一种多幂次滑模趋近律设计与分析

张瑶; 马广富; 郭延宁; 曾添一

doi:10.16383/j.aas.2016.c150377

一种多幂次滑模趋近律设计与分析

doi: 10.16383/j.aas.2016.c150377

张瑶^1,,
马广富^1,,
郭延宁^1, ,,
曾添一^2,

1.
哈尔滨工业大学控制科学与工程系哈尔滨 150006
2.
北京理工大学自动化学院北京 100081

基金项目:

国家自然科学基金 61403103

中央高校基本科研业务费专项基金 HIT.NSRIF.2014035

国家自然科学基金 61174200

国家重点基础研究发展计划(973计划) 2012CB720000

中国博士后科学基金 2014M550195

详细信息

作者简介:
张瑶哈尔滨工业大学控制科学与工程系博士研究生.主要研究方向为航天器姿态控制及滑模控制理论.E-mail:yaozhanghit@outlook.com

马广富哈尔滨工业大学控制科学与工程系教授.主要研究方向为航天器姿态控制, 卫星编队控制.E-mail:magf@hit.edu.cn

曾添一北京理工大学自动化学院博士研究生.主要研究方向为多电机驱动控制及机构参数与控制器一体化设计.E-mail:blessno@163.com

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出版历程
- 收稿日期: 2015-06-16
- 录用日期: 2015-11-06
- 刊出日期: 2016-03-01

A Multi Power Reaching Law of Sliding Mode Control Design and Analysis

1.
Department of Control Science and Engineering, Harbin Institute of Technology, Harbin 150006
2.
School of Automation, Beijing Institute of Technology, Beijing 100081

Funds:

National Natural Science Foundation of China 61403103

the Fundamental Research Funds for the Central Universities HIT.NSRIF.2014035

National Natural Science Foundation of China 61174200

National Basic Research Program of China(973 Program) 2012CB720000

China Postdoctoral Science Foundation 2014M550195

More Information

Author Bio:
Ph. D. candidate in the Department of Control Science and Engineering, Harbin Institute of Technology. Her research interest covers attitude control of spacecraft and sliding mode control

Professor in the Department of Control Science and Engineering, Harbin Institute of Technology. His research interest covers attitude control of spacecraft and satellite formation control

Ph. D. candidate at the School of Automation, Beijing Institute of Technology. His research interest covers motor drive control and integration of mechanism parameters and controller design

Corresponding author: GUO Yan-Ning Associate professor in the Department of Control Science and Engineering, Harbin Institute of Technology. His research interest covers attitude control of spacecraft. Corresponding author of this paper

摘要

摘要: 针对传统滑模趋近律使系统存在抖振现象、收敛速度较慢及动态响应不平滑等问题, 提出一种多幂次滑模趋近律.该趋近律通过三个幂次项系数在系统趋近过程不同阶段进行针对性地调节, 使系统动态响应过程的收敛速度大幅度提高, 且无抖振现象.理论验证了其存在性、可达性及稳定性, 并详细推导了趋近速率及干扰稳定界.以航天器姿态机动控制系统为例, 对比仿真结果表明该趋近律下, 系统的动态过程有较大改善并消除了抖振, 且在存在模型不确定性及外加干扰作用下, 系统仍可较快地收敛到平衡点附近的邻域内.
- 多幂次趋近律 /
- 滑模控制 /
- 趋近速率 /
- 干扰稳定界
Abstract: A multi power reaching law of sliding mode control is proposed in this paper, which aims at reducing chattering phenomenon, fastening convergence speed and making dynamic process smoothly. The proposed reaching law has three exponential terms to adjust the convergence process, so that the system has a faster convergence speed obviously and no chattering phenomenon. It is indicated through theoretical analysis that the system under the proposed reaching law has existence, accessibility and stability. The convergence speed and interference stability boundary are deduced in detail. Simulation results show that the dynamic process is improved and the chattering is reduced, as compared with the exponential reaching law, single power reaching law and double power reaching law. Furthermore, when there exists interference or uncertainty, the system can converge to a neighborhood of the origin quickly.
- Multi power reaching law /
- sliding-mode control /
- convergence speed /
- interference stability boundary

HTML全文

图 1 不同趋近律下航天器姿态跟踪情况

Fig. 1 Attitude tracking under reaching laws

下载: 全尺寸图片幻灯片

图 2 不同趋近律下s随时间变化情况

Fig. 2 Condition of s under reaching laws

下载: 全尺寸图片幻灯片

图 3 不同趋近律下控制器输出u随时间变化情况

Fig. 3 Controller output u under reaching laws

下载: 全尺寸图片幻灯片

图 4 外加干扰下s的收敛情况

Fig. 4 Convergence condition of s with interference

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图 5 外加干扰下ds的收敛情况

Fig. 5 Convergence condition of ds with interference

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表 1 各趋近律仿真参数

Table 1 Simulation parameters of every reaching law

a b c d

k_a=0.9 k_b=0.7 k_c1=0.7 k₁=0.7

ε_a=0.5 α_b=1.1 k_c2=0.9 k₂=0.9

α_c=1.1 k₃=1.1

β_c=0.8 k₄=1.4

α=1.7

β=0.5

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