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Research Papers

Robust Negative Input Shapers for Vibration Suppression

[+] Author and Article Information
Joshua Vaughan, Aika Yano

The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405

William Singhose

The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405singhose@gatech.edu

J. Dyn. Sys., Meas., Control 131(3), 031014 (Mar 23, 2009) (9 pages) doi:10.1115/1.3072155 History: Received January 29, 2008; Revised December 02, 2008; Published March 23, 2009

Input shaping is a control method that limits motion-induced oscillation in vibratory systems by intelligently shaping the reference command. As with any control method, the robustness of input shaping to parameter variations and modeling errors is an important consideration. For input shaping, there exists a fundamental compromise between robustness to such errors and system rise time. For all types of shapers, greater robustness requires a longer duration shaper, which degrades rise time. However, if a shaper is allowed to contain negative impulses, then the shaper duration may be shortened with only a small cost of robustness and possible high-mode excitation. This paper presents a thorough analysis of the compromise between shaper duration, robustness, and possible high-mode excitation for several negative input-shaping methods. In addition, a formulation for specified negative amplitude, specified insensitivity shapers is presented. These shapers provide a continuous spectrum of solutions for the duration/robustness/high-mode excitation trade-off. Experimental results from a portable bridge crane verify the theoretical predictions.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

The input-shaping process

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Figure 2

Sensitivity curves for (UM-)ZV and (UM-)ZVD shapers

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Figure 3

ZV, UM-ZV, and UM-ZVD sensitivity curves

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Figure 4

Sensitivity curves for UM-EI method shapers

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Figure 5

Sensitivity curves for several UM-SI shapers

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Figure 6

Graphical representation of a five-impulse SNA-SI shaper

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Figure 7

SNA-SI shaper frequency sampling solution method

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Figure 8

Sensitivity curves for SI, SNA, and UM-SI shapers for I(5%)=0.5

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Figure 9

I(5%) as a function of shaper duration

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Figure 10

I(5%) as a function of shaper duration for several SNA-SI shapers

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Figure 11

Insensitivity as a function of shaper duration and maximum negative amplitude

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Figure 12

Efficiency of insensitivity

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Figure 13

Average high-mode excitation

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Figure 14

Average high-mode excitation as a function of negative impulse amplitude

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Figure 15

Portable bridge crane

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Figure 16

Vibration amplitudes for unshaped, UM-ZV, and UM-SI [I(5%)=0.5] shaped motions

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Figure 17

Experimental sensitivities of UM-ZV and UM-ZVD shapers

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Figure 18

Experimental sensitivities of UM-EI and two-hump UM-EI shapers

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Figure 19

Experimental sensitivity of UM-SI [I(5%)=0.5] shaper

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Figure 20

Experimental sensitivity of SNA(0.25) [I(5%)=0.5] shaper

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Figure 21

Experimental sensitivity of SNA(0.50) [I(5%)=0.5] shaper

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Figure 22

Experimental sensitivity of SNA(0.75) [I(5%)=0.5] shaper

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