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Research Papers

Iterative Learning Velocity and Tension Control for Single Span Axially Moving Materials

[+] 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. Dyn. Sys., Meas., Control 130(5), 051003 (Aug 01, 2008) (6 pages) doi:10.1115/1.2957625 History: Received June 28, 2005; Revised July 20, 2007; Published August 01, 2008

Precise tension and speed control of axially moving material systems enables high speed processing of paper, plastics, fibers, and films. A single span model is developed that includes distributed longitudinal vibration, a torque-controlled roller at the left boundary, and a speed-controlled roller at the right boundary. The speed trajectory of the right roller is assumed periodic but unknown. A proportional and derivative (PD) feedback and iterative learning control (ILC) feedforward control law is developed for the left roller torque based on the measured tension and speed at the left boundary. PD tension/speed control is proven to ensure boundedness of distributed displacement and tension. ILC is proven to provide the same theoretical result but greatly improved simulated response to an aggressive stop/start right roller speed trajectory.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of an axially moving material system

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Figure 2

Open loop response of the system: (a) disturbance position, uL(t); (b) disturbance velocity, u̇L(t); (c) velocity error, υ̇(0,t); and (d) tension error, PD−P(0,t)

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Figure 3

Closed loop response of the system under PD control (thin) and ILC (thick): (a) velocity error, υ̇(0,t); (b) learning term, Δ(t); (c) tension error, PD−P(0,t); and (d) control effort, f0(t)

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