This paper presents a control design technique which enables approximate reference trajectory tracking for a class of underactuated mechanical systems. The control law comprises two terms. The first involves feedback of the trajectory tracking error in the actuated coordinates. Building on the concept of vibrational control, the second term imposes high-frequency periodic inputs that are modulated by the tracking error in the unactuated coordinates. Under appropriate conditions on the system structure and the commanded trajectory, and with sufficient separation between the time scales of the vibrational forcing and the commanded trajectory, the approach provides convergence in both the actuated and unactuated coordinates. The procedure is first described for a two degree-of-freedom (DOF) system with one input. Generalizing to higher-dimensional, underactuated systems, the approach is then applied to a 4DOF system with two inputs. A final example involves control of a rigid plate that is flapping in a uniform flow, a 3DOF system with one input. More general applications include biomimetic locomotion systems, such as underwater vehicles with articulating fins and flapping wing micro-air vehicles.
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July 2015
Research-Article
A Control Design Method for Underactuated Mechanical Systems Using High-Frequency Inputs
Sevak Tahmasian,
Sevak Tahmasian
Department of Engineering Science
and Mechanics,
e-mail: sevakt@vt.edu
and Mechanics,
Virginia Tech
,Blacksburg, VA 24061
e-mail: sevakt@vt.edu
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Craig A. Woolsey
Craig A. Woolsey
1
Professor
Department of Aerospace
and Ocean Engineering,
e-mail: cwoolsey@vt.edu
Department of Aerospace
and Ocean Engineering,
Virginia Tech
,Blacksburg, VA 24061
e-mail: cwoolsey@vt.edu
1Corresponding author.
Search for other works by this author on:
Sevak Tahmasian
Department of Engineering Science
and Mechanics,
e-mail: sevakt@vt.edu
and Mechanics,
Virginia Tech
,Blacksburg, VA 24061
e-mail: sevakt@vt.edu
Craig A. Woolsey
Professor
Department of Aerospace
and Ocean Engineering,
e-mail: cwoolsey@vt.edu
Department of Aerospace
and Ocean Engineering,
Virginia Tech
,Blacksburg, VA 24061
e-mail: cwoolsey@vt.edu
1Corresponding author.
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 3, 2015; final manuscript received January 12, 2015; published online March 4, 2015. Editor: Joseph Beaman.
J. Dyn. Sys., Meas., Control. Jul 2015, 137(7): 071004 (11 pages)
Published Online: July 1, 2015
Article history
Received:
January 3, 2015
Revision Received:
January 12, 2015
Online:
March 4, 2015
Citation
Tahmasian, S., and Woolsey, C. A. (July 1, 2015). "A Control Design Method for Underactuated Mechanical Systems Using High-Frequency Inputs." ASME. J. Dyn. Sys., Meas., Control. July 2015; 137(7): 071004. https://doi.org/10.1115/1.4029627
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