Research Papers

A Control Design Method for Underactuated Mechanical Systems Using High-Frequency Inputs

[+] Author and Article Information
Sevak Tahmasian

Department of Engineering Science
and Mechanics,
Virginia Tech,
Blacksburg, VA 24061
e-mail: sevakt@vt.edu

Craig A. Woolsey

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 137(7), 071004 (Jul 01, 2015) (11 pages) Paper No: DS-15-1003; doi: 10.1115/1.4029627 History: Received January 03, 2015; Revised January 12, 2015; Online March 04, 2015

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.

Copyright © 2015 by ASME
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Fig. 3

Notation for the oscillating wing

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Fig. 1

Time history of actuated coordinates θ1 and θ2

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Fig. 2

Time history of unactuated coordinates θ3 and θ4

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Fig. 4

Aerodynamic and control forces on the flapping device

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Fig. 6

Variations of y with respect to time in hovering motion using modified controller

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Fig. 7

Variations of y, z, and θ following a harmonic trajectory with ω=50 rad/s

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Fig. 8

Variations of y, z, and θ following a harmonic trajectory with ω=17 rad/s

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Fig. 5

Variations of y, z, and θ with respect to time in hovering motion




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