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Journal of Vibration and Acoustics | Volume 127 | Issue 4 | TECHNICAL PAPERS
TECHNICAL PAPERS

Friction-Compensating Command Shaping for Vibration Reduction

[+] Author and Article Information
Jason Lawrence, William Singhose

Woodruff School of Mechanical Engineering,  Georgia Institute of Technology, Atlanta, GA

Keith Hekman

Department of Mechanical Engineering,  The American University in Cairo, Cairo, Egypt

J. Vib. Acoust 127(4), 307-314 (Sep 03, 2004) (8 pages) doi:10.1115/1.1924637 History: Received June 25, 2003; Revised September 03, 2004
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Fast and accurate point-to-point motion is a common operation for industrial machines, but vibration will frequently corrupt such motion. This paper develops commands that can move machines without vibration, even in the presence of Coulomb friction. Previous studies have shown that input shaping can be used on linear systems to produce point-to-point motion with no residual vibration. This paper extends command-shaping theory to nonlinear systems, specifically systems with Coulomb friction. This idea is applied to a PD-controlled mass with Coulomb friction to ground. The theoretical developments are experimentally verified on a solder cell machine. The results show that the new commands allow the proportional gain to be increased, resulting in reduced rise time, settling time, and steady-state error.
Copyright © 2005 by American Society of Mechanical Engineers
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+Comparison of ZVS and ZVC commands with experimentally determined optimal two-step commands
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Comparison of ZVS and ZVC commands with experimentally determined optimal two-step commands
Figure 15

Comparison of ZVS and ZVC commands with experimentally determined optimal two-step commands

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+Average steady-state error across all two-step commands at each proportional gain
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Average steady-state error across all two-step commands at each proportional gain
Figure 16

Average steady-state error across all two-step commands at each proportional gain

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+Applying the ZVC shaper to improve system response
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Applying the ZVC shaper to improve system response
Figure 17

Applying the ZVC shaper to improve system response

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+Experimental data: Comparison of step, ZVS, and ZVC responses
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Experimental data: Comparison of step, ZVS, and ZVC responses
Figure 13

Experimental data: Comparison of step, ZVS, and ZVC responses

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+Experimental data: Performance measures for various two-step commands at different proportional gains
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Experimental data: Performance measures for various two-step commands at different proportional gains
Figure 14

Experimental data: Performance measures for various two-step commands at different proportional gains

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+Model of system
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Model of system
Figure 1

Model of system

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+Stribeck curve
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Stribeck curve
Figure 2

Stribeck curve

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+Friction model used in this study
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Friction model used in this study
Figure 3

Friction model used in this study

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+Comparison of step response with and without Coulomb friction
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Comparison of step response with and without Coulomb friction
Figure 4

Comparison of step response with and without Coulomb friction

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+Effect of proportional gain on final steady-state error
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Effect of proportional gain on final steady-state error
Figure 5

Effect of proportional gain on final steady-state error

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+Effects of proportional and derivative gain on overshoot and rise time
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Effects of proportional and derivative gain on overshoot and rise time
Figure 6

Effects of proportional and derivative gain on overshoot and rise time

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+Using a ZVS input shaper to eliminate vibration
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Using a ZVS input shaper to eliminate vibration
Figure 7

Using a ZVS input shaper to eliminate vibration

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+Strategy for designing the ZVC shaper
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Strategy for designing the ZVC shaper
Figure 8

Strategy for designing the ZVC shaper

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+Simulated step and ZVC responses
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Simulated step and ZVC responses
Figure 9

Simulated step and ZVC responses

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+Comparison of residual vibration and rise time for step, ZVS and ZVC responses
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Comparison of residual vibration and rise time for step, ZVS and ZVC responses
Figure 10

Comparison of residual vibration and rise time for step, ZVS and ZVC responses

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+Experimental setup
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Experimental setup
Figure 11

Experimental setup

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+Sample step response showing peaks and troughs
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Sample step response showing peaks and troughs
Figure 12

Sample step response showing peaks and troughs

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