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.

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.

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.

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.

Disturbance rejection via iterative learning control with a disturbance observer for active magnetic bearing systems

Although standard iterative learning control(ILC) approaches can achieve perfect tracking for active magnetic bearing(AMB) systems under external disturbances, the disturbances are required to be iteration-invariant.In contrast to existing approaches, we address the tracking control problem of AMB systems under iteration-variant disturbances that are in different channels from the control inputs. A disturbance observer based ILC scheme is proposed that consists of a universal extended state observer(ESO) and a classical ILC law. Using only output feedback, the proposed control approach estimates and attenuates the disturbances in every iteration. The convergence of the closed-loop system is guaranteed by analyzing the contraction behavior of the tracking error.Simulation and comparison studies demonstrate the superior tracking performance of the proposed control approach.

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.

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.

Self-sensing active magnetic bearing using real-time duty cycle

In a self-sensing active magnetic bearing (AMB) system driven by pulse width modulation (PWM) switching power amplifiers, the rotor position information can be extracted from coil current and voltage signals by a specific signal demodulation process. In this study, to reduce the complexity of hardware, the coil voltage signal was not filtered but measured in the form of a duty cycle by the eCAP port of DSP (TMS320F28335). A mathematical model was established to provide the relationship between rotor position, current ripple, and duty cycle. Theoretical analysis of the amplitude-frequency characteristic of the coil current at the switching frequency was presented using Fourier series, Jacobi-Anger identity, and Bessel function. Experimental results showed that the time-varying duty cycle causes infinite side frequencies around the switching frequency. The side frequency interval depends on the varying frequency of the duty cycle. Rotor position can be calculated by measuring the duty cycle and demodulating the coil current ripple. With this self-sensing strategy, the rotor system supported by AMBs can steadily rotate at a speed of 3000 r/min.

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。

基于粒子群算法的分数阶PID主动磁轴承控制

针对主动磁轴承(AMB)四自由度间强耦合、非线性导致控制器控制效果不佳的问题,将分数阶PID(FOPID)控制器引入AMB控制系统,提出了基于粒子群(PSO)算法的FOPID控制器以提高控制器的响应速度并抑制转轴位移超调量,提高控制精度。采用时间乘以误差绝对值积分(ITAE)作为性能指标,在限制电流模块不同幅值条件下,将FOPID控制器与PID控制器进行比较。仿真结果显示,PSO算法可以简化FOPID控制器参数的调节过程;随着限制电流的提升,FOPID控制器的控制效果明显优于PID控制器,在5 A输入电流的限制下其性能指标高出PID控制器约1.05%;随限制电流幅值增加,在60 A输入电流的限制下性能指标可高出PID控制器约26.25%。

主动磁轴承系统建模与准谐振自抗扰振动抑制

为了建立更准确的磁轴承数学模型,优化其控制性能,对磁轴承的电磁力非线性特性和系统固有干扰源进行了分析,通过转子动力学分析建立了含干扰源的主动磁轴承径向耦合系统模型。为抑制系统的振动,提出了一种磁轴承准谐振自抗扰振动抑制方法。通过扩张状态观测器实现系统解耦,简化控制流程,提升系统抗干扰能力;在此基础上,并入准谐振控制器对正弦周期性振动进行抑制。与传统方法相比,该方法控制结构简单,所需整定参数较少。仿真与试验结果表明,所提方法可以有效降低转子位移振动幅值,系统内常见的1、3、5倍频周期性振动得到显著抑制,具有良好的振动抑制效果。

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。

高速内置式永磁电动机转子系统的模态特性

针对含多组件的高速内置式永磁同步电动机转子结构等效弹性模量准确获取难度大,忽略轴承支承阻尼引起的模态分析误差大的问题,提出一种基于悬臂梁模型的等效弹性模量解析法,采用复数里卡蒂传递矩阵法建立考虑支承阻尼的转子系统动力学模型,分析了轴承支承特性和等效弹性模量对模态特性的影响,并进行了仿真和试验验证。结果表明:增加轴承刚度将增大转子系统的刚性临界转速并降低系统稳定裕度,增加轴承阻尼将减小刚性临界转速并增大系统稳定性;当转子系统阻尼比增加到0.4左右时,锥动刚性模态消失;等效弹性模量主要影响转子系统的弯曲模态,而对刚性模态几乎无影响。

Investigation of Rotor Radial Rotating Error upon AMB System

This paper first suggests the use of the Fourier frequency transmission method of two dimensions function （ 2D FFT） to analyze radial rotating errors that occurred in a rotor. Based on this method a magnetic rotor is measured. The authors point out that the main cause to affect radial rotating accuracy of the rotating shaft at a high speed is the dynamic imbalance of the shaft itself. Finally the feedforward control scheme is suggested to improve the accuracy of the shaft in an active magnetic bearing （ AMB ） system.

计及磁路分布特性的电磁轴承解析模型建立与支撑性能影响因素研究

综合考虑磁路分布特性的电磁轴承解析模型是对电磁轴承优化设计的快速有效手段。该文通过计及铁心材料非线性磁导率、磁极边缘效应、磁场透入深度等影响因素,研究了磁极宽度对电磁轴承定子结构参数及其最大静态电磁力的影响,揭示了定子结构参数与磁路动态磁阻之间的规律,构建了计及磁路分布特性的电磁轴承解析模型。在此基础上,以异极径向电磁轴承结构参数为研究对象,分别以构建的解析模型和有限元法对其结构与最大电磁力及气隙磁通密度的影响规律进行计算对比,同时搭建了对应的实验平台进行验证分析,验证了解析模型的准确性和有效性。另一方面,基于构建的电磁轴承解析模型,揭示了定子极弧系数、励磁电流、气隙长度对于电磁轴承支撑性能的影响规律,为径向结构电磁轴承的设计及运行控制提供理论参考。

电磁轴承支承的船舶推进轴系纵向振动变刚度控制方法研究

船舶推进轴系纵向非定常激励激发壳体结构振动和辐射噪声,严重影响航行隐蔽性。针对这一问题,结合电磁轴承支承特性主动可控优势,首先提出了一种采用电磁轴承支承的推进轴系结构,然后推导了含推力电磁轴承结构及控制参数的轴系纵向振动频率方程,最后提出了一种基于纵向激励频率的变刚度控制方法。仿真结果表明,在推力电磁轴承可变等效刚度范围内,增大控制器比例系数,可有效提高轴系一阶纵向固有频率,对高阶纵向固有频率影响不大;轴系在不同转速下工作时可以选用不同比例系数,实时调节轴系纵向振动传递特性,有效减小纵向激励向壳体传递。

主动电磁轴承–柔性转子系统过多个临界转速区的同频振动抑制

为了对电磁轴承(active magnetic bearings,AMBs)–柔性转子系统在多阶弯曲临界转速范围内的同频不平衡振动行有效控制,首先建立AMBs–柔性转子系统的动力学模型,分析线性自抗扰控制器和相位偏移最小均方(least mean square,LMS)算法。然后,提出一种基于相位偏移LMS的扰动跟踪补偿方法,并将相位偏移LMS算法用在同频扰动的跟踪中,以解决扩展状态观测器不能准确估计高频同频不平衡扰动的问题。接着,从补偿方法、补偿有效性和闭环系统稳定性等方面分析相位偏移LMS的补偿特性。最后,在AMBs–多盘柔性转子系统试验台上进行试验。结果表明,所提出的基于相位偏移LMS扰动补偿策略无需切换极性和相位,就能够有效地抑制柔性转子在跨越系统的刚体平动、刚体锥动、一阶弯曲和二阶弯曲临界转速区的同频不平衡振动,使转子系统在高于二阶弯曲临界转速的转速区稳定工作。

考虑界面接触的磁悬浮转子高阶模态自激振动抑制研究

在磁悬浮叶轮机械中,叶轮与转子装配界面的接触引入了附加接触刚度,减弱了转子系统模态阻尼,并降低磁悬浮轴承转子系统的性能及稳定性,激发出转子高频模态振动。目前关于磁悬浮轴承系统中接触界面引起的转子高频模态振动的研究相对较少且传统PID控制器无法有效抑制此类振动。为解决上述问题,设计基于柔性转子的H∞鲁棒控制器。首先对考虑界面接触的磁悬浮轴承转子系统进行动力学分析,探究其模态振动特性。之后对磁悬浮轴承转子系统进行扫频试验得到频响曲线,在传统磁悬浮轴承刚性转子系统建模的基础上,基于柔性转子模态理论将转子传递函数模型进行重构,并基于此模型对转子系统扫频曲线进行拟合,得到转子系统的高阶模态参数,最终建立考虑高阶模态特性的被控对象模型,设计H∞鲁棒控制器。试验结果表明,基于柔性转子模型的鲁棒控制器可以对接触界面引起的转子高频模态振动进行有效抑制。

磁悬浮轴承控制系统及控制技术研究

磁悬浮轴承技术因其无接触、无需润滑、无磨损的优良特性特别适用于高速传动应用场景。其通常采用分散的PID控制,且刚度与阻尼的选择决定了系统的稳定性与动态性能。文章针对典型的磁悬浮轴承控制系统,研究了其控制策略。同时,对不同刚度与阻尼条件下的系统进行了仿真分析。

磁悬浮轴承刚度、阻尼特性研究

与传统机械轴承相比,刚度、阻尼可调节是磁悬浮轴承的一个主要特点与技术优势,在不改变轴承结构的前提下,磁悬浮轴承系统的响应主要取决于控制器的设计,即可通过在线改变磁悬浮轴承的刚度和阻尼,适应实际运行工况的瞬态响应,从而保证转子在受到扰动时悬浮稳定。为此,探究磁悬浮轴承刚度、阻尼的变化趋势对于磁悬浮系统来说至关重要。