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Journal of Dynamic Systems, Measurement, and Control | Volume 130 | Issue 5 | Research Paper
Research Papers

Command Shaping for Flexible Systems Subject to Constant Acceleration Limits

[+] Author and Article Information
Jon Danielson, Jason Lawrence

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

William Singhose

Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332bill.singhose@me.gatech.edu

For a ZVD shaper, the derivative of the sensitivity curve at the designed frequency is zero (4) EI, SI, and other shapers have there own unique constraints (11,40).

J. Dyn. Sys., Meas., Control 130(5), 051011 (Aug 04, 2008) (8 pages) doi:10.1115/1.2963045 History: Received January 25, 2007; Revised March 25, 2008; Published August 04, 2008
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Input shaping is an effective means of eliminating vibration in many types of flexible systems. This paper discusses how input shaper performance is affected by a fixed acceleration limit. This type of limit is a common occurrence in many mechanical drive systems because it corresponds to a constant force or torque input. It is shown that some input shapers are not affected by an acceleration limit under certain conditions. A test criterion is developed to determine what types of input shapers are negatively affected, and a method is proposed to compensate for the detrimental effects of the constant acceleration limit. Experimental results from an industrial crane support the main theoretical results.
Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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+Unshaped and shaped-step commands
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Unshaped and shaped-step commands
Figure 1

Unshaped and shaped-step commands

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+Payload response to unshaped and shaped commands
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Payload response to unshaped and shaped commands
Figure 2

Payload response to unshaped and shaped commands

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+Zero-vibration shaped step
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Zero-vibration shaped step
Figure 3

Zero-vibration shaped step

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+Effect of acceleration limiting
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Effect of acceleration limiting
Figure 4

Effect of acceleration limiting

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+Zero-vibration response to two impulses
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Zero-vibration response to two impulses
Figure 5

Zero-vibration response to two impulses

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+Sensitivity curves for ZV, ZVD, and EI shapers
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Sensitivity curves for ZV, ZVD, and EI shapers
Figure 6

Sensitivity curves for ZV, ZVD, and EI shapers

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+Sensitivity curve for SI shaper
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Sensitivity curve for SI shaper
Figure 7

Sensitivity curve for SI shaper

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+Nonlinear system is reduced to a linear system
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Nonlinear system is reduced to a linear system
Figure 8

Nonlinear system is reduced to a linear system

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+Command decomposition
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Command decomposition
Figure 9

Command decomposition

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+Sensitivity curve for ZV shaper
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Sensitivity curve for ZV shaper
Figure 10

Sensitivity curve for ZV shaper

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+Amplitude of residual vibration as a function of α for various shapers
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Amplitude of residual vibration as a function of α for various shapers
Figure 11

Amplitude of residual vibration as a function of α for various shapers

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+Acceleration for three-step velocity command
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Acceleration for three-step velocity command
Figure 12

Acceleration for three-step velocity command

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+Sensitivity curves for ZVD and ALZVD input shapers
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Sensitivity curves for ZVD and ALZVD input shapers
Figure 13

Sensitivity curves for ZVD and ALZVD input shapers

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+Sensitivity curves for EI and ALEI input shapers
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Sensitivity curves for EI and ALEI input shapers
Figure 14

Sensitivity curves for EI and ALEI input shapers

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+Sensitivity curves for SI and ALSI input shapers
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Sensitivity curves for SI and ALSI input shapers
Figure 15

Sensitivity curves for SI and ALSI input shapers

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+An example of a shaped and an unshaped multistep command
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An example of a shaped and an unshaped multistep command
Figure 16

An example of a shaped and an unshaped multistep command

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+Shaper sensitivity to damping ratio
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Shaper sensitivity to damping ratio
Figure 17

Shaper sensitivity to damping ratio

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