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.

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.

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.

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.

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.

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.

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.

Experimental Study of Active Magnetic Bearing on a 150 M^(3)Turbo Oxygen Gas Expander

This paper is concerned with the investigation, experiment and design analyses on the application of active magnetic bearings for a 150M 3 turbo oxygen gas expander having 1.16 kg weight and 30 mm diameter rotor, which was supported by two aerostatic bearings formerly. Now, the machine can work steady at a rotation speed of 92,000 r/min, and can be run up to a maximum rotation speed of 104,000 r/min.

Improving Kinetic Energy Storage for Vehicles through the Combination of Rolling Element and Active Magnetic Bearing

The demand for short term energy storage providing high power for electric and hybrid-electric vehicles is increasing drastically. Stationary FESS （flywheel energy storage systems） is established as UPS （uninterruptible power supply） and represent an emerging market. In contrast, mobile FESSs are currently only used in a few application, e.g., in motor sports. To enable a wider use in personal and public transportation the life-span of the flywheel＇s bearings needs to be increased significantly. This paper presents an alternative approach to extend the lifespan of the flywheel＇s bearings significantly by using a CREAMB （combination of rolling element and active magnetic bearings）.

Variable Parameters PD Control and Stability of a High Rate Rigid Rotor-Journal Active Magnetic Bearing System

Stability is a key problem that means whether a high rate rotor-active magnetic bearings system works reliably or not. Aiming at a bearings system described with nonlinear equations, this paper built a linear model according to the system behavior. Considering realization of the control system and behavior of a high rate rotor system (magnetic force is far smaller than input force produced by mass eccentricity) this paper proposes a design method of variable parameters PD control algorithm that can be used universally. The control system was simplified and a mass of adjusting work of control parameters was reduced. Analysis and simulation indicated that the bearings system could get a wider stable region of harmonic motion, and proved that the algorithm is robust and advanced. The control system can be realized because the winding electric currents are positive. The method is convenient for operation and can easily be used for engineering practice.

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.

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.

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.

STUDY ON CATASTROPHIC MECHANISM FOR ROTOR DROP TRANSIENT VIBRATION FOLLOWING MAGNETIC BEARING FAILURE

The nonlinear and transient vibration of a rotor, which dropped onto back-up bearings when its active magnetic bearings were out of order, was investigated. After strictly deriving its equations of motion and performing numerical simulations, the time-histories of rotating speed of the dropping rotor, and normal force at the rubbing contact point as well as the frequency spectrum of the vibration displacement of back-up bearings are fully analyzed. It is found that the strong and unsteady forced bending vibration of the unbalanced and, damped rotor decelerating through : its first. bending vibtation of the unbalanced and, damped rotor decelerating through its,first critical speed as well as chattering at high frequencies caused by the nonlinearity at the rubbing contact point between, the journal and back-up bearings may lead to the catastrophic damage. of the system.

A Novel Model Calibration Method for Active Magnetic Bearing Based on Deep Reinforcement Learning

Active magnetically suspended control moment gyro is a novel attitude control actuator for satellites.It is mainly composed of rotor,active magnetic bearing(AMB)and motor.As a crucial supporting component of control moment gyro,the performance of AMB is directly related to the stability of the rotor system and pointing precision of the satellites.Therefore,calibrating the parameters of AMB is essential for the realization of super-quiet satellites.This paper proposed a model calibration method,known as the deep reinforcement learningbased model calibration frame(DRLMC).First,the dynamics of magnetic bearing with damage degradation over its life cycle are modeled.Subsequently,the calibration process is formulated as a Markov Decision Process(MDP),and reinforcement learning(RL)is employed to infer the degradation parameters.In addition,experience replay and target network update mechanism are introduced to guarantee stability.Simulation results demonstrate that the proposed method identi¯es force-current factor of AMB during its degradation process e®ectively.Furthermore,additional experiments con¯rm the robustness of the DRLMC approach.

Control of a flexible rotor active magnetic bearing test rig: a characteristic model based all-coefficient adaptive control approach

Active magnetic bearings （AMBs） have found a wide range of applications in high-speed rotating machinery industry. The instability and nonlinearity of AMBs make controller designs difficult, and when AMBs are coupled with a flexible rotor, the resulting complex dynamics make the problems of stabilization and disturbance rejection, which are critical for a stable and smooth operation of the rotor AMB system, even more difficult. Proportional-integral-derivative （PID） control dominates the current AMB applications in the field. Even though PID controllers are easy to implement, there are critical performance limitations associated with them that prevent the more advanced applications of AMBs, which usually require stronger robustness and performance offered by modern control methods such as H-infinity control and if-synthesis. However, these advanced control designs rely heavily on the relatively accurate plant models and uncertainty characterizations, which are sometimes difficult to obtain. In this paper, we explore and report on the use of the characteristic model based all-coefficient adaptive control method to stabilize a flexible rotor AMB test rig. In spite of the simple structure of such a characteristic model based all-coefficient adaptive controller, both simulation and experimental results show its strong performance.

Fuzzy-Immune PID Control for AMB Systems

In order to improve the dynamic performance of active magnetic hearing systems with highly nonlinear and naturally unstable dynamics, a new nonlinear fuzzy-immune proportional integral-derivative （PID） controller is proposed by combining the immune feedback law with linear PID con trol. This controller consists of a PID controller and a basic immune proportional controller in cascaded connection, the nonlinear function of the immune proportional controller is realized by using fuzzy reasoning. Simulation results demon strate that the active magnetic bearing system with the proposed controller has better dynamic performance and disturbance rejection ability than using the linear PID controller.

Dynamic Responses of Rotor Drops onto Double-decker Catcher Bearing

In an active magnetic bearing （AMB） system, the catcher bearings （CBs） are indispensable to protect the rotor and stator in case the magnetic bearings fail. Most of the former researches associated with CBs are mainly focused on the dynamic responses of the rotor drops onto traditional single-decker catcher bearings （SDCBs）. But because of the lower limited speed of SDCB, it cannot withstand the ultra high speed rotation after rotor drop. In this paper, based on the analysis of the disadvantages of SDCBs, a new type of double-decker catcher bearings （DDCBs） is proposed to enhance the CB work performance in AMB system. In order to obtain thc accurate rotor movements before AMB failure, the dynamic characteristics of AMB are theoretically derived. Detailed simulation models containing rigid rotor model, contact model between rotor and inner race, DDCB force model as well as heating model after rotor drop are established. Then, using those established models the dynamic responses of rotor drops onto DDCBs and SDCBs are respectively simulated. The rotor orbits, contact forces, spin speeds of various parts and heat energies after AMB failure are mainly analyzed. The simulation results show that DDCBs can effectively improve the CBs limit rotational speed and reduce the following vibrations, impacts and heating. Finally, rotor drop experiments choosing different types of CBs are carried out on the established AMB test bench. Rotor orbits, inner race temperatures as well as the rotating speeds of both inner race and intermediate races after rotor drop are synchronously measured. The experiment results verify the advantages of DDCB and the correctness of theoretical analysis. The studies provide certain theoretical and experimental references for the application of DDCBs in AMB system.