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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April 2016
Research-Article
Vibration Reduction Using Near Time-Optimal Commands for Systems With Nonzero Initial Conditions
Joshua Vaughan,
Joshua Vaughan
Assistant Professor
Department of Mechanical Engineering,
University of Louisiana at Lafayette,
Lafayette, LA 70504
e-mail: joshua.vaughan@louisiana.edu
Department of Mechanical Engineering,
University of Louisiana at Lafayette,
Lafayette, LA 70504
e-mail: joshua.vaughan@louisiana.edu
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William Singhose
William Singhose
Professor
George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: singhose@gatech.edu
George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: singhose@gatech.edu
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Abhishek Dhanda
Joshua Vaughan
Assistant Professor
Department of Mechanical Engineering,
University of Louisiana at Lafayette,
Lafayette, LA 70504
e-mail: joshua.vaughan@louisiana.edu
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
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. Apr 2016, 138(4): 041006 (9 pages)
Published Online: February 17, 2016
Article history
Received:
December 10, 2014
Revised:
November 20, 2015
Citation
Dhanda, A., Vaughan, J., and Singhose, W. (February 17, 2016). "Vibration Reduction Using Near Time-Optimal Commands for Systems With Nonzero Initial Conditions." ASME. J. Dyn. Sys., Meas., Control. April 2016; 138(4): 041006. https://doi.org/10.1115/1.4032064
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