Adaptive vibration isolation for axially moving strings: theory and experiment

High-speed transport of continuous materials such as belts, webs, filaments, or bands can cause unwanted vibration. Vibration control for these systems often focuses on restricting the response resulting from external disturbances (e.g. support roller eccentricity or aerodynamic excitation) to areas...

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Bibliographic Details
Published inAutomatica (Oxford) Vol. 38; no. 3; pp. 379 - 390
Main Authors Li, Yugang, Aron, Dan, Rahn, Christopher D.
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 01.03.2002
Elsevier
Subjects
Applied sciences
Axially moving string
Computer science; control theory; systems
Control system analysis
Control theory. Systems
Distributed parameter systems
Exact sciences and technology
Lyapunov theory
Vibration isolation
Axially moving string
Lyapunov theory
Distributed parameter systems
Vibration isolation
Positioning
Vibration
Axial speed
Eccentricity
Differential equation
Aerodynamics
Translation motion
Adaptive control
Modeling
Partial differential equation
Asymptotic stability
Vibration damping
High speed
World wide web
Vibration control
Asymptotic approximation
Internet
Strip material
Distributed parameter system
Actuator
Lyapunov function
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Summary:High-speed transport of continuous materials such as belts, webs, filaments, or bands can cause unwanted vibration. Vibration control for these systems often focuses on restricting the response resulting from external disturbances (e.g. support roller eccentricity or aerodynamic excitation) to areas not requiring high precision positioning. This paper introduces vibration controllers for an axially moving string system consisting of a controlled span coupled to a disturbed span via an actuator. The system model includes a partial differential equation for the two spans and an ordinary differential equation for the actuator. Exact model knowledge and adaptive isolation controllers, based on Lyapunov theory, regulate the controlled span from bounded disturbances in the adjacent, uncontrolled span. Assuming distributed damping in the uncontrolled span, the exact model knowledge and adaptive controllers exponentially and asymptotically drive the controlled span displacement to zero, respectively, while ensuring bounded uncontrolled span displacement and control force. Experiments demonstrate the effectiveness of the proposed controller in isolating the controlled span from disturbances and damping the controlled span displacement.
ISSN:0005-1098
1873-2836
DOI:10.1016/S0005-1098(01)00219-9