Motion stability of high-speed maglev systems in consideration of aerodynamic effects: a study of a single magnetic suspension system

In this study, the intrinsic mechanism of aerodynamic effects on the motion stability of a high-speed maglev system was investigated. The concept of a critical speed for maglev vehicles considering the aerodynamic effect is proposed. The study was carried out based on a single magnetic suspension system, which is convenient for proposing relevant concepts and obtaining explicit expressions. This study shows that the motion stability of the suspension system is closely related to the vehicle speed when aerodynamic effects are considered. With increases of the vehicle speed, the stability behavior of the system changes. At a certain vehicle speed,the stability of the system reaches a critical state, followed by instability. The speed corresponding to the critical state is the critical speed. Analysis reveals that when the system reaches the critical state, it takes two forms, with two critical speeds, and thus two expressions for the critical speed are obtained. The conditions of the existence of the critical speed were determined, and the effects of the control parameters and the lift coefficient on the critical speed were analyzed by numerical analysis. The results show that the first critical speed appears when the aerodynamic force is upward,and the second critical speed appears when the aerodynamic force is downward. Moreover, both critical speeds decrease with the increase of the lift coefficient.

Vibration characteristics of a multi-block high-temperature superconducting maglev system

The multi-block high-temperature superconducting （HTS） maglev system has more complicated dynamic characteristics than the single-block HTS maglev system. To study its vibration characteristics, we designed a maglev measurement system. The system responses at the excitation frequencies of 2, 3 and 15 Hz were examined. Results show that the responses under excitation frequencies of 2 and 3 Hz include a 6 Hz component, which means that the maglev system is a critical nonlinear system. Moreover, the 6 Hz component is much stronger than the 2 Hz or 3 Hz components in the response spectra. There is the interaction between excitation and response. Under an excitation frequency of 15 Hz, intensified low-frequency perturbations were observed.

Computation and Analysis of Propellant and Levitation Forces of a Maglev System Using FEM Coupled to External Circuit Model

This paper studies the propellant and levitation forces of a prototype maglev system where the propellant forces are provided by a linear motor system. For this purpose, the mathematical model and method using finite element method coupled to external circuit model is developed. The details of the propellant and levitation forces for a prototype maglev system under different operating conditions are investigated, and some directions are given for practical engineering applications.

Sliding Mode Control with Auto-Tuning Law for Maglev System

This paper presents a control strategy for maglev system based on the sliding mode controller with auto-tuning law. The designed adaptive controller will replace the conventional sliding mode control (SMC) to eliminate the chattering resulting from the SMC. The stability of maglev system is ensured based on the Lyapunov theory. Simulation results verify the effectiveness of the proposed method. In addition, the advantages of the proposed controller are indicated in comparison with a traditional sliding mode controller.

A novel refined dynamic model of high-speed maglev train-bridge coupled system for random vibration and running safety assessment

Running safety assessment and tracking irregularity parametric sensitivity analysis of high-speed maglev train-bridge system are of great concern,especially need perfect refinement models in which all properties can be well characterized based on various stochastic excitations.A three-dimensional refined spatial random vibration analysis model of high-speed maglev train-bridge coupled system is established in this paper,in which multi-source uncertainty excitation can be considered simultaneously,and the probability density evolution method(PDEM)is adopted to reveal the system-specific uncertainty dynamic characteristic.The motion equation of the maglev vehicle model is composed of multi-rigid bodies with a total 210-degrees of freedom for each vehicle,and a refined electromagnetic force-air gap model is used to account for the interaction and coupling effect between the moving train and track beam bridges,which are directly established by using finite element method.The model is proven to be applicable by comparing with Monte Carlo simulation.By applying the proposed stochastic framework to the high maglev line,the random dynamic responses of maglev vehicles running on the bridges are studied for running safety and stability assessment.Moreover,the effects of track irregularity wavelength range under different amplitude and running speeds on the coupled system are investigated.The results show that the augmentation of train speed will move backward the sensitive wavelength interval,and track irregularity amplitude influences the response remarkably in the sensitive interval.

Disturbance decoupled fault diagnosis for sensor fault of maglev suspension system

A disturbance decoupled fault diagnosis strategy is proposed.This disturbance decoupled fault diagnosis is both robust to disturbances and sensitive to sensor faults of magnetic levitation control system.First,a robust controller based on a novel disturbance observer is devised to improve the disturbance attenuation ability,which greatly enhances the robustness of the system.Second,a fault reconstruction technique with adaptive method is presented,along with a strict verification for guaranteeing the robustness of fault.This fault reconstruction technique provides an accurate sensor fault reconstruction.From the results of simulation and experiments conducted on the CMS-04 maglev train,the integrated strategy is robust to model uncertainties of the system and the fault reconstruction algorithm is able to reconstruct the dynamic uncertain faults.

A practical robust nonlinear controller for maglev levitation system

In order to explore the precise dynamic response of the maglev train and verify the validity of proposed controller,a maglev guideway-electromagnet-air spring-cabin coupled model is developed in the first step.Based on the coupled model,the stresses of the modules are analyzed,and it is pointed 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 the maglev engineering.Furthermore,a feedback linearization controller based on the mathematical model of a maglev module is derived,in which the nonlinearity,coupling and misalignments are taken into account.Then,to attenuate the effect of external disturbances,a disturbance observer is proposed and the dynamics of the estimation error is analyzed using the input-to-state stability theory.It shows that the error is negligible under a low-frequency disturbance.However,at the high-frequency range,the error is unacceptable and the disturbances can not be compensated in time,which lead to over designed fluctuations of levitation gap,even a clash between the upper surface of electromagnet and lower surface of guideway.To solve this problem,a novel nonlinear acceleration feedback is put forward to enhancing the attenuation ability of fast varying disturbances.Finally,numerical comparisons show that the proposed controller outperforms the traditional feedback linearization controller and maintains good robustness under disturbances.

Vibration analysis of maglev three-span continuous guideway considering control system

The dynamic interaction between maglev vehicle and three-span continuous guideway is discussed. With the consideration of control system, the dynamic interaction model has been developed. Numerical simulation has been performed to study dynamic characteristics of the guideway. The results show that bending rigidity, vehicle speed, span ratio and primary frequency all have important influences on the dynamic characteristics of the guideway and there is no distinct trend towards resonance vibration when fl/（v/l） equals 1.0. The definite way is to control impact coefficient and acceleration of the guideway. The conclusions can serve the design of high-speed maglev three-span continuous guideway.

Coupling vibration analysis of high-speed maglev train-viaduct systems with control loop failure

The risk of failure of the control loop can occur when a high-speed maglev train runs on viaduct.Meanwhile,the failure of the levitation magnets which balances the gravity of the maglev train could cause the train collision with track.To study the dynamic response of the train and the viaduct when the levitation magnet control loop failure occurs,a high-speed maglev train-viaduct coupling model,which includes a maglev controller fitted by measured force-gap data and considers the actual structure of train and viaduct,is established.Then the accuracy and effectiveness of the established approach are validated by comparing the computed dynamic responses and frequencies with the measurement results.After that,the dynamic responses of maglev train and viaduct are discussed under normal operation and control loop failures,and the most disadvantageous combination of control loop failures is obtained.The results show that when a single control loop fails,it only has a great influence on the failed electromagnet,and the maglev response of adjacent electromagnets has no obvious change and no collision occurs.But there is a risk of rail collisions when the dual control loop fails.

Levitation mechanism modelling for maglev transportation system

A novel maglev transportation system was proposed for large travel range ultra precision motion.The system consists of a levitation subsystem and a propulsion subsystem.During the propulsion subsystem driving the moving platform along the guideway,the levitation subsystem uses six pairs of electromagnets to steadily suspend the moving platform over the guideway.The model of the levitation system,which is a typical nonlinear multi-input multi-output coupling system and has many inner nonlinear coupling characteristics,was deduced.For testifying the model,the levitation mechanism was firstly controlled by proportional-integral-differential(PID) control,and then a lot of input-output data were collected for model parameter identification.The least-square parameter identification method was used.The identification results prove that the model is feasible and suitable for the real system.

Self-excited vibration problems of maglev vehicle-bridge interaction system

The self-excited vibration problems of maglev vehicle-bridge interaction system were addressed, which greatly degrades the stability of the levitation control, decreases the ride comfort, and restricts the cost of the whole system. Firstly, the coupled model containing the quintessential parts was built, and the mechanism of self-excited vibration was explained in terms of energy transmission from levitation system to bridge. Then, the influences of the parameters of the widely used integral-type proportion and derivation(PD) controller and the delay of signals on the stability of the interaction system were analyzed. The result shows that the integral-type PD control is a nonoptimal approach to solve the self-excited vibration completely. Furthermore, the differential-type PD controller can guarantee the passivity of levitation system at full band. However, the differentiation of levitation gap should be filtered by a low-pass filter due to noise of gap differentiation. The analysis indicates that a well tuned low-pass filter can still keep the coupled system stable.

Experimental investigation on vibration characteristics of the medium-low-speed maglev vehicle-turnout coupled system

The steel turnout is one of the key components in the medium–low-speed maglev line system.However,the vehicle under active control is prone to vehicle–turnout coupled vibration,and thus,it is necessary to identify the vibration characteristics of this coupled system through field tests.To this end,dynamic performance tests were conducted on a vehicle–turnout coupled system in a medium–low-speed maglev test line.Firstly,the dynamic response data of the coupled system under various operating conditions were obtained.Then,the natural vibration characteristics of the turnout were analysed using the free attenuation method and the finite element method,indicating a good agreement between the simulation results and the measured results;the acceleration response characteristics of the coupled system were analysed in detail,and the ride quality of the vehicle was assessed by Sperling index.Finally,the frequency distribution characteristics of the coupled system were discussed.All these test results could provide references for model validation and optimized design of medium–low-speed maglev transport systems.

Vibration Analysis of Continuous Maglev Guideway Considering the Magnetic Levitation System

The dynamic interaction between moving vehicles and two-span continuous guideway was discussed. With the consideration of the magnetic levitation system, the maglev vehicle/guideway dynamic interaction model was developed. Numerical simulation was performed to understand dynamic characteristics of the guideway used in practice. The results show that vehicle speed, span length and primary frequency of the guideway have an important influence on the dynamic responses of the guideway and there is no distinct trend towards resonance vibration when fl equals 1.0. The definite way is to control the impact coefficient and acceleration of the guideway. The conclusions can serve the design of high speed maglev guideway.

μ-Syntheses of Suspension Systems for EMS and EDS Maglev Vehicles

Under model uncertainty and complex disturbance, the robust control strategy should be used in suspension control systems for various Maglev vehicles to obtain ride comfort of passengers. In this paper, the robust controllers are synthesized using μ approach for levitation system of electromagnetic Maglev vehicle and active suspension system of super conducting Maglev vehicle. The numerical simulations for different parameter perturbations and different disturbances are accomplished, and a comparison of μ control and H ∞ control is performed. The simulation results show that, both H ∞ control and μ control for two kinds of Maglev vehicles exhibit good stability robustness to plant model uncertainty, but μ control exhibits better performance robustness than H ∞ control, therefore better ride quality could be obtained by μ control.

A Permanent Magnet Linear Synchronous Motor Drive for HTS Maglev Transportation Systems

A permanent magnet linear synchronous motor （PMLSM） for a high temperature superconducting （HTS） maglev system has been studied, including the motor structure, control strategy, and analysis techniques. Finite element analysis （FEA） of magnetic field is conducted to accurately calculate major motor parameters. Equivalent electrical circuit is used to predict the drive＇s steady-state characteristics, and a phase variable model is applied to predict the dynamic performance. Preliminary experiment with a prototype has been made to verify the theoretical analysis and the HTS-PM synchronous driving technology.

Design of relative position sensing system for high-speed maglev train

In the high-speed maglev system,accurate real-time information of the train position is essential forstable,safe and efficient train operation.To detect the relative position of the high-speed maglev trainfrom a reference position,a location method based on long stator slot detection was proposed.Besides,aprototype system has been successfully developed.The hardware structure of the system,as well as itsworking principle was described.Moreover,a subdivision algorithm for calculating the pole location anglesignal was elucidated.Experiments show that the proposed method is feasible.The technical indexes ofthe detection system satisfy the requirements of the vehicle operation control system.The relative positionsensing system can be put into practice.

A nonlinear control method for the electromagnetic suspension system of the maglev train

To deal with the inherent nonlinearity and open-loop instability of the electromagnetic suspension（EMS） system,a new nonlinear control method is proposed.The simulation results show that,for a PID controller,the over-shoot of the system response to an airgap step disturbance is about 3 mm,and the transient time is 6 s;however,for the proposed nonlinear controller,there is no overshoot and transient time within 2 s.The proposed method has a faster response and stronger robustness.With a designed bi-DSP suspension controller,this nonlinear control method was implemented on the Shanghai Urban Maglev Test Line（SUMTL） to validate its effectiveness and feasibility.

Research on the H_∞ Controller Synthesis for Maglev Suspension System

The performances of a single magnet model, which is the simplified model of Maglev suspension, are analyzed. The H ∞ controller synthesized for the single magnet model is presented. The synthesis results show that the control performance and robustness performance are satisfactory and the application of the H ∞ controller to Maglev suspension is feasible and effective.

Aerodynamic Features of High-Speed Maglev Trains with Different Marshaling Lengths Running on a Viaduct under Crosswinds

The safety and stability of high-speed maglev trains traveling on viaducts in crosswinds critically depend on their aerodynamic characteristics.Therefore,this paper uses an improved delayed detached eddy simulation(IDDES)method to investigate the aerodynamic features of high-speed maglev trains with different marshaling lengths under crosswinds.The effects of marshaling lengths(varying from 3-car to 8-car groups)on the train’s aerodynamic performance,surface pressure,and the flow field surrounding the train were investigated using the three-dimensional unsteady compressible Navier-Stokes(N-S)equations.The results showed that the marshaling lengths had minimal influence on the aerodynamic performance of the head and middle cars.Conversely,the marshaling lengths are negatively correlated with the time-average side force coefficient(CS)and time-average lift force coefficient(Cl)of the tail car.Compared to the tail car of the 3-car groups,the CS and Cl fell by 27.77%and 18.29%,respectively,for the tail car of the 8-car groups.It is essential to pay more attention to the operational safety of the head car,as it exhibits the highest time average CS.Additionally,the mean pressure difference between the two sides of the tail car body increased with the marshaling lengths,and the side force direction on the tail car was opposite to that of the head and middle cars.Furthermore,the turbulent kinetic energy of the wake structure on the windward side quickly decreased as marshaling lengths increased.