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TECHNICAL BRIEFS

On the Control of Axially Moving Material Systems

[+] Author and Article Information
Haiyu Zhao

Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA 16803

Christopher D. Rahn

Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA 16803cdrahn@psu.edu

J. Vib. Acoust 128(4), 527-531 (Jan 27, 2006) (5 pages) doi:10.1115/1.2202170 History: Received July 05, 2005; Revised January 27, 2006

Vibration control can improve the performance of many axially moving material systems (e.g., web handling machines and tape drives). Researchers have used Lyapunov analysis to develop vibration stabilizing controllers for distributed parameter models of axially moving material systems. Both the material and regular time derivatives have been used in these analyses despite the fact that they give different results. This paper proves that for a pinned axially moving string model: (i) Lyapunov stability analysis using the material derivative incorrectly predicts that a time-varying functional is constant and (ii) neglect of the coupled domain in boundary control analysis is ill posed and incorrectly predicts bounded forced response and exponentially decaying transients.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Pinned axially moving string Eulerian VE(t) (dashed) and Lagrangian VL(t) (solid) functionals versus time

Grahic Jump Location
Figure 2

Boundary control for: (a) axially moving string; (b) stationary string; (c) axially moving beam; and (d) stationary beam

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