In this paper, general in-plane trajectory tracking problem of a flexible beam is studied. To obtain the dynamic equations of motion of the beam, Hamiltonian dynamics is used and then Lagrange’s equations of beam dynamics and corresponding expressions for boundary conditions are derived. Resulting equations show that the coupled beam dynamics including beam vibration and its rigid in-plane motion take place in two different time domains. By using two-time scale (TTS) control theory, a control scheme is elaborated that makes the orientation and position of the mass center of the beam track a desired trajectory while suppressing its vibration. TTS composite controller has two parts: one is a tracking controller designed for the slow (rigid) subsystem, and the other one is a stabilizing controller for the fast (flexible) subsystem. For the fast subsystem, the proposed boundary control (BC) method does not require any information about vibration along the beam except at the end points, nor requires discretizing the partial differential equation of beam vibration to a set of ordinary differential equations. So, the method avoids the need for instruments to measure data from vibration of any point along the beam or designing an observer for estimating this information. Also, the proposed method prevents control spillover due to discretization. Simulation results show that fast BC is able to remove undesirable vibration of the flexible beam and the slow controller provides very good trajectory tracking with acceptable actuating forces/moments.
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e-mail: lotfavar@shirazu.ac.ir
e-mail: eghtesad@shirazu.ac.ir
e-mail: alinajafi62@gmail.com
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October 2008
Research Papers
Vibration Control and Trajectory Tracking for General In-Plane Motion of an Euler–Bernoulli Beam Via Two-Time Scale and Boundary Control Methods
Amir Lotfazar,
Amir Lotfazar
Ph.D. Candidate
Department of Mechanical Engineering,
e-mail: lotfavar@shirazu.ac.ir
Shiraz University
, Mollasadra Avenue, Shiraz, Fars 71348-51154, Iran
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Mohammad Eghtesad,
Mohammad Eghtesad
Associate Professor
Department of Mechanical Engineering,
e-mail: eghtesad@shirazu.ac.ir
Shiraz University
, Mollasadra Avenue, Shiraz, Fars 71348-51154, Iran
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Ali Najafi
Ali Najafi
Ph.D. Candidate
Department of Mechanical Engineering,
e-mail: alinajafi62@gmail.com
Shiraz University
, Mollasadra Avenue, Shiraz, Fars 71348-51154, Iran
Search for other works by this author on:
Amir Lotfazar
Ph.D. Candidate
Department of Mechanical Engineering,
Shiraz University
, Mollasadra Avenue, Shiraz, Fars 71348-51154, Irane-mail: lotfavar@shirazu.ac.ir
Mohammad Eghtesad
Associate Professor
Department of Mechanical Engineering,
Shiraz University
, Mollasadra Avenue, Shiraz, Fars 71348-51154, Irane-mail: eghtesad@shirazu.ac.ir
Ali Najafi
Ph.D. Candidate
Department of Mechanical Engineering,
Shiraz University
, Mollasadra Avenue, Shiraz, Fars 71348-51154, Irane-mail: alinajafi62@gmail.com
J. Vib. Acoust. Oct 2008, 130(5): 051009 (11 pages)
Published Online: August 14, 2008
Article history
Received:
July 1, 2007
Revised:
March 30, 2008
Published:
August 14, 2008
Citation
Lotfazar, A., Eghtesad, M., and Najafi, A. (August 14, 2008). "Vibration Control and Trajectory Tracking for General In-Plane Motion of an Euler–Bernoulli Beam Via Two-Time Scale and Boundary Control Methods." ASME. J. Vib. Acoust. October 2008; 130(5): 051009. https://doi.org/10.1115/1.2948406
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