Vibration Suppression for Active Magnetic Bearings Using Adaptive Filter with Iterative Search Algorithm

Active Magnetic Bearing(AMB) is a kind of electromagnetic support that makes the rotor movement frictionless and can suppress rotor vibration by controlling the magnetic force. The most common approach to restrain the rotor vibration in AMBs is to adopt a notch filter or adaptive filter in the AMB controller. However, these methods cannot obtain the precise amplitude and phase of the compensation current. Thus, they are not so effective in terms of suppressing the vibrations of the fundamental and other harmonic orders over the whole speed range. To improve the vibration suppression performance of AMBs,an adaptive filter based on Least Mean Square(LMS) is applied to extract the vibration signals from the rotor displacement signal. An Iterative Search Algorithm(ISA) is proposed in this paper to obtain the corresponding relationship between the compensation current and vibration signals. The ISA is responsible for searching the compensating amplitude and shifting phase online for the LMS filter, enabling the AMB controller to generate the corresponding compensation force for vibration suppression. The results of ISA are recorded to suppress vibration using the Look-Up Table(LUT) in variable speed range. Comprehensive simulations and experimental validations are carried out in fixed and variable speed range, and the results demonstrate that by employing the ISA, vibrations of the fundamental and other harmonic orders are suppressed effectively.

Research on heat dissipation characteristics of magnetic fluid bearings under multiple field coupling effects

This paper analyzes the sources of heat losses in magnetic fluid bearings,proposes various cou-pling relationships of physical fields,divides the coupled heat transfer surfaces while ensuring the continuity of heat flux density,and analyzes the overall heat dissipation pathways of the bearings.By changing parameters such as input current,rotor speed,and inlet oil flow rate,the study applies a multi-physics field coupling method to investigate the influence of different parameters on the temper-ature field and heat dissipation patterns of the bearings,which is then validated through experi-ments.This research provides a theoretical basis for the optimal design of magnetic fluid bearing sys-tems.

Control System Design for Low PowerMagnetic Bearings in a Flywheel Energy Storage System

This paper presents a theoretical and experimental study on controller design for the AMBs in a small-scale flywheel energy storage system,where the main goals are to achieve low energy consumption and improved rotordynamic stability.A H-infinity optimal control synthesis procedure is defined for the permanent-magnet-biased AMB-rotor system with 4 degrees of freedom.Through the choice of design weighting functions,notch filter characteristics are incorporated within the controller to reduce AMB current components caused by rotor vibration at the synchronous frequency and higher harmonics.Experimental tests are used to validate the controller design methodology and provide comparative results on performance and efficiency.The results show that the H-infinity controller is able to achieve stable rotor levitation and reduce AMB power consumption by more than 40%(from 4.80 to 2.64 Watts)compared with the conventional PD control method.Additionally,the H-infinity controller can prevent vibrational instability of the rotor nutation mode,which is prone to occur when operating with high rotational speeds.

Unbalance Vibratory Displacement Compensation for Active Magnetic Bearings

As the dynamic stiffness of radial magnetic bearings is not big enough, when the rotor spins at high speed, unbalance displacement vibration phenomenon will be produced. The most effective way for reducing the displacement vibration is to enhance the radial magnetic bearing stiffness through increasing the control currents, but the suitable control currents are not easy to be provided, especially, to be provided in real time. To implement real time unbalance displacement vibration compensation, through analyzing active magnetic bearings （AMB） mathematical model, the existence of radial displacement runout is demonstrated. To restrain the runout, a new control scheme-adaptive iterative learning control （A1LC） is proposed in view of rotor frequency periodic uncertainties during the startup process. The previous error signal is added into AILC learning law to enhance the convergence speed, and an impacting factor/3 influenced by the rotor rotating frequency is introduced as learning output coefficient to improve the rotor control effects, As a feed-forward compensation controller, AILC can provide one tmknown and perfect compensatory signal to make the rotor rotate around its geometric axis through power amplifier and radial magnetic bearings. To improve AMB closed-loop control system robust stability, one kind of incomplete differential PID feedback controller is adopted. The correctness of the AILC algorithm is validated by the simulation of AMB mathematical model adding AILC compensation algorithm through MATLAB soft. And the compensation for fixed rotational frequency is implemented in the actual AMB system. The simulation and experiment results show that the compensation scheme based on AILC algorithm as feed-forward compensation and PID algorithm as close-loop control can realize AMB system displacement minimum compensation at one fixed frequency, and improve the stability of the control system. The proposed research provides a new adaptive iterative/earning control algorithm and control strategy for AMB displacement minimum compensation, and provides some references for time-varied displacement minimum compensation.

Real-time Feed-forward Force Compensation for Active Magnetic Bearings System Based on H∞ Controller

There are two kinds of unbalance vibrations—force vibration and displacement vibration due to the existence of unbalance excitation in active magnetic bearings（AMB） system. And two unbalance compensation methods—closed-loop feedback and open loop feed-forward are presented to reduce the force vibration. The transfer function order of the control system directly influencing the system stability will be increased when the closed-loop method is adopted, which makes the real-time compensation not easily achieved. While the open loop method would not increase the primary transfer function order, it provides conditions for real-time compensation. But the real-time compensation signals are not easy to be obtained in the open loop method. To implement real-time force compensation, a new method is proposed to reduce the force vibration caused by the rotor unbalance on the basis of AMB active control. The method realizes real-time and on-line force auto-compensation based on H∞ controller and one novel feed-forward compensation controller, which makes the rotor rotate around its inertia axis. The time-variable feed-forward compensatory signal is provided by a modified adaptive variable step-size least mean square（VSLMS） algorithm. And the relevant least mean square（LMS） algorithm parameters are used to solve the H∞ controller weighting functions. The simulation of the new method to compensate some frequency-variable and sinusoidal signals is completed by MATLAB programming, and real-time compensation is implemented in the actual AMB experimental system. The simulation and experiment results show that the compensation scheme can improve the robust stability and the anti-interference ability of the whole AMB system by using H∞ controller to achieve close-loop control, and then real-time force unbalance compensation is implemented. The proposed research provides a new control strategy containing real-time algorithm and H∞ controller for the force compensation of AMB system. And the stability of the control system is finally improved.

CONTROL SYSTEM OF MAGNETIC BEARINGS BASED ON LINEAR QUADRATIC METHOD OF OPTIMAL CONTROL STRATEGY

A state equation for radical 4-degree-of-freedom active magnetic bearings isbuilt, and the approach on how to use linear quadratic method of optical control theory to design acentralized and decentralized parameters control system is introduced, and also Matlab language isused to simulate and analyze. The simulation results have proved that the differences are smallbetween centralized parameters and decentralized parameters control system. The conclusions ofexperiments have shown that decentralized controllers designed from optimal state feedback theorymeet the requirements of active magnetic bearing system. The vibration amplitude of the rotor isabout 20 mu m when the speed of the rotor runs between 0 to 60 000 r/min. This method may be used inthe study and design of controllers of magnetic bearings.

Design and Analysis of a Magnetic Bearings with Three Degrees of Freedom

The current research of supporting and transmission system in flywheel energy storage system(FESS) focuses on the low consumption design. However, friction loss is a non-negligible factor in the high-speed but lightweight FESS energy and momentum storage with mechanical-type supporting system. In order to realize the support system without mechanical loss and to maximize the e ciency of the flywheel battery, a permanent magnet biased magnetic bearings(PMBMB) is applied to the FESS with the advantages of low loss, high critical speed, flexible controllability and compact structure. In this frame, the relevant research of three degrees of freedom(3-DOF) PMBMB for a new type FESS is carried out around the working principle, structural composition, coupling characteristics analysis, mathematical model, and structural design. In order to verify the performance of the 3-DOF PMBMB, the radial force mathematical model and the coupling determination equations of radial two DOF are calculated according to an equivalent magnetic circuit, and radial–axial coupling is analyzed through finite element analysis. Moreover, a control system is presented to solve the control problems in practical applications. The rotor returns to the balanced position in 0.05 s and maintains stable suspension. The displacement fluctuation is approximately 40 μm in the y direction and 30 μm in the x direction. Test results indicate that the dynamic rotor of the proposed flywheel energy storage system with PMBMB has excellent characteristics, such as good start-of-suspension performance and stable suspension characteristics. The proposed research provides the instruction to design and control a low loss support system for FESS.

STUDY ON THE COUPLED ELECTROMECHANICAL DYNAMICS OF ROTOR SYSTEM EQUIPPED WITH MAGNETIC BEARINGS

The influences of thrust magnetic bearing and journal tilt on dynamiccharacteristics of rotor system are studied mainly. The Outcome shows that the influences ofcoupling effects of thrust magnetic bearing and tilt of journal on critical rotational speeds ofsystem are very large, and the stability of system reduces greatly. That shows it is important thatthe influence of coupling effects of thrust and radial magnetic bearings due to the rotor tiltingmust be considered in the study of rotor-magnetic bearings system dynamic characteristics, and alsoshows it is important that the rotor is mounted and debugged in ideal alignment of magneticbearings.

TRANSIENT RESPONSE OF FLEXIBLE ROTOR WITH ACTIVE MAGNETIC BEARINGS DURING ROTOR DROP

A new technique so-called finite modes condensation based on modal analysis is presented to simplify a long and complicated rotor system with distributed mass into a simplified rotor model with adjustablenumber of degrees of freedom. By means of this new method, a practical example study shows that it can bedone to calculate transient response for any cross-section of a flexible rotor with enough accuracy during itsdrop in case that there exist several active magnetic bearings and traditional bearings.

A Study on the Levitation Control of the Multi-degrees-of-Freedom Rotational Machine Supported by Magnetic Bearings Using Flux Feedback

This paper deals with an open-loop characteristic of a magnetically levitated system including flux feedback. In order to design a controller to obtain a good disturbance rejection and to be insensitive to parameter variations, it might be useful to employ a flux feedback loop. The air gap flux which can be sensed by a proper sensor has linear relationship with respect to the change of the current and the air gap. This linear property decreases the inherent nonlinearity of the magnetic suspension system that is caused by the coupling between the electrical actuator and the mechanical plant. Simulation results achieved from a multi-degree-of-freedom numerical model show that the flux feedback loop makes an improvement of the performance of the magnetic suspension system against the load variations.

COMPENSATION CONTROL OF REAL-TIME UNBALANCE FORCE FOR ACTIVE MAGNETIC BEARING SYSTEM

Aiming at the stability and others properties of active magnetic bearing （AMB） system influenced by the periodic unbalance stimulation synchronous with rotor rotational speed, a new real-time adaptive feed-forward unbalance force compensation scheme is proposed based on variable step-size least mean square（LMS） algorithm as the feed-forward compensation controller. The controller can provide some suitable sinusoidal signals to com- pensate the feedback unbalance response signals synchronous with the rotary frequency, then reduce the fluctua- tion of the control currents and weaken the active control of AMB system. The variable step-size proportional to the rotational frequency is deduced by analyzing the principle of normal LMS algorithm and its deficiency in the application of real-time filtering of AMB system. Experimental results show that the new method can implement real-time unbalance force compensation in a wide frequency band, reduce the effect of unbalance stimulant force on the housing of AMB system, and provide convenience to improve rotational speed.

Modeling and Analysis of Novel Integrated Radial Hybrid Magnetic Bearing for Magnetic Bearing Reaction Wheel

Conventional ball bearing reaction wheel used to control the attitude of spacecraft can＇t absorb the centrifugal force caused by imbalance of the wheel rotor,and there will be a torque spike at zero speed,which seriously influences the accuracy and stability of spacecraft attitude control.Compared with traditional ball-bearing wheel,noncontact and no lubrication are the remarkable features of the magnetic bearing reaction wheel,and which can solve the high precision problems of wheel.In general,two radial magnetic bearings are needed in magnetic bearing wheel,and the design results in a relatively large axial dimension and smaller momentum-to-mass ratios.In this paper,a new type of magnetic bearing reaction wheel（MBRW） is introduced for satellite attitude control,and a novel integrated radial hybrid magnetic bearing（RHMB） with permanent magnet bias is designed to reduce the mass and minimize the size of the MBRW,etc.The equivalent magnetic circuit model for the RHMB is presented and a solution is found.The stiffness model is also presented,including current stiffness,position negative stiffness,as well as tilting current stiffness,tilting angular position negative stiffness,force and moment equilibrium equations.The design parameters of the RHMB are given according to the requirement of the MBRW with angular momentum of 30 N ？ m ？ s when the rotation speed of rotor reaches to 5 kr/min.The nonlinearity of the RHMB is shown by using the characteristic curves of force-control current-position,current stiffness,position stiffness,moment-control current-angular displacement,tilting current stiffness and tilting angular position stiffness considering all the rotor position within the clearance space and the control current.The proposed research ensures the performance of the radial magnetic bearing with permanent magnet bias,and provides theory basis for design of the magnetic bearing wheel.

RESEARCH ON CONTROL OF FLYWHEEL SUSPENDED BY ACTIVE MAGNETIC BEARING SYSTEM WITH SIGNIFICANT GYROSCOPIC EFFECTS

Traditional PID controllers are no longer suitable formagnetic-bearing-supported high-speed flywheels with significant gyroscopic effects. Becausegyroscopic effects greatly influence the stability of the flywheel rotor, especially at highrotational speeds. Velocity cross feedback and displacement cross feedback are used to overcomeharmful effects of nutation and precession modes, and stabilize the rotor at high rotational speeds.Theoretical analysis is given to show their effects. A control platform based on RTLinut and a PCis built to control the active magnetic bearing (AMB) system, and relevant results are reported.Using velocity cross feedback and displacement cross feedback in a closed loop control system, theflywheel successfully runs at over 20000 r/min.

MATLAB WEB SERVER AND ITS APPLICATION IN REMOTE COLLABORATIVE DESIGN OF MAGNETIC BEARING SYSTEMS

Acclimatizing itself to the development of network,Math Works Inc constructed a MATLAB Web Server environment by dint of which one can browse the calculation and plots of MATLAB through Internet directly.The installation and use of the environment is introduced.A code established on the platform of MATLAB,which deals with the modal analysis of magnetic bearing system(MBS) supporting rotors of five degrees of freedom and considering the coupling of thrust bearing with radical bearings is modified to work in the environment.The purpose is to realize a remote call of the code by users through Internet for the performance analysis of the system.Such an application is very important to the concurrent design of MBS and for the utilization of distributive knowledge acquisition resources in collaborative design.The work on modification and realization is described and the results are discussed.

UNBALANCE RESPONSE AND TOUCH-RUBBING THRESHOLD SPEED OF ROTOR SUBJECTED TO NONLINEAR MAGNETIC FORCES

Because of the effect of unbalance excitation and nonlinear magnetic force, the large vibration of the rotor supported by active magnetic bearing（AMB） will go beyond the radial gap of the bearing, even causing mechanical touch-rubbing when the system works at an operational speed closer to the critical speed. In order to investigate this problem, the linear model and nonlinear model of the single mass symmetric rigid rotor system supported by AMB are established respectively and the corresponding transfer functions of close-loop system are given. To pass through the numerical calculation by using MATLAB/Simulink, the effect of both the unbalance response and threshold speed of touch-rubbing of the system subjected to nonlinear magnetic forces and nonlinear output current of power amplifier are studied. Furthermore, threshold speed of touch-rubbing of the rotor-bearing system is defined and the results of numerical simulation are presented. Finally, based on above studies, two methods of increasing the touch-rubbing threshold speed are discussed.

Estimation of optimum operating point for thrust magnetic bearing with solid magnet

A carrying capacity-temperature rise analysis model has been established for analysis of the carrying capacity, temperature rise and carrying capacity-temperature rise characteristic of a thrust magnetic bearing with solid magnet. The results indicate that there must be an optimal operating point for the thrust magnetic bearing with solid magnet. The main factors having effect on carrying capacity-temperature rise include static gap and/or ampere-turns. With proper static gap chosen, the bearing can be run near the optimal operating point by adjhusting ampere-turns, thereby optimizing the bearing properties.

Analysis on Dynamic Performance for Active Magnetic Bearing-Rotor System

In the application of active magnetic bearings (AMB), one of the key problems to be solved is the safety and stability in the sense of rotor dynamics. The project related to the present paper deals with the method for analyzing bearing rotor systems with high rotation speed and specially supported by active magnetic bearings, and studies its rotor dynamics performance, including calculation of the natural frequencies with their distribution characteristics, and the critical speeds of the system. One of the targets of this project is to formulate a theory and method valid for the analysis of the dynamic performance of the active magnetic bearing rotor system by combining the traditional theory and method of rotor dynamics with the analytical theory and design method based on modern control theory of the AMB system.

Design Method for the Magnetic Bearing Control System with Fuzzy-PID Approach

The five degree freedom magnetic bearing is researched and its structure and working principles are introduced also. Based on the fuzzy control technology, combining fuzzy algorithm and PID control method, identifying the transition process mode of the online system to get the PID parameters＇ self-adjusting, the magnetic beating system＇s Fuzzy-PID nonlinear controller is designed by analyzing the system control demands. The Fuzzy-PID nonlinear controller can deal with the magnetic bearing system＇ s open loop instability and strong nonlinearity, and the approach could improve the system＇s rapidity, adaptability, stability and dynamic characteristics. Comparative analysis and experiments are conducted between linear PID and nonlinear fuzzy- PID control methods, the results show that the fuzzy-PID controller is better, and the five-freedom magnetic bearing＇ s rotary precision experiments are conducted by the fuzzy-PID controller, it satisfies the control rotary precision demands and realizes the hearing＇s steady floating and rotating.

Experimental Investigation on Vibration Control of Rotor-bearing System with Active Magnetic Exciter

Vibration control is an efficient way to minimize a rotating machine’s vibration level so that its vibration fault-free can be realized.While,several factors,such as unbalance,misalignment and instability,contribute to the serious vibration of rotating machines.It is necessary that one apparatus can depress vibration caused by two or more reasons.The fault self-recovery(FSR) mechanism is introduced and investigated.Strategies of vibration control are investigated theoretically using numerical method firstly.Active magneticelectric exciter(AME) are selected as the actuator of a FSR device because it can provide suitable force by varying the control current in the exciters depending upon a proportional and derivative control law.By numerical study,it is indicate that only a small control force is needed to improve stability margins of the compressor and prevent subsynchronous vibration fault efficiently.About synchronous vibration,three control strategies,searching in whole circle,fast optimizing control(FOC),and none mistaking control,are investigated to show which of the control strategy can realize the fault self-recovery in the shortest time.Experimental study is conducted on a test rig with variable rotating speed.Results of the test indicate that the non-mistake control strategy can minimize synchronous vibration in less than three seconds.The proposed research can provide a new insight for subsynchronous and synchronous vibration restraining about centrifugal compressor.

Synchronous Vibration Suppression of Magnetic Bearing Systems without Angular Sensors

Active Magnetic Bearing(AMB)levitates rotor by magnetic force without friction,and it can provide active control force to suppress vibration while rotating.Most of vibration suppressing methods need angular speed sensors to obtain rotating speed,but in many occasions,angular speed sensor is difficult to install or is difficult to guarantee reliability.This paper proposed a vibration suppressing strategy without angular speed sensor based on generalized integrator and frequency locked loop(GI-FLL)and phase shift generalized integrator(PSGI).GI-FLL and high-pass filter estimate frequency from control current,PSGI is applied to generate compensating signal.Firstly,model of AMB system expressed by transfer function is established and effect of centrifugal force is analyzed.Then,principle and process of vibration suppressing strategy is introduced.Influence of parameters are analyzed by root locus and bode diagram.Simulation results display the process of frequency estimation and performance of displacement.Experiments are carried on a test rig,results of simulations and experiments demonstrate the effectiveness of proposed vibration suppressing strategy.