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

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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Figure 15

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

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Figure 16

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

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Figure 17

Applying the ZVC shaper to improve system response

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Figure 13

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

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Figure 14

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

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Figure 3

Friction model used in this study

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Figure 4

Comparison of step response with and without Coulomb friction

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Figure 5

Effect of proportional gain on final steady-state error

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Figure 6

Effects of proportional and derivative gain on overshoot and rise time

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Figure 7

Using a ZVS input shaper to eliminate vibration

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Figure 8

Strategy for designing the ZVC shaper

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Figure 9

Simulated step and ZVC responses

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Figure 10

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

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Figure 11

Experimental setup

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Figure 12

Sample step response showing peaks and troughs





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