Maglev Vehicle Research Articles

Conceptual Design of Electrodynamic Wheels Based on HTS Halbach Array Magnets

Maglev technologies have been extensively studied for modern transport systems; however, their main applications are limited to transportation systems with fixed tracks. On-road vehicles could have a broader outlook if combined with maglev technologies, for which electrodynamic wheels (EDWs) have provided a possible solution. Conventional EDWs are designed based on permanent magnets (PMs), which generate limited thrust and lift forces while having a low power density. In order to enhance the feasibility of EDWs in maglev vehicles, a novel design of EDWs based on high-temperature superconducting (HTS) Halbach array magnets (HAMs) has been proposed in this paper. The suggested design is made of the second generation (2G) superconducting coils, which have been modeled with the A-formulation and T-formulation based finite element methods. Simulation results show that the proposed HTS HAM EDW can generate higher thrust and lift forces, improve the magnetic flux density distribution in the airgap, and greatly reduce the weight of the magnets compared with the conventional design. This paper provides a possibility for future on-road maglev vehicles.

Robust nonsingular sliding mode control of the maglev train system: case study

This paper deals with a new approach to explore the precise dynamic response of the maglev system train and its control. Magnetic-suspension systems are characterized by high nonlinearity and open-loop instability which are the core components of maglev vehicles. Firstly, we use the electromagnetics and mechanics laws to derive the mathematical expressions of the proposed maglev system. Analytical investigation and theoretical calculation show that for the specific values of the control system parameters, the maglev system train can be significantly improved. It points out that the inherent nonlinearity, the inner coupling, misalignments between the sensors and actuators, and external disturbances are the main issues that should be considered for maglev engineering. Secondly, a control strategy based on the precise model of a nonsing ular robust sliding mode control is designed to reduce the upper bound of both the uncertainty and interference of the sliding mode controller. This approach presents an added value compared to the new sliding control methods in terms of overshoot and speed of convergence which is designed to control the vertical position of the proposed system. By using rigorous mathematical transformation associated with the adaptation laws in the frequency domain, a sufficient condition is drawn for the stability of the dynamical error based on the Lyapunov theory. This allows us a great possibility for interpreting the operation of the maglev train system. Numerical results are presented to show the effectiveness of our proposed control scheme.

A Non-Iterative Integration Scheme Enriching the Solution to the Coupled Maglev Vehicle–Bridge System

A non-iterative integration scheme is presented in this study to enrich the solutions to the coupled equations of the maglev vehicle–bridge system. The proposed integration scheme is composed of two integration methods aiming at providing the solutions to equation of motion and state-space equation. First, the equation of motion of the simply supported girder bridge is transformed by the modal superposition method. Then the state-space equation is used to describe the motions of both the vehicle and the suspension control system, with the associated matrices assembled using the fully computerized approach. By adopting this integration scheme, only pure vector calculations arise in the solution process, regardless of the existence of time-dependent displacement and velocity on the right-hand sides of the two coupled equations. The proposed integration method is of the second-order accuracy with and without damping. Being equipped with adequate numerical dissipation and dispersion, the method also possesses the characteristic of little computing errors, as can be achieved through the use of different pairs of parameters. Finally, numerical simulations have been conducted to assess the influence of different feedback gains, three types of bridges with different lengths, and guideway irregularity on the maglev vehicle–bridge system.

The Stability of HTS Maglev Vehicle Through Grade Change Point

High-temperature superconducting (HTS) maglev system, based on the magnetic flux pinning characteristic of non-ideal type II superconductors, can realize self-stable above permanent magnets. HTS maglev possesses the advantages of low-energy consumption, simple mechanical structure and environment-friendly, which make it an ideal high-speed transportation mode. When an HTS maglev vehicle crosses a ramp, the levitation height will fluctuate due to the rapid change of the track curve, which may affect the safety and stability of the system. In this paper, first, a levitation force model was obtained based on experimental data. Based on this model, a dynamic model of the HTS maglev vehicle-bridge coupled system was established. The dynamic response of the maglev train was simulated and analyzed when it operated through track grade change points under different track slopes, vertical curve radii and speeds. The influence of these parameters on the stability of the system was investigated, and the optimized design parameters for the vehicle and the track slope are proposed as well. This study provides references for the future engineering development of HTS maglev transportation.

Deep Learning Based Semi-Supervised Control for Vertical Security of Maglev Vehicle With Guaranteed Bounded Airgap

The vertical security problem of maglev train is challenging for nonlinearity, external disturbances, unmeasurable airgap velocity and constrained output. To solve this problem, a semi-supervised controller based on deep belief network (DBN) algorithm is proposed in the presence of unknown external disturbances. Firstly, the extended state observer (ESO) is designed to ensure fast convergence of observation errors with high enough estimation precision. An output-constrained controller is designed by backstepping method, and the estimated value of ESO is introduced to ensure that the output airgap is constrained within a bounded range. Then, the stability of this method is proved based on the symmetric Barrier Lyapunov function. Subsequently, a semi-supervised controller is presented based on DBN algorithm and the output-constrained controller. The numerical simulation results show that this method can effectively deal with unmeasurable airgap velocity and generalized external disturbances, and guarantee the vertical security with output airgap within a bounded range. Finally, experiments are implemented on a full-scale maglev vehicle and the experimental results demonstrate that the developed deep learning controller can ensure the vertical security.

Offset-free Nonlinear Model Predictive Control by the Example of Maglev Vehicles

Abstract Offset-free action of model predictive control (MPC) for nonlinear systems with the number of measured outputs greater than controlled outputs is a nontrivial problem. Motivated by investigating the possible application of MPC for the control system of magnetic levitation (Maglev) vehicles – tracking only the gap while measuring the gap, acceleration, and current – for higher speeds than hitherto travelled, different possible offset-free nonlinear MPC strategies are reviewed and discussed. Moreover, a novel approach based on a two-stage observer is introduced, requiring less effort to design an offset-free MPC. The different strategies are applied and analyzed in detail for a realistic model of the control system of the latest Transrapid vehicle, called TR09. Unlike usual offset-free MPC studies, the controller performance is also studied in a typical dynamic scenario, revealing the conflict and trade-off between the requirements for speed of command response and the robustness of closed-loop stability.

Optimization on Size of Halbach Array Permanent Magnets for Magnetic Levitation System for Permanent Magnet Maglev Train

A permanent magnet suspension (PMS) magnetic levitation (Maglev) system consisted of magnetic rail magnets and carriage magnets are investigated for PMS Maglev vehicle. The characteristics of magnetic flux line and magnetic flux density distribution in the suspension gap region are analyzed by using finite element method. The results show that the Halbach Array stack structure generates strong sinusoidal periodic magnetic field in the suspension gap region. The size of Halbach Array permanent magnets stacked structure model was simulated and optimized, and the optimal size factor was obtained. In addition, a levitation force model describing the relationship between magnetic levitation force, permanent magnet size and levitation height was established by molecular current method. The correctness of the levitation force model is evaluated. Finite element simulation and experiment verify the validity of the levitation force model. The results show that the optimized Halbach Array permanent magnets can generate large suspension force and good stability, which is of great significance to improve the utilization rate of permanent magnet materials and save costs, and is conducive to the further development of permanent magnet maglev train. The study is useful for analysis and design optimization of maglev train.

The Concept of Development and Implementation of High-Speed Transport

The article discusses the issues of implementation and organization of high-speed transport. The objective of the article is to consider possible options for implementing highspeed (HS) motion systems using the principle of magnetic levitation, which will ensure high speeds for delivery of goods and carrying people over long distances. To achieve this objective, it is necessary to develop an engine and technical solutions for design of HS rolling stock, make decisions on energy supply infrastructure and the HS track, address safety issues and new control systems considering the state of the infrastructure and its design elements. The article discusses several options for implementation of high-speed transport systems, differing in the power supply system, current collection and track based on the magnetic levitation approach. An original approach is proposed in implementation of magnetic levitation transport using the technology of electromagnetic guns designed to implement traction forces of a magnetic levitation vehicle. The advantage of this approach is that it opens the possibility of maneuvering for the vehicle while driving. This allows to abandon switch turnouts, now significantly limiting the use of magnetic levitation transport. A mathematical model describing interaction of an electromagnetic gun and supermagnets located on the track is considered. In constructing the model, methods of the theory of electromagnetic field and interaction of magnetic bodies were used, and when constructing a model of interaction of rolling stock with a magnetic track, methods of mathematical algebra and the Cauchy theorem were used. The article discusses various principles of organization of movement using the magnetic levitation for urban, suburban, and intercity transport.

Static and Dynamic Modeling of the Electromagnets of the Maglev Vehicle Transrapid

This work provides a new approach for modeling the electromagnets of the magnetic levitation (Maglev) vehicle Transrapid intending to effectively and efficiently represent the statics and the dynamics in a frequency range relevant for Maglev control design and for the use in mechatronic simulation models. It includes the effects of magnetic reluctances, fringing and leakage flux, magnetic saturation, and eddy currents. The modeling follows a systematic approach by setting up the equivalent magnetic and electric circuits, and coupling the equations using Ampère's circuital law and Faraday's law of induction resulting in a system of differential algebraic equations. It allows to study effects occurring in the magnet design process or different operating points, resulting, e.g., from aerodynamic uplift, for which an extended validity range is needed. Since the computational effort of such models is significant, additionally, a numerical procedure for model reduction is presented yielding a simplified version, which possesses a nearly identical input-output behavior and is usable for control design or in large vehicle models. The proposed approach can be applied to any levitation or guidance magnet of the vehicle and is shown exemplarily for a Transrapid's levitation magnet. The model is validated for the parameters of the latest Transrapid vehicle, called TR09, showing good correspondence with the measured static force-current-gap characteristics and the inductance.

An Accurate GNSS-Based Redundant Safe Braking System for Urban Elevated Rail Maglev Trains

The association of elevated rail structures and Maglev (magnetic levitation) trains is a promising alternative for urban transportation. Besides being cost-effective in comparison with underground solutions, the Maglev technology is a clean and low-noise mass transportation. In this paper, we propose a low-cost automatic braking system for Maglev trains. There is a myriad of sensors and positioning techniques used to improve the accuracy, precision and stability of train navigation systems, but most of them result in high implementation costs. In this paper, we develop an affordable solution, called Redundant Autonomous Safe Braking System (RASBS), for the MagLev-Cobra train, a magnetic levitation vehicle developed at the Federal University of Rio de Janeiro (UFRJ), Brazil. The proposed braking system employs GNSS (Global Navigation Satellite System) receivers at the stations and trains, which are connected via an ad-hoc wireless network. The proposed system uses a cooperative error correction algorithm to achieve sub-meter distance precision. We experimentally evaluate the performance of RASBS in the MagLev prototype located at the campus of UFRJ, Brazil. Results show that, using RASBS, the train is able to dynamically set the precise location to start the braking procedure.

Stability and control of maglev vehicle–girder coupled system considering torsional vibration of the girder

The EMS (Electro-Magnetic Suspension) maglev vehicle uses controlled electromagnetic forces to achieve stable levitation; however, the interactions between the vehicle and the flexible girder may induce strong coupled resonances. Recently, a new type of girder resonance has been encountered, and field measurements indicate that this resonance is caused by torsional vibration of the girder. However, up to now, the principle of the girder torsional resonance has not been studied, and related control strategies have not been developed either. In this paper, a typical maglev girder with a steel track is investigated through finite element analysis, and a searching algorithm is proposed to obtain a best fit of the girder transfer function. Then, a maglev vehicle with twenty levitation control units is considered, and together with the girder model, the vehicle–girder coupled system is established. Factors that affect the coupled resonances are analyzed, and it is found that the velocity feedback of the electromagnet, which is effective to suppress the bending resonance of the girder, may lead to torsional resonance of the girder. This conclusion is validated by experiments in a real maglev system. To solve this problem, a distributed virtual tuned mass damper scheme is discussed, and suggestions to avoid the torsional resonances are also presented. This work not only interprets the principle underlying the vehicle–girder coupled torsional resonance, but also presents a methodology for dealing with the maglev vehicle–girder coupled resonance problems.

Design and Innovative Test of a Linear Induction Motor for Urban MagLev Vehicles

This article presents the design and innovative test of a linear induction motor (LIM) to be used in the urban superconducting magnetic levitated vehicle named MagLev-Cobra. This levitation method, based on the flux pinning property of high-temperature superconductors in the proximity of rare-earth permanent magnets, has constraints related to the lifting forces. This issue is even more critical as there is no control of the levitation gap, which changes according to the load. The motor design is based on analytical equations and computational simulations by finite element methods. An innovative workbench for tests was developed to measure values of interest, such as end effects, forces, electrical currents, magnetic flux densities, and others. Numerical and experimental results support the desired performance of the proposed LIM.

Research on dynamics of a new high-speed maglev vehicle

The levitation bogie of the TR-series maglev vehicle is redesigned by adding an intermediate buffer layer between the levitationbogie and the levitation module to improve the curve negotiation capacity of the high-speed maglev vehicle and reduce the vertical coupleddynamic effect of the vehicle and the track beam. As the existing TR08 maglev vehicle dynamic model has been verified by experiments, anew type of dynamic model of maglev vehicle is constructed by transplanting the functional module of TR08 model. The vehicle-elastic trackbeam coupled dynamic model and the vehicle-curved track dynamic model are established. Simulation analyses of the dynamic response ofvehicles and track beams show that: the curve negotiation capacity of the new-type maglev vehicle is better than that of TR08 type maglevvehicle; the resonance effect does not occur between the vehicle and the track beam; the vertical dynamic displacement of the track beammid-span decreases by 23% compared with the TR08 type; the redesigned levitation bogie structure and the track beam have less dynamicinteraction, indicating that the working environment of the electromagnet in the new maglev vehicle has been improved, which can effectivelyreduce the burden of electrical decoupling of the control system.

RBF Neural Network-Based Supervisor Control for Maglev Vehicles on an Elastic Track With Network Time Delay

When the electromagnetic suspension (EMS) type maglev vehicle is traveling over a track, the airgap must be maintained between the electromagnet and the track to prevent contact with that track. Because of the open-loop instability of the EMS system, the current must be actively controlled to maintain the target airgap. However, the maglev system suffers from the strong nonlinearity, force saturation, track flexibility, and feedback signals with network time-delay, hence making the controller design even more difficult. In this article, the minimum levitation unit of the maglev vehicle system has been established. An amplitude saturation controller (ASC), which can ensure the generation of only saturated unidirectional attractive force, is thus proposed. The stability and convergence of the closed-loop signals are proven based on the Lyapunov method. Subsequently, ASC is improved based on the radial basis function neural networks, and a neural network-based supervisor controller (NNBSC) is thus designed. The ASC plays the main role in the initial stage. As the neural network learns the control trend, it will gradually transition to the neural network controller. Simulation results are provided to illustrate the specific merit of the NNBSC. The hardware experimental results of a full-scale IoT EMS maglev train are included to validate the effectiveness and robustness of the presented control method as regards to time delay.

Instability of vibrations of an oscillator moving at high speed through a tunnel embedded in soft soil

This paper investigates the instability of vertical vibrations of an object moving uniformly through a tunnel embedded in soft soil. Using the indirect Boundary Element Method in the frequency domain, the equivalent dynamic stiffness of the tunnel-soil system at the point of contact with the moving object, modelled as a mass-spring system or as the limiting case of a single mass, is computed numerically. Using the equivalent stiffness, the original 2.5D model is reduced to an equivalent discrete model, whose parameters depend on the vibration frequency and the object’s velocity. The critical velocity beyond which the instability of the object vibration may occur is found, and it is the same for both the oscillator and the single mass. This critical velocity turns out to be much larger than the operational velocity of high-speed trains and ultra-high-speed transportation vehicles. This means that the model adopted in this paper does not predict the vibrations of Maglev and Hyperloop vehicles to become unstable. Furthermore, the critical velocity for resonance of the system is found to be slightly smaller than the velocity of Rayleigh waves, which is very similar to that for the model of a half-space with a regular track placed on top (with damping). However, for that model, the critical velocity for instability is only slightly larger than the critical velocity for resonance (of the undamped system), while for the current model the critical velocity for instability is much larger than the critical velocity for resonance due to the large stiffness of the tunnel and the radiation damping of the waves excited in the tunnel. A parametric study shows that the thickness and material damping ratio of the tunnel, the stiffness of the soil and the burial depth have a stabilising effect, while the damping of the soil may have a slightly destabilising effect (i.e., lower critical velocity for instability). In order to investigate the instability of the moving object for velocities larger than the identified critical velocity for instability, we employ the D-decomposition method and find instability domains in the space of system parameters. In addition, the dependency of the critical mass and stiffness on the velocity is found. We conclude that the higher the velocity, the smaller the mass of the object should be to ensure stability (single mass case); moreover, the higher the velocity, the larger the stiffness of the spring should be when a spring is added (oscillator case). Finally, in view of the stability assessment of Maglev and Hyperloop vehicles, the approach presented in this paper can be applied to more advanced models with more points of contact between the moving object and the tunnel, which resembles reality even better.

Model-based Simulation and Verification on Typical Function Scenes of High-Speed Maglev Vehicle Operation Control System

Under the new situation, high-speed maglev transportation has gradually become the new development direction of the railway field in the future. Its vehicle operation control system (VOCS for short) as a key subsystem has a great impact on the safety and stability of the entire high-speed maglev train control system. The high-speed maglev VOCS has the characteristics of complex system structure and frequent interaction between its modules. Finding hidden safety hazards and design errors in the system design and development process and ensuring the safety and efficiency of system design and development has become an important task of related projects. On this background, modelling and simulation of typical scenarios of high-speed maglev VOCS are absolutely necessary in the early stage of project development, drawing on the traditional wheel-rail vehicle system simulation verification research results, with the help of advanced computer simulation methods. Using Simulink / Stateflow tools for the parking point stepping functional scenario as an example, the validity and correctness of the high-speed maglev VOCS were verified to ensure the operation safety of the high-speed maglev train through.

Design and Implementation of auto-filling liquid nitrogen for HTS maglev vehicles based on Kalman filter algorithm

The cryostat equipped with superconducting materials is one of the most important component of high-temperature superconducting maglev vehicles. However, due to the multiple energy disturbance forms in the cryostat, such as AC losses of superconductors, vibration of the cryostat and so on, the evaporation of liquid nitrogen (LN2) will be stimulated to accelerate, which will seriously threaten the vehicle safety. Therefore, this paper designs an intelligent controller which can realize the function of auto-filling LN2 based on the Kalman filter (KF) algorithm. Moreover, in this publication the corresponding methodology will be described as well in detail. Initially, the platinum resistance sensors were used to study the relationship between the temperature and LN2 level, meanwhile, the system state equation and observation equation were established. Then, the KF algorithm was introduced to estimate the true LN2 level. Based on the feedback signal of LN2 level, the system utilizes the STM32 microprocessor as control chip to control the solenoid valves and realizes the function of auto-filling. The controller has been implemented and the total time for filling one cryostat was reduced from 86 min to 16 min. This result is very encouraging and inspiring for the practical application of HTS maglev systems.

Study on stability and bifurcation of electromagnet-track beam coupling system for EMS maglev vehicle

The stability and bifurcation behavior of the electromagnet-track beam coupling system of the electromagnetic suspension maglev vehicle are studied by the theoretical and numerical analyses. The stability domain of three key dynamics parameters of the track beam as well as the Lyapunov coefficient at the degenerated equilibrium point is calculated. The topological structure of the solution to the coupling system near the Bautin bifurcation point is determined. The results show that in the engineering practice, the intermediate frequency should be avoided in the natural frequency of the track beam; when a low frequency is taken, it should be reduced as much as possible; when a high frequency is taken, it should be increased as much as possible and the damping ratio should also be increased, so that the system can remain stable while a lighter-weight track beam is used, thereby reducing the engineering costs. Besides, when the parameters are near the Bautin bifurcation point, the system will have complex dynamics behaviors. Within a certain parameter range, multiple stable and unstable limit cycles exist simultaneously, so that the system tends to have different stable solutions under different initial disturbances.

Vertical–Lateral Coupling Force Relation of the High-Temperature Superconducting Magnetic Levitation System

A high-temperature superconducting (HTS) magnetic levitation (maglev), based on YBaCuO bulk superconductors and permanent magnet guideways, shows the potential to be applied in the future rail transportation. The maglev forces (levitation and guidance force) of the HTS maglev system, which bond the vehicle and the guideway, are the key factors of its dynamics studies. In practical operation, the HTS maglev vehicle moves in both the vertical and lateral directions, but the previous force models are in single degree of freedom. In this article, an experiment was designed to study the vertical-lateral coupled effect of the levitation and guidance force. A 2-D coupling model was proposed to fit the experimental data. Furthermore, the motion stability and the dynamical characteristics of the HTS maglev system in 2-D space were studied. The simulation results show that the vertical-lateral coupling effect in maglev forces cannot be neglected, and one direction motion can affect the motion in the other direction. It also shows that the proposed force model is suitable for HTS maglev dynamics' calculations.

Optimized Linear Motor for Urban Superconducting Magnetic Levitation Vehicles

The normal force that exists between primary and secondary of a linear motor plays an important role in Magnetically Levitated (MagLev) trains. In the particular case of the superconducting magnetic levitation (SML) method, based on the diamagnetic property of high-temperature superconductors (HTS) in the proximity of rare-earth permanent magnets, this issue is even more critical, as there is no control of the levitation gap, which changes according to the load. In this article, the previous experience of traction systems of MagLev trains in commercial operation serves as a background for the study and will be reviewed. The experience of other SML projects will also be considered to reach the proposed topology, similarly to the process of genetic evolution. The proposed solution for the normal force issue consists of a linear induction motor (LIM) optimized for an urban SML vehicle. Analytical equations and simulations with the finite element method (FEM) are presented. An innovative workbench for velocity tests was developed to measure the parameters of interest. Simulation and experimental results confirm the improved performance of the proposed LIM. The final results with the short primary LIM, designed and tested, showed excellent results. The LIM can be qualified as 3 times low: low-cost solution, for low-speed SML vehicles, and with low-normal force amplitudes.