Introduction The working principle of active magnetic bearings (AMBs) is mainly based on the interaction of electromagnetic force and magnetic field. Specifically, the AMBs detects the position deviation signals of the rotor through the position sensor and sends these signals to the controller. According to these signals, the controller controls the current of the electromagnet through a power amplifier, resulting in a change in the electromagnetic force, so that the spindle is suspended in the specified position. Advantages of AMBs include high speed, low power consumption, long life, no lubrication, and the ability to operate in vacuum and over a wide temperature range. These advantages make AMBs have obvious advantages compared with traditional bearings in many application fields. Among the vibration control methods of an AMBs high speed motor rigid rotor system, the linear quadratic regulator (LQR) can realize the optimal control of rotor vibration and control current, and is not limited to the specific vibration form. Purpose The purpose of this paper is using LQR to control the rotor vibration and energy consumption of the high speed motor rotor system. Since the linear quadratic regulator (LQR) not only can easily obtain the optimal control rate of the state linear feedback of the high speed motor rotor system, but also expediently form the closed-loop optimal control, it is often used to control the rotor vibration and energy consumption of the high speed motor rotor system. Aiming at the LQR control of the active magnetic bearings (AMBs)-high speed motor rigid rotor system, the four-degree-of freedom motion equation given in the form of state space is usually taken as the constraint condition, and the rotor vibration and control current are used to construct the objective function J which is the quadratic function of both rotor vibration and control current. Methods The main methods include: (1) aiming at the LQR control of the active magnetic bearings (AMBs)-high speed motor rigid rotor system, the four-degree-of freedom motion equation given in the form of state space is taken as the constraint condition, and the rotor vibration and control current are used to construct the objective function J which is the quadratic function of both rotor vibration and control current. (2) the state feedback controller K controlled by LQR needs to minimize J, and K is only determined by the weight matrices Q and R. Therefore, the choice of Q and R is particularly significant. (3) due to the differences between the supporting modes of traditional sliding bearings and that of AMBs, the LQR control used in the traditional bearings is not suitable for the AMBs high speed motor rigid rotor system, so it is necessary to explore the design method of LQR of the AMBs high speed motor rigid rotor system. Results These three steps result that the design method of LQR in the AMBs high speed motor rigid rotor system and the influence of weight matrix Q and R on the control performance are studied in this paper. Discussion The four-degree-of-freedom motion equation of the rigid rotor system of AMBs high speed motor is taken as the constraint condition, and appropriate state variables are selected to construct the objective function with rotor vibration and control current as the performance index. By selecting the appropriate <Emphasis Type="BoldItalic">Q</Emphasis> and <Emphasis Type="BoldItalic">R</Emphasis> weight matrices to design the LQR controller, the optimal state feedback controller <Emphasis Type="BoldItalic">K</Emphasis> is obtained to realize the closed-loop control of an AMBs high speed motor rigid rotor system. At the same time, the design method of LQR and the selection principle of weight matrices are given. Finally, the experimental results show that the vibration control method based on LQR can effectively control the rotor vibration of an AMBs high speed motor rigid rotor system in the full speed range including two rigid body modes. Conclusion The principle of LQR control was introduced in this paper, which considered the power amplifier loss and rotor vibration control in the rigid rotor system of high speed motor. Then, the LQR controller of the rigid rotor system of high speed motor was designed according dynamic motion equation of a four-degree-of-freedom rotor. After that, the performance index of the system was constructed from the rotor vibration and the output current of the power amplifier, and the expression of the control rate was given. The effects of LQR controller parameters Q11, Q22 and R on the performance of rigid rotor system of AMBs high speed motor were further studied. Finally, the vibration control effect of rigid rotor system of AMBs high speed motor under LQR control was verified by simulation and experiment.

Vibration Control of Full Rotational Speed Range for Magnetically Levitated High-Speed Motors Based on Linear Quadratic Regulator

期刊论文
发表日期：

2025年1月15日

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Lei Gong,
Pai He,
Wang Yichen,
Dang Zhaoyang,
Changsheng Zhu

摘要

Introduction

The working principle of active magnetic bearings (AMBs) is mainly based on the interaction of electromagnetic force and magnetic field. Specifically, the AMBs detects the position deviation signals of the rotor through the position sensor and sends these signals to the controller. According to these signals, the controller controls the current of the electromagnet through a power amplifier, resulting in a change in the electromagnetic force, so that the spindle is suspended in the specified position. Advantages of AMBs include high speed, low power consumption, long life, no lubrication, and the ability to operate in vacuum and over a wide temperature range. These advantages make AMBs have obvious advantages compared with traditional bearings in many application fields. Among the vibration control methods of an AMBs high speed motor rigid rotor system, the linear quadratic regulator (LQR) can realize the optimal control of rotor vibration and control current, and is not limited to the specific vibration form.

Purpose

The purpose of this paper is using LQR to control the rotor vibration and energy consumption of the high speed motor rotor system. Since the linear quadratic regulator (LQR) not only can easily obtain the optimal control rate of the state linear feedback of the high speed motor rotor system, but also expediently form the closed-loop optimal control, it is often used to control the rotor vibration and energy consumption of the high speed motor rotor system. Aiming at the LQR control of the active magnetic bearings (AMBs)-high speed motor rigid rotor system, the four-degree-of freedom motion equation given in the form of state space is usually taken as the constraint condition, and the rotor vibration and control current are used to construct the objective function J which is the quadratic function of both rotor vibration and control current.

Methods

The main methods include: (1) aiming at the LQR control of the active magnetic bearings (AMBs)-high speed motor rigid rotor system, the four-degree-of freedom motion equation given in the form of state space is taken as the constraint condition, and the rotor vibration and control current are used to construct the objective function J which is the quadratic function of both rotor vibration and control current. (2) the state feedback controller K controlled by LQR needs to minimize J, and K is only determined by the weight matrices Q and R. Therefore, the choice of Q and R is particularly significant. (3) due to the differences between the supporting modes of traditional sliding bearings and that of AMBs, the LQR control used in the traditional bearings is not suitable for the AMBs high speed motor rigid rotor system, so it is necessary to explore the design method of LQR of the AMBs high speed motor rigid rotor system.

Results

These three steps result that the design method of LQR in the AMBs high speed motor rigid rotor system and the influence of weight matrix Q and R on the control performance are studied in this paper.

Discussion

The four-degree-of-freedom motion equation of the rigid rotor system of AMBs high speed motor is taken as the constraint condition, and appropriate state variables are selected to construct the objective function with rotor vibration and control current as the performance index. By selecting the appropriate Q and R weight matrices to design the LQR controller, the optimal state feedback controller K is obtained to realize the closed-loop control of an AMBs high speed motor rigid rotor system. At the same time, the design method of LQR and the selection principle of weight matrices are given. Finally, the experimental results show that the vibration control method based on LQR can effectively control the rotor vibration of an AMBs high speed motor rigid rotor system in the full speed range including two rigid body modes.

Conclusion

The principle of LQR control was introduced in this paper, which considered the power amplifier loss and rotor vibration control in the rigid rotor system of high speed motor. Then, the LQR controller of the rigid rotor system of high speed motor was designed according dynamic motion equation of a four-degree-of-freedom rotor. After that, the performance index of the system was constructed from the rotor vibration and the output current of the power amplifier, and the expression of the control rate was given. The effects of LQR controller parameters Q₁₁, Q₂₂ and R on the performance of rigid rotor system of AMBs high speed motor were further studied. Finally, the vibration control effect of rigid rotor system of AMBs high speed motor under LQR control was verified by simulation and experiment.