The anti-disturbance property of a closed-loop system of 1-d wave equation with boundary control matched disturbance

We study the anti-disturbance problem of a 1-d wave equation with boundary control matched disturbance. In earlier literature, the authors always designed the controller such as the sliding mode control and the active disturbance rejection control to stabilize the system. However, most of the corres...

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Bibliographic Details
Published in:Applications of mathematics (Prague) 2019-12, Vol.64 (6), p.695-714
Main Authors: Wang, Xiao-Rui, Xu, Gen-Qi
Format: Article
Language:English
Subjects:
Active control
Analysis
Applications of Mathematics
Boundary control
Classical and Continuum Physics
Closed loop systems
Control systems design
Feedback control
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Nonlinear control
Nonlinear systems
Optimization
Sliding mode control
Theoretical
Wave equations
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Summary:We study the anti-disturbance problem of a 1-d wave equation with boundary control matched disturbance. In earlier literature, the authors always designed the controller such as the sliding mode control and the active disturbance rejection control to stabilize the system. However, most of the corresponding closed-loop systems are boundedly stable. In this paper we show that the linear feedback control also has a property of anti-disturbance, even if the disturbance includes some information of the system. By choosing suitable parameters introduced in the proof, we can ensure the solution of the closed-loop system is bounded in an admissible range. As an application, we discuss the control problem of a nonlinear system. As a result, it is shown that the bounded estimation of the solution is suitable.
ISSN:0862-7940
1572-9109
DOI:10.21136/AM.2019.0070-18