A Lyapunov-Based Piezoelectric Controller for Flexible Cartesian Robot Manipulators
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Published:2004-06-01
Issue:2
Volume:126
Page:347-358
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ISSN:0022-0434
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Container-title:Journal of Dynamic Systems, Measurement, and Control
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language:en
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Short-container-title:
Author:
Dadfarnia Mohsen12, Jalili Nader12, Xian Bin12, Dawson Darren M.12
Affiliation:
1. Department of Mechanical Engineering, Robotics and Mechatronics Laboratory, Clemson University, Clemson, South Carolina 29634 2. Department of Electrical and Computer Engineering, Robotics and Mechatronics Laboratory, Clemson University, Clemson, South Carolina 29634
Abstract
A Lyapunov-based control strategy is proposed for the regulation of a Cartesian robot manipulator, which is modeled as a flexible cantilever beam with a translational base support. The beam (arm) cross-sectional area is assumed to be uniform and Euler-Bernoulli beam theory assumptions are considered. Moreover, two types of damping mechanisms; namely viscous and structural dampings, are considered for the arm material properties. The arm base motion is controlled utilizing a linear actuator, while a piezoelectric (PZT) patch actuator is bonded on the surface of the flexible beam for suppressing residual beam vibrations. The equations of motion for the system are obtained using Hamilton’s principle, which are based on the original infinite dimensional distributed system. Utilizing the Lyapunov method, the control force acting on the linear actuator and control voltage for the PZT actuator are designed such that the base is regulated to a desired set-point and the exponential stability of the system is attained. Depending on the composition of the controller, some favorable features appear such as elimination of control spillovers, controller convergence at finite time, suppression of residual oscillations and simplicity of the control implementation. The feasibility of the controller is validated through both numerical simulations and experimental testing.
Publisher
ASME International
Subject
Computer Science Applications,Mechanical Engineering,Instrumentation,Information Systems,Control and Systems Engineering
Reference27 articles.
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, 1987, “Application of Discrete-Time Model Reference Adaptive Control to a Flexible Single-Link Robot,” J. Rob. Syst., 4, pp. 621–630. 3. Ge, S. S., Lee, T. H., and Zhu, G., 1997, “A Nonlinear Feedback Controller for a Single-Link Flexible Manipulator Based on a Finite Element Method,” J. Rob. Syst., 14(3), pp. 165–178. 4. de Querioz, M. S., Dawson, D. M., Agrawal, M., and Zhang, F., 1999, “Adaptive Nonlinear Boundary Control of a Flexible Link Robot Arm,” IEEE Trans. Rob. Autom., 15(4), pp. 779–787. 5. de Querioz, M. S., Dawson, D. M., Nagarkatti, S. P., and Zhang, F., 2000, Lyapunov-based Control of Mechanical Systems, Birkhauser, Boston.
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