磁悬浮直驱式无油涡旋压缩机模糊PID控制研究

段振云; 刘洋; 孙凤; 史策; 徐方超; 金俊杰; 张晓友; 陈熙

doi:10.3969/j.issn.0258-2724.20240600

磁悬浮直驱式无油涡旋压缩机模糊PID控制研究

doi: 10.3969/j.issn.0258-2724.20240600

段振云^1,,
刘洋¹,
孙凤^1, ,,
史策¹,
徐方超¹,
金俊杰¹,
张晓友^{1, 2},
陈熙¹

1.
沈阳工业大学机械工程学院，辽宁沈阳 110870
2.
日本工业大学机械工程学院，日本琦玉 345-8501

基金项目: 国家自然基金项目（52375258，52405284）；国家重点研发计划（2024YFB3410002）；中国博士后科学基金（2024M762160）；辽宁省科技厅项目（2023-BS-127）；辽宁省教育厅项目（LJ222410142008，JYTMS20231191，LJ212410142015）

详细信息

作者简介:
段振云（1971—），男，教授，研究方向为复杂曲面加工及齿轮技术，E-mail：13604045543@139.com

通讯作者:
孙凤（1978—），男，教授，研究方向为机械系统多元驱动及其控制技术，E-mail：sunfeng@sut.edu.cn

中图分类号: TH455
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出版历程
- 收稿日期: 2024-11-18
- 修回日期: 2025-02-10
- 网络出版日期: 2025-04-29

Research on Fuzzy Proportional Integral Differential Control of Magnetic Drive Oil-free Scroll Compressor

DUAN Zhenyun^1
,,
LIU Yang¹,
SUN Feng^{1
, ,},
SHI Ce¹,
XU Fangchao¹,
JIN Junjie¹,
ZHANG Xiaoyou^{1, 2},
CHEN Xi¹

1.
School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China
2.
Department of Mechanical Engineering, Nippon Institute of Technology, Saitama 345-8501, Japan

摘要

摘要:
磁悬浮直驱式无油涡旋压缩机采用电磁力非接触式驱动动涡盘运动. 本文针对压缩机系统非线性较强、PID控制下轨迹跟踪误差较大的问题设计了一种模糊PID控制器，可以在线实时修正控制参数，提高轨迹跟踪效果. 首先，介绍了磁悬浮直驱式无油涡旋压缩机的结构和工作原理，建立电磁驱动力的数学模型和系统动力学模型并进行系统稳定性分析；其次，添加模糊逻辑，进行模糊控制器设计；最后，在控制参数相同的情况下，将PID与模糊PID 2种控制下的阶跃响应与轨迹跟踪结果进行对比分析. 结果表明：相较于PID控制，模糊PID控制下，阶跃响应时的稳定时间减少了0.461 s，稳态误差减小了0.012 mm；轨迹跟踪时，X、Y方向达到稳定跟踪的时间分别减少了0.365、0.090 s；X、Y方向的最大轨迹跟踪误差减小了0.043、0.060 mm，最大相对误差减小了50%、60%.
- 磁力驱动 /
- 无油涡旋压缩机 /
- 模糊PID控制 /
- 轨迹跟踪
Abstract:
Magnetic drive oil-free scroll compressor (MDOFSC) adopts electromagnetic force to drive the orbiting scroll in a non-contact manner. The problems of strong nonlinearity in the compressor system and large trajectory tracking errors under proportional integral differential (PID) control were analyzed, and a fuzzy PID controller was designed to adjust control parameters online and improve trajectory tracking performance. Firstly, the structure and working principle of MDOFSC were introduced, and the mathematical model of electromagnetic drive and the system dynamics model were established; the system stability was analyzed. Secondly, fuzzy logic was added for fuzzy controller design; finally, the step response and trajectory tracking results under both PID and fuzzy PID control were compared under the same control parameters. The results show that under the fuzzy PID control, the stabilization time during the step response is reduced by 0.461 s, and the steady state error is reduced by 0.012 mm; the time to reach the stable tracking in the X and Y directions during the trajectory tracking is reduced by 0.365 s and 0.090 s, respectively, and the maximal trajectory tracking error in the X and Y directions is reduced by 0.043 mm and 0.060 mm; the maximal relative error is reduced by 50% and 60%, respectively.
- magnetic drive /
- oil-free scroll compressor /
- fuzzy PID control /
- trajectory tracking

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图 1 磁悬浮直驱式无油涡旋压缩机结构

Figure 1. Structure of MDOFSC

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图 2 电磁驱动机构的结构参数

Figure 2. Structural parameters of electromagnetic actuator

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图 3 系统受力分析图

Figure 3. System force analysis

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图 4 磁悬浮直驱式无油涡旋压缩机模糊PID控制原理

Figure 4. Fuzzy PID control principle of MDOFSC

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图 5 输入、输出变量的隶属函数

Figure 5. Membership functions of input and output variables

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图 6 0.1 mm位移阶跃响应仿真

Figure 6. Step response simulation at 0.1 mm displacement

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图 7 PID控制下轨迹跟踪仿真

Figure 7. Trajectory tracking simulation under PID control

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图 8 模糊PID控制下轨迹跟踪仿真

Figure 8. Trajectory tracking simulation under fuzzy PID control

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图 9 负载突变下模糊PID控制仿真

Figure 9. Simulation of fuzzy PID control under sudden load changes

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图 10 原理样机实验系统

Figure 10. Principle prototype control system

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图 11 Y方向阶跃响应实验

Figure 11. Step response experiment for Y direction

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图 12 PID控制下轨迹跟踪实验结果

Figure 12. Experimental results of trajectory tracking under PID control

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图 13 模糊PID控制下轨迹跟踪实验结果

Figure 13. Experimental results of trajectory tracking under fuzzy PID control

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图 14 负载突变下模糊PID控制实验

Figure 14. Fuzzy PID control experiment under sudden load changes

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表 1 系统参数

Table 1. System parameters

结构参数	数值
J/(kg•m²)	1.51 × 10⁻³
m/kg	1.7
k_iX/(N•A⁻¹)	150
k_dX/(N•m⁻¹)	−75 × 10⁻³
k_iY/(N•A⁻¹)	180
k_dY/(N•m⁻¹)	−57 × 10⁻³
k_n/(N•mm⁻¹)	4.544
c/(N•s•m⁻¹)	40 × 10³
H/m	0.0195
L/m	0.021

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表 2 ΔK_P模糊规则表

Table 2. Fuzzy control rules of ΔK_P

e	c_e
e	NB	NM	NS	ZO	PS	PM	PB
NB	PB	PB	PM	PM	PS	ZO	ZO
NM	PB	PB	PM	PS	PS	ZO	NS
NS	PM	PM	PM	PS	ZO	NS	NS
ZO	PM	PM	PS	ZO	NS	NM	NM
PS	PS	PS	ZO	NS	NS	NM	NM
PM	PS	ZO	NS	NM	NM	NM	NB
PB	ZO	ZO	NM	NM	NM	NB	NB

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表 3 ΔK_I模糊规则表

Table 3. Fuzzy control rules of ΔK_I

e	c_e
e	NB	NM	NS	ZO	PS	PM	PB
NB	NB	NB	NM	NM	PS	NS	ZO
NM	NB	NB	NM	NS	NS	ZO	ZO
NS	NB	NM	NS	NS	ZO	PS	PS
ZO	NM	NM	NS	ZO	PS	PM	PM
PS	NM	NS	ZO	PS	PS	PM	PB
PM	ZO	ZO	PS	PS	PM	PB	NB
PB	ZO	ZO	PS	PM	PM	PB	PB

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表 4 ΔK_D模糊规则表

Table 4. Fuzzy control rules of ΔK_D

e	c_e
e	NB	NM	NS	ZO	PS	PM	PB
NB	PS	NS	NB	NB	NB	NM	PS
NM	PS	NS	NB	NM	NM	NS	ZO
NS	ZO	NS	NM	NM	ZO	NS	ZO
ZO	ZO	NS	NS	NM	NB	NS	ZO
PS	PS	PS	ZO	NS	NS	NM	NM
PM	PS	ZO	NS	NM	NM	NM	NB
PB	ZO	ZO	NM	NM	NM	NB	NB

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