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Research Papers

Vibration Reduction Using Near Time-Optimal Commands for Systems With Nonzero Initial Conditions

[+] Author and Article Information
Abhishek Dhanda

San Jose Research Center,
HGST,
San Jose, CA 95135
e-mail: adhanda@gmail.com

Joshua Vaughan

Assistant Professor
Department of Mechanical Engineering,
University of Louisiana at Lafayette,
Lafayette, LA 70504
e-mail: joshua.vaughan@louisiana.edu

William Singhose

Professor
George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: singhose@gatech.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 10, 2014; final manuscript received November 20, 2015; published online February 17, 2016. Assoc. Editor: Fu-Cheng Wang.

J. Dyn. Sys., Meas., Control 138(4), 041006 (Feb 17, 2016) (9 pages) Paper No: DS-14-1521; doi: 10.1115/1.4032064 History: Received December 10, 2014; Revised November 20, 2015

The control of flexible systems has been an active area of research for many years because of its importance to a wide range of applications. The majority of previous research on time-optimal control has concentrated on the rest-to-rest problem. However, there are many cases when flexible systems are not at rest or are subjected to disturbances. This paper presents an approach to design optimal vibration-reducing commands for systems with nonzero initial conditions. The problem is first formulated as an optimal control problem, and the optimal solution is shown to be bang-bang. Once the structure of the optimal command is known, a parametric problem formulation is presented for the computation of the switching times. Solutions are experimentally verified using a portable bridge crane by moving the payload through a commanded motion while removing initial payload swing.

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Figures

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Fig. 1

Three impulse vibration reduction filter based on switching control

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Fig. 2

Comparison of various control schemes for rest-to-rest motion with command saturation: (a) shaped control using UM filter, (b) shaped control using PS filter, and (c) closed-form control

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Fig. 3

Ideal case of time-optimal control

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Fig. 4

Time-optimal control interrupted during motion

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Fig. 6

Vibration sensitivity for optimal ICZV and ICZVD filters designed for ω = 1, initial condition {yf0 ,vf0}=[0.1,−0.1], and final condition x(T)=[1, 0]

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Fig. 7

Transition shaping

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Fig. 8

Acceleration responses from TS filters designed to cancel mode at ω = 10 rad/s and yref = 100

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Fig. 9

Representing impulses on a vector diagram

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Fig. 10

Resultant vibration vector from adding impulses

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Fig. 11

Input-shaper design using the vector diagram

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Fig. 12

Vector diagram representation of initial conditions

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Fig. 13

Five-impulse sequence to cancel initial conditions

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Fig. 14

Portable bridge crane

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Fig. 15

Residual vibration amplitude for unshaped, ICZV-shaped, and ICZVD-shaped moves

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Fig. 16

Theoretical and experimental sensitivity of the ICZV command

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Fig. 17

Theoretical and experimental sensitivity of the ICZVD command

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