure, at the suspension control point without the fault-tolerant control algorithm (the 3rd suspension point), the actuator failure reduces the effective magnetic poles, resulting in the mismatch between the actual model and the designed model. The suspension system cannot stably suspend, and the suspension current increases, causing the electromagnet to continuously heat up, which easily damages the magnetic poles. With the intervention of the fault-tolerant control algorithm, the current at the 1st suspension point is basically the same as before the fault, only the current fluctuation increases, not exceeding 1A up and down, and the gap remains stable.

[0044] The experimental results of 33% actuator failure are as Figure 11 and Figure 12 shown. At the suspension control point without the fault-tolerant control algorithm, the gap cannot stably suspend, and the current also increases to about 33A, which is worse than the case of connecting 5 magnetic poles in series. However, with the intervention of the proposed fault-tolerant control algorithm, the amplitude of the current at the 1st suspension point slightly increases, and the average value is about 25A, with an increased fluctuation. The gap fluctuation increases compared with the case of connecting 5 magnetic poles in series, not exceeding ±1mm, which does not affect the suspension performance. Without adding the fault-tolerant control algorithm, the current amplitude increases, and in severe working conditions, it will cause the suspension system to become unstable. After adding the fault-tolerant control algorithm, the suspension control system can still maintain stable suspension under the condition of actuator failure, and the fluctuations of the current and the gap increase.

[0045] Based on the above embodiments, the present application designs a fault-tolerant control method for the actuator failure of a high-speed maglev train suspension system for some actuator failures of the maglev train suspension system, realizing the stable suspension of the maglev train. In particular, the suspension gap is stably near the desired position within a finite time. At the same time, it is possible to suppress the influence of the inability to accurately obtain the suspension system parameters in a complex operating environment on the stable suspension. The asymptotic stability of the control system is strictly theoretically analyzed using the Schur complement theory and the bounded real lemma, and the stability of the suspension system at the equilibrium point under partial actuator failures is proved. 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 a multi-point coupled suspension system.

[0046] Based on the same principle as the method provided in the embodiments of the present application, the embodiments of the present application also provide a fault-tolerant control system for the actuator failure of a high-speed maglev train, as Figure 13 shown, the system includes: A system model construction module 1301, configured to introduce actuator failure and system parameter uncertainty factors, and construct a dynamic model of a single-point suspension system under actuator failure; A controller construction module 1302, configured to determine the H ∞A robust fault-tolerant controller is designed, and the closed-loop asymptotic stability of the single-point levitation system under actuator faults is proven by using the Schur complement theory and the bounded real lemma.

[0047] In the embodiments of this application, for the actuator faults in the single-point levitation system of maglev trains, the factors of actuator faults and system parameter uncertainties are introduced, the actuator faults in the single-point levitation system are modeled, and the dynamic model of the single-point levitation system under actuator faults is constructed. A state feedback control law and linear matrix inequalities are used to design H ∞ a robust fault-tolerant controller, and the closed-loop asymptotic stability of the single-point levitation system is strictly proven based on the Schur complement theory and the bounded real lemma. Therefore, in the embodiments of this application, the actuator faults and system parameter uncertainties are considered in the design of the controller, improving the control performance of the controller.

[0048] The fault-tolerant control system for actuator faults of the high-speed maglev train provided by the embodiments of this application can achieve Figures 1 to 12 each process implemented in the method embodiments. To avoid repetition, it will not be elaborated here.

[0049] The fault-tolerant control system for actuator faults of the high-speed maglev train in the embodiments of this application can execute the fault-tolerant control method for actuator faults of the high-speed maglev train provided by the embodiments of this application. Their implementation principles are similar. The actions performed by each module and unit in the fault-tolerant control system for actuator faults of the high-speed maglev train in the embodiments of this application correspond to the steps in the fault-tolerant control method for actuator faults of the high-speed maglev train in the embodiments of this application. For the detailed function descriptions of each module of the fault-tolerant control system for actuator faults of the high-speed maglev train, reference can specifically be made to the descriptions in the corresponding fault-tolerant control method for actuator faults of the high-speed maglev train shown above. It will not be elaborated here.

[0050] The above description is only for the preferred embodiments of this application and the explanation of the applied technical principles. Those skilled in the art should understand that the scope of disclosure involved in this application is not limited to the technical solutions formed by the specific combination of the above technical features, but also covers other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above disclosure concept. For example, the technical solutions formed by mutually replacing the above features with (but not limited to) the technical features with similar functions disclosed in this application.

Claims

1. A fault-tolerant control method for high-speed maglev train actuators, characterized in that, The method includes: Introduce actuator faults and system parameter uncertainties, and construct the dynamic model of the single-point suspension system with actuator faults; The state feedback control law is used to determine the H ∞ robust fault-tolerant controller of the single-point suspension system under actuator faults, and the closed-loop asymptotic stability of the single-point suspension system under actuator faults is proved by using the Schur complement theory and the bounded real lemma; The dynamic model of the single-point suspension system with actuator faults is: In the formula, , , , , , is the system parameter uncertainty matrix, where is the identity matrix, is the known weight matrix, and the state variable ; 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, is the external disturbance force, is the number of turns of the suspension electromagnet winding, A is the magnetic area of the suspension electromagnet, is the air magnetic permeability, is the equivalent resistance of the magnetic circuit, is the control input considering the system actuator failure, is the normal output signal of the actuator when no failure occurs; is the output signal considering the actuator failure, is the actuator failure coefficient; The robust fault-tolerant controller of the single-point suspension system under actuator faults is determined by using the state feedback control law, and the closed-loop asymptotic stability of the single-point suspension system under actuator faults is proved by using the Schur complement theory and the bounded real lemma, including: H ∞ ​ For the dynamic model of the single-point suspension system with actuator faults, select the state feedback control law: wherein, is the controller gain; And for a given , the closed-loop transfer function from the external disturbance to the output satisfies: In the formula, , is the identity matrix, is a complex variable defined in the domain of Laplace transform; Theorem 1 is given: For the dynamic model of the single-point suspension system with actuator faults, if there exist constants , matrix and symmetric positive definite matrix such that the linear matrix inequality holds: For any actuator fault gain , there exists a robust fault-tolerant controller , where , under its action, the dynamic model of the single-point suspension system with actuator faults has H ∞ norm bound ; Proof of Theorem 1 is carried out using the Schur complement theory and the bounded real lemma to determine H ∞ the existence of a robust fault-tolerant controller and the closed-loop asymptotic stability of the single-point suspension system under actuator faults.

2. The fault-tolerant control method for the actuator failure of a high-speed maglev train according to claim 1, wherein Prove Theorem 1 by using the Schur complement theory and the bounded real lemma to determine H ∞ the existence of a robust fault-tolerant controller and the closed-loop asymptotic stability of the single-point suspension system under actuator faults, including: Give the lemma for proving Theorem 1; the lemma includes the Schur complement theory and the bounded real lemma; Based on the above lemma, it is proved that there exists H ∞ a robust fault-tolerant controller such that the linear matrix inequality shown in Theorem 1 holds; Based on the lemma, 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 with actuator faults; Based on the above lemma, it is proved that the linear matrix inequality shown in Theorem 1 can ensure that the single-point suspension system under actuator faults has H ∞ norm bound .

3. The fault-tolerant control method for the actuator failure of a high-speed maglev train according to claim 2, wherein The lemma also includes Lemma 1: For matrices of appropriate orders , and , the following inequality holds: The Schur complement theory is as follows: for a given symmetric matrix , where , the following three conditions are equivalent: （1） ； （2） ； （3） ； The bounded real lemma is: For the following system: wherein, is the system state; is the external disturbance input; is the controlled output of the system, is a matrix of appropriate order; The closed-loop transfer function from the external disturbance to the controlled output is as follows: , let the constant , the system is asymptotically stable and satisfies The necessary and sufficient condition for this is that there exists a positive definite matrix satisfying the condition: 。 4. The fault-tolerant control method for the actuator failure of a high-speed maglev train according to claim 3, characterized in that, Based on the above lemma, it is proved that there exists H ∞ a robust fault-tolerant controller such that the linear matrix inequality shown in Theorem 1 holds, including: Let the auxiliary matrix : Multiply the auxiliary matrix on the left and right respectively with a diagonal matrix to obtain: It can be seen from Lemma 1 that the first matrix inequality: Therefore, scale the second matrix to obtain the second matrix inequality: After arranging the second matrix inequality, the third matrix inequality can be obtained: Let and . According to the Schur complement theory, the linear matrix can be obtained. Therefore, there exists H ∞ robust fault-tolerant controller such that the linear matrix inequality holds.

5. The fault-tolerant control method for the actuator failure of a high-speed maglev train according to claim 3, characterized in that, The proof 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 with actuator faults based on the lemma includes: Select the Lyapunov function: The time derivative of the Lyapunov function along any trajectory of the single-point suspension system with actuator faults is: Combining the dynamic model of the single-point suspension system with actuator faults and the time derivative of the Lyapunov function along any trajectory of the single-point suspension system with actuator faults, the first function is obtained: Let , the first function can be arranged into the second function: When interference is not considered, that is from the linear matrix inequality and Schur complement theory, it can be seen that: Therefore, the inequality holds. According to Lyapunov stability theorem, it can be known that the single-point suspension system is uniformly asymptotically stable under actuator faults; because the linear matrix inequality takes into account the situation of actuator failure, the single-point suspension system under actuator faults also has robust fault-tolerant performance.

6. The fault-tolerant control method for the actuator failure of a high-speed maglev train according to claim 3, wherein Based on the above lemma, it is proved that the linear matrix inequality can ensure that the single-point suspension system under actuator faults has H ∞ norm bound , including: Assume the initial state , introduce the function: The robust stability of the single-point suspension system in case of actuator failure ensures that boundedness and , so, under zero initial conditions, for any , the following inequality holds: The closed-loop transfer function from the external disturbance to the controlled output is as follows: , let the constant , the necessary and sufficient condition for the single-point suspension system to be asymptotically stable and satisfy under actuator faults is that there exists a positive definite matrix satisfying the conditions: Therefore, according to the bounded real lemma, the single-point suspension system under actuator faults has H ∞ a norm bound .

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

8. A fault-tolerant control system for a high-speed maglev train actuator, characterized in that, The system includes: A system model construction module for introducing actuator faults and system parameter uncertainties and constructing the dynamic model of the single-point suspension system with actuator faults; A controller construction module is used to determine the robust fault-tolerant controller of the single-point suspension system under actuator faults by using the state feedback control law, and prove the closed-loop asymptotic stability of the single-point suspension system under actuator faults by using the Schur complement theory and the bounded real lemma; H ∞ ​ The dynamic model of the single-point suspension system with actuator faults is: wherein , , , , , is the system parameter uncertainty matrix, where is the identity matrix, is the known weight matrix, and the state variable ; 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, is the external disturbance force, is the number of turns of the suspension electromagnet winding, A is the magnetic area of the suspension electromagnet, is the air magnetic permeability, is the equivalent resistance of the magnetic circuit, is the control input considering the system actuator failure, is the normal output signal of the actuator when no failure occurs; is the output signal considering the actuator failure, is the actuator failure coefficient; The robust fault-tolerant controller of the single-point suspension system under actuator faults is determined by using the state feedback control law, and the closed-loop asymptotic stability of the single-point suspension system under actuator faults is proved by using the Schur complement theory and the bounded real lemma, including: H ∞ ​ For the dynamic model of the single-point suspension system with actuator faults, select the state feedback control law: wherein, is the controller gain; And for a given , the closed-loop transfer function from the external disturbance to the output satisfies: wherein, , is the identity matrix, is a complex variable defined in the Laplace transform domain; Theorem 1 is given: For the dynamic model of the single-point suspension system with actuator faults, if there exist constants , matrix and symmetric positive definite matrix such that the linear matrix inequality holds: For any actuator fault gain , there exists a robust fault-tolerant controller , where , under its action, the dynamic model of the single-point suspension system with actuator faults has H ∞ norm bound ; Proof of Theorem 1 is carried out by using the Schur complement theory and the bounded real lemma to determine H ∞ the existence of the robust fault-tolerant controller and the closed-loop asymptotic stability of the single-point suspension system under actuator faults.

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