主动磁悬浮轴承系统不平衡振动补偿研究
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摘要
在主动磁悬浮轴承系统中，由于转子存在不平衡，会产生与转速同频的不平衡振动。为了减小这些同频振动对主动磁悬浮轴承系统的不利影响，本文进行了惯性力最小和位移最小振动补偿研究。
针对惯性力最小振动补偿，主要是通过消除反馈位移信号中的同频振动来减弱主动磁悬浮轴承系统的控制电流，控制电流的减小有利于降低磁悬浮轴承定子的电磁力以及对转子的约束力，使转子在离心力作用下尽可能地绕其惯性主轴转动，最终达到减小转子惯性力以及磁悬浮轴承电磁力的目的。本文先后采用了三种惯性力最小补偿策略，首先，在标准LMS算法自适应滤波的基础上，提出了在固定频率处的惯性力最小切换补偿策略，即在主动磁悬浮轴承原反馈控制系统中添加标准LMS算法作为滤波器，通过切换有效消除反馈位移信号中对应某些固定转动频率的同频振动，实现了转子在300Hz和400Hz转动频率处的惯性力最小切换补偿，补偿后的控制电流幅值相对于未加补偿时分别衰减了大约90%和95%；然后，为了实现实时惯性力最小补偿，即在转动频率连续变化时实现惯性力最小补偿，论文提出了一种变步长LMS算法，其核心是提供时变的前馈信号来补偿位移反馈信号中的同频振动，与未加补偿相比，补偿后的控制电流幅值在转动频率为300Hz时衰减了97.4%，且转动频率越高补偿效果越明显；考虑到前两种补偿策略对主动磁悬浮轴承原控制系统存在干扰影响，论文又提出了一种将H∞算法和一种新的改进变步长LMS算法相结合的惯性力最小实时前馈补偿策略，提高了控制系统的抗干扰能力和鲁棒稳定性，转动频率达到300Hz时，补偿后的控制电流幅值同样衰减了97.4%，且转动频率越高补偿效果越好。
针对位移最小振动补偿，考虑到转子启动以及停车过程中不平衡振动信号的周期是变化的，论文提出了一种基于自适应迭代学习控制算法的位移最小前馈补偿策略，该算法可以自适应地提供所需的不平衡补偿信号，以便减小由于算法学习周期不一致而对主动磁悬浮轴承控制系统造成的干扰，研究结果表明所提补偿策略实现了系统在固定转动频率处的位移最小补偿，显著减小了转子径向跳动，补偿后转子径向跳动较未加补偿时衰减了91.3%。
观察到主动磁悬浮轴承系统存在拍振现象，从理论上分析了主动磁悬浮轴承系统参数与拍振的内在关系，研究结果表明，通过改变主动磁悬浮轴承系统广义动刚度能够有效减弱拍振对控制系统的不利影响。
In active magnetic bearings (AMB) system, unbalance vibrations synchronous with the rotationalspeed will be produced because of the rotor’s mass unbalance. To reduce the bad influence of theseunbalance vibrations, force minimum compensation and displacement minimum compensation arestudied in this paper.
Aiming at the inertial force minimum vibration compensation, the major solution is weakeningAMB system control current through eliminating the unbalance vibrations in feedback displacements.The decrease of the control currents helps to weaken the electromagnetic force of magnetic baeringstators and the radial constraint on the rotor, and make the rotor spin around its inertia axis under thecentrifugal force. Finally, the purposes of reducing the effects of rotor inertia force andelectromagnetic force of magnetic baerings are implemented. Three kinds of compensation schemesare adopted in this paper. Firstly, a scheme of switching compensation control in fixed frequencyusing adaptive filter based on norm LMS algorithm is presented. As a filter, the norm LMS algorithmis added into the primary feedback control loop, and the unbalance vibration at some fixed rotationalfrequencies in the feedback displacement can be filtered effectively through switching. Inertial forceminimum switching compensation is achieved at300Hz and400Hz, and the amplitudes of controlcurrent after compensation are attenuated90%and95%compared with the amplitudes beforecompensation, respectively. Secondly, in order to realize real-time inertial force minimumcompensation, implementing inertial force minimum compensation with changing rotationalfrequencies, a new variable step LMS algorithm is presented, and its core is providing feed-forwardsignal to compensate the unbalance vibration. The control current amplitudes after compensation isattenuated97.4%at300Hz, and the compensatory effects become better with the increase of the rotorrotational frequency. Thirdly, in view of the interference influence of the two proposed compensatoryschemes on the primary control system of AMB, another real-time inertial force minimumfeed-forward compensation scheme combined by H∞algorithm and a new modified variable stepLMS algorithm is proposed. This compensatory scheme also realizes inertial force minimumcompensation for AMB system at any frequency, and improves the anti-jamming capability andstability of the control system. The amplitudes of control current after compensation can alsoattenuate97.4%at300Hz, and the higher rotational frequency the better compensatory effects can beachieved.
Aiming at the displacement minimum vibration compensation, a feed-forward displacement minimum compensatory scheme is proposed based on a new adaptive iterative learning controlalgorithm in consideration of the periodic variation of unbalance interference in the processes of rotorstart and shutoff. In the compensation scheme, this algorithm can reduce the interference to AMBcontrol system due to the inconformity of learning circle and can adaptively provide expectedunbalance compensatory signals. Study results show that the proposed scheme can achievedisplacement minimum compensation for AMB system in fixed rotation frequency, and observablyreduce the rotor radial runout. The radial displacement after compensation has reduced by93.1%.
The beat vibration phenomenon existing in the AMB system is discovered, and the internalrelation between beat vibration and the parameters of AMB system is theoretically analyzed.Simulation and experiment results show the unfavorable effects of beat on the control system can beeffectively weakened by changing the generalized dynamical stiffness of AMB.
针对惯性力最小振动补偿，主要是通过消除反馈位移信号中的同频振动来减弱主动磁悬浮轴承系统的控制电流，控制电流的减小有利于降低磁悬浮轴承定子的电磁力以及对转子的约束力，使转子在离心力作用下尽可能地绕其惯性主轴转动，最终达到减小转子惯性力以及磁悬浮轴承电磁力的目的。本文先后采用了三种惯性力最小补偿策略，首先，在标准LMS算法自适应滤波的基础上，提出了在固定频率处的惯性力最小切换补偿策略，即在主动磁悬浮轴承原反馈控制系统中添加标准LMS算法作为滤波器，通过切换有效消除反馈位移信号中对应某些固定转动频率的同频振动，实现了转子在300Hz和400Hz转动频率处的惯性力最小切换补偿，补偿后的控制电流幅值相对于未加补偿时分别衰减了大约90%和95%；然后，为了实现实时惯性力最小补偿，即在转动频率连续变化时实现惯性力最小补偿，论文提出了一种变步长LMS算法，其核心是提供时变的前馈信号来补偿位移反馈信号中的同频振动，与未加补偿相比，补偿后的控制电流幅值在转动频率为300Hz时衰减了97.4%，且转动频率越高补偿效果越明显；考虑到前两种补偿策略对主动磁悬浮轴承原控制系统存在干扰影响，论文又提出了一种将H∞算法和一种新的改进变步长LMS算法相结合的惯性力最小实时前馈补偿策略，提高了控制系统的抗干扰能力和鲁棒稳定性，转动频率达到300Hz时，补偿后的控制电流幅值同样衰减了97.4%，且转动频率越高补偿效果越好。
针对位移最小振动补偿，考虑到转子启动以及停车过程中不平衡振动信号的周期是变化的，论文提出了一种基于自适应迭代学习控制算法的位移最小前馈补偿策略，该算法可以自适应地提供所需的不平衡补偿信号，以便减小由于算法学习周期不一致而对主动磁悬浮轴承控制系统造成的干扰，研究结果表明所提补偿策略实现了系统在固定转动频率处的位移最小补偿，显著减小了转子径向跳动，补偿后转子径向跳动较未加补偿时衰减了91.3%。
观察到主动磁悬浮轴承系统存在拍振现象，从理论上分析了主动磁悬浮轴承系统参数与拍振的内在关系，研究结果表明，通过改变主动磁悬浮轴承系统广义动刚度能够有效减弱拍振对控制系统的不利影响。
In active magnetic bearings (AMB) system, unbalance vibrations synchronous with the rotationalspeed will be produced because of the rotor’s mass unbalance. To reduce the bad influence of theseunbalance vibrations, force minimum compensation and displacement minimum compensation arestudied in this paper.
Aiming at the inertial force minimum vibration compensation, the major solution is weakeningAMB system control current through eliminating the unbalance vibrations in feedback displacements.The decrease of the control currents helps to weaken the electromagnetic force of magnetic baeringstators and the radial constraint on the rotor, and make the rotor spin around its inertia axis under thecentrifugal force. Finally, the purposes of reducing the effects of rotor inertia force andelectromagnetic force of magnetic baerings are implemented. Three kinds of compensation schemesare adopted in this paper. Firstly, a scheme of switching compensation control in fixed frequencyusing adaptive filter based on norm LMS algorithm is presented. As a filter, the norm LMS algorithmis added into the primary feedback control loop, and the unbalance vibration at some fixed rotationalfrequencies in the feedback displacement can be filtered effectively through switching. Inertial forceminimum switching compensation is achieved at300Hz and400Hz, and the amplitudes of controlcurrent after compensation are attenuated90%and95%compared with the amplitudes beforecompensation, respectively. Secondly, in order to realize real-time inertial force minimumcompensation, implementing inertial force minimum compensation with changing rotationalfrequencies, a new variable step LMS algorithm is presented, and its core is providing feed-forwardsignal to compensate the unbalance vibration. The control current amplitudes after compensation isattenuated97.4%at300Hz, and the compensatory effects become better with the increase of the rotorrotational frequency. Thirdly, in view of the interference influence of the two proposed compensatoryschemes on the primary control system of AMB, another real-time inertial force minimumfeed-forward compensation scheme combined by H∞algorithm and a new modified variable stepLMS algorithm is proposed. This compensatory scheme also realizes inertial force minimumcompensation for AMB system at any frequency, and improves the anti-jamming capability andstability of the control system. The amplitudes of control current after compensation can alsoattenuate97.4%at300Hz, and the higher rotational frequency the better compensatory effects can beachieved.
Aiming at the displacement minimum vibration compensation, a feed-forward displacement minimum compensatory scheme is proposed based on a new adaptive iterative learning controlalgorithm in consideration of the periodic variation of unbalance interference in the processes of rotorstart and shutoff. In the compensation scheme, this algorithm can reduce the interference to AMBcontrol system due to the inconformity of learning circle and can adaptively provide expectedunbalance compensatory signals. Study results show that the proposed scheme can achievedisplacement minimum compensation for AMB system in fixed rotation frequency, and observablyreduce the rotor radial runout. The radial displacement after compensation has reduced by93.1%.
The beat vibration phenomenon existing in the AMB system is discovered, and the internalrelation between beat vibration and the parameters of AMB system is theoretically analyzed.Simulation and experiment results show the unfavorable effects of beat on the control system can beeffectively weakened by changing the generalized dynamical stiffness of AMB.
引文
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