基于模糊PID控制的准零刚度磁悬浮隔振平台的设计与实现

翟明达; 张博; 李晓龙; 龙志强

doi:10.3969/j.issn.0258-2724.20220880

基于模糊PID控制的准零刚度磁悬浮隔振平台的设计与实现

doi: 10.3969/j.issn.0258-2724.20220880

国防科技大学智能科学学院，湖南长沙 410000

基金项目: 国家重点研发计划（2016YFB1200601, 2016YFB1200602）

详细信息

作者简介:
翟明达（1990—），男，助理研究员，博士，研究方向为悬浮控制与优化，E-mail：zhaimd@126.com

通讯作者:
李晓龙（1979—），男，副研究员，研究方向为悬浮控制、磁浮隔振，E-mail：13787786254@163.com

中图分类号: TP273
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- 文章访问数: 1238
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- PDF下载量: 51
- 被引次数: 0
出版历程
- 收稿日期: 2022-12-21
- 修回日期: 2023-05-04
- 网络出版日期: 2023-06-17
- 刊出日期: 2023-05-06

Design and Implementation of Magnetic Suspension Vibration Isolation Platform with Quasi-Zero Stiffness Based on Fuzzy PID Control

College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410000, China

摘要

摘要:
为有效降低系统固有频率，获得外部振动在多频段的强衰减，以永磁电磁混合作动器为负刚度结构提出并设计了一种准零刚度的磁悬浮隔振平台，实现了基于模糊PID (proportional integral differential)算法的振动主动控制系统. 首先，通过特性分析与参数计算，基于准零刚度理论完成了准零刚度磁悬浮隔振平台的方案设计；其次，建立磁悬浮隔振系统模型，提出基于模糊PID算法的振动主动控制策略，可主动调节系统的等效刚度和阻尼；最后，基于Speedgoat实时目标机开发振动主动控制系统，搭建隔振测试平台，并开展了隔振性能测试. 研究结果表明：本文设计的准零刚度磁悬浮隔振平台通过采用模糊PID的控制策略能够主动调节PID参数，动态调整系统的等效刚度和阻尼；外部振动频率在20～100 Hz频率段内，振动衰减率大于80%；外部振动频率在100～500 Hz频率段内，振动衰减率大于90%.
- 隔振 /
- 准零刚度 /
- 磁悬浮 /
- 永磁电磁混合作动器 /
- 模糊PID
Abstract:
In order to effectively reduce the natural frequency of systems and realize the strong attenuation of external vibrations in multiple frequency bands, a magnetic suspension vibration isolation platform with quasi-zero stiffness was designed, in which the permanent-magnet and electromagnetic hybrid actuator was the negative stiffness structure, and an active vibration control system based on fuzzy PID (proportional integral differential) algorithm was implemented. Firstly, based on the theory of quasi-zero stiffness, the scheme of the magnetic suspension vibration isolation platform with quasi-zero stiffness was designed through characteristic analysis and parameter calculation; secondly, the model of the magnetic suspension vibration isolation system was established, and the active vibration control strategy based on fuzzy PID algorithm was designed to actively adjust the equivalent stiffness and damping of the system; finally, an active vibration control system was developed based on the Speedgoat real-time target machine. A vibration isolation test platform was built, and a series of vibration isolation performance tests were carried out. The results show that the magnetic suspension vibration isolation platform with quasi-zero stiffness can actively adjust PID parameters by adopting a fuzzy PID control strategy and dynamically adjust the equivalent stiffness and damping of the system. When the external vibration frequency is 20–100 Hz, the vibration attenuation rate is greater than 80%; when the external vibration frequency is 100–500 Hz, the vibration attenuation rate is greater than 90%.
- vibration isolation /
- quasi-zero stiffness /
- magnetic suspension /
- permanent-magnet and electromagnetic hybrid actuator /
- fuzzy PID

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图 1 准零刚度隔振器工作原理

Figure 1. Working principle of quasi-zero stiffness vibration isolator

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图 2 准零刚度磁悬浮隔振平台

Figure 2. Magnetic suspension vibration isolation platform with quasi-zero stiffness

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图 3 永磁电磁混合作动器的结构

Figure 3. Structure of permanent-magnet and electromagnetic hybrid actuator

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图 4 永磁电磁混合作动器三维有限元模型

Figure 4. Three-dimensional finite element model of permanent-magnet and electromagnetic hybrid actuator

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图 5 电流环动态结构

Figure 5. Dynamic structure of current loop

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图 6 电磁铁的阶跃响应曲线

Figure 6. Step response curve of electromagnet

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图 7 模糊PID算法的流程图

Figure 7. Flow chart of fuzzy PID algorithm

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图 8 PID与模糊PID控制算法隔振效果对比

Figure 8. Comparison of vibration isolation effects of PID and fuzzy PID control algorithms

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图 9 隔振效果

Figure 9. Vibration isolation effect

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表 1 永磁体具体参数

Table 1. Detailed parameters of permanent magnet

参数名称	参数符号	参数值
剩余磁感应强度/T	B_r	1.2
矫顽力/（kA•m⁻¹）	H_c	896
相对磁导率	$\mu_{{\rm{r}}}$	1.05

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表 2 永磁体在工作点附近产生的电磁吸力

Table 2. Electromagnetic attraction generated by permanent magnet near working point N

永磁体厚度/mm	悬浮间隙/mm
永磁体厚度/mm	9.5	10.0	10.5
7	465.1	430.4	399.0
8	532.5	493.9	459.3
9	595.4	553.1	515.6
10	652.2	608.9	567.8
11	705.5	658.7	615.3
12	753.2	704.2	659.3
13	797.1	747.0	699.9

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表 3 模糊控制器参数

Table 3. Parameters of fuzzy controller

模糊变量	基本论域	模糊论域	映射系数
$ e $	[−0.0025，0.0025]	[−1，1]	400
$ \delta $	[−0.05，0.05]	[−1，1]	20
$\Delta K_{{\rm{P}}}$	[−5000，5000]	[−1，1]	0.0002
$\Delta K_{{\rm{I}}}$	[−10，10]	[−1，1]	0.1
$\Delta K_{{\rm{D}}}$	[−50，50]	[−1，1]	0.02

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表 4 $\Delta K_{{\rm{P}}}$整定规则

Table 4. Setting rules of $\Delta K_{{\rm{P}}}$

e	δ
e	NB	NM	NS	ZE	PS	PM	PB
NB	NB	NB	NM	NM	NM	ZE	ZE
NM	NB	NM	NM	NM	NS	ZE	PS
NS	NM	NM	NS	NS	ZE	PS	PS
ZE	NM	NS	NS	ZE	PS	PS	PM
PS	NS	NS	ZE	PS	PS	PM	PM
PM	NS	ZE	PS	PM	PM	PM	PB
PB	ZE	ZE	PM	PM	PM	PB	PB

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表 5 $\Delta K_{{\rm{I}}}$整定规则

Table 5. Setting rules of $\Delta K_{{\rm{I}}}$

e	δ
e	NB	NM	NS	ZE	PS	PM	PB
NB	ZE	ZE	ZE	ZE	ZE	ZE	ZE
NM	ZE	ZE	ZE	ZE	ZE	ZE	ZE
NS	PS	PS	PS	PS	PS	PS	PS
ZE	PS	PS	PS	PS	PS	PS	PS
PS	PS	PS	PS	PS	PS	PS	PS
PM	ZE	ZE	ZE	ZE	ZE	ZE	ZE
PB	ZE	ZE	ZE	ZE	ZE	ZE	ZE

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表 6 $\Delta K_{{\rm{D}}}$整定规则

Table 6. Setting rules of $\Delta K_{{\rm{D}}}$

e	δ
e	NB	NM	NS	ZE	PS	PM	PB
NB	NB	NB	PM	PM	PS	ZE	ZE
NM	NB	NB	PM	PS	PS	ZE	ZE
NS	NB	NM	PS	PS	ZE	NS	NS
ZE	NM	NS	PS	ZE	NS	NS	NM
PS	NS	NS	ZE	NS	NS	NM	NB
PM	ZE	ZE	NS	NS	NM	NB	NB
PB	ZE	ZE	NS	NM	NM	NB	NB

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表 7 振动衰减率和振动传递率

Table 7. Vibration attenuation rate and vibration transmission rate

振动频率/Hz	振动衰减率/%	振动传递率/dB
20	83.64	−15.72
50	90.55	−19.83
100	91.91	−21.84
200	92.60	−22.61
300	93.52	−23.77
500	95.35	−26.66

下载: 导出CSV

参考文献(18)

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[2]	REN C, YANG D, QIN H. Mechanical performance of multidirectional buckling-based negative stiffness metamaterials: an analytical and numerical study[J]. Materials, 2018, 11(7): 1078.1-1078.19.
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[4]	YAN B, YU N, WU C Y. A state-of-the-art review on low-frequency nonlinear vibration isolation with electromagnetic mechanisms[J]. Applied Mathematics and Mechanics, 2022, 43(7): 1045-1062. doi: 10.1007/s10483-022-2868-5
[5]	ZHANG F, SHAO S B, TIAN Z, et al. Active-passive hybrid vibration isolation with magnetic negative stiffness isolator based on Maxwell normal stress[J]. Mechanical Systems and Signal Processing, 2019, 123: 244-263. doi: 10.1016/j.ymssp.2019.01.022
[6]	沈铖武. 车载光电瞄准平台主被动隔振关键技术研究[D]. 北京: 中国科学院大学, 2021.
[7]	黄翠翠,李晓龙,杨洋,等. 基于自抗扰技术的机械-电磁悬浮复合隔振控制[J]. 西南交通大学学报,2022,57(3): 582-587,617. doi: 10.3969/j.issn.0258-2724.20210850 HUANG Cuicui, LI Xiaolong, YANG Yang, et al. Mechanical-electromagnetic suspension compound vibration isolation control based on active disturbance rejection technology[J]. Journal of Southwest Jiaotong University, 2022, 57(3): 582-587,617. doi: 10.3969/j.issn.0258-2724.20210850
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e	δ
e	NB	NM	NS	ZE	PS	PM	PB
NB	NB	NB	NM	NM	NM	ZE	ZE
NM	NB	NM	NM	NM	NS	ZE	PS
NS	NM	NM	NS	NS	ZE	PS	PS
ZE	NM	NS	NS	ZE	PS	PS	PM
PS	NS	NS	ZE	PS	PS	PM	PM
PM	NS	ZE	PS	PM	PM	PM	PB
PB	ZE	ZE	PM	PM	PM	PB	PB

e	δ
e	NB	NM	NS	ZE	PS	PM	PB
NB	ZE	ZE	ZE	ZE	ZE	ZE	ZE
NM	ZE	ZE	ZE	ZE	ZE	ZE	ZE
NS	PS	PS	PS	PS	PS	PS	PS
ZE	PS	PS	PS	PS	PS	PS	PS
PS	PS	PS	PS	PS	PS	PS	PS
PM	ZE	ZE	ZE	ZE	ZE	ZE	ZE
PB	ZE	ZE	ZE	ZE	ZE	ZE	ZE

e	δ
e	NB	NM	NS	ZE	PS	PM	PB
NB	NB	NB	PM	PM	PS	ZE	ZE
NM	NB	NB	PM	PS	PS	ZE	ZE
NS	NB	NM	PS	PS	ZE	NS	NS
ZE	NM	NS	PS	ZE	NS	NS	NM
PS	NS	NS	ZE	NS	NS	NM	NB
PM	ZE	ZE	NS	NS	NM	NB	NB
PB	ZE	ZE	NS	NM	NM	NB	NB

e	δ
e	NB	NM	NS	ZE	PS	PM	PB
NB	NB	NB	NM	NM	NM	ZE	ZE
NM	NB	NM	NM	NM	NS	ZE	PS
NS	NM	NM	NS	NS	ZE	PS	PS
ZE	NM	NS	NS	ZE	PS	PS	PM
PS	NS	NS	ZE	PS	PS	PM	PM
PM	NS	ZE	PS	PM	PM	PM	PB
PB	ZE	ZE	PM	PM	PM	PB	PB

e	δ
e	NB	NM	NS	ZE	PS	PM	PB
NB	ZE	ZE	ZE	ZE	ZE	ZE	ZE
NM	ZE	ZE	ZE	ZE	ZE	ZE	ZE
NS	PS	PS	PS	PS	PS	PS	PS
ZE	PS	PS	PS	PS	PS	PS	PS
PS	PS	PS	PS	PS	PS	PS	PS
PM	ZE	ZE	ZE	ZE	ZE	ZE	ZE
PB	ZE	ZE	ZE	ZE	ZE	ZE	ZE

e	δ
e	NB	NM	NS	ZE	PS	PM	PB
NB	NB	NB	PM	PM	PS	ZE	ZE
NM	NB	NB	PM	PS	PS	ZE	ZE
NS	NB	NM	PS	PS	ZE	NS	NS
ZE	NM	NS	PS	ZE	NS	NS	NM
PS	NS	NS	ZE	NS	NS	NM	NB
PM	ZE	ZE	NS	NS	NM	NB	NB
PB	ZE	ZE	NS	NM	NM	NB	NB

基于模糊PID控制的准零刚度磁悬浮隔振平台的设计与实现

doi: 10.3969/j.issn.0258-2724.20220880

作者简介: 翟明达（1990—），男，助理研究员，博士，研究方向为悬浮控制与优化，E-mail：zhaimd@126.com

通讯作者: 李晓龙（1979—），男，副研究员，研究方向为悬浮控制、磁浮隔振，E-mail：13787786254@163.com

计量

出版历程

Design and Implementation of Magnetic Suspension Vibration Isolation Platform with Quasi-Zero Stiffness Based on Fuzzy PID Control

计量

出版历程

目录

作者简介:
翟明达（1990—），男，助理研究员，博士，研究方向为悬浮控制与优化，E-mail：zhaimd@126.com

通讯作者:
李晓龙（1979—），男，副研究员，研究方向为悬浮控制、磁浮隔振，E-mail：13787786254@163.com

e	δ
e	NB	NM	NS	ZE	PS	PM	PB
NB	NB	NB	NM	NM	NM	ZE	ZE
NM	NB	NM	NM	NM	NS	ZE	PS
NS	NM	NM	NS	NS	ZE	PS	PS
ZE	NM	NS	NS	ZE	PS	PS	PM
PS	NS	NS	ZE	PS	PS	PM	PM
PM	NS	ZE	PS	PM	PM	PM	PB
PB	ZE	ZE	PM	PM	PM	PB	PB

e	δ
e	NB	NM	NS	ZE	PS	PM	PB
NB	ZE	ZE	ZE	ZE	ZE	ZE	ZE
NM	ZE	ZE	ZE	ZE	ZE	ZE	ZE
NS	PS	PS	PS	PS	PS	PS	PS
ZE	PS	PS	PS	PS	PS	PS	PS
PS	PS	PS	PS	PS	PS	PS	PS
PM	ZE	ZE	ZE	ZE	ZE	ZE	ZE
PB	ZE	ZE	ZE	ZE	ZE	ZE	ZE

e	δ
e	NB	NM	NS	ZE	PS	PM	PB
NB	NB	NB	PM	PM	PS	ZE	ZE
NM	NB	NB	PM	PS	PS	ZE	ZE
NS	NB	NM	PS	PS	ZE	NS	NS
ZE	NM	NS	PS	ZE	NS	NS	NM
PS	NS	NS	ZE	NS	NS	NM	NB
PM	ZE	ZE	NS	NS	NM	NB	NB
PB	ZE	ZE	NS	NM	NM	NB	NB