论文总字数：23910字

摘 要

磁悬浮飞轮储能系统中根据电磁转换原理，通过控制输入电流的大小，使得磁轴承产生可以约束的电磁力，从而使得定转子能够分离，达到两者间不接触的旋转，减少因相互接触而引起的摩擦损耗，提高储能效率。在转子转速很高时，磁轴承径向间会产生陀螺耦合效应，造成系统失去稳定性，不能达到控制要求。与此同时飞轮转子在高速旋转时还会受到来自外界的各种干扰从而使得系统失去稳定性造成系统运行状况的崩溃。本文采用交叉反馈控制方法消除了磁轴承因陀螺耦合效应造成的失稳，使得系统能够在高转速情况下保持系统的稳定性。

首先第一部分主要对径向四自由度磁轴承的转子进行了力学分析和数学建模，分析了所建立的模型中转子在旋转过程中受到的磁力、负荷力和因质量不等而引起的不平衡力。第二部分主要对陀螺耦合效应产生的原理进行了数学公式的推导进行解释。同时也详细的阐述了弹性支承、阻尼支承、位移交叉反馈支承和速度交叉反馈支承这四种支承方式。

因为PID控制器只适应于低转速情况下，此时各自由度之间的耦合可以忽略。但当转速上升时会产生陀螺效应使得系统失去稳定性。所以本文采用交叉反馈控制，在传统PID控制器的基础上加入了速度和位移在空间上相角超前的交叉反馈进行补偿，通过对零极点图对比分析了交叉反馈控制对提高稳定性的实验依据，通过转子质心轨迹图得出系统趋稳的走势，从而得出交叉反馈在高转速的情况下能够使得系统的稳定性得到提高。

通过Matlab中Simulink对系统的控制器和本体模型进行仿真，得出转子在额定转速20000 rpm下转子质心运动轨迹和转子趋稳的图形，从而验证了交叉反馈具有良好的解除耦合的作用，可以在高转速的情况下可以消除因陀螺耦合效应对系统造成的干扰。

关键词：飞轮储能 动力学分析 四自由度建模 交叉反馈

Research on Cross-Feedback Control of Magnetic Suspension Flywheel

ABSTRACT

Magnetic levitation flywheel energy storage system according to the principle of electromagnetic conversion, by controlling the size of the input current, so that the magnetic bearing can generate a constrained electromagnetic force, so that the stator and rotor can be separated to achieve the rotation between the two contact, reducing the contact caused by the contact The friction loss increases the energy storage efficiency. When the rotational speed of the rotor is high, a gyroscopic coupling effect will occur between the magnetic bearings in the radial direction, causing the system to lose stability and fail to meet the control requirements. At the same time, the flywheel rotor also receives various disturbances from the outside while rotating at a high speed, which causes the system to lose stability and cause the system to run down. In this paper, cross-feedback control method is used to eliminate the instability of the magnetic bearing due to the gyro coupling effect, so that the system can maintain the stability of the system at high speed.

In the first part of the second chapter, the mechanical analysis and mathematical modeling of the rotor of a radial four-degree-of-freedom magnetic bearing are mainly carried out. The magnetic force, load force and the quality of the rotor in the rotation of the model are analyzed. Unbalanced force caused. The second part mainly explains the mathematical formula derivation of the principle of gyro coupling effect. At the same time, the four support modes of elastic support, damping support, displacement cross feedback support and velocity cross feedback support are also described in detail.

Because the PID controller is only suitable for low speed conditions, the coupling between the degrees of freedom can be ignored. But when the speed increases, the gyroscopic effect will cause the system to lose stability. So in this paper, cross feedback control is adopted to compensate the cross feedback of speed and displacement in space above the phase angle on the basis of the traditional PID controller. By comparing the zero pole graph, the experimental basis of the cross feedback control to improve the stability is analyzed. Finally, the intersection and fork feedback can be obtained at high speed. The stability of the system is improved.

Through the simulation of the system controller and the ontology model in Matlab, the rotor centroid motion trajectory and the rotor stabilization pattern at the rated speed of 20000 r/min are obtained, which proves that the cross feedback has a good decoupling effect, that can eliminate the interference caused by the gyroscope coupling effect at high speed.

KEYWORDS: Flywheel energy storage dynamics analysis cross feedback

four degree of freedom modeling

目 录

摘 要 II

ABSTRACT III

第一章 绪论 1

1.1 课题的研究背景及意义 1

1.2 磁轴承简介 2

1.2.1 磁轴承研究及应用现状 2

1.3 磁悬浮飞轮转子的控制算法研究 4

1.4 课题研究内容 4

第二章 磁轴承转子系统建模与陀螺效应分析 6

2.1磁轴承转子运动模型与受力分析 6

2.1.1 径向四自由度磁悬浮飞轮转子系统建模 6

2.1.2 转子受力情况分析 10

2.2 磁轴承转子陀螺效应分析 13

2.2.1 转子陀螺效应原理及特性 13

2.2.2 转子陀螺力矩与支承力矩分析 14

2.3 本章小结 16

第三章 控制算法设计分析与分析 17

3.1 PID控制算法设计与分析 17

3.2 交叉反馈控制算法设计与分析 20

3.3 本章小结 23

第四章 陀螺效应抑制仿真分析 24

4.1 交叉反馈系统控制器仿真 24

4.2 PID系统控制器仿真 29

4.3 本章小结 33

第五章 总结与展望 34

5.1工作总结 34

5.2工作展望 35

参考文献 36

致谢 38

第一章 绪论

1.1 课题的研究背景及意义

人类社会的发展进步历史就是不断对能源需求不断增加以及开发各种形式能源的历史。当前电力能源系统已具有多种形式的能源储能方式，比较常见的存储方式有物理形式储能，比如热能；化学形式的储能：如镍镉电池；还有诸如超导磁储能、电容器储能^[1]等；

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