Stabilization of a Wave Equation with a Tip Mass Based on Disturbance Observer of Time-Varying Gain

Stabilization of a Wave Equation with a Tip Mass Based on Disturbance Observer of Time-Varying Gain In this paper, we consider the stabilization problem of a wave equation with a tip mass, which undergoes the external disturbances at the tip mass end. Here, the disturbance may be exponentially increasing. For such a model, the usual sliding mode control method cannot be applied. Therefore, we employ the active disturbance rejection control (ADRC) approach to investigate this problem. At first, by the ADRC method, we design a disturbance observer that has time-varying gain so that the disturbance can be estimated exponentially. We show the disturbance observer is an exponential-type observer. Then, we use the estimate term as negative feedback so as to cancel disturbance. Finally, we prove that the resulted closed-loop system is well-posedness and exponentially stable. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Dynamical and Control Systems Springer Journals

Stabilization of a Wave Equation with a Tip Mass Based on Disturbance Observer of Time-Varying Gain

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Publisher
Springer US
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Engineering; Vibration, Dynamical Systems, Control; Calculus of Variations and Optimal Control; Optimization; Analysis; Applications of Mathematics; Systems Theory, Control
ISSN
1079-2724
eISSN
1573-8698
D.O.I.
10.1007/s10883-016-9349-0
Publisher site
See Article on Publisher Site

Abstract

In this paper, we consider the stabilization problem of a wave equation with a tip mass, which undergoes the external disturbances at the tip mass end. Here, the disturbance may be exponentially increasing. For such a model, the usual sliding mode control method cannot be applied. Therefore, we employ the active disturbance rejection control (ADRC) approach to investigate this problem. At first, by the ADRC method, we design a disturbance observer that has time-varying gain so that the disturbance can be estimated exponentially. We show the disturbance observer is an exponential-type observer. Then, we use the estimate term as negative feedback so as to cancel disturbance. Finally, we prove that the resulted closed-loop system is well-posedness and exponentially stable.

Journal

Journal of Dynamical and Control SystemsSpringer Journals

Published: Dec 17, 2016

References

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