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TECHNICAL BRIEFS

Adaptive Input Shaping for Nonlinear Systems: A Case Study

[+] Author and Article Information
John Stergiopoulos

Electrical and Computer Engineering Department, University of Patras, Rio, Achaia 26500, Greece

Anthony Tzes

Electrical and Computer Engineering Department, University of Patras, Rio, Achaia 26500, Greecetzes@ee.upatras.gr

J. Dyn. Sys., Meas., Control 129(2), 219-223 (Jul 14, 2006) (5 pages) doi:10.1115/1.2431815 History: Received June 25, 2005; Revised July 14, 2006

Input shaping is a technique that seeks to reduce residual vibrations of lightly damped systems through modification of the command input to the system. Although several input shaping techniques have been derived primarily from linear system theory, theoretical results are hard to be traced for their application to nonlinear systems. In most of the reported cases, a fixed shaper is designed based on the linearized version around an operating point of the nonlinear system. In this paper, an adaptive form of the input shaper is proposed for a class of nonlinear lightly damped systems. The adaptive shaper adjusts the magnitude and relative time difference between its impulses according to the instant frequency and damping of the linearized systems. The efficacy of the proposed scheme and its comparison to a fixed shaper is investigated through its application to a pendulum system. The adaptive shaper’s parameters vary according to the pendulum’s angle. The illustrative examples indicate the deficiencies of the fixed case and demonstrate the efficacy of the designed controller.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 2

System’s shaped response (case study 1)

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Figure 3

(a) Reference and shaped (adaptive case) commands and (b) evolution of relative impulse spacing in time (case study 1)

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Figure 4

System’s shaped response (case study 2)

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Figure 5

(a) Reference and shaped (adaptive case) commands and (b) evolution of relative impulse spacing in time (case study 2)

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