A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt Damping
This paper deals with the numerical approximation problem of the optimal control problem governed by the Euler-Bernoulli beam equation with local Kelvin-Voigt damping, which is a nonlinear coefficient control problem with control constraints. The goal of this problem is to design a control input num...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/982574 |
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| author | Xin Yu Zhigang Ren Qian Zhang Chao Xu |
| author_facet | Xin Yu Zhigang Ren Qian Zhang Chao Xu |
| author_sort | Xin Yu |
| collection | DOAJ |
| description | This paper deals with the numerical approximation problem of the optimal control problem governed by the Euler-Bernoulli beam equation with local Kelvin-Voigt damping, which is a nonlinear coefficient control problem with control constraints. The goal of this problem is to design a control input numerically, which is the damping and distributes locally on a subinterval of the region occupied by the beam, such that the total energy of the beam and the control on a given time period is minimal. We firstly use the finite element method (FEM) to obtain a finite-dimensional model based on the original PDE system. Then, using the control parameterization method, we approximate the finite-dimensional problem by a standard optimal parameter selection problem, which is a suboptimal problem and can be solved numerically by nonlinear mathematical programming algorithm. At last, some simulation studies will be presented by the proposed numerical approximation method in this paper, where the damping controls act on different locations of the Euler-Bernoulli beam. |
| format | Article |
| id | doaj-art-6235895127474f6aac10440baee5d978 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-6235895127474f6aac10440baee5d9782025-02-03T05:47:21ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/982574982574A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt DampingXin Yu0Zhigang Ren1Qian Zhang2Chao Xu3Laboratory of Information & Control Technology, Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, ChinaThe State Key Laboratory of Industrial Control Technology and Institute of Cyber-Systems & Control, Zhejiang University, Hangzhou 310027, ChinaLaboratory of Information & Control Technology, Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, ChinaThe State Key Laboratory of Industrial Control Technology and Institute of Cyber-Systems & Control, Zhejiang University, Hangzhou 310027, ChinaThis paper deals with the numerical approximation problem of the optimal control problem governed by the Euler-Bernoulli beam equation with local Kelvin-Voigt damping, which is a nonlinear coefficient control problem with control constraints. The goal of this problem is to design a control input numerically, which is the damping and distributes locally on a subinterval of the region occupied by the beam, such that the total energy of the beam and the control on a given time period is minimal. We firstly use the finite element method (FEM) to obtain a finite-dimensional model based on the original PDE system. Then, using the control parameterization method, we approximate the finite-dimensional problem by a standard optimal parameter selection problem, which is a suboptimal problem and can be solved numerically by nonlinear mathematical programming algorithm. At last, some simulation studies will be presented by the proposed numerical approximation method in this paper, where the damping controls act on different locations of the Euler-Bernoulli beam.http://dx.doi.org/10.1155/2014/982574 |
| spellingShingle | Xin Yu Zhigang Ren Qian Zhang Chao Xu A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt Damping Journal of Applied Mathematics |
| title | A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt Damping |
| title_full | A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt Damping |
| title_fullStr | A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt Damping |
| title_full_unstemmed | A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt Damping |
| title_short | A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt Damping |
| title_sort | numerical method of the euler bernoulli beam with optimal local kelvin voigt damping |
| url | http://dx.doi.org/10.1155/2014/982574 |
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