Research Papers

Adjustable-Smooth Polynomial Command-Shaping Control With Linear Hoisting

[+] Author and Article Information
Khalid A. Alghanim

Department of Mechanical Engineering,
Kuwait University,
P.O. Box 5969,
Safat 13060, Kuwait
e-mail: khalid.ghanim@ku.edu.kw

Majed A. Majeed

Department of Mechanical Engineering,
Kuwait University,
P.O. Box 5969,
Safat 13060, Kuwait
e-mail: m.majeed@ku.edu.kw

Khaled A. Alhazza

Department of Mechanical Engineering,
Kuwait University,
P.O. Box 5969,
Safat 13060, Kuwait
e-mail: kalhazza@vt.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 5, 2017; final manuscript received May 4, 2018; published online June 18, 2018. Assoc. Editor: Maurizio Porfiri.

J. Vib. Acoust 140(6), 061013 (Jun 18, 2018) (9 pages) Paper No: VIB-17-1483; doi: 10.1115/1.4040236 History: Received November 05, 2017; Revised May 04, 2018

Great amount of work has been dedicated to eliminate residual vibrations in rest-to-rest motion. Considerable amount of these methods is based on convolving a general input signal with a sequence of timed impulses. These impulses usually have large jumps in their profiles and are chosen depending on the system modal parameters. Furthermore, classical input shaping methods are usually used for constant cable length and are sensitive to any change in the system parameters. To overcome these limitations, polynomial command shapers with adjustable maneuvering time are proposed. The equation of motion of a simple pendulum with the effect of hoisting is derived, linearized, and solved in order to eliminate residual vibrations in rest-to-rest maneuvers. Several cases including smooth, semi-smooth and unsmooth continuous shapers are simulated numerically and validated experimentally on an experimental overhead crane. Numerical and experimental results show that the proposed polynomial command shaper eliminates residual vibrations effectively. The effect of linear hoisting is also included and discussed. To enhance the shaper performance, extra parameters are added to the polynomial function to reduce shaper sensitivity. Results show that the effect of adding these parameters greatly enhances the shaper performance.

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Fig. 1

Schematic diagram of an overhead crane with hoisting capability [30]

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Fig. 2

Overhead crane model with variable cable length

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Fig. 3

Numerical results of shaped jib acceleration and velocity profiles for constant cable lengths

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Fig. 4

Numerical results of unshaped and shaped payload angles for constant cable lengths

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Fig. 5

Numerical results of payload angle and jib acceleration for different hoisting time: Li=0.5 m and Lf=0.4 m

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Fig. 6

Numerical results of payload angle and jib acceleration for three different jib acceleration: Li=0.5 m and Lf=0.4 m

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Fig. 7

Residual oscillations at the end of the maneuver as function of the length ratio β for the very-smooth input, +1, +2 and +3 optimized jib acceleration: Li=0.4 m and Lf=0.3 m

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Fig. 8

Experimental setup of scaled overhead crane model

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Fig. 9

Jib velocity, payload angle, and cable length of the very smooth input: Li=0.2 m and Lf=0.14 m

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Fig. 10

Jib velocity, payload angle, and cable length of the semi-smooth input: Li=0.5 m and Lf=0.4 m



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