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TECHNICAL PAPERS

Robust Input Shaper Control Design for Parameter Variations in Flexible Structures

[+] Author and Article Information
Lucy Y. Pao, Mark A. Lau

Electrical & Computer Engineering Department, University of Colorado, Boulder, CO 80309-0425

J. Dyn. Sys., Meas., Control 122(1), 63-70 (Oct 04, 1999) (8 pages) doi:10.1115/1.482429 History: Received October 04, 1999
Copyright © 2000 by ASME
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References

Figures

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Sensitivity curves relative to normalized frequency for ZV, ZVD, and EI input shapers (ωmodel=1 rad/sec,ζmodel=0.01,tv=4π sec).
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Shaper lengths for optimal shaper designs assuming uniform (top) and Gaussian (bottom) variation in the natural frequency. The ZVD and EI shaper lengths (which are equal) are also shown for comparison.
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Comparison of the 5 percent insensitivity Wf levels assuming for optimal shaper designs uniform (top) and Gaussian (bottom) variation in the natural frequency.
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Comparison of the expected residual vibration (J) assuming for optimal shaper designs uniform (left) and Gaussian (right) variation in the natural frequency. For smaller parameter uncertainties, the ZVD is more optimal; and as the parameter uncertainty increases, the EI shaper becomes closer to optimal.
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Comparison of the magnitude of shaper zeros assuming for optimal shaper designs uniform (left) and Gaussian (right) variation in the natural frequency.  
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Shaper length of minimal expected residual vibration shapers assuming uniform and Gaussian variation in both frequency and damping. For lightly damped systems, optimal shapers yield shorter shaper lengths than those obtained from traditional ZVD and EI shaper designs.
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Expected residual vibration (J) assuming for optimal shaper designs uniform (top) and Gaussian (bottom) variation in both frequency and damping. Optimal shapers yield lower expected residual vibration than those of ZVD and EI designs.
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Angle deviation of optimal shaper zeros from system poles for uniform (top) and Gaussian (bottom) variation in frequency and damping. The angle deviation is negative for the optimal shaper zeros meaning that their location is shifted toward a line of lower damping.
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Shaper lengths for different uniform frequency uncertainties. The optimal shapers yield shorter shaper lengths compared with traditional ZV shaper designs.
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Expected residual vibration for different uniform uncertainty ranges in frequency. The optimal shapers yield lower expected residual vibration compared with the traditional ZV shaper designs.

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