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Copyright © 2010 Alexandre Molter et al. Alexandre Molter et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents a control design for flexible manipulators using piezoelectric actuators bonded on nonprismatic links. The dynamic model of the manipulator is obtained in a closed form through the Lagrange equations. Each link is discretized using finite element modal formulation based on Euler-Bernoulli beam theory. The control uses the motor torques and piezoelectric actuators for controlling vibrations. An optimization problem with genetic algorithm (GA) is formulated for the location and size of the piezoelectric actuator and sensor on the links. The natural frequencies and mode shapes are computed by the finite element method, and the irregular beam geometry is approximated by piecewise prismatic elements. The State-Dependent Riccati Equation (SDRE) technique is used to derive a suboptimal controller for a robot control problem. A state-dependent equation is solved at each new point obtained for the variables from the problem, along the trajectory to obtain a nonlinear feedback controller. Numerical tests verify the efficiency of the proposed optimization and control design.

Details

Title
Simultaneous Piezoelectric Actuator and Sensor Placement Optimization and Control Design of Manipulators with Flexible Links Using SDRE Method
Author
Molter, Alexandre; Otávio A. Alves da Silveira; Ono Fonseca, Jun S; Bottega, Valdecir
Publication year
2010
Publication date
2010
Publisher
John Wiley & Sons, Inc.
ISSN
1024123X
e-ISSN
15635147
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
856980411
Copyright
Copyright © 2010 Alexandre Molter et al. Alexandre Molter et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.