On limit cycle chattering in sliding mode control systems under the influence of sampling intervals based on describing function approach
In this paper, the influence of sampling intervals on the chattering in sliding mode （SM） control systems is considered. The describing function （DF） approach is employed to analyze the chattering characteristics in the sampling SM control. By the DF calculations and limit cycle existence conditions...
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| Published in | Journal of China universities of posts and telecommunications Vol. 23; no. 1; pp. 55 - 59 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.02.2016
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1005-8885 |
| DOI | 10.1016/S1005-8885(16)60008-0 |
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| Abstract | In this paper, the influence of sampling intervals on the chattering in sliding mode （SM） control systems is considered. The describing function （DF） approach is employed to analyze the chattering characteristics in the sampling SM control. By the DF calculations and limit cycle existence conditions, an unstable limit cycle and two stable limit cycles are found in the SM control system. The frequencies and amplitudes of the two limit cycles can also be estimated by graphical calculations. The estimation accuracy of chattering parameters is evaluated by the simulations. The results of simulations show that the system could converge to a large and a small limit cycle from different initial conditions. |
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| AbstractList | In this paper, the influence of sampling intervals on the chattering in sliding mode (SM) control systems is considered. The describing function (DF) approach is employed to analyze the chattering characteristics in the sampling SM control. By the DF calculations and limit cycle existence conditions, an unstable limit cycle and two stable limit cycles are found in the SM control system. The frequencies and amplitudes of the two limit cycles can also be estimated by graphical calculations. The estimation accuracy of chattering parameters is evaluated by the simulations. The results of simulations show that the system could converge to a large and a small limit cycle from different initial conditions. In this paper, the influence of sampling intervals on the chattering in sliding mode （SM） control systems is considered. The describing function （DF） approach is employed to analyze the chattering characteristics in the sampling SM control. By the DF calculations and limit cycle existence conditions, an unstable limit cycle and two stable limit cycles are found in the SM control system. The frequencies and amplitudes of the two limit cycles can also be estimated by graphical calculations. The estimation accuracy of chattering parameters is evaluated by the simulations. The results of simulations show that the system could converge to a large and a small limit cycle from different initial conditions. |
| Author | Kang Hongbo Shen YU |
| AuthorAffiliation | Institute of Electrical and Control Engineering, Chang＇an University, Xi＇an 710064, China College of Automation, Xi＇an University of Posts Communications, Xi＇an 710121, China School of Computer and Information Science, Southwest University, Chongqing 400715, China |
| Author_xml | – sequence: 1 givenname: Kang surname: Hongbo fullname: Hongbo, Kang organization: Institute of Electrical and Control Engineering, Chang'an University, Xi'an 710064, China – sequence: 2 givenname: Shen surname: Yu fullname: Yu, Shen email: shenyuxd@swu.edu.cn organization: School of Computer and Information Science, Southwest University, Chongqing 400715, China |
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| Cites_doi | 10.1109/TAC.2010.2041973 10.1007/s11071-008-9410-y 10.1016/j.arcontrol.2007.08.001 10.1023/A:1020565510218 10.1007/s11071-011-9983-8 10.1109/TAC.2004.829615 10.1109/9.940930 10.7498/aps.63.068701 10.1109/41.370376 10.1109/TAC.2008.2007171 10.1109/TIE.2012.2203777 |
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| Keywords | describing function approach sampling interval multiple limit cycle analysis chattering parameters |
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| Notes | sampling interval, chattering parameters, describing function approach, multiple limit cycle analysis 11-3486/TN In this paper, the influence of sampling intervals on the chattering in sliding mode （SM） control systems is considered. The describing function （DF） approach is employed to analyze the chattering characteristics in the sampling SM control. By the DF calculations and limit cycle existence conditions, an unstable limit cycle and two stable limit cycles are found in the SM control system. The frequencies and amplitudes of the two limit cycles can also be estimated by graphical calculations. The estimation accuracy of chattering parameters is evaluated by the simulations. The results of simulations show that the system could converge to a large and a small limit cycle from different initial conditions. ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
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| References | Shen, Qiu (bib13) 2014; 33 Levant (bib3) 2010; 55 Lee, Utkin (bib10) 2007; 31 Wu, Chen (bib6) 2013; 60 Fridman (bib2) 2001; 46 Huang, Wang (bib9) 2002; 30 Boiko, Fridman, Castellanos (bib12) 2004; 49 Boiko (bib11) 2008; 53 Shen (bib14) 2014 Wang, Xu (bib5) 2014; 63 Duarte, Machado (bib7) 2009; 56 Atherton (bib4) 1975 Oliveira, Kienitz, Misawa (bib8) 2011; 67 Gao, Wang, Homaifa (bib1) 1995; 42 Boiko (10.1016/S1005-8885(16)60008-0_bib12) 2004; 49 Duarte (10.1016/S1005-8885(16)60008-0_bib7) 2009; 56 Wu (10.1016/S1005-8885(16)60008-0_bib6) 2013; 60 Wang (10.1016/S1005-8885(16)60008-0_bib5) 2014; 63 Shen (10.1016/S1005-8885(16)60008-0_bib13) 2014; 33 Atherton (10.1016/S1005-8885(16)60008-0_bib4) 1975 Huang (10.1016/S1005-8885(16)60008-0_bib9) 2002; 30 Boiko (10.1016/S1005-8885(16)60008-0_bib11) 2008; 53 Gao (10.1016/S1005-8885(16)60008-0_bib1) 1995; 42 Oliveira (10.1016/S1005-8885(16)60008-0_bib8) 2011; 67 Shen (10.1016/S1005-8885(16)60008-0_bib14) 2014 Lee (10.1016/S1005-8885(16)60008-0_bib10) 2007; 31 Fridman (10.1016/S1005-8885(16)60008-0_bib2) 2001; 46 Levant (10.1016/S1005-8885(16)60008-0_bib3) 2010; 55 |
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| SubjectTerms | chattering parameters Control systems describing function approach Describing functions Initial conditions Intervals Mathematical analysis multiple limit cycle analysis Sampling sampling interval Simulation Vibration 估计精度 图形计算 存在性条件 抖振 描述函数法 极限环 滑模控制系统 采样间隔 |
| Title | On limit cycle chattering in sliding mode control systems under the influence of sampling intervals based on describing function approach |
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