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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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Figure 1

Unshaped and shaped-step commands

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Figure 2

Payload response to unshaped and shaped commands

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Figure 3

Zero-vibration shaped step

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Figure 4

Effect of acceleration limiting

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Figure 5

Zero-vibration response to two impulses

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Figure 6

Sensitivity curves for ZV, ZVD, and EI shapers

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Figure 7

Sensitivity curve for SI shaper

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Figure 8

Nonlinear system is reduced to a linear system

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Figure 9

Command decomposition

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Figure 10

Sensitivity curve for ZV shaper

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Figure 11

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

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Figure 12

Acceleration for three-step velocity command

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Figure 13

Sensitivity curves for ZVD and ALZVD input shapers

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Figure 14

Sensitivity curves for EI and ALEI input shapers

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Figure 15

Sensitivity curves for SI and ALSI input shapers

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Figure 16

An example of a shaped and an unshaped multistep command

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Figure 17

Shaper sensitivity to damping ratio

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