Stabilization and disturbance rejection for the wave equation
Author(s)
Date
1998-01Source Title
IEEE Transactions on Automatic Control
Print ISSN
0018-9286
Publisher
Institute of Electrical and Electronics Engineers
Volume
43
Issue
1
Pages
89 - 95
Language
English
Type
ArticleItem Usage Stats
206
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Abstract
We consider a system described by the one-dimensional linear wave equation in a bounded domain with appropriate boundary conditions. To stabilize the system, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the proposed controller is a proper rational function of the complex variable s and may contain a single pole at the origin and a pair of complex conjugate poles on the imaginary axis, provided that the residues corresponding to these poles are nonnegative; the rest of the transfer function is required to be a strictly positive real function. We then show that depending on the location of the pole on the imaginary axis, the closed-loop system is asymptotically stable. We also consider the case where the output of the controller is corrupted by a disturbance and show that it may be possible to attenuate the effect of the disturbance at the output if we choose the controller transfer function appropriately. We also present some numerical simulation results which support this argument.
Keywords
Boundary control systemsDistributed parameter systems
Disturbance rejection
Semigroup theory
Stability
Asymptotic stability
Boundary conditions
Closed loop control systems
Computer simulation
Distributed parameter control systems
Poles and zeros
Transfer functions
Disturbance rejection
Linear wave equation
Semigroup theory
System stability
Permalink
http://hdl.handle.net/11693/25328Published Version (Please cite this version)
http://dx.doi.org/10.1109/9.654893Collections
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