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.

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).

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.

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.

A novel superconducting magnetic levitation method to support the laser fusion capsule by using permanent magnets

A novel magnetic levitation support method is proposed, which can relieve the perturbation caused by traditional support methods andprovide more accurate position control of the capsule. This method can keep the perfect symmetry of the octahedral spherical hohlraum and hasthe characteristics in stability, tunability and simplicity. It is also favorable that all the results, such as supporting forces acting on the super-conducting capsule, are calculated analytically, and numerical simulations are performed to verify these results. A typical realistic design isproposed and discussed in detail. The superconducting coating material is suggested, and the required superconducting properties are listed.Damped oscillation of the floating capsule in thin helium gas is discussed, and the restoring time is estimated.

Research on magnetic levitation absolute vibration measurement method in vehicles

This paper presents a design for a magnetic levitation absolute- vibration test system which can be used by vehicles to measure the road surface roughness. The relationship between the vibration test system output voltage and measured speed of the object was obtained through testing,the power spectrum of the measured signal was obtained by virtual instrument analysis,the vibration waveforms of the vehicle over gentle and steep slopes were measured respectively and the road surface roughness was obtained by waveform analysis. Data was saved where the waveforms exceeded threshold. Finally,the steep slope was located using a GPS system. Experimental results show that the magnetic levitation absolute- vibration measurement method has characteristics of high sensitivity and a wide frequency range. This lays the foundation for research into multi- dimensional vibration measurements through magnetic levitation vibration test systems in vehicles.

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.

UAQ4 Magnetic Levitating Train： Propulsion System for Urban Transportation

This paper discusses the design of the propulsion system of the UAQ4 （University of L＇Aquila, model 4） magnetic levitating train which is used for transportation applications in urban environments. UAQ4 is the only magnetic levitating vehicle with resistance motion, except for aerodynamic drag and with energy consumption near zero at low speed. The feasibility of the system has been successfully verified and tested in the laboratory. Propulsion and braking are provided by a novel direct-current linear stepper motor, with the primary formed by permanent magnets distributed on central beam of the track, and the secondary by coils on board the vehicle, instead of the present alternate current linear motors that have well-known disadvantages. The motor working principles are described, and its performances are analyzed, by a finite element numerical model which allows modifying the most important parameters of the system. The main components of a full scale motor for urban transportation are measured and discussed.

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.

STABILITY ANALYSES ON DYNAMIC CONTROL FOR A MOVING BODY LEVITATED MAGNETICALLY OVER ELASTIC GUIDEWAYS

Based on the Floquet theory on ordinary differential equationswith periodically variable coefficients and the bifurcation approachto nonlinear equations, a numerical approach to determining thestability region of control parameters is established for a dynamiccontrol system composed of a moving body levitated magnetically overflexible guideways. The system is nonlinearly coupled among theelastic deformation of guideways, disturbance the levitation positionof the body and electromagnet- ic control forces.

Vibration Measurement of Pedestrian Bridge Using Double Magnetic Suspension Vibrator Based on Wavelet Analysis

Aiming at the problem of pedestrian bridge vibration measurement,a vibration measurement system of pedestrian bridge with dual magnetic suspension vibrator structure was designed according to absolute vibration measurement principle. The relationship between the magnetic repulsion force of vibrator and its displacement was obtained by the experimental method and the least square fitting method. The vibration equations of two magnetic suspension vibrators were deduced respectively,and the measurement sensitivity of the system was deduced. The amplitude-frequency characteristic of the system was studied. A simulation model of vibrator measurement system with double magnetic suspension vibrator was established. The analysis shows that the sensitivity of the vibration measurement system with double magnetic suspension vibrator is higher than that with single magnetic suspension vibrator. The four vibration waveforms were measured,that is,no one passes through a pedestrian bridge,there are cars running under the pedestrian bridge,single pedestrian passes through the pedestrian bridge and multiple pedestrians pass through the pedestrian bridge. The multi-scale one-dimensional wavelet decomposition function was used to analyze the vibration signals. The vibration characteristics were obtained using one dimension wavelet decomposition function under four different conditions. Finally,the vibration waveforms of four cases were reconstructed. The measured results show that the vibration measurement system of pedestrian bridge with double magnetic suspension vibrator structure has high measurement sensitivity. The design has a certain value to monitor a pedestrian bridge.

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.

Current-Bounded Commutation of a Long-Stroke Magnetically Levitated Stage with Moving Coils

Magnetically levitated stages（MLS） have potentials to obtain good motion performances in high vacuum environment. Yet the electromagnetic forces/torques corresponding to six degrees of freedom（DOF） motions have coupling relationship with each current of coil array, and this coupling is still associated with the relative positions between the mover and the stator of the stage. So it is quite difficult to control the 6-DOF motions of the stage. By reasonable commutation of coil array, this complicated coupling relationship can be decoupled. The analytical force/torque-decomposing model of the stage is established first. Then the initial currents of coil array are commutated based on the pseudo inverse of the analytical force/torque-decomposing model matrix. And then the coil array currents are commutated again with different current bounds given to the initial currents as well as in the sense of minimum 2-norm of currents vector. Using the long stroke magnetically levitated stage with moving coils under investigation as examples, the currents of coil array are commutated with different current bounds adopting the proposed commutation method, the determination of current bound and the current bounds＇ influences on the heat-losses in coil array are analyzed, and the effectiveness of implementation algorithm of proposed commutation method is discussed. Simulation, analysis and discussion results indicate that the currents of coil array within the given current bound can be solved analytically by proposed commutation method, and the implementation algorithm does not need any searching or iteration. By the current-bounded commutation method proposed, the amplitude of coil array currents can be limited within an appropriate current bound（This is very beneficial to the improvement of the reliability and motion performance of the stage）, as well as these currents can also generate the desired forces and torques.

VERTICAL NONCONTACT POSITIONING H_∞ ROBUST CONTROL FOR MAGNETICALLY LEVITATED SURFACE MOTOR

To fulfill the stringent requirement, super-precision positioning and ultra cleanness, a surface motor with the integrated chip fabrication equipment is constructed by using permanent magnets and electromagnet coils as primary actuating components. It consists of stator and mover, and the mover is isolated from the stator by the magnetic beating. The magnetic bearing in the stator is composed of eight air core electromagnet coils, the propulsion in the stator is composed of iron core and electromagnetic coils, and the mover is composed of NdFeB permanent magnets and levitated stage. Based on Lorentz law, some parameters, including permanent magnets dimensions, currents and levitation height, which may affect the stability, are analyzed and optimized. To improve the positioning accuracy in the vertical direction of the magnetic levitation surface motor, a robust controller is proposed using H∞ mixed sensitivity control theory. The simulation results show that by choosing appropriate weight functions, the controller can ensure the robustness of the closed loop system under the presence of uncertainties, and the H∞ robust controller is excellent for reducing steady error and increasing response speed.

Excessive levitation for the efficient loading of large-volume optical dipole traps

We study the excessive levitation effect in the magnetically levitated loading process of ultracohl Cs atoms into a large-volume crossed optical dipole trap. We analyze the motion of atoms with a non-zero combined gravito-magnetic force during the loading, where the magnetically levitated force catches up with and surpasses the gravity. We present the theoretical variations of both acceleration and velocity with levitation time and magnetic field gradient. We measure the evolution of the number of trapped atoms with the excessive levitation time at different magnetic field gradients. The dependence of the number of atoms on the magnetic field gradient is also measured for different excessive levitation times. The theoretical analysis shows reasonable agreement with the experimental results. Our investigation illustrates that the excessive levitation can be used to reduce the heating effect of atoms in the magnetically levitated loading process, and to improve the loading rate of a large-volume optical dipole trap.

Development of a Small Scale Magnetically Levitated Train as Demonstrator for Undergraduate Mechatronics Students

At the Institute of Electrical Machines of the Rheinisch Westfalilische Technische Hochschule Aachen University, there is a project financed by student fees for the realization of a magnetically levitated train in the scale of 1：50. Undergraduate students are supposed to get the possibility to design and build up a real train which serves as demonstrator for a mechatronic system. This project strengthens the motivation of students, since a practical demonstration of electromagnetic forces is given in addition to theoretical courses. This paper introduces the major project steps and explains the learning targets for the students. It focuses on analytical magnetic circuit design, numerical field simulation, modeling and control of a multi degree of freedom system, electronic circuit design, measurement setups and a first prototype test bench.

Seismic Response of Magnetically Levitated House

This study explored the seismic response of a house supporting base sides with a polymeric displacement control material and by magnetically levitating the foundation base. In this paper, we explore the possibility and efficacy of a seismic-isolated detached house as described above from both a shaking table experiment of model and three-dimensional finite element analysis. The seismic-isolated model showed stable response and its acceleration response was significantly reduced compared to the base-fixed model in the shaking table test. Three-dimensional finite element analysis was possible to simulate the experimental results. In the seismic response analysis of a full-scale detached house, the seismic-isolated model showed response reduction and its residual displacement was smaller than that of the sliding-base isolation model.

Magnetic levitation using diamagnetism:Mechanism,applications and prospects

As a typical contact-free manipulation technique that removes friction and contamination risk,levitation has gradually become a preferred candidate for various applications.Magnetic levitation using diamagnetism,beyond Earnshaw’s theorem,is a kind of passive stable levitation that can be achieved at normal temperatures with no energy input.Appealingly,most seemingly nonmagnetic materials can be levitated in a magnetic field and can stabilize free levitation of magnetic materials.This review focuses on the fundamental principles of magnetic levitation using diamagnetism,with emphasis on its burgeoning applications.The theoretical basis associated with the magnetic levitation using diamagnetism is discussed by elucidating the characteristics of diamagnetic materials,and the key levitation mechanisms are clarified.Afterwards,state-of-the-art applications in various aspects,including sensing and measurement,actuating and micromanipulation,energy harvesting and magnetic gravity compensation,are summarized and compared.Finally,the review concludes with a brief outlook on future perspectives.