Dynamic control of an Euler-Bernoulli equation with time-delay and disturbance in the boundary control

The boundary control problem of a cantilever Euler- Bernoulli is considered in this paper. If the control at the right end of the beam is of the form w xxx (1, t) = u(t − τ) + r(t), where τ > 0 is the input time-delay and r(t) is an unknown external disturbance, a dynamic feedback control strateg...

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Published inInternational journal of control Vol. 92; no. 1; pp. 27 - 41
Main Authors Shang, YingFeng, Xu, Genqi
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.01.2019
Taylor & Francis Ltd
Subjects
Active control
ADRC
Boundary control
Delay
disturbance
Dynamic control
dynamic feedback control
Euler-Bernoulli equation
Feedback control
Time-delay
Online AccessGet full text
ISSN0020-7179
1366-5820
DOI10.1080/00207179.2017.1334264

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Abstract The boundary control problem of a cantilever Euler- Bernoulli is considered in this paper. If the control at the right end of the beam is of the form w xxx (1, t) = u(t − τ) + r(t), where τ > 0 is the input time-delay and r(t) is an unknown external disturbance, a dynamic feedback control strategy based on the methods of partial state predictor and active disturbance rejection control is used to stabilise the system. Under some assumptions on r(t), it is proven that the state of the system exponentially converges to and stays in the compact set . The radius ϵ is determined by the time-delay τ and the properties of r(t). The simulations are provided to compare the influence of τ and r(t) on the radius ϵ.
AbstractList The boundary control problem of a cantilever Euler- Bernoulli is considered in this paper. If the control at the right end of the beam is of the form w xxx (1, t) = u(t - τ) + r(t), where τ > 0 is the input time-delay and r(t) is an unknown external disturbance, a dynamic feedback control strategy based on the methods of partial state predictor and active disturbance rejection control is used to stabilise the system. Under some assumptions on r(t), it is proven that the state of the system exponentially converges to and stays in the compact set [Formula omitted.] . The radius [GREEK LUNATE EPSILON SYMBOL] is determined by the time-delay τ and the properties of r(t). The simulations are provided to compare the influence of τ and r(t) on the radius [GREEK LUNATE EPSILON SYMBOL].
The boundary control problem of a cantilever Euler- Bernoulli is considered in this paper. If the control at the right end of the beam is of the form w xxx (1, t) = u(t − τ) + r(t), where τ > 0 is the input time-delay and r(t) is an unknown external disturbance, a dynamic feedback control strategy based on the methods of partial state predictor and active disturbance rejection control is used to stabilise the system. Under some assumptions on r(t), it is proven that the state of the system exponentially converges to and stays in the compact set . The radius ϵ is determined by the time-delay τ and the properties of r(t). The simulations are provided to compare the influence of τ and r(t) on the radius ϵ.
Author Xu, Genqi
Shang, YingFeng
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10.1109/9.186332
10.1109/9.975475
10.1016/j.amc.2010.08.021
10.1080/00207179.2013.861931
10.1002/asjc.279
10.1080/00207179.2011.584197
10.1016/j.sysconle.2012.07.012
10.1137/120873212
10.1137/090781140
10.1109/TAC.1982.1103023
10.3934/cpaa.2011.10.667
10.1051/cocv:2006021
10.1109/TAC.2012.2218669
10.1137/060648891
10.1007/978-1-4471-0419-3
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cit0005
cit0016
cit0002
cit0013
cit0024
cit0014
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  doi: 10.1007/s00028-009-0004-z
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  doi: 10.1137/0327028
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  doi: 10.1016/j.automatica.2011.01.064
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  doi: 10.1137/120873212
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  doi: 10.1137/090781140
– ident: cit0001
  doi: 10.1109/TAC.1982.1103023
– ident: cit0014
  doi: 10.3934/cpaa.2011.10.667
– volume-title: Families of exponentials. The method of moments in controllability problems for distributed parameter systems
  year: 1995
  ident: cit0003
– ident: cit0024
  doi: 10.1051/cocv:2006021
– ident: cit0006
  doi: 10.1109/TAC.2012.2218669
– ident: cit0017
  doi: 10.1137/060648891
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Snippet The boundary control problem of a cantilever Euler- Bernoulli is considered in this paper. If the control at the right end of the beam is of the form w xxx (1,...
The boundary control problem of a cantilever Euler- Bernoulli is considered in this paper. If the control at the right end of the beam is of the form w xxx (1,...
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SubjectTerms Active control
ADRC
Boundary control
Delay
disturbance
Dynamic control
dynamic feedback control
Euler-Bernoulli equation
Feedback control
Time-delay
Title Dynamic control of an Euler-Bernoulli equation with time-delay and disturbance in the boundary control
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Volume 92
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