具有采样反馈的力控制系统稳定性

王在华; 胡海岩

doi:10.6052/0459-1879-16-102

具有采样反馈的力控制系统稳定性

王在华^1,3, ,,
胡海岩^2,3

1.
解放军理工大学理学院, 南京 211101
2. 北京理工大学宇航学院, 北京 100081
3. 南京航空航天大学机械结构力学及控制国家重点实验室, 南京 210016

基金项目: 国家自然科学基金资助项目（11372354，11290151）.

详细信息

通讯作者:
王在华,教授,主要研究方向:时滞系统及分数阶系统的动力学与控制,非线性动力学.E-mail:zhwang@nuaa.edu.cn

中图分类号: O317⁺.1;O302
计量
- 文章访问数: 1066
- HTML全文浏览量: 143
- PDF下载量: 764
出版历程
- 收稿日期: 2016-04-17
- 修回日期: 2016-06-05
- 刊出日期: 2016-11-17

STABILITY OF A FORCE CONTROL SYSTEM WITH SAMPLED-DATA FEEDBACK

Wang Zaihua^1,3, ,,
Hu Haiyan^2,3

1.
Institute of Science, PLA University of Science and Technology, Nanjing 211101, China
2. School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
3. State Key Lab of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

摘要

摘要: 基于计算机的数字采样控制对离散信号进行运算并向作动器提供控制输入，是当前的主流控制技术.数字采样控制系统是这样一类控制系统，其控制对象由微分方程（组）描述，而控制律由离散采样信号给出.以采样PD（proportional-derivative）反馈作用下的单自由度力控制系统为例，基于离散系统的稳定性分析方法，研究采样控制律对控制系统稳定性的影响.为了突出采样反馈的作用，将系统取为无刚度、无阻尼的最简单形式.不同于已有研究假设位移采样信号与速度采样信号相互同步，本文研究当位移采样信号与速度采样信号不同步时受控系统的稳定性，发现位移采样信号与速度采样信号的采样周期不同组合对受控系统在增益平面上的稳定性区域有重要影响.结果表明，对所关心的三种数字采样反馈控制律，当位移采样信号滞后于速度采样信号一个采样周期时，受控系统具有最大的稳定性区域且对相同的增益值可以有最好的稳定效果.论文对这种现象进行分析，给出了一种力学解释.
- 数字控制 /
- 采样反馈 /
- 时滞反馈 /
- 稳定性
Abstract: Sampled-data control, or digital control, is a major control technology in modern engineering. Based on digital computers, it provides actuators with control inputs in terms of discrete signals. A sampled-data control system is a controlled time-continuous system under sampled-data control. The paper investigates the effects of sampled-data controls on the system stability via an SDOF force control system under sampled PD (proportional-derivative) feedbacks, by means of stability analysis for discrete systems. In order to highlight the role of the sampled-data controls, the uncontrolled system is assumed to be fully free. Unlike in the previous studies where the sampled displacement signal and the sampled velocity signal are synchronic, the study focuses on the system stability for the case when the sampled displacement signal and the sampled velocity signal are not synchronic. A key observation is that when the controller uses the sampled velocity signal as well as the sampled displacement signal delayed an additional sampling period, the controlled system admits a largest stable region of the feedback gains and it decays fastest to the unique equilibrium, among the three sampled-data controllers. The paper gives a discussion of this phenomenon from the viewpoint of mechanics.
- digital control /
- sampled-data feedback /
- delayed feedback /
- stability

HTML全文

参考文献(30)

1 Ackermann J. Sampled-Data Control Systems:Analysis and Synthesis, Robust System Design. Berlin and Heidelberg:Springer-Verlag, 1985

2 Chen TW, Francis BA. Optimal Sampled-Data Control. London:Springer-Verlag, 1995

3 张德江. 计算机控制系统. 北京:科学出版社, 2011(Zhang Dejiang. Computer Controlled Systems. Beijing:Science Press, 2011(in Chinese))

4 胡勇, 徐李佳, 解永春. 针对失控翻滚目标航天器的交会对接控制. 宇航学报, 2015, 36(1):47-57(Hu Yong, Xu Lijia, Xie Yongchun. Control for rendezvous and docking with a tumbling target spacecraft. Journal of Astronautics, 2015, 36(1):47-57(in Chinese))

5 Wan Y, Wen G, Cao J, et al. Distributed node-to-node consensus of multi-agent systems with stochastic sampling. International Journal of Robust and Nonlinear Control, 2016, 26(1):110-124

6 Wu H, Li R, Wei H, et al. Synchronization of a class of memristive neural networks with time delays via sampled-data control. International Journal of Machine Learning and Cybernetics, 2015, 6(3):365-373

7 Monaco S, Normand-Cyrot D. An introduction to motion planning under multirate digital control. In:Proceedings of the 31st IEEE Conference on Decision and Control, 1992, 2:1780-1785

8 Furuta K, Kajiwara H, Kosuge K. Digital control of a double inverted pendulum on an inclined rail. International Journal of Control, 1980, 32(5):907-924

9 藏强, 梅平, 郑柏超等. 非线性微分-代数系统的反馈镇定:基于线性采样控制. 自动化学报, 2015, 41(10):1831-1836(Zang Qiang, Mei Ping, Zheng Baichao, et al. Output feedback stabilization of nonlinear differential-algebraic equations system based on linear sampled-data control. Acta Automatica Sinica, 2015, 41(10):1831-1836(in Chinese))

10 郭雷. 关于控制理论发展的某些思考. 系统科学与数学, 2011, 31(9):1014-1018(Guo Lei. Some thoughts on the development of control theory. Journal of Systems Science and Mathematical Science, 2011, 31(9):1014-1018(in Chinese))

11 Fridman E, Seuret A, Richard JP. Robust sampled-data stabilization of linear systems:an input delay approach. Automatica, 2004, 40(8):1441-1446

12 Fridman E. A refined input delay approach to sampled-data control. Automatica, 2010, 46(2):421-427

13 Sakthivel R, Arunkumar A, Mathiyalagan K. Robust sampled-data H_∞ control for mechanical systems. Complexity, 2015, 20(4):19-29

14 Nagahara M., Yamamoto Y. Digital repetitive controller design via sampled-data delayed signal reconstruction. Automatica, 2015, 65(3):203-209

15 Palmeira AHK, Gomes da Silva Jr JM, Tarbouriech S, et al. Sampled-data control under magnitude and rate saturating actuators. International Journal of Robust and Nonlinear Control, 2016, doi: 10.1002/rnc.3503

16 Naghshtabrizi P, Hespanha JP, Teel AR. Exponential stability of impulsive systems with application to uncertain sampled-data systems. Systems and Control Letters, 2008, 57(5):378-385

17 Mansour M. A note on the stability of linear discrete systems and Lyapunov method. IEEE Transactions on Automatic Control, 1982, 27(3):707-708

18 Martynyuk AA. Stability analysis of discrete systems. International Applied Mechanics, 2000, 36(7):835-865

19 Rabbath CA, Lechevin N. Discrete-Time Control Design with Applications. New York:Springer-Verlag, 2014

20 Insperger T, Stepan G. Stability improvements of robot control by periodic variations of the gain parameters. In:Tian Huang ed. Proc. of the 11th World Congress in Mechanism and Machine Science. Beijing:China Machine Press, 2004, 1816-1820

21 Insperger T, Stepan G. Semi-discretization for Time-Delay Systems:Stability and Engineering Applications. Berlin and Heidelberg:Springer-Verlag, 2011

22 Habib G, Rega G, Stepan G. Delayed digital position control of a single-DOF system and the nonlinear behavior of the act-and-wait controller. Journal of Vibration and Control, 2016, 22(2):481-495

23 Habib G, Rega G, Stepan G. Stability analysis of a two-DOF mechanical system subjected to proportional-derivative digital position control. Journal of Vibration and Control, 2015, 21(8):1539-1555

24 Zhou J, Zhang H, Xiang L, et al. Sampled-data synchronization of coupled harmonic oscillators with controller failure and communication delays. Theoretical and Applied Mechanics Letters, 2013, 3(6):063002

25 赵艳影, 徐鉴. 时滞非线性动力吸振器的减振机理. 力学学报, 2008, 40(1):98-106(Zhao Yanying, Xu Jian. Mechanism analysis of delayed nonlinear vibration absorber. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(1):98-106(in Chinese))

26 陈龙祥, 蔡国平. 旋转运动柔性梁的时滞主动控制实验研究. 力学学报, 2008, 40(4):520-527(Chen Longxiang, Cai Guoping. Experimental study on active control of a rotating flexible beam with time delay. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(4):520-527(in Chinese))

27 王在华, 李俊余. 时滞状态正反馈在振动控制中的新特征. 力学学报, 2010, 42(5):933-942(Wang Zaihua, Li Junyu. New features of time-delayed positive feedbacks in vibration control. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(5):933-942(in Chinese))

28 王在华, 胡海岩. 时滞动力系统的稳定性与分岔:从理论走向应用. 力学进展, 2013, 43(1):3-20(Wang Zaihua, Hu Haiyan. Stability and bifurcation of delayed dynamic systems:From theory to application. Advances in Mechanics, 2013, 43(1):3-20(in Chinese))

29 Wang ZH. A very simple criterion for characterizing the crossing direction of time-delay systems. International Journal of Bifurcation and Chaos, 2012, 29(2):1250048

30 Kuang Y. Delay Di erential Equation with Application to Population Dynamics. San Diego:Academic Press, 1993

施引文献(9)

期刊类型引用(7)

1.	曹天成，张舒. 含有采样反馈的二连杆系统稳定性. 动力学与控制学报. 2023(11): 10-18 . 百度学术
2.	张博，丁虎，陈立群. 基于压电纤维复合材料的旋转叶片主动控制. 力学学报. 2021(04): 1093-1102 . 本站查看
3.	郭梓龙，王琳，倪樵，贾青青，杨文正. 接地惯容式减振器对悬臂输流管稳定性和动态响应的影响研究. 力学学报. 2021(06): 1769-1780 . 本站查看
4.	刘楚源，刘泽森，宋汉文. 基于主动控制策略的机翼颤振特性模拟. 力学学报. 2019(02): 333-340 . 本站查看
5.	柴凯，楼京俊，杨庆超，俞翔. 高静低动隔振系统的双时延反馈混沌化. 船舶力学. 2019(05): 611-620 . 百度学术
6.	王强，梁松，王在华. 基于采样PD反馈的倒立摆控制系统的稳定性. 动力学与控制学报. 2018(04): 377-384 . 百度学术
7.	张舒，徐鉴. 时滞耦合系统非线性动力学的研究进展. 力学学报. 2017(03): 565-587 . 本站查看