主动电磁轴承-柔性转子系统振动位移的高精度跟踪和估计方法

doi:10.19595/j.cnki.1000-6753.tces.220519

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Abstract

Supporting by active magnetic bearings (AMBs), the AMBs-flexible rotor system works near and above the first-order bending critical speed. Because of the deformation of the shaft, the displacement of other positions on the shaft cannot be inferred from the displacement of the two AMBs through simple mathematical calculations. Therefore, when controlling other positions is needed, an estimator construct by the observer is the key to tracking and obtaining the real-time displacement.
As the classical observer in control theory, the Luenberger observer can obtain the state of system by output. However, the design of the Luenberger observer needs to consider mathematical model error and continuous disturbance, which leads to less application in industry and lagging tracking. The Unknown Input Observer (UIO) is designed to keep track of unknown inputs in the system. Since the unbalance force in AMBs-flexible rotor system can be regarded as unknown input. It can be estimated by UIO to realize fast tracking and estimation.
There are two preconditions in the design of UIO. The first one is that the invariant zeros of the system (A, C_m, B_u) are all in the left half plane. This condition is equivalent to the disturbance input matrix B_u being full of rank and the system matrix A being stable. Since the AMB under the PID controller can provide positive stiffness and damping similar to mechanical bearings, the system matrix A is considered stable. The second condition is the observer matching condition, requiring rank(C_mB_u)=rank(B_u). While meeting these two conditions, the form of UIO can be designed as follows.

However, the observer matching condition is only satisfied in some systems. In the AMBs-flexible rotor system, the output matrix C_m is the position of the displacement sensors, and the unbalanced force acts on the acceleration of the system, resulting in rank (C_mB_u)=0. In order to achieve the matching of observers, this paper proposes an implementation method for constructing auxiliary outputs. By taking the second derivative of the output equation, the new output includes the original output y and auxiliary output $ \ddot{\boldsymbol{y}}-\boldsymbol{C}_{\mathrm{m}} A \boldsymbol{B} \boldsymbol{u}-\boldsymbol{C}_{\mathrm{m}} \boldsymbol{B} \dot{\boldsymbol{u}}$. The new input matrix C_mAB_u is full of rank, satisfying the matching condition.
The state observability needs to be solved before observing the AMBs-flexible rotor system. The first is the observable condition of the disturbance system, which requires that the number of disturbances cannot exceed the number of sensors. The second is the observable condition of the flexible rotor system, which requires at least n displacement sensors to estimate n nodes, including rigid modes. When observing the first-order bending mode, six displacement sensors are required. In addition, the observability of the system is calculated using the Gramian factor, and the positioning node of the sensor cannot be located near the mode shape node.
The tracking performance of the observers is studied by calculating the frequency response in the SISIO case. Compared with the Luenberger observer, the LESO with an extended disturbance state performs better but still suffers from phase lag when the input frequency exceeds the observer bandwidth. The UIO with auxiliary output can track the physics system accurately over a large frequency area.
Simulations and experiments are carried out to verify the proposed method. Tracking performance refers to the ability of the observer to track the existing output. Estimation performance refers to the ability to obtain the target position. In this paper, the existing outputs are 6 sensors of AMBs and disk A. The position to be estimated is the node of disk B. Simulations verify the estimating and tracking performance of UIO and the observability conditions. In the experiment, the second derivative in the auxiliary output is replaced by the square of the frequency multiplied by-1. A synchronous resonator is used to suppress the noise effect. The experimental result proves that the proposed method can track all system outputs with high precision in the region of 0~6 000 r/min and accurately estimate the displacement of the target position.

Key words： Active magnetic bearing flexible rotor state observer

Received: 06 April 2022

PACS:

TM133.3

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Cite this article:

Li Wengheng,Zhu Changsheng. High Precision Tracking and Estimation Method for Vibration Displacement of Active Magnetic Bearings-Flexible Rotor System[J]. Transactions of China Electrotechnical Society, 2023, 38(12): 3151-3164.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.220519 OR https://dgjsxb.ces-transaction.com/EN/Y2023/V38/I12/3151

[1] Maslen E H, Schweitzer G.Magnetic bearings: theory, design, and application to rotating machinery[M]. Berlin, Heidelberg: Springer, 2009.
[2] Siva Srinivas R, Tiwari R, Kannababu C.Application of active magnetic bearings in flexible rotordynamic systems-a state-of-the-art review[J]. Mechanical Systems and Signal Processing, 2018, 106: 537-572.
[3] 巩磊, 杨智, 祝长生. 主动电磁轴承-刚性转子系统加速响应的鲁棒性[J]. 电工技术学报, 2021, 36(2): 268-281.
Gong Lei, Yang Zhi, Zhu Changsheng.Acceleration responses robustness of active magnetic bearings-rigid rotor system[J]. Transactions of China Elec-trotechnical Society, 2021, 36(2): 268-281.
[4] 禹春敏, 邓智泉, 梅磊, 等. 基于精确磁路的新型混合型轴向-径向磁悬浮轴承研究[J]. 电工技术学报, 2021, 36(6): 1219-1228.
Yu Chunmin, Deng Zhiquan, Mei Lei, et al.Research of new hybrid axial-radial magnetic bearing based on accurate magnetic circuit[J]. Transactions of China Electrotechnical Society, 2021, 36(6): 1219-1228.
[5] 张静, 宋宝林, 谢松霖, 等. 基于状态估计的高速受电弓鲁棒预测控制[J]. 电工技术学报, 2021, 36(5): 1075-1083.
Zhang Jing, Song Baolin, Xie Songlin, et al.Robust predictive control of high-speed pantograph based on state estimation[J]. Transactions of China Electro-technical Society, 2021, 36(5): 1075-1083.
[6] Luenberger D G.Observing the state of a linear system[J]. IEEE Transactions on Military Electronics, 1964, 8(2): 74-80.
[7] Meier L, Luenberger D.Approximation of linear constant systems[J]. IEEE Transactions on Automatic Control, 1967, 12(5): 585-588.
[8] Tang T S, Huang G M.On control of large space structure[C]//1990 American Control Conference, San Diego, CA, USA, 2009: 2965-2970.
[9] Balas M J.Active control of flexible systems[J]. Journal of Optimization Theory and Applications, 1978, 25(3): 415-436.
[10] 曲志强, 高为炳. 大型柔性空间结构的状态估计及变结构控制[J]. 北京航空航天大学学报, 1989, 15(3): 17-25.
Qu Zhiqiang, Gao Weibing.State estimation and variable structure control of flexible spacecrafts[J]. Journal of Beijing University of Aeronautics and Astronautics, 1989, 15(3): 17-25.
[11] 王霈霈. 主动电磁轴承-柔性转子系统的振动分析与控制[D]. 杭州: 浙江大学, 2020.
[12] 耿晓晓. 电磁轴承-柔性转子系统过一阶弯曲临界转速区的滑膜振动控制[D]. 杭州: 浙江大学, 2020.
[13] Gosiewski Z, Kulesza Z.Virtual collocation of sensors and actuators for a flexible rotor supported by active magnetic bearings[C]//Proceedings of the 14th International Carpathian Control Conference (ICCC), Rytro, Poland, 2013: 94-99.
[14] Chen Wenhua, Yang Jun, Guo Lei, et al.Disturbance-observer-based control and related methods—an overview[J]. IEEE Transactions on Industrial Elec-tronics, 2015, 63(2): 1083-1095.
[15] Peng Cong, Fang Jiancheng, Xu Xiangbo.Mismatched disturbance rejection control for voltage-controlled active magnetic bearing via state-space disturbance observer[J]. IEEE Transactions on Power Electronics, 2015, 30(5): 2753-2762.
[16] Gong Lei, Zhu Changsheng.Vibration suppression for magnetically levitated high-speed motors based on polarity switching tracking filter and disturbance observer[J]. IEEE Transactions on Industrial Elec-tronics, 2021, 68(6): 4667-4678.
[17] 韩京清. 一类不确定对象的扩张状态观测器[J]. 控制与决策, 1995, 10(1): 85-88.
Han Jingqing.The “extended state observer” of a class of uncertain systems[J]. Control and Decision, 1995, 10(1): 85-88.
[18] 郭凯旋. 基于自抗扰理论的磁悬浮轴承控制系统设计与研究[D]. 南京: 南京航空航天大学, 2017.
[19] 朱良红, 张国强, 李宇欣, 等. 基于级联扩张观测器的永磁电机无传感器自抗扰控制策略[J]. 电工技术学报, 2022, 37(18): 4614-4624.
Zhu Lianghong, Zhang Guoqiang, Li Yuxin, et al.Active disturbance rejection control for position sensorless permanent magnet synchronous motor drives based on cascade extended state observer[J]. Transactions of China Electrotechnical Society, 2022, 37(18): 4614-4624.
[20] 李思毅, 苏健勇, 杨贵杰. 基于自抗扰控制的永磁同步电机弱磁控制策略[J]. 电工技术学报, 2022, 37(23): 6135-6144.
Li Siyi, Su Jianyong, Yang Guijie.Flux weakening control strategy of permanent magnet synchronous motor based on active disturbance rejection control[J]. Transactions of China Electrotechnical Society, 2022, 37(23): 6135-6144.
[21] Bhattacharyya S.Observer design for linear systems with unknown inputs[J]. IEEE Transactions on Auto-matic Control, 1978, 23(3): 483-484.
[22] Kudva P, Viswanadham N, Ramakrishna A.Observers for linear systems with unknown inputs[J]. IEEE Transa-ctions on Automatic Control, 1980, 25(1): 113-115.
[23] Darouach M, Zasadzinski M, Xu S J.Full-order observers for linear systems with unknown inputs[J]. IEEE Transactions on Automatic Control, 1994, 39(3): 606-609.
[24] Darouach M, Zasadzinski M, Hayar M.Reduced-order observer design for descriptor systems with unknown inputs[J]. IEEE Transactions on Automatic Control, 1996, 41(7): 1068-1072.
[25] Bara G I, Rafaralahy H, Zasadzinski M, et al.State observers for a class of bilinear descriptor systems subjected to unmeasurable disturbances[C]//Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, AZ, USA, 2002: 85-87.
[26] Kalsi K, Lian Jianming, Hui S, et al.Sliding-mode observers for systems with unknown inputs: a high-gain approach[J]. Automatica, 2010, 46(2): 347-353.
[27] 张建成, 朱芳来. 匹配条件不满足时线性系统未知输入观测器设计[J]. 控制理论与应用, 2017, 34(4): 441-448.
Zhang Jiancheng, Zhu Fanglai.Linear system unknown input observer design when the observer matching condition is not satisfied[J]. Control Theory & Applications, 2017, 34(4): 441-448.
[28] Gao Zhiqiang, Hu Shaohua, Jiang Fangjun.A novel motion control design approach based on active disturbance rejection[C]//Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, FL, USA, 2002: 4877-4882.
[29] 孟占峰, 韩潮. 模态密集柔性空间结构二阶内平衡降阶[J]. 航空学报, 2008, 29(2): 364-372.
Meng Zhanfeng, Han Chao.Second-order balanced reduction for flexible space structures with close modes[J]. Acta Aeronautica et Astronautica Sinica, 2008, 29(2): 364-372.