Sliding mode control to stabilization of cascaded heat PDE–ODE systems subject to boundary control matched disturbance
In this paper, we are concerned with the boundary feedback stabilization of a cascade of heat PDE–ODE system with Dirichlet/Neumann interconnection and with the external disturbance flowing the control end. In order to deal with the disturbance, the sliding model control (SMC) is integrated with the...
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| Published in | Automatica (Oxford) Vol. 52; pp. 23 - 34 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.02.2015
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| Abstract | In this paper, we are concerned with the boundary feedback stabilization of a cascade of heat PDE–ODE system with Dirichlet/Neumann interconnection and with the external disturbance flowing the control end. In order to deal with the disturbance, the sliding model control (SMC) is integrated with the backstepping approach, where the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop system are proved, and the monotonicity of the “reaching condition” is presented without differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed-loop system. Finally the numerical simulations validate the effectiveness of this method for the system with periodic and normal random disturbances respectively. |
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| AbstractList | In this paper, we are concerned with the boundary feedback stabilization of a cascade of heat PDE–ODE system with Dirichlet/Neumann interconnection and with the external disturbance flowing the control end. In order to deal with the disturbance, the sliding model control (SMC) is integrated with the backstepping approach, where the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop system are proved, and the monotonicity of the “reaching condition” is presented without differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed-loop system. Finally the numerical simulations validate the effectiveness of this method for the system with periodic and normal random disturbances respectively. |
| Author | Ren, Beibei Wang, Jun-Min Chen, Jinhao Liu, Jun-Jun |
| Author_xml | – sequence: 1 givenname: Jun-Min surname: Wang fullname: Wang, Jun-Min email: jmwang@bit.edu.cn organization: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China – sequence: 2 givenname: Jun-Jun surname: Liu fullname: Liu, Jun-Jun email: mathjun@163.com organization: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China – sequence: 3 givenname: Beibei surname: Ren fullname: Ren, Beibei email: beibei.ren@ttu.edu organization: Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA – sequence: 4 givenname: Jinhao surname: Chen fullname: Chen, Jinhao email: jinhao.chen@ttu.edu organization: Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA |
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| Snippet | In this paper, we are concerned with the boundary feedback stabilization of a cascade of heat PDE–ODE system with Dirichlet/Neumann interconnection and with... |
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| SubjectTerms | Backstepping Boundary control Cascade systems Disturbance rejection Sliding mode control |
| Title | Sliding mode control to stabilization of cascaded heat PDE–ODE systems subject to boundary control matched disturbance |
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