Simultaneous Piezoelectric Actuator and Sensor Placement Optimization and Control Design of Manipulators with Flexible Links Using SDRE Method

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-...

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Bibliographic Details
Published in:Mathematical Problems in Engineering 2010-01, Vol.2010 (1), p.1275-1297-074
Main Authors: Molter, Alexandre, da Silveira, Otávio A. Alves, Fonseca, Jun S. Ono, Bottega, Valdecir
Format: Article
Language:English
Subjects:
Beam theory (structures)
Control systems design
Dependent variables
Design optimization
Dynamic models
Euler-Bernoulli beams
Euler-Lagrange equation
Feedback control
Finite element method
Flexible manipulators
Genetic algorithms
Links
Mechanical engineering
Nonlinear control
Nonlinear feedback
Partial differential equations
Piezoelectric actuators
Resonant frequencies
Riccati equation
Robot arms
Robot control
Robots
Sensors
Studies
Trajectory control
Trajectory optimization
Vibration
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Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2010/362437