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Different from common cylindrical magnetic bearings, the spherical radial AC HMB has obvious advantages in suppressing the gyroscopic effect, thus it is very suitable for application in flywheel battery systems. In this study, a precise mathematical model of suspension forces is deduced adopting wide-area and universal modeling theories in detail for the spherical radial AC HMB. Different from the traditional Maxwell tensor method based on a cylindrical two-dimensional coordinate system, the improved Maxwell tensor method based on a spherical coordinate system has a wider range and versatility. Then, the detailed explanation about the accuracy, wide-area and universality are given. Further, based on the model, the control system is designed, which includes the overall schematic, hardware and software designs. Finally, stiffness and performance tests are conducted. The good results of the stiffness tests indicate the error between the proposed model and the force-deflection stiffness test results is less than 2.8%. The good performance test results show that, based on the established model and control system, the rotor will soon return to equilibrium position under the disturbance of vehicle action. [ABSTRACT FROM AUTHOR]

At present, the stability study of the flywheel battery system under the influence of road conditions is only limited to the analysis of dynamic characteristics but also lacks effective controller considering road disturbances. In order to solve this defect and further improve the robust performance of vehicular flywheel battery systems under road disturbances, a robust controller considering interference of road surface roughness is proposed. Firstly, on the basis of a brief introduction to flywheel battery system structure, the influence degree of the flywheel by road condition is compared to find the key areas most affected by road disturbance factors. Then the nonlinear dynamic model of the axial suspension system is constructed, and the actual road surface roughness is regarded as the unmodeled dynamics of the external disturbance emphatically. Following, the established unknown system dynamics is approximated by radial basis function (RBF) neural network based on the minimum parameter learning method, the control input is generated by sliding-mode control law, and the weight adjustment of neural network is replaced by the designed adaptive law of parameter estimation. The effects of different levels of road surface roughness on the system are simulated, and the robustness of the proposed controller is verified based on the Lyapunov method. Finally, the experimental platform to simulate road disturbances is designed ingeniously. Experimental results show that the proposed controller can make the flywheel battery system have good robustness under different road conditions. [ABSTRACT FROM AUTHOR]

A nonlinear magnetic suspension system is considered in this paper. A novel online algorithm based on analytical approach is presented to stabilize the suspended mass. The new algorithm employs a single analytical function to create the ball position and velocity profiles. The reference ball position is described by a series of time dependent exponential functions. Boundary conditions at both initial and final states are automatically satisfied. Moreover, feasible ball position and velocity profiles are ensured by evaluating one algorithm parameter (an exponential factor). The exponential factor is analytically computed by minimizing the peak of electrical power. This new algorithm is capable of generating the well-suited coil voltage that guarantees the stability of the system with a small closed-loop command. Gain Shechting method is used to obtain the closed-loop effort in order to track the analytical reference profiles. Compared to the prior magnetic suspension algorithms, the proposed analytical scheme is qualified to handle very large dispersions in initial ball position while satisfying the ball position and coil voltage constraints. Monte-Carlo simulations with change in initial ball position are presented. The simulation results demonstrated the great reliable performance of the proposed algorithm despite the wide range of initial ball position dispersions.

Sliding Mode Control (SMC) is a robust control strategy that is insensitive to system uncertainties and external disturbances. It is widely used in designing controllers, observers and differentiators. However, the inevitable chattering problem affects the SMC applications in real-life engineering. This paper presents an improved SMC algorithm based on discrete second-order time optimal control (TOC). The proposed algorithm adopts a simple method to calculate the distance from the state variable to the sliding surface, and it can adjust the linear or nonlinear control law according to the calculated distance. On the other hand, the control law deviation in the two-step reachable region is corrected. The improved control algorithm shortens the convergence time and reduces the chattering problem of the system. It is applied to the design of magnetic suspension controllers. This allows the system to achieve a fast, accurate and stable suspension target when the system has external disturbances and internal parameter perturbations.

Different from common cylindrical magnetic bearings, the spherical radial AC HMB has obvious advantages in suppressing the gyroscopic effect, thus it is very suitable for application in flywheel battery systems. In this study, a precise mathematical model of suspension forces is deduced adopting wide-area and universal modeling theories in detail for the spherical radial AC HMB. Different from the traditional Maxwell tensor method based on a cylindrical two-dimensional coordinate system, the improved Maxwell tensor method based on a spherical coordinate system has a wider range and versatility. Then, the detailed explanation about the accuracy, wide-area and universality are given. Further, based on the model, the control system is designed, which includes the overall schematic, hardware and software designs. Finally, stiffness and performance tests are conducted. The good results of the stiffness tests indicate the error between the proposed model and the force-deflection stiffness test results is less than 2.8%. The good performance test results show that, based on the established model and control system, the rotor will soon return to equilibrium position under the disturbance of vehicle action.

In this article, a magnetic suspension technique was introduced into the field of vibration absorption. Using the advantage of adjustable control parameters of a magnetic suspension system, a type of a magnetic suspension dynamic vibration absorber that can achieve broadband vibration suppression was designed. First, the theoretical model of a magnetic suspension dynamic vibration absorber was established. Then, the cantilever beam with sinusoidal excitation is seen as the main system of vibration suppression; combined with the fixed point theory (Seto K (2013) Dynamic Vibration Absorber and its Application. Mechanic Industry Press), the specific structure of the magnetic suspension dynamic vibration absorber was designed. Based on that, the simulation study of vibration suppression performance of the magnetic suspension dynamic vibration absorber was carried out. The results indicated that the vibration of the main system at the 1st modal frequency was reduced by 65.38% under the action of the magnetic suspension dynamic vibration absorber, compared with that without the action of the magnetic suspension dynamic vibration absorber. Furthermore, the vibration of the main system can be suppressed in the frequency band of [16 Hz, 32 Hz]. Finally, a vibration test rig of the magnetic suspension dynamic vibration absorber was built up for experimental study. And the results showed that the absorber can decrease the vibration of the main system by 43.03% at the 1st modal frequency compared with that without the action of magnetic suspension dynamic vibration absorber and had a certain suppression effect (decrease varies from 0 to 43.03%) on the vibration of the main system in the frequency band of [20 Hz, 32 Hz]. [ABSTRACT FROM AUTHOR]

At present, the stability study of the flywheel battery system under the influence of road conditions is only limited to the analysis of dynamic characteristics but also lacks effective controller considering road disturbances. In order to solve this defect and further improve the robust performance of vehicular flywheel battery systems under road disturbances, a robust controller considering interference of road surface roughness is proposed. Firstly, on the basis of a brief introduction to flywheel battery system structure, the influence degree of the flywheel by road condition is compared to find the key areas most affected by road disturbance factors. Then the nonlinear dynamic model of the axial suspension system is constructed, and the actual road surface roughness is regarded as the unmodeled dynamics of the external disturbance emphatically. Following, the established unknown system dynamics is approximated by radial basis function (RBF) neural network based on the minimum parameter learning method, the control input is generated by sliding-mode control law, and the weight adjustment of neural network is replaced by the designed adaptive law of parameter estimation. The effects of different levels of road surface roughness on the system are simulated, and the robustness of the proposed controller is verified based on the Lyapunov method. Finally, the experimental platform to simulate road disturbances is designed ingeniously. Experimental results show that the proposed controller can make the flywheel battery system have good robustness under different road conditions.

This paper proposes a new type of noncontact magnetic suspension system using two permanent magnets driven by rotary actuators. The paper aims to explain the proposed concept, configuration of the suspension system, and basic analyses for feasibility by FEM analyses. Two bar-shaped permanent magnets are installed as they are driven by rotary actuators independently. Attractive forces of two magnets act on the iron ball which is located under the magnets. Control of the angles of two magnets can suspend the iron ball stably without mechanical contact and changes the position of the ball. FEM analyses have been carried out for the arrangement of two permanent magnets and forces are simulated for noncontact suspension. Hence, successfully the required enough force against the gravity of the iron ball can be generated and controlled. Control of the horizontal force is also confirmed by the rotation of the permanent magnets. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to propose a GSA-tuning IPD control technique for magnetic suspension systems. An educational demonstration on a magnetic-field sensed magnetic suspension system is examined for effectiveness. For the magnetic-field sensed magnetic suspension system (FSMSS), the current transducer is employed for measuring the electromagnetic coil current, and a Hall effect device is used for detecting the position of the suspended object. To achieve optimal performance, the gravitational search algorithm (GSA) is adopted for tuning the integral-proportional-derivative (IPD) controller. The IPD control includes the specified PD controller and an integrator. The specified PD control is employed for stabilizing the inherently unstable FSMSS, whereas the integral control is utilized for eliminating the steady-state error. The GSA can tune the IPD control parameters to enable optimal FSMSS performance. We achieved excellent results from the simulations and hands-on experiments for the proposed control strategies and structures.

Magnetic suspension systems are mechatronic systems and crucial in several engineering applications, such as the levitation of high-speed trains, frictionless bearings, and wind tunnels. Magnetic suspension systems are nonlinear and unstable systems; therefore, they are suitable educational benchmarks for testing various modeling and control methods. This paper presents the digital modeling and control of magnetic suspension systems. First, the magnetic suspension system is stabilized using a digital proportional-derivative controller. Subsequently, the digital model is identified using recursive algorithms. Finally, a digital mixed linear quadratic regulator (LQR)/H∞ control is adopted to stabilize the magnetic suspension system robustly. Simulation examples and a real-world example are provided to demonstrate the practicality of the study results. In this study, a digital magnetic suspension system model was developed and reviewed. In addition, equivalent state and output feedback controls for magnetic suspension systems were developed. Using this method, the controller design for magnetic suspension systems was simplified, which is the novel contribution of this study. In addition, this paper proposes a complete digital controller design procedure for magnetic suspension systems.

In order to asymptotically track the desired trajectory of nonlinear systems with unidirectional control input under various uncertainties, a modified saturated learning-based control law with adaptive notch filter (ANF) is presented in this paper. The proposed control law ensures the asymptotic convergence of the tracking error by utilizing a saturated function and a repetitive learning-based estimator, which allows the learning of the periodic dynamic behavior of the nonlinear system online to make compensations. Simultaneously, an ANF is integrated with the proposed control law to estimate the frequency of the periodic dynamics online. Differing from the existing methodologies in the literatures, the control law proposed in this paper only requires the unknown dynamics be bounded (the parameters, structure, and period of the unknown dynamics is not required to be known). Finally, applying the proposed control law to the electromagnetic suspension system, simulation, and experimental results are included to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A method of suppressing vibration in lateral directions is investigated based on varying stiffness strategy. A vertically controlled magnetic suspension system is often subjected to vibration in lightly damped lateral directions. In this paper, a novel approach is proposed to detect the lateral displacement of such magnetic suspension system, and how this displacement can be used to reduce vibration by varying stiffness control is presented. The principle of edge effect is applied to detect the lateral displacement in a magnetic suspension system operated in differential mode. A switching stiffness control and a modified control strategies are used to vary the stiffness of the system in order to reduce lateral vibration. Several experiments are carried out to validate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper describes 2 types of 2 DOF magnetic suspension systems which suspend two iron balls or an iron stick type object. Both suspension system controls 2 DOF of suspended object(s). The magnetic suspension forces are controlled by a generator of magnetomotive force. This suspension system must control two degrees of freedom without mechanical contacts. In iron stick suspension system, a vertical displacement and a horizontal rotation of the object should be controlled. This paper proves the feasibility of these noncontact suspension systems. A theoretical analysis will be done on the model of these suspension systems and numerical simulations carried out for confirmation of performances. [ABSTRACT FROM AUTHOR]

In this paper, a model based intelligent PID controller tuning is attempted for a Magnetic Suspension System (MSS) using Bacterial Foraging Optimization (BFO) algorithm. MSS is an Electro- Mechanical system with highly non linear dynamics and exhibits unstable steady state behavior around the nominal operating range. In this work, Integral Time Absolute Error (ITAE) based performance criterion is employed to guide the BFO to search the optimized controller parameters such as Kp, Ki, and Kd. The work is substantiated through a comparative study with Particle Swarm Optimization (PSO) algorithm by using PID and modified PID controller structure. The effectiveness of the proposed scheme has been validated with a simulation study and the results show that the proposed method provides better result in the control of the unstable MSS system with effective setpoint tracking and load disturbance rejection. [ABSTRACT FROM AUTHOR]

The objective of this paper were to determine by computer simulation and laboratory test the dynamic characteristics of a Sliding mode controller in magnetic levitation (Maglev) systems. In maglev trains, magnetic suspension system is required to operate over large variations in air gap. As a result, the nonlinearities inherent in most types of suspensions have a significant impact on performance. Specifically, it may be difficult to design a linear controller which gives satisfactory performance, stability, and disturbance rejection over a wide range of operating points. One way to solve this problem is through the use of nonlinear control techniques such as Sliding mode control. In this paper a sliding controller is proposed for controlling the two groups of electromagnets embed in the module of the maglev train and the superiority of nonlinear controllers over conventional controllers for systems with large variations in operating point via simulations and experiments on our system is demonstrated. Simulations and experiments show that the controller can effectually control double-electromagnet suspension system. [ABSTRACT FROM AUTHOR]

This work presents a newly developed six-axis magnetic suspension stage for precision motion control. The designed travel volume is 4×4×2 mm in translation and 1°×1°×2° in rotation. A dynamic model of the feedback linearized and uncoupled stage is developed for the purpose of motion control. Model parameter variations are demonstrated through closed-loop system identification. In motion control, a parameter variation model is proposed in conjunction with a reduced order observer to compensate the joined effect of disturbance, modeling error, and cross coupling. Experimental results in terms of positioning stability, motion resolution, rotational motion control, model regulation, large travel multiaxis contouring, and disturbance rejection are shown. Uniform positioning stability and invariant dynamic response within the designed travel volume are illustrated. [ABSTRACT FROM PUBLISHER]

Magnetically suspended frictionless manipulator is designed to improve the resolution and position accuracy. In order to increase the dynamic stability, the magnetically suspended manipulator is constructed using push-and-push forces. Using the force analysis, the design and modeling processes of the manipulator are achieved. The proposed modeling process is experimentally verified from free vibration of the manipulator. Comparison is made between the natural frequencies from the modeled dynamic equation and those from experimentally obtained. [ABSTRACT FROM AUTHOR]