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.

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.

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.

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.

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.

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.

Nonlinear optimal control of rotating flexible shaft in active magnetic bearings

The optimal control of nonlinear systems has been studied for years by many researchers. However, the application of optimal control problem to nonlinear non-affine systems needs more attention. In this paper we propose an optimal control design technique for a class of nonlinear and control non-affine equations. The dynamic equations of a flexible shaft supported by a pair of active magnetic bearings (AMBs) are used as the nonlinear control non-affine equations. Mathematical model for the flexible beam is chosen to be the well known Timoshenko beam model, which takes rotary inertia and shear deformations into account, and it is assumed that the shaft is supported by two frictionless bearings at the ends. The effective control of such systems is extremely important for very high angular velocity shafts which are a feature of many modern machines. The control must be able to cope with unbalanced masses and hence be very robust. We shall approach the problem by discretising the Timoshenko beam model and using standard difference formulae to develop a finite-dimensional model of the system. Then we use a recently developed technique for controlling nonlinear systems by reducing the problem to a sequence of linear time-varying (LTV) systems. An optimal control designed for each approximating linear, time-varying system and recent results show that this method will converge uniformly on compact time intervals to the optimal solution.

Model-free adaptive control for three-degree-of-freedom hybrid magnetic bearings

Mathematical models are disappointing due to uneven distribution of the air gap magnetic field and significant un- modeled dynamics in magnetic bearing systems. The effectiveness of control deteriorates based on an inaccurate mathematical model, creating slow response speed and high jitter. To solve these problems, a model-free adaptive control （MFAC） scheme is proposed for a three-degree-of-freedom hybrid magnetic bearing （3-DoF HMB） control system. The scheme for 3-DoF HMB depends only on the control current and the objective balanced position, and it does not involve any model information. The design process of a parameter estimation algorithm is model-free, based directly on pseudo-partial-derivative （PPD） derived online from the input and output data information. The rotor start-of-suspension position of the HMB is regulated by auxiliary bearings with different inner diameters, and two kinds of operation situations （linear and nonlinear areas） are present to analyze the validity of MFAC in detail. Both simulations and experiments demonstrate that the proposed MFAC scheme handles the 3-DoF HMB control system with start-of-suspension response speed, smaller steady state error, and higher stability.

Riccati difference equation in optimal control formagnetic bearings

A model predictive optimal control method for magnetically suspended flywheel is presented.In order to suppress the conical whirl of the rotor caused by gyroscopic effect,the synchronization error is added to the traditional quadratic performance index.The target performance index is composed of the translatory error,the synchronization error,and the control output predicted by the discrete-time state model.The optimal controller is obtained by means of iterating a Riccati difference equation(RDE).Stability of the control scheme is investigated through fake algebraic Riccati technique(FART).The robust performance of the controller with respect to control parameters is studied by simulation.Results of the simulation and experiment on a compact magnetically suspended flywheel demonstrate that the proposed controller with consideration of the synchronization error is very effective to suppress the conical whirl caused by gyroscopic effect.

Characteristics of motorized spindle supported by active magnetic bearings

A motorized spindle supported by active magnetic bearings（AMBs） is generally used for ultra-high-speed machining. Iron loss of radial AMB is very great owing to high rotation speed, and it will cause severe thermal deformation. The problem is particularly serious on the occasion of large power application, such as all electric aero-engine. In this study, a prototype motorized spindle supported by five degree-of-freedom AMBs is developed. Homopolar and heteropolar AMBs are independently adopted as radial bearings. The influences of the two types of radial AMBs on the dynamic characteristics of the motorized spindle are comparatively investigated by theoretical analysis, test modal analysis and actual operation of the system. The iron loss of the two types of radial AMBs is analyzed by finite element software and verified through run-down experiments of the system. The results show that the structures of AMB have less influence on the dynamic characteristics of the motorized spindle. However, the homopolar structure can effectively reduce the iron loss of the radial AMB and it is useful for improving the overall performance of the motorized spindle.

Dynamic analysis and identification of unbalance and misalignment in a rigid rotor with two offset discs levitated by active magnetic bearings:a novel trial misalignment approach

Rotating machinery is an essential and crucial component of numerous mechanical systems in modern industries,transport vehicles,and in several other applications.Excessive vibrations on rotating equipment due to multiple faults may cause catastrophic failure in machines and lead to hazardous accidents.So,there is a need for perceiving the dynamic nature and identifying the faults for the safe,smooth and effective operation of machines.This paper proposes a novel trial misalignment approach to estimate the misalignment with a similar concept as the trial unbalance in the rotor balancing.Active magnetic bearing(AMB)misalignment with the rotor has been investigated with residual misalignment and additional trial misalignment cases.Additional trial misalignments are provided in addition to the unknown misalignments of the residual misalignment case.For the execution of this methodology,the dynamic model of a four-degree-of-freedom unbalanced and misaligned rigid rotor with two offset discs supported by two active magnetic bearings has been mathematically developed.The offset discs result in the gyroscopic effect at high rotor speeds.Equations of motion of the rotor-AMB system have been derived and solved to generate the time domain rotor displacement and controlling current responses at AMB positions.A fast Fourier transform technique has been utilized to convert the time domain responses into the frequency domain for estimation of unbalance eccentricities and phases together with force-displacement and forcecurrent stiffnesses of misaligned AMBs as well as AMB's constant forces using the developed identification algorithm.Identified values of AMB's parameters for both residual and additional trial misalignment cases are evaluated to estimate the four unknown misalignments.Testing of the algorithm has also been carried out at multiple spin speeds against measurement signal noise in rotor responses and bias errors in rotor system parameters to check its effectiveness and robustness.The algorithm is found to be exhibiting excellent.

Nonlinear vibration analysis of a rotor supported by magnetic bearings using homotopy perturbation method

In this paper,the effects of nonlinear forces due to the electromagnetic field of bearing and the unbalancing force on nonlinear vibration behavior of a rotor is investigated.The rotor is modeled as a rigid body that is supported by two magnetic bearings with eightpolar structures.The governing dynamics equations of the system that are coupled nonlinear second order ordinary differential equations(ODEs)are derived,and for solving these equations,the homotopy perturbation method(HPM)is used.By applying HPM,the possibility of presenting a harmonic semi-analytical solution,is provided.In fact,with equality the coefficient of auxiliary parameter(p),the system of coupled nonlinear second order and non-homogenous differential equations are obtained so that consists of unbalancing effects.By considering some initial condition for displacement and velocity in the horizontal and vertical directions,free vibration analysis is done and next,the forced vibration analysis under the effect of harmonic forces also is investigated.Likewise,various parameters on the vibration behavior of rotor are studied.Changes in amplitude and response phase per excitation frequency are investigated.Results show that by increasing excitation frequency,the motion amplitude is also increases and by passing the critical speed,it decreases.Also it shows that the magnetic bearing system performance is in stable maintenance of rotor.The parameters affecting on vibration behavior,has been studied and by comparison the results with the other references,which have a good precision up to 2nd order of embedding parameter,it implies the accuracy of this method in current research.

Model Development and Adaptive Imbalance Vibration Control of Magnetic Suspended System

A system model is developed to describe the translational and rotational motion of an active-magnetic-bearing-suspended rigid rotor in a single-gimbal control moment gyro onboard a rigid satellite. This model strictly reflects the motion characteristics of the rotor by considering the dynamic and static imbalance as well as the coupling between the gimbal＇s and the rotor＇s motion on a satellite platform. Adaptive auto-centering control is carefully constructed for the rotor with unknown dynamic and static imbalance. The rotor makes its rotation about the principal axis of inertia through identifying the small rotational angles between the geometric axis and the principal axis as well as the displacements from the geometric center to the mass center so as to tune a stabilizing controller composed of a decentralized PD controller with cross-axis proportional gains and high- and low-pass filters. The main disturbance in the wheel spinning can thereby be completely removed and the vibration acting on the satellite attenuated.

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.

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.

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.

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.