Stabilization analysis of Euler-Bernoulli beam equation with locally distributed disturbance
In order to enrich the system stability theory of the control theories, taking Euler-Bernoulli beam equation as the research subject, the stability of Euler-Bernoulli beam equation with locally distributed disturbance is studied. A feedback controller based on output is designed to reduce the effect...
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doaj-06691f3b898446adb6465a68e24ef6772020-11-25T01:59:21ZzhoHebei University of Science and TechnologyJournal of Hebei University of Science and Technology1008-15422017-12-0138653654110.7535/hbkd.2017yx06005b201706005Stabilization analysis of Euler-Bernoulli beam equation with locally distributed disturbancePengcheng HAN0Danhong LIU1Mathematics Department, Tianjin University, Tianjin 300350, ChinaMathematics Department, Tianjin University, Tianjin 300350, ChinaIn order to enrich the system stability theory of the control theories, taking Euler-Bernoulli beam equation as the research subject, the stability of Euler-Bernoulli beam equation with locally distributed disturbance is studied. A feedback controller based on output is designed to reduce the effects of the disturbances. The well-posedness of the nonlinear closed-loop system is investigated by the theory of maximal monotone operator, namely the existence and uniqueness of solutions for the closed-loop system. An appropriate state space is established, an appropriate inner product is defined, and a non-linear operator satisfying this state space is defined. Then, the system is transformed into the form of evolution equation. Based on this, the existence and uniqueness of solutions for the closed-loop system are proved. The asymptotic stability of the system is studied by constructing an appropriate Lyapunov function, which proves the asymptotic stability of the closed-loop system. The result shows that designing proper anti-interference controller is the foundation of investigating the system stability, and the research of the stability of Euler-bernoulli beam equation with locally distributed disturbance can prove the asymptotic stability of the system. This method can be extended to study the other equations such as wave equation, Timoshenko beam equation, Schrodinger equation, etc.http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201706005&flag=1&journal_theory of stabilityEuler-Bernoulli beam equationlocal feedback controllocally distributed disturbancewell-posednessasymptotic stabilization |
collection |
DOAJ |
language |
zho |
format |
Article |
sources |
DOAJ |
author |
Pengcheng HAN Danhong LIU |
spellingShingle |
Pengcheng HAN Danhong LIU Stabilization analysis of Euler-Bernoulli beam equation with locally distributed disturbance Journal of Hebei University of Science and Technology theory of stability Euler-Bernoulli beam equation local feedback control locally distributed disturbance well-posedness asymptotic stabilization |
author_facet |
Pengcheng HAN Danhong LIU |
author_sort |
Pengcheng HAN |
title |
Stabilization analysis of Euler-Bernoulli beam equation with locally distributed disturbance |
title_short |
Stabilization analysis of Euler-Bernoulli beam equation with locally distributed disturbance |
title_full |
Stabilization analysis of Euler-Bernoulli beam equation with locally distributed disturbance |
title_fullStr |
Stabilization analysis of Euler-Bernoulli beam equation with locally distributed disturbance |
title_full_unstemmed |
Stabilization analysis of Euler-Bernoulli beam equation with locally distributed disturbance |
title_sort |
stabilization analysis of euler-bernoulli beam equation with locally distributed disturbance |
publisher |
Hebei University of Science and Technology |
series |
Journal of Hebei University of Science and Technology |
issn |
1008-1542 |
publishDate |
2017-12-01 |
description |
In order to enrich the system stability theory of the control theories, taking Euler-Bernoulli beam equation as the research subject, the stability of Euler-Bernoulli beam equation with locally distributed disturbance is studied. A feedback controller based on output is designed to reduce the effects of the disturbances. The well-posedness of the nonlinear closed-loop system is investigated by the theory of maximal monotone operator, namely the existence and uniqueness of solutions for the closed-loop system. An appropriate state space is established, an appropriate inner product is defined, and a non-linear operator satisfying this state space is defined. Then, the system is transformed into the form of evolution equation. Based on this, the existence and uniqueness of solutions for the closed-loop system are proved. The asymptotic stability of the system is studied by constructing an appropriate Lyapunov function, which proves the asymptotic stability of the closed-loop system. The result shows that designing proper anti-interference controller is the foundation of investigating the system stability, and the research of the stability of Euler-bernoulli beam equation with locally distributed disturbance can prove the asymptotic stability of the system. This method can be extended to study the other equations such as wave equation, Timoshenko beam equation, Schrodinger equation, etc. |
topic |
theory of stability Euler-Bernoulli beam equation local feedback control locally distributed disturbance well-posedness asymptotic stabilization |
url |
http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201706005&flag=1&journal_ |
work_keys_str_mv |
AT pengchenghan stabilizationanalysisofeulerbernoullibeamequationwithlocallydistributeddisturbance AT danhongliu stabilizationanalysisofeulerbernoullibeamequationwithlocallydistributeddisturbance |
_version_ |
1724964964620304384 |