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.

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.

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.

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.

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.

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.

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

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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.

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.

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.

Dynamic Stiffness Analysis and Experimental Verification of Axial Magnetic Bearing Based on Air Gap Flux Variation in Magnetically Suspended Molecular Pump

Current and displacement stiffness are important parameters of axial magnetic bearing(AMB)and are usually considered as constants for the control system.However,in actual dynamic work situations,time-varying force leads to time-varying currents and air gap with a specific frequency,which makes the stiffness of appear decrease and even worsens control performance for the whole system.In this paper,an AMB dynamic stiffness model considering the flux variation across the air gap due to frequency is established to obtain the accurate dynamic stiffness.The dynamic stiffness characteristics are analyzed by means of the dynamic equivalent magnetic circuit method.The analytical results show that the amplitude of current and displacement stiffness decreases with frequency increasing.Moreover,compared with the stiffness model without considering the variation of flux density across the air gap,the improved dynamic stiffness results are closer to the actual results.Through the dynamic stiffness measurement method of AMB,experiments of AMB in magnetically suspended molecular pump(MSMP)are carried out and the experimental results are consistent with theoretical analysis results.This paper proposes the dynamic stiffness model of axial magnetic bearing considering the variation of flux density across the air gap,which improves the accuracy of the AMB stiffness analysis.

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.

主动磁悬浮轴承系统保护轴承热特性研究及减摩设计

针对主动磁悬浮轴承系统(AMBs)转子跌落过程中转子与保护轴承碰摩产生巨大冲击、振动和大量摩擦热,易使保护轴承失效的问题,对立式转子跌落到保护轴承过程中的热特性进行了研究,分析了转子跌落对保护轴承造成破坏的主要影响因素,进而提出了一种采用磁控溅射技术在保护轴承关键表面沉积固体润滑薄膜(类石墨碳基薄膜,GLC)的减摩方法,并对镀膜、未镀膜的保护轴承进行了转子跌落试验。研究结果表明:跌落转速为20000 r/min时,保护轴承的最高温度为210.60℃,出现在转子与轴承内圈端面高速碰摩阶段,该温度超过了轴承钢160℃的回火温度,导致轴承烧伤而失效。在跌落试验中,镀有GLC薄膜的自润滑保护轴承试验后的沟道和端面外观明显优于未镀膜保护轴承,由碰摩发热导致的内圈端面硬度下降也较轻,质心轨迹和轴向位移更加平稳,温升更低,GLC薄膜起到了关键的自润滑和减摩功能,提高了保护轴承的使用寿命和服役可靠性,为解决主动磁悬浮轴承系统中保护轴承易失效而发生重大事故的问题提供了一种思路和方法。

基于特征结构配置的电磁轴承-刚性转子系统动态补偿器的设计

由于电磁轴承-转子系统的动力学特性与控制器的结构和参数密切相关,若要使系统安全、稳定及可靠地运行,控制器的设计尤为重要。针对电磁轴承-刚性转子系统,提出一种基于特征结构配置的动态补偿器的设计方法。首先,通过模态解耦,将平动和锥动运动相互耦合的四自由度电磁轴承-刚性转子系统解耦为2个单自由度平动子系统和2个单自由度锥动子系统。然后,基于特征结构配置,建立引入动态补偿器后的闭环系统的特征值和特征向量与补偿器参数之间的关系。之后,限定特征值的变化范围,以使系统具备稳定性和良好的动态性能,构造优化目标函数,以同时抑制转子系统的不平衡位移和不平衡控制电流,从而使系统具备所需的动力特性。最后,通过数值仿真和试验,验证所设计的动态补偿器的有效性。

基于改进型双模分数阶重复控制器的高速磁悬浮电机谐波电流抑制

主动磁悬浮轴承系统的转子不平衡和传感器跳动会使系统产生谐波电流,从而导致谐波振动。重复控制器能同时抑制同频和倍频谐波,但传统重复控制器必须确保控制系统的采样频率与实际转频之比为整数,极大地限制了其适用性。为解决此问题,设计了一种改进型双模分数阶重复控制器。采用拉格朗日插值法将分数阶变为整数,解决了重复控制的非整数延迟问题;通过双支路独立地消除奇偶次谐波,第1次、2次、3次、4次和5次谐波分别降低了87.9%、61.3%、86.9%、36.9%和85.3%。仿真和试验结果验证了改进型重复控制器对谐波电流抑制的精确性和有效性。

磁悬浮轴承系统跌落转子-保护轴承的动态响应分析

保护轴承是磁悬浮轴承系统发生失稳、掉电等故障后保护系统的重要部件,其动态性能直接影响磁悬浮轴承系统的安全性和可靠性。通过有限元软件Abaqus和舍弗勒轴承动力学软件Caba3D建立了柔性转子和保护轴承的动力学模型,开展了从转子开始跌落到转子-保护轴承系统相对稳定状态的动态响应研究,分析了转子和保护轴承内圈转速、转子质心轨迹、转子与保护轴承内圈的碰撞力、球之间的碰撞力、球与内圈之间滑动速度随时间的变化过程。结果表明:在转子的驱动下,保护轴承内圈转速先以极高的加速度升高,当内圈转速与转子接近时,转子和内圈转速又以极低的减速度降低;当保护轴承内圈加速时,转子的质心轨迹紊乱,转子与内圈的碰撞力较大,并且内圈与球之间的滑动速度随着时间增加逐渐增加;当保护轴承内圈减速时,转子与内圈的碰撞力较小,并且内圈与球之间的滑动速度随着时间增加逐渐降低。

基于迭代策略的自适应ADRC磁轴承控制仿真

针对磁悬浮轴承位置控制过程中存在非线性耦合、内外部扰动不确定性的问题,提出了一种基于自抗扰控制的四自由度磁轴承迭代学习控制策略。首先依据四自由度磁悬浮轴承系统模型搭建自抗扰控制器,其次将估计的总扰动通过间接迭代控制在线调整扩张状态观测器的带宽,实现不同增益下观测器参数的自适应整定。Simulink仿真实验数据表明:系统约在0.14 s处达到稳定,加入干扰后约0.05 s恢复稳定;基于迭代控制的自适应ADRC四自由度磁悬浮轴承控制性能好,同时调节速度快,具有较强的抗干扰能力。经比例-微分型间接迭代学习控制律在线更新带宽后,超调量小且跟踪目标误差积分性能指标小。

基于惯性运动自适应前馈的磁轴承基座扰动抑制

为抑制主动磁轴承中基座的运动造成转子的振动增大,设计并实现了一种基于惯性运动的前馈控制方法。首先,针对基座运动状态下的磁轴承系统,建立了基座运动的五自由度磁轴承转子动力学模型,然后,分析了在基座进行小幅度复杂运动时转子受扰动力的动力学,提出了一种基于自适应算法的惯性前馈方法。最后,采用搭建的实验平台对不同扰动下开启前馈控制前后转子的响应进行了实验研究。实验结果表明:自适应前馈控制器使能后,磁轴承转子的位移减少了80%以上。设计的自适应前馈控制方法能够有效抑制磁悬浮系统基座扰动对转子振动的影响,大幅提高了磁轴承转子的运行精度,且设计的系统仅需增加一个小体积的惯性微机电测量单元,满足实际工程应用需求。