论文总字数：25221字

摘 要

磁悬浮飞轮系统存在着惯性耦合、陀螺耦合、非线性、同频扰动等控制难题，目前仍没有得到很好的解决，因此本文基于H_∞控制理论对磁悬浮飞轮轴承的控制系统进行了以下研究工作：

本文分析了磁悬浮飞轮轴承系统的各个环节，包括轴承-转子结构、控制器、功率放大器和传感器等，根据动力学理论，考虑所选用模型的各部分参数，分析和计算各控制量以及中间转化的数据，建立了单自由度和五自由度磁悬浮飞轮轴承-转子数学模型，为便于分析以及计算，对其进行了强制解耦。分别对传感器和控制器在径向和轴向的传递函数模型进行了基本的分析，给出了具体的传递函数矩阵。

针对磁悬浮飞轮H_∞控制系统不确定性的问题，引入对广义受控对象的描述，结合系统模型以及线性定常系统动态方程，分析了广义受控对象在控制系统中的传递函数矩阵，并得出控制系统从输入到输出的闭环传递函数。求证了实际系统中以闭环传递函数H_∞范数最小为指标设计出的控制器是最优控制器，并指出将次优控制问题转化为最优问题，即标准H_∞控制问题的求解问题。详细讨论了H_∞控制所包含的各类控制问题，分别将它们通过模型转化、等量变换归结到统一的求解标准H_∞控制问题，这样就可以用一致的标准来衡量控制器的性能，化简了各类模型结构，便于分析计算。

详细讨论了基于H_∞混合灵敏度控制的加权函数的选择方法，研究了它们的约束条件，频率曲线特性以及一般选择规律。由于磁悬浮飞轮系统一般会存在多种控制问题，考虑了各种控制方式的优缺点，本文采用H_∞混合灵敏度控制方法，分析及计算了单自由度上的H_∞混合灵敏度控制器参数以及系统传递函数，并通过仿真探讨了该控制器对外界干扰的抑制性能和对输入信号的跟踪性能。对于磁悬浮飞轮径向单自由度和轴向单自由度的控制，本文分别分析和设计了相对应的H_∞混合灵敏度控制器。本文还在Matlab/Simulink环境中分别进行了系统仿真，根据运行出的控制器数据和得出的各曲线图进行分析，经多次调试后得到的H_∞控制器具有良好稳定的信号跟踪以及抑制干扰的性能。

关键词:磁悬浮飞轮轴承 H_∞控制 混合灵敏度 加权函数

H-infinity Control of Magnetic Suspended Flywheel System

Abstract

The magnetically suspended flywheel system exists coupling inertia, gyroscopic coupling, nonlinear and same frequency disturbance control problems , there is no good solutions until now. Therefore, this paper has carried out the following research study based on H-infinity control theory of magnetic bearing flywheel control system:

In this paper, the various links of the magnetic bearing system are analyzed, including the bearing rotor structure, the power amplifier, the sensor and the controller. The mathematical model of the single degree of freedom and the five degree of freedom bearing rotor bearing is established, which is convenient for analysis and calculation., and forced them to be decoupled. Made the basic analysis of the transfer function model for sensors and controllers in the radial and axial direction , and the specific transfer function matrix is given.

For the uncertain systems in magnetically suspended flywheel H-infinity control causing problems, introduced description of generalized controlled object, in combination with the system model and linear constant system dynamic equation, analysed transfer function matrix of the generalized controlled object in control system , and obtained control system from the input to the output of the closed-loop transfer function. Verified a closed loop transfer function H-infinity norm minimum design index of the controller is optimal controller in the actual system , and points out that the suboptimal control problem can transform into the optimal problem, namely standard H-infinity control problem . Discussed in detail all kinds of control problems in the H-infinity control system, respectively transformed them through model and equivalent transformation boils to the unified standards for solving the H-infinity control problem. So that it can be used to measure the standard of controller performance, also simplified structure of various types of model for calculation and analysis.

Discussed in detail the weighting function selection method based on H-infinity mixed sensitivity controlling , studied their constraints , frequency characteristic curve and the general selection rules . Due to magnetic levitation flywheel system usually has variety of control problems, took into advantages and disadvantages of various control modes , the H-infinity mixed sensitivity control method are adopted in this paper, analyzed and calculated the single degree of freedom on the H-infinity mixed sensitivity controller parameters and the system transfer function, through simulation discussing the effects of the controller for external disturbance and the input signal tracking performance. For the magnetic levitation flywheel radial single degree and axial single degree of freedom controlling, analyzed and designed the corresponding H-infinity mixed sensitivity controller. Under the situation of Matlab / Simulink , The system simulation and analysis is carried out ,according to the operation controller data and draw the curve graph, after several debugging the H-infinity controller obtained has good and stable signal tracking and disturbance rejection performance.

Keywords: Magnetic; flywheel; bearing; H-infinity control; Mixed-sensitivity; weighting function

目录

摘要 I

Abstract II

第一章 绪论 1

1.1 背景与意义 1

1.2 磁悬浮飞轮的研究与应用现状 1

1.3 磁悬浮飞轮的控制 2

1.4 本文研究内容 4

第二章 磁悬浮飞轮系统结构与模型分析 6

2.1系统结构及工作原理 6

2.2.单自由度转子的数学模型 6

2.3 五自由度磁悬浮飞轮转子的数学模型 8

2.4 位移传感器和功率放大器数学模型 10

2.4.1 位移传感器 10

2.4.2 功率放大器 10

2.5控制电路引入的增益 11

2.6磁悬浮飞轮模型的数值分析与变换 11

第三章 H_∞控制原理分析 16

3.1 磁悬浮飞轮系统不确定性的描述 16

3.2 范数 17

3.3 广义受控对象的描述 17

3.4 H_∞控制的标准问题 18

3.5 H_∞控制的各类控制问题分析 19

3.5.1 灵敏度极小化问题 19

3.5.2 鲁棒镇定问题 19

3.5.3 混合灵敏度问题 21

第四章 磁悬浮飞轮的H_∞混合灵敏度控制 22

4.1 H_∞混合灵敏度控制的系统结构 22

4.2 加权函数的选择 22

4.3 控制器仿真 25

4.3.1 径向自由度 25

4.3.2 轴向自由度 29

第五章 总结与思考 32

5.1 论文的主要工作 32

5.2 研究过程中的思考 32

参考文献 34

致谢 36

第一章 绪论

1.1 背景与意义

磁悬浮飞轮是一种具有广阔应用前景的新型机电技术，飞轮储能具有转速高，储能大，功率高，适用广，寿命长，易维护等优点，在多个领域开展了广泛的研究及生产应用。主动磁悬浮轴承由于具有转速高、无磨损、转子可超高速运行及环境友好等突出优点，可以应用于真空环境，为磁悬浮飞轮的研发提供了条件^[1,2]，磁悬浮飞轮技术的研究是建立在磁悬浮轴承技术的基础之上的。

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