Sliding Mode and Active Disturbance Rejection Control to Stabilization of One-Dimensional Anti-Stable Wave Equations Subject to Disturbance in Boundary Input

In this technical note, we are concerned with the boundary stabilization of a one-dimensional anti-stable wave equation subject to boundary disturbance. We propose two strategies, namely, sliding mode control (SMC) and the active disturbance rejection control (ADRC). The reaching condition, and the...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 58; no. 5; pp. 1269 - 1274
Main Authors: Guo, Bao-Zhu, Jin, Feng-Fei
Format: Journal Article
Language:English
Published: IEEE 01.05.2013
Subjects:
Aerospace electronics
Boundary control
Closed loop systems
Continuous wavelet transforms
disturbance rejection
Eigenvalues and eigenfunctions
Equations
Mathematical model
sliding mode control (SMC)
wave equation
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:In this technical note, we are concerned with the boundary stabilization of a one-dimensional anti-stable wave equation subject to boundary disturbance. We propose two strategies, namely, sliding mode control (SMC) and the active disturbance rejection control (ADRC). The reaching condition, and the existence and uniqueness of the solution for all states in the state space in SMC are established. The continuity and monotonicity of the sliding surface are proved. Considering the SMC usually requires the large control gain and may exhibit chattering behavior, we then develop an ADRC to attenuate the disturbance. We show that this strategy works well when the derivative of the disturbance is also bounded. Simulation examples are presented for both control strategies.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2012.2218669