Output feedback stabilisation of an axially moving string subject to a spring-mass-dashpot

Jun-Min  Wang; Jing Wang; Han-Wen  Zhang

doi:10.1080/00207179.2022.2085180

Output feedback stabilisation of an axially moving string subject to a spring-mass-dashpot

Jun-Min Wang, Jing Wang^*, Han-Wen Zhang

^*Corresponding author for this work

Mathematical Physics

Research output: Contribution to journal › Article › Scientific › peer-review

1 Citation (Scopus)

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Abstract

In this paper, we consider the output feedback stabilisation of an axially moving string system subject to a spring-mass-dashpot boundary condition. By constructing an invertible backstepping transformation, we design a state feedback controller to stabilise the system. Next, we present an observer to estimate the states of the system, and based on the estimated states, we design an output-feedback controller. The closed-loop system is proved to be exponentially stable by Lyapunov analysis. Numerical simulations are presented to verify the effectiveness of the proposed controller.

Original language	English
Pages (from-to)	2157-2166
Number of pages	10
Journal	International Journal of Control
Volume	96
Issue number	9
DOIs	https://doi.org/10.1080/00207179.2022.2085180
Publication status	Published - 2022

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

backstepping
Moving string
PDE-ODE
spring-mass-dashpot
vibration control

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10.1080/00207179.2022.2085180

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abstract = "In this paper, we consider the output feedback stabilisation of an axially moving string system subject to a spring-mass-dashpot boundary condition. By constructing an invertible backstepping transformation, we design a state feedback controller to stabilise the system. Next, we present an observer to estimate the states of the system, and based on the estimated states, we design an output-feedback controller. The closed-loop system is proved to be exponentially stable by Lyapunov analysis. Numerical simulations are presented to verify the effectiveness of the proposed controller.",

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N2 - In this paper, we consider the output feedback stabilisation of an axially moving string system subject to a spring-mass-dashpot boundary condition. By constructing an invertible backstepping transformation, we design a state feedback controller to stabilise the system. Next, we present an observer to estimate the states of the system, and based on the estimated states, we design an output-feedback controller. The closed-loop system is proved to be exponentially stable by Lyapunov analysis. Numerical simulations are presented to verify the effectiveness of the proposed controller.

AB - In this paper, we consider the output feedback stabilisation of an axially moving string system subject to a spring-mass-dashpot boundary condition. By constructing an invertible backstepping transformation, we design a state feedback controller to stabilise the system. Next, we present an observer to estimate the states of the system, and based on the estimated states, we design an output-feedback controller. The closed-loop system is proved to be exponentially stable by Lyapunov analysis. Numerical simulations are presented to verify the effectiveness of the proposed controller.

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Output feedback stabilisation of an axially moving string subject to a spring-mass-dashpot

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