Simultaneous piezoelectric actuator and sensor placement optimization and control design of manipulators with flexible links using SDRE method
type: Item
instance of: scholarly article
title: Simultaneous piezoelectric actuator and sensor placement optimization and control design of manipulators with flexible links using SDRE method
zbMATH Open document ID: 1206.93078
DOI: 10.1155/2010/362437
author: Alexandre Molter
author: Otávio A. Alves Da Silveira
author: J. S. O. Fonseca
author: Valdecir Bottega
published in: Mathematical Problems in Engineering
publication date: 2011-02-09T00:00:00Z
full work available at URL: https://eudml.org/doc/229562
review text: 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.
Mathematics Subject Classification ID: 93C85
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 70Q05
zbMATH DE Number: 5849031
zbMATH Keywords: control design for flexible manipulators
zbMATH Keywords: Lagrange equations
zbMATH Keywords: finite element modal formulation
zbMATH Keywords: Euler-Bernoulli beam theory
zbMATH Keywords: state-dependent Riccati equation (SDRE) technique
Wikidata QID: Q58653035
MaRDI profile type: Publication
OpenAlex ID: W2158638369
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description: scientific article; zbMATH DE number 5849031