Disturbance rejection tube model predictive levitation control of maglev trains

Magnetic levitation control technology plays a significant role in maglev trains.Designing a controller for the levitation system is challenging due to the strong nonlinearity,open-loop instability,and the need for fast response and security.In this paper,we propose a Disturbance-Observe-based Tube Model Predictive Levitation Control(DO-TMPLC)scheme combined with a feedback linearization strategy for the levitation system.The proposed strategy incorporates state constraints and control input constraints,i.e.,the air gap,the vertical velocity,and the current applied to the coil.A feedback linearization strategy is used to cancel the nonlinearity of the tracking error system.Then,a disturbance observer is implemented to actively compensate for disturbances while a TMPLC controller is employed to alleviate the remaining disturbances.Furthermore,we analyze the recursive feasibility and input-to-state stability of the closed-loop system.The simulation results indicate the efficacy of the proposed control strategy.

Research on modeling and self-excited vibration mechanism in magnetic levitation-collision interface coupling system

The modeling and self-excited vibration mechanism in the magnetic levitation-collision interface coupling system are investigated.The effects of the control and interface parameters on the system's stability are analyzed.The frequency range of self-excited vibrations is investigated from the energy point of view.The phenomenon of self-excited vibrations is elaborated with the phase trajectory.The corresponding control strategies are briefly analyzed with respect to the vibration mechanism.The results show that when the levitation objects collide with the mechanical interface,the system's vibration frequency becomes larger with the decrease in the collision gap;when the vibration frequency exceeds the critical frequency,the electromagnetic system continues to provide energy to the system,and the collision interface continuously dissipates energy so that the system enters the self-excited vibration state.

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.

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.

Structure analysis of levitation chassis of medium-to-low speed maglev vehicles based on left-right decoupling

Levitation chassis, as an extremely important component of maglev vehicles, provides functions of transmitting levitation force and steering force, and directly affects the safety performance of the vehicle. Based on the vertical dynamics model of the levitation chassis, kinetic equations of the model are established, and a simulation program is designed to analyze the structural decoupling function of the chassis, especially under the influence of elastic constraints between the left and right modules, which are exclusively owned by maglev vehicles. A finite element model of the levitation chassis based on left-right decoupling is constructed. Analysis results of the model show that the mechanical properties of the chassis tailored for the vehicle meet the design requirements, and the stiffness and strength is adequate to bear the weight of the whole vehicle.

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.

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.

Levitation force analysis of medium and low speed maglev vehicles

The rule of levitation force variation with different structure and electromagnetic parameters provides a basis for electromagnet design of electromagnetic suspension （EMS） medium and low speed maglev vehicles. In order to acquire accurate calculation results of levitation force, different calculation methods, including analytical method, 2D FEM （finite element method）, and 3D FEM, are applied to investigate the impact of various structural parameters, such as excitation current, air gap, lateral offset, and pole width, on levitation force. The analytical analysis is based on the classic mathematical model of levitation force between electromagnet and rail and performed with MATLAB. In the 2D and 3D FEMs, the numerical calculation of the levitation force is conducted with Ansoft by taking the magnetic saturation into account. In addition, the longitudinal end effect on the levitation force calculation is considered in the 3D FEM. The results show that the 3D FEM is the most accurate among the above three methods for calculating the levitation force, and the analytical method can only work for small current and/or large air gap conditions. A lateral- offset between vehicle and rail will reduce the levitation force; the levitation force descends sharply once the lateral offset exceeds the threshold, i.e., 8% of the pole width for U-shaped electromagnets. The maximum lift-to-weight ratio emerges when the pole width ratio of F type rail to electromagnet is 6：7. This may offer a reference for EMS maglev vehicle design and application.

Modeling and Validation of Diamagnetic Rotor Levitated by Permanent Magnetics

As an innovative,low-power consuming,and low-stiffness suspension approach,the diamagnetic levitation technique has attracted considerable interest because of its potential applicability in miniaturized mechanical systems.The foundation of a diamagnetic levitation system is mathematical modeling,which is essential for operating performance optimization and stability prediction.However,few studies on systematic mathematical modeling have been reported.In this study,a systematic mathematical model for a disc-shaped diamagnetically levitated rotor on a permanent magnet array is proposed.Based on the proposed model,the magnetic field distribution characteristics,diamagnetic levitation force characteristics(i.e.,levitation height and stiffness),and optimized theoretical conditions for realizing stable levitation are determined.Experiments are conducted to verify the feasibility of the proposed mathematical model.Theoretical predictions and experimental results indicate that increasing the levitation height enlarges the stable region.Moreover,with a further increase in the rotor radius,the stable regions of the rotor gradually diminish and even vanish.Thus,when the levitation height is fixed,a moderate rotor radius permits stable levitation.This study proposes a mathematical modeling method for a diamagnetic levitation system that has potential applications in miniaturized mechanical systems.

Efficient loading of cesium atoms in a magnetic levitated dimple trap

We report a detailed study of magnetically levitated loading of ultracold ^(133)Cs atoms in a dimple trap.The atomic sample was produced in a combined red-detuned optical dipole trap and dimple trap formed by two small waist beams crossing a horizontal plane.The magnetic levitation for the ^(133)Cs atoms forms an effective potential for a large number of atoms in a high spatial density.Dependence of the number of atoms loaded and trapped in the dimple trap on the magnetic field gradient and bias field is in good agreement with the theoretical analysis.This method has been widely used to obtain the Bose–Einstein condensation atoms for many atomic species.

Effective method to control the levitation force and levitation height in a superconducting maglev system

The influence of the width of the middle magnet in the permanent magnet guideways （PMGs） on the levitation force and the levitation height of single-domain yttrium barium copper oxide （YBCO） bulks has been investigated at 77 K under the zero field cooled （ZFC） state. It is found that the largest levitation force can be obtained in the system with the width of the middle magnet of the PMG equal to the size of the YBCO bulk when the gap between the YBCO bulk and PMG is small. Both larger levitation force and higher levitation height can be obtained in the system with the width of the middle magnet of the PMG larger than the size of the YBCO bulk. The stiffness of the levitation force between the PMG and the YBCO bulk is higher in the system with a smaller width of the middle magnet in the PMG. These results provide an effective way to control the levitation force and the levitation height for the superconducting maglev design and applications.

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.

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.

Study on Dynamic Characteristics of Superconducting Electrodynamic Maglev Train

This study considers a superconducting electrodynamic maglev train of MLX01 type.The characteristics of the electromagnetic spring coefficient of a single bogie under different magnetomotive force(MF) of the superconducting coil and standard air gap(Sag) were explored.In view of the small electromagnetic damping,a passive damping control strategy and an active damping control strategy were designed to increase the electromagnetic damping force between the superconducting coil and ground coil.Combined with the coupling numerical model of a single bogie,the vibration characteristics of the bogie in different directions with different damping control strategies were studied when the Sag and MF were fixed.The results can provide important theoretical support for stable operation control of maglev trains.

Control of magnetic levitation positioning stage with an eddy current damper

To enhance the system damping,a permanent magnet set which served as an eddy current damper was added to the magnetic levitation positioning stage which consists of a moving table,four Halbach permanent magnetic arrays,four stators and displacement sensors.The dynamics model of this stage was a complex nonlinear,strong coupling system which made the control strategy to be a focus research.The nonlinear controller of the system was proposed based on the theory of differential geometry.Both simulation and experimental results show that either the decoupling control of the movement can be realized in horizontal and vertical directions,and the control performance was improved by the damper,verifying the validity and efficiency of this method.

Levitation现象研究进展

漂浮(Levitation)现象可以定义为这样一种稳定情况,即在垂直振荡流体中颗粒的重力被完全抵消而仅在某一固定位置附近做振荡运动。作者分析了国内外研究现状,综述了以往学者对该现象进行的实验研究、理论分析以及数值模拟等工作。通过对Levitation现象研究文献的综述,总结了以往学者的一些研究成果,分析了他们所开展的研究之间的共性和分歧,在此基础上提出了目前对Levitation现象研究需解决的问题并对Levitation现象今后研究需要进一步解决的问题做了探讨。

A practical nonlinear controller for levitation system with magnetic flux feedback

This work proposes a practical nonlinear controller for the MIMO levitation system. Firstly, the mathematical model of levitation modules is developed and the advantages of the control scheme with magnetic flux feedback are analyzed when compared with the current feedback. Then, a backstepping controller with magnetic flux feedback based on the mathematical model of levitation module is developed. To obtain magnetic flux signals for full-size maglev system, a physical method with induction coils installed to winding of the electromagnet is developed. Furthermore, to avoid its hardware addition, a novel conception of virtual magnetic flux feedback is proposed. To demonstrate the feasibility of the proposed controller, the nonlinear dynamic model of full-size maglev train with quintessential details is developed. Based on the nonlinear model, the numerical comparisons and related experimental validations are carried out. Finally, results illustrating closed-loop performance are provided.

ELECTROMAGNETIC MODEL OF LEVITATION MELTING WITH COLD CRUCIBLE

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Physical Properties of Liquid Terbium Measured by Levitation Techniques

To understand the nature and behavior of rare earth metals in their liquid phases, accurate values of their physical properties are essential. However, to measure their physical properties, the samples should be maintained in liquid phases for prolonged time, and this raises a formidable challenge. This is mainly explained by their high melting temperatures （e.g., 1629 K for Tb）, high vapor pressure, and the risk of melt contamination with a crucible or support. An electrostatic levitation furnace alleviated these difficulties and allowed the determination of density, surface tension, and viscosity of several metals above their melting temperature. Here, first, the levitation furnace facility and the noncontact diagnostic procedures were briefly discussed, followed by the explanation of their thermophysical property measurements over wide temperature ranges. The density was obtained using an ultraviolet-based imaging technique that allowed excellent illumination, even at elevated temperatures. Over the 1615 to 1880 K temperature span, the density measurements could be expressed as p（T） =7.84 × 10^3 -0.47 （T - Tm） （kg · m^-3） with Tm = 1629 K, yielding a volume expansion coefficient a（T） = 6.0 × 10^-5 （K^-1）. In addition, the surface tension and the viscosity could be determined by inducing a drop oscillation to a molten sample. Using this technique, the surface tension data could be expressed as σ（T） = 8.93 × 10^2 - 0.10 （T - Tm）（mN· m^-1） and those for viscosity as η（T） =0.583 exp [4.1 × 10^4/（RT）] （MPa·s） over the 1690 to 1980 K temperature range

THE ELECTROMAGNETIC FIELD CALCULATION AND ANALYSIS OF LEVITATION MELTING WITH COLD CRUCIBLE

In this paper, using the quasi-3D coupled current method, the influences of structure of cold crucible, the power frequency, the electricity property of melt, the coil position and current on the electromagnetic field (EMF) and the levitation characteristics in the melting processes are analyzed. It is shown that in the processes of levitation melting with cold crucible, the power frequency and cold crucible structure are the decisive factors for the ability of magnetic flux penetrating into cold crucible. The magnetic flux density in cold crucible is reduced as the increasing of power frequency, and this tendency becomes stronger when the power frequency is higher than 100kHz. The segmented structure of cold crucible can reduce the induction eddy in itself effectively, and the higher the power frequency is, the better the result is. So, a cold crucible can be segmented into 16-20 sectors for high frequency electromagnetic field and/or 8-12 sectors for lower frequency one. It is also shown that the levitation force of melting charge is related to coil current as a parabolic function.