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 the control of other position is needed, an estimator construct by the observer is the keyway to track and obtain 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 Luenberger observer does not take into account the problem of 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 of 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 system (A, C_m, B_u) are all in the left half plane. This condition is actually equivalent to fact that the disturbance input matrix B_u is full of rank and the system matrix A is stable. Since the AMB under PID controller can provide positive stiffness and damping similar to mechanical bearings, the system matrix A be 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.
$ \left\{\begin{array}{l} \dot{\bar{z}}=G \bar{A} \hat{\bar{x}}+G B u+L(\bar{y}-\bar{C} \hat{\bar{x}}) \\ \hat{\bar{x}}=z+H \bar{y} \end{array}\right.$
However, the observer matching condition is not satisfied in many systems. In the AMBs - flexible rotor system, the output matrix C_m is the position of the displacement sensors, while the unbalanced force acts on the acceleration of the system, resulting 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 outputs y and auxiliary output $ \ddot{y}-C_{\mathrm{m}} A B u-C_{\mathrm{m}} B \dot{u}$. The new input matrix C_mAB_u is full of rank, satisfying the matching condition.
Before observing the AMBs - flexible rotor system, the state observability needs to be solved. The first is the observable condition of 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, a total of 6 displacement sensors are required. In addition, the observability of the system is calculated using the Gramian factor, and the position 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 extended disturbance state performs better, but still suffers from phase lag when the input frequency is above the observer bandwidth. The UIO with auxiliary output can track the physics system accurately over a large frequency area.
In order to verify the validity of the method proposed in this paper, simulations and experiments are carried out. 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 analyzed above. In the experiment, the second derivative in the auxiliary output is replace 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 method proposed in this paper can track all system outputs with high precision in the region of 0-6000 rpm and estimate the displacement of the target position accurately.

Key words： active magnetic bearing flexible rotor state observer

PACS:

TM133.3

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	LI Weng-heng
	ZHU Chang-sheng

Cite this article:

LI Weng-heng,ZHU Chang-sheng. High Precision Tracking and Estimation Method for Vibration Displacement of Active Magnetic Bearings - Flexible Rotor System[J]. Transactions of China Electrotechnical Society, 0, (): 9-9.

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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/Y0/V/I/9

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