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Technical Briefs

Command Shaping Under Nonsymmetrical Acceleration and Braking Dynamics

[+] Author and Article Information
Thomas H. Bradley, Jon Danielson, Jason Lawrence, William Singhose

 Georgia Institute of Technology, Atlanta, GA 30332-0405

J. Vib. Acoust 130(5), 054503 (Aug 13, 2008) (5 pages) doi:10.1115/1.2948385 History: Received February 19, 2007; Revised February 26, 2008; Published August 13, 2008

The conventional unity magnitude zero vibration (UM-ZV) command shaping technique is an effective means for eliminating vibration in linear mechanical systems with on-off actuators. This paper discusses how the UM-ZV command shaping technique is affected by a common nonlinearity: nonsymmetrical accelerating and braking dynamics. Two approaches for creating new types of UM-ZV shaped commands are presented: a closed-form analytic solution and a numerical optimization approach. Both methods reduce residual vibration of the nonlinear system more effectively than the conventional UM-ZV shaped commands. Simulations and experiments on a bridge crane confirm the effectiveness of the new commands.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 10

Simulated and experimental responses for different UM-ZV shaped commands

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Figure 9

Simulated residual vibration of UM-ZV shaped commands for nonlinear system

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Figure 8

Flowchart for the UM‐ZVo numerical optimization routine

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Figure 7

Residual vibration for UM-ZV and UM‐ZVc shaped commands as a function of tp (τa=0.117s, τb=0.065s)

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Figure 6

Constraints on τa∕T and τb∕T for the UM‐ZVc shaped command

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Figure 5

Phasor diagram for UM-ZV input shaper ramp-up command

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Figure 4

Residual vibration using unshaped and UM-ZV shaped commands as a function of tp (τa=0.117s, τb=0.065s)

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Figure 3

Payload residual vibration using UM-ZV commands as a function of tp and τb(τa=0.117s)

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Figure 2

Block diagram of the control and the actuation system

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Figure 1

UM-ZV shaper and UM-ZV shaped pulse

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