非定向磁轴承的模糊RBF神经网络PID控制策略

谢文海; 谢振宇; 许绍瀚; 肖锋

doi:10.13224/j.cnki.jasp.20240827

非定向磁轴承的模糊RBF神经网络PID控制策略

doi: 10.13224/j.cnki.jasp.20240827

南京航空航天大学直升机传动技术重点实验室，南京 210016

详细信息

作者简介:
谢文海（2000-），男，硕士，主要从事磁悬浮轴承控制研究。E-mail：xiewenhai@nuaa.edu.cn

通讯作者:
谢振宇（1968-），男，副教授，博士，主要从事磁悬浮轴承研究。E-mail：xiezy@nuaa.edu.cn

中图分类号: V233；TH133
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出版历程
- 收稿日期: 2024-12-07
- 网络出版日期: 2025-07-15

Fuzzy RBF neural network PID control strategy for non-directional magnetic bearing

National Key Laboratory of Science and Technology on Helicopter Transmission，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，China

摘要

摘要:
采用非定向差动控制方式，通过分别控制各差动磁极对，提高径向磁轴承的承载能力。常规PID（proportion integration differentiation）控制面对复杂非线性的磁轴承系统，难以满足控制要求。提出基于非定向差动控制方式的模糊RBF（radial basis function）神经网络PID控制策略，通过在线训练模型实现PID参数的在线整定，以满足复杂的工况。以16磁极径向磁轴承为例，对常规差动控制方式与非定向差动控制方式的工作原理进行分析，对比两者的名义最大承载力。理论计算结果表明，非定向磁轴承的名义最大承载力提高了30.66%。利用Simulink对模糊RBF神经网络PID控制策略进行仿真，仿真结果表明，该控制策略具有更好的静态和动态性能。通过搭建试验台进行径向磁轴承实际最大承载力试验和系统高速旋转试验，试验结果表明，非定向磁轴承的实际最大承载力提高了26.07%，模糊RBF神经网络PID控制策略具有较好的控制效果。
- 径向磁轴承 /
- 非定向差动控制方式 /
- 名义最大承载力 /
- 模糊RBF神经网络PID控制 /
- 动态性能
Abstract:
With introduction of non-directional differential control method, the bearing capacity of the radial magnetic bearing was improved by independently controlling each differential magnetic pole pair. As the conventional PID (proportion integration differentiation) control was found difficult to meet the control requirements of the complex nonlinear magnetic bearing system, the fuzzy RBF (radial basis function) neural network PID control strategy based on the non-directional differential control method was proposed to realize the online adjustment of PID parameters through an online training model so as to meet complex working conditions. Taking the 16-pole radial magnetic bearing as an example, the working principle of the conventional differential control method and the non-directional differential control method was analyzed, and the nominal maximum bearing capacity of the two control methods was compared. The theoretical calculation results showed that the nominal maximum bearing capacity of the radial magnetic bearing based on the non-directional differential control method increased by 30.66%. Simulink software was adopted to simulate the PID control strategy of the fuzzy RBF neural network. The simulation results showed that the control strategy had better static and dynamic performance. By setting up a test bench, actual maximum bearing capacity tests for radial magnetic bearing and high-speed rotation tests for the system were conducted. The test results showed that the actual maximum bearing capacity of the radial magnetic bearing based on the non-directional differential control method increased by 26.07%, and the fuzzy RBF neural network PID control strategy had better control effect compared with the conventional PID control strategy.
- radial magnetic bearing /
- non-directional differential control method /
- nominal maximum bearing capacity /
- fuzzy RBF neural network PID control /
- dynamic performance

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图 1 16磁极径向磁轴承磁极对分布

Figure 1. 16 pole pairs distribution of radial magnetic bearings

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图 2 常规差动控制方式磁极组分布

Figure 2. Distribution of pole groups under conventional differential control method

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图 3 常规差动控制方式系统框图

Figure 3. Block diagram of the conventional differential control method

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图 4 非定向差动控制方式磁极对分布

Figure 4. Distribution of pole groups under non-directional differential control method

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图 5 非定向差动控制方式系统框图

Figure 5. Block diagram of the non-directional differential control method

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图 6 16磁极径向磁轴承各差动磁极对作用力分布图

Figure 6. Force distribution diagram of each differential magnetic pole pair of the 16-pole radial magnetic bearing

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图 7 两种控制方式在0°～90°下的磁轴承电磁力

Figure 7. Electromagnetic force of magnetic bearing at 0°—90° in two control methods

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图 8 两种控制方式在0°～360°下的磁轴承电磁力

Figure 8. Electromagnetic force of magnetic bearing at 0°—360°in two control methods

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图 9 磁轴承系统结构框图

Figure 9. Block diagram of magnetic bearing system

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图 10 磁轴承转子系统机械结构

1 左径向位移传感器；2 左径向磁轴承；3轴向磁轴承；4 右径向磁轴承；5 右径向位移传感器；6 轴向位移传感器；7 轴向保护轴承；8 右径向保护轴承；9 转子；10 内置式电动机；11 左径向保护轴承。

Figure 10. Mechanical structure of the magnetic bearing rotor system

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图 11 转子受力分析

Figure 11. Analysis of rotor forces

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图 12 模糊RBF神经网络PID控制结构框图

Figure 12. Structure block diagram of fuzzy RBF neural network PID control

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图 13 模糊RBF神经网络结构图

Figure 13. Structure diagram of fuzzy RBF neural network

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图 14 模糊RBF神经网络PID控制器仿真模型

Figure 14. Simulation model of fuzzy RBF neural network PID controller

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图 15 各控制器阶跃响应仿真曲线

Figure 15. Step response simulation curves of each controller

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图 16 各控制器正弦波扰动仿真曲线

Figure 16. Sine wave disturbance simulation curves of each controller

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图 17 磁悬浮系统试验平台

1 变频器；2 磁轴承转子系统；3 磁轴承控制系统；4 示波器；5 计算机。

Figure 17. Magnetic levitation system test bench

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图 18 悬挂砝码转子受力示意图

Figure 18. Force diagram of rotor under suspension weight

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图 19 PID控制下线圈电流

Figure 19. Coil current by PID control

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图 20 模糊RBF神经网络PID控制下线圈电流

Figure 20. Coil current by fuzzy RBF neural network PID control

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图 21 PID控制下转子位移

Figure 21. Rotor displacement by PID control

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图 22 模糊RBF神经网络PID控制下转子位移

Figure 22. Rotor displacement by fuzzy RBF neural network PID control

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表 1 常规与非定向差动控制方式所需硬件数量

Table 1. Amount of hardware required for conventional versus non-directional differential control methods

硬件	常规差动控制	非定向差动控制
传感器电路	2	2
控制器	2	4
功率放大器	4	8
位移分解电路	0	1

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表 2 径向磁轴承设计参数

Table 2. Design parameters for radial magnetic bearings

参数	数值
磁极有效面积/mm²	68
线圈匝数	48
偏置电流/A	5
气隙/mm	0.25
单边保护气隙/mm	0.1

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表 3 符号说明及转子相关参数

Table 3. Symbols and rotor parameters

参数	含义	数值
x_a、y_a	转子左径向x、y方向位移
F_ax、F_ay	转子左径向x、y方向受力
x_c、y_c	转子质心x、y方向位移
${\theta _x}$、${\theta _y}$	转子绕质心x、y轴转角
ω	转子绕z轴角速度
x_b、y_b	转子右径向x、y方向位移
F_bx、F_by	转子右径向x、y方向受力
m/kg	转子质量	6
l_a/mm	转子质心与左径向磁轴承距离	108.3
l_b/mm	转子质心与右径向磁轴承距离	79.7
L/mm	转子两径向磁轴承距离	188
J/（g·m²）	转子绕x、y轴的转动惯量	50.4
J_z/（g·m²）	转子绕z轴的转动惯量	1.68

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表 4 3个修正参数的模糊控制规则表

Table 4. Fuzzy control rule table with three modified parameters

x_d	x_dc
x_d	NB	NM	NS	ZO	PS	PM	PB
NB	PB/NB/PS	PB/NB/NS	PM/NM/NB	PM/NM/NB	PS/NS/NB	ZO/ZO/NM	ZO/ZO/PS
NM	PB/NB/PS	PB/NB/NS	PM/NM/NB	PS/NS/NM	PS/NS/NM	ZO/ZO/NS	NS/ZO/ZO
NS	PM/NB/ZO	PM/NM/NS	PM/NS/NM	PM/NS/NM	ZO/ZO/NS	NS/PS/NS	NS/PS/ZO
ZO	PM/NM/ZO	PM/NM/NS	PS/NS/NS	ZO/ZO/NS	NS/PS/NS	NM/PM/NS	NM/PM/ZO
PS	PS/NM/ZO	PS/NS/ZO	ZO/ZO/ZO	NS/PS/ZO	NS/PS/ZO	NM/PM/ZO	NM/PB/ZO
PM	PS/ZO/PB	ZO/ZO/NS	NS/PS/PS	NM/PS/PS	NM/PM/PS	NM/PB/PS	NB/PB/PB
PB	ZO/ZO/PB	ZO/ZO/PM	NM/PS/PM	NM/PM/PM	NM/PM/PS	NB/PB/PB	NB/PB/PB

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表 5 不同控制方式最大承载力

Table 5. Maximum bearing capacity adopting different control methods

承载力	常规差动控制方式	非定向差动控制方式	提升百分比/%
名义最大承载力/N	142.68	186.43	30.66
实际最大承载力/N	96.14	121.2	26.07

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