Inversion control has been very successful in the control of nonlinear dynamical systems. However, when applied to flexible manipulators, inverse dynamics through direct integration in temporal space causes unbounded controller command. For nearly three decades, researchers have exhausted all possible solutions. Still, a perfect solution does not exist that would yield a perfect tip tracking. It has been suggested that seeking an inverse dynamics solution for a given tip trajectory is an ill-posed problem. It has also been suggested that increasing model accuracy by including more terms in a truncated beam model worsens the controller’s ability of stability. In this paper, we seek to understand the nature of the inverse dynamics instability. We use one assumed mode to approximate the beam deflection in a single link manipulator. The mode shape is chosen to ensure a boundedness of the inverse dynamics solution. Such solution is then applied in an inversion controller. Numerical simulations and experiments have both been conducted to show its performance.
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ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 30–September 2, 2009
San Diego, California, USA
Conference Sponsors:
- Design Engineering Division and Computers in Engineering Division
ISBN:
978-0-7918-4898-2
PROCEEDINGS PAPER
Stable Inversion Using the Assumed-Modes Rayleigh-Ritz Approximation for Tip Tracking of an Elastic Beam Available to Purchase
Priyanka Mandali,
Priyanka Mandali
University of Calgary, Calgary, AB, Canada
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Qiao Sun
Qiao Sun
University of Calgary, Calgary, AB, Canada
Search for other works by this author on:
Priyanka Mandali
University of Calgary, Calgary, AB, Canada
Qiao Sun
University of Calgary, Calgary, AB, Canada
Paper No:
DETC2009-87794, pp. 1509-1514; 6 pages
Published Online:
July 29, 2010
Citation
Mandali, P, & Sun, Q. "Stable Inversion Using the Assumed-Modes Rayleigh-Ritz Approximation for Tip Tracking of an Elastic Beam." Proceedings of the ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 1: 22nd Biennial Conference on Mechanical Vibration and Noise, Parts A and B. San Diego, California, USA. August 30–September 2, 2009. pp. 1509-1514. ASME. https://doi.org/10.1115/DETC2009-87794
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