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.

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.

Design and Implementation of Digital Fractional Order PID Controller Using Optimal Pole-Zero Approximation Method for Magnetic Levitation System

The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(MLS),which is inherently nonlinear and unstable system.The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller.An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored.The controller parameters are tuned using dynamic particle swarm optimization(d PSO)technique.Effectiveness of the proposed control scheme is verified by simulation and experimental results.The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers.It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance.

Maximization of Acoustic Levitating Force for a Single-Axis Acoustic Levitation System Using the Finite Element Method

We investigate single-axis acoustic levitation using standing waves to levitate particles freely in a medium bounded by a driver and a reflector. The acoustic pressure at the pressure antinode of the standing wave counteracts the downward gravitational force of the levitating object. The optimal relationship between the air gap and the driving frequency leads to resonance and hence maximization of the levitating force. Slight deviation from the exact resonance condition causes a reduction in acoustic pressure at the pressure antinodes. This results in a significant reduction of the levitating force. The driving frequency is kept constant while the air gap is varied for different conditions. The optimal air gap for maximizing the levitation force is studied for first three resonance modes. Furthermore, a levitating particle is introduced between the driver and the reflector. The dependence of the resonance condition on the size of the levitating particle as well as the position of the particle between the driver and the reflector has also been studied. As the size of the levitating particle increases, the resonance condition also gets modified. Finite element results show a good agreement with the validated results available in the literature. Furthermore, the finite element approach is also used to study the variation of acoustic pressure at the pressure antinode with respect to the size of the reflector. The optimum diameter of the reflector is calculated for maximizing the levitating force for three resonance modes.

Lateral magnetic stiffness under different parameters in a high-temperature superconductor levitation system

Magnetic stiffness determines the stability of a high-temperature superconductor(HTS)magnetic levitation system.The quantitative properties of the physical and geometrical parameters that affect the stiffness of HTS levitation systems should be identified for improving the stiffness by some effective methods.The magnetic stiffness is directly related to the first-order derivative of the magnetic force with respect to the corresponding displacement,which indicates that the effects of the parameters on the stiffness should be different from the relationships between the forces and the same parameters.In this paper,we study the influences of some physical and geometrical parameters,including the strength of the external magnetic field(B0)produced by a rectangular permanent magnet(PM),critical current density(Jc),the PM-to-HTS area ratio(α),and thickness ratio(β),on the lateral stiffness by using a numerical approach under zero-field cooling(ZFC)and field cooling(FC)conditions.In the first and second passes of the PM,the lateral stiffness at most of lateral positions essentially increases with B0 increasing and decreases withβincreasing in ZFC and FC.The largest lateral stiffness at every lateral position is almost produced by the minimum value of Jc,which is obviously different from the lateral force–Jc relation.Theα-dependent lateral stiffness changes with some parameters,which include the cooling conditions of the bulk HTS,lateral displacement,and movement history of the PM.These findings can provide some suggestions for improving the lateral stiffness of the HTS levitation system.

An improvement of frozen-image model and its application in a HTS levitation system

This paper mainly reports an improvement of frozen-image model which can qualitatively describe the influence of lateral moving speed on vertical force in a HTS levitation system under lateral movement with field-cooling condition.The model is improved by introducing a dipole which represents the influence of lateral moving speed and modifying the rule of diamagnetic dipole based on frozen-image model.The vertical and lateral forces that are obtained by this improved model agree with the previous measurements qualitatively.This model can also describe the effect of finite scale of superconductor sample in a levitation system.

Dynamic Analysis of Micro-machined Diamagnetic Stable Permanent Magnet Levitation System

A novel micro-machined diamagnetic stable.levitation system （MDSLS） which is composed of a free permanent magnetic rotor, a ring lifting permanent magnet and two diamagnetic stabilizers was presented. The static and dynamic stable characters of MDSLS were analyzed. The coupled non-linear differential equations were used to describe six-degree-of-freedom motion of the levitated rotor, and the equivalent surface current and combined dia- magnetic image current method were utilized to model the interaction forces and torques between the lifting perma- nent magnet and rotor permanent magnet and also between the rotor permanent magnet and diamagnetic sub- strates. Because of difficulty to get analytical solution, the numerical calculation based on Runge-Kutta method was used to solve the dynamic model. The vibration frequencies were identified b~ fast Fourier transform （FFT） analysis. According to their resonance characteristics and parameters, the translational and angular dynamic stiff- ness were also calculated. The results show that the levitation of the rotor in MDSLS is stable, and the MDSLS is potential for the application in levitation inertial sensor.

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.

Decentralized control design and implementation for magnetic levitation systems with extended state observer

This paper focuses on control design and synthesize for a class of magnetic levitation systems,which have a decentralized control for each suspension point.Due to the existence of mechanical coupling among four suspension points,large modeling uncertainties,unpredictable disturbances during the operation,and measurement noises,becomes challenging.To estimate and compensate for the effects of lumped uncertainties,this study employs the extended state observer(ESO)in conjunction with active disturbance rejection control(ADRC).Specifically,a novel ESO is proposed that utilizes output signals and their derivatives to estimate the lumped uncertainties more accurately,which simplifies the convergence proof conditions and has well engineering performance.This article is written in honor of B.M.Chen on the occasion of his 60th birthday.Specifically,this paper is inspired by his pioneering work on composite nonlinear feedback,which combines linear feedback and nonlinear compensator to enhance system performance Chen et al.(IEEE Trans Autom Control,40:427-439,2003).

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.

Miniature optical force levitation system

Optical levitation technology is a new levitation technology for trapping micro/nano-particles.By taking advantage of the mechanical effect of light,it has the characteristics of non-contact and high sensitivity.However,the traditional optical levitation system is large in volume,complex in adjustment,and greatly affected by the external environment.Herein,a miniature optical levitation system based on a laser diode,miniature lenses,and a micro-electro-mechanical system(MEMS) particles cavity is proposed.First,we analyze the output spot characteristics of the laser diode.Being compared the characteristics of different kinds of laser diodes,the type,wavelength,and power of diodes in the levitation system are determined.Then,the micro-particles cavity is fabricated based on the MEMS process.The MEMS process is widely used in the manufacturing of micro-electronic devices because of its advantages of small size,high precision,and easy mass production.The particle cavity processed in this way can not only ensure the advantage of small volume,but also possesses high processing repeatability.The volume of the entire package including the light source,focusing lenses,and MEMS cavity is just Φ10 mm×33 mm,which is the smallest optical levitation system reported,to the best of our knowledge.After the entire levitation system is designed and set up,one silica particle of 10 μm diameter is stably trapped in the atmospheric environment.Finally,the micro-displacement and vibration signal are detected by a four-quadrant photoelectric detector to evaluate the stiffness of the optical levitation system.

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.

Design and Development of Impeller Synergic Systems of Electromagnetic Type to Levitation/Suspension Flight of Symmetrical Bodies

Using certain models of twistor surfaces for fields of force and the mathematical relationships that lie among fields, lines, surfaces and flows of energy, it has been designed and developed a flight electromagnetic type system based on the synergic study of their electromagnetic field geodesics to generate vehicle levitation, suspension and movement without being in contact with the surface. The idea of such work is to obtain a new flight and impulse patent of an electromagnetic vehicle by principles of super-conduction and some laws of the current like Eddy currents and principles which are very similar to mechanics of sidereal objects like galaxies or stars under models of twistor surfaces. This vehicle will be controlled by one microchip that will be programmed by conscience operators algebra of electromagnetic type that leads to the flow of Eddy currents, the iso-rotations and suspension of the special geometrical characteristics vehicle, generating also on the vehicle structure certain “magnetic conscience” that provokes all movements like succeeding to the sidereal objects in the universe.

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.

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.

Single-axis ultrasound levitation system with annular clamping forces

Based on the principle of acoustic levitation,a single-axis ultrasonic levitation system(SAULS) with convex sides was designed.A normal SAULS only provides a levitation force(LF) against the gravity of the sample.While,such systems also provide an annular clamping force(ACF) surrounding the levitated samples,and improve levitation stability of samples in the standing wave field.Using the finite-difference time-domain method,we investigated the force distributions in different resonance cavities and the factors that influence the magnitude of the levitation force in optimizing the SAULS and the ACF.The theoretical analyses and experimental results indicate that the stability of levitation in this special SAULS is improved with the ACF from its designed convex-side feature.It can be developed into a simple device in levitating and moving samples steadily in related experiments and applications.

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.

Controllability and Observability of 2-DOF Permanent Magnet Maglev System with Linear Control

A new type of 2-DOF(degree of freedom) magnetic levitation system for multi-DOF levitation is proposed. In this system, the force of permanent magnets are used for levitation and controlled by adjusting the reluctance of the magnetic circuit. Using permanent magnets, the feature of this system is effective for saving energy and avoiding heat generation. First, the principle of the levitation system and typical reluctance control methods are described. Second, an experimental device based on the principle is introduced. Finally, the feasibility of this system is considered from linear control theory.

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。