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Arbitrary Decay Rate for Euler-Bernoulli Beam by Backstepping Boundary Feedback
Smyshlyaev, Andrey1; Guo, Bao-Zhu2,3; Krstic, Miroslav1
2009-05-01
Source PublicationIEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN0018-9286
Volume54Issue:5Pages:1134-1140
AbstractWe consider a problem of stabilization of the Euler-Bernoulli beam. The beam is controlled at one end (using position and moment actuators) and has the "sliding" boundary condition at the opposite end. We design the controllers that achieve any prescribed decay rate of the closed loop system, removing a long-standing limitation of classical "boundary damper" controllers. The idea of the control design is to use the well-known representation of the Euler-Bernoulli beam model through the Schrodinger equation, and then adapt recently developed backstepping designs for the latter in order to stabilize the beam. We derive the explicit integral transformation (and its inverse) of the closed-loop system into an exponentially stable target system. The transformation is of a novel Volterra/Fredholm type. The design is illustrated with simulations.
KeywordBackstepping boundary control distributed parameter systems Euler-Bernoulli beam Riesz basis
DOI10.1109/TAC.2009.2013038
Language英语
WOS Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000266174100032
PublisherIEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/7615
Collection系统科学研究所
Corresponding AuthorSmyshlyaev, Andrey
Affiliation1.Univ Calif San Diego, Dept Mech & Aerosp Engn, La Jolla, CA 92093 USA
2.Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg Wits, South Africa
3.Acad Sinica, Acad Math & Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Smyshlyaev, Andrey,Guo, Bao-Zhu,Krstic, Miroslav. Arbitrary Decay Rate for Euler-Bernoulli Beam by Backstepping Boundary Feedback[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL,2009,54(5):1134-1140.
APA Smyshlyaev, Andrey,Guo, Bao-Zhu,&Krstic, Miroslav.(2009).Arbitrary Decay Rate for Euler-Bernoulli Beam by Backstepping Boundary Feedback.IEEE TRANSACTIONS ON AUTOMATIC CONTROL,54(5),1134-1140.
MLA Smyshlyaev, Andrey,et al."Arbitrary Decay Rate for Euler-Bernoulli Beam by Backstepping Boundary Feedback".IEEE TRANSACTIONS ON AUTOMATIC CONTROL 54.5(2009):1134-1140.
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