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Research Papers

Vibration Analysis and Mitigation of Dead-Zone on Systems Using Two-Impulse Zero-Vibration Input Shaping

[+] Author and Article Information
Khalid L. Sorensen1

 Georgia Institute of Technology, Woodruff School of Mechanical Engineering, 813 Ferst Street, Atlanta, GA 30332khalids@gatech.edu

Patrick W. Cross, William E. Singhose, Shashvat Prakash

 Georgia Institute of Technology, Woodruff School of Mechanical Engineering, 813 Ferst Street, Atlanta, GA 30332

Modern variable-frequency drives provide precise speed control of ac induction motors. They are capable of enforcing a variety of kinematic constraints on the driven motors through the use of embedded configurable parameters. While constraints such as dead-zone and rate limiting are configurable, the configured values are limited by the physical capability of the drive. For example, instantaneous speed change is not possible. This constitutes an upper threshold on rate limiting. Likewise, variable-frequency drives cannot actuate a motor at very low speeds. The lower speed limit constitutes a lower threshold on the programmable dead-zone width.

1

Corresponding author.

J. Comput. Nonlinear Dynam 6(1), 011011 (Oct 05, 2010) (7 pages) doi:10.1115/1.4001818 History: Received April 01, 2008; Revised November 03, 2009; Published October 05, 2010; Online October 05, 2010

Input shaping is an effective method for reducing oscillatory motion in linear systems. Many physical systems, however, exhibit discontinuous dynamics, such as saturation, rate limiting, backlash, and dead-zone. These hard nonlinearities can degrade the vibration reducing properties of shaped signals. This paper investigates the detrimental effects of dead-zone on a class of input-shaped commands. A mitigation strategy is proposed for reducing these detrimental effects when the value of the dead-zone can be estimated. The robustness of this mitigation approach to uncertainties in the dead-zone width is also determined. Theoretical developments are experimentally verified using an industrial 10 ton bridge crane.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Input shaping process

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Figure 2

Input shaping implemented on a system with dead-zone

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Figure 3

Response of a harmonic oscillator to an arbitrary command

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Figure 4

Oscillatory effects of dead-zone on ZV-shaped and -unshaped step commands

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Figure 5

10 ton bridge crane

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Figure 6

Crane actuation block diagram

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Figure 7

P-values for a system with dead-zone

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Figure 8

P̂-values for a system with dead zone and rate limiting

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Figure 9

Oscillatory effects of acceleration-limited, dead-zone commands

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Figure 10

Velocity command and system response for d=25% maximum velocity

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Figure 11

Experimental and theoretical effects of dead-zone on ZV-shaped step commands

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Figure 12

Mitigation technique for eliminating the effects of dead-zone

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Figure 13

ZV-shaped step command modified by dead-zone and inverse-dead-zone

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Figure 14

Inverse-mitigation robustness: relative uncertainty

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Figure 15

Inverse-mitigation robustness: absolute uncertainty

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Figure 16

Experimental and theoretical inverse-mitigation robustness

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