A Galerkin-Parameterization Method for the Optimal Control of Smart Microbeams
Joint Authors
Abukhaled, Marwan
Sadek, Ibrahim S.
Source
Mathematical Problems in Engineering
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-12-16
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
A proposed computational method is applied to damp out the excess vibrations in smart microbeams, where the control action is implemented using piezoceramic actuators.
From a mathematical point of view, we wish to determine the optimal boundary actuators that minimize a given energy-based performance measure.
The minimization of the performance measure over the actuators is subjected to the full motion of the structural vibrations of the micro-beams.
A direct state-control parametrization approach is proposed where the shifted Legendre polynomials are employed to solve the optimization problem.
Legendre operational matrix and the properties of Kronecker product are utilized to find the approximated optimal trajectory and optimal control law of the lumped parameter systems with respect to the quadratic cost function by solving linear algebraic equations.
Numerical examples are provided to demonstrate the applicability and efficiency of the proposed approach.
American Psychological Association (APA)
Abukhaled, Marwan& Sadek, Ibrahim S.. 2009. A Galerkin-Parameterization Method for the Optimal Control of Smart Microbeams. Mathematical Problems in Engineering،Vol. 2009, no. 2009, pp.1-15.
https://search.emarefa.net/detail/BIM-479070
Modern Language Association (MLA)
Abukhaled, Marwan& Sadek, Ibrahim S.. A Galerkin-Parameterization Method for the Optimal Control of Smart Microbeams. Mathematical Problems in Engineering No. 2009 (2009), pp.1-15.
https://search.emarefa.net/detail/BIM-479070
American Medical Association (AMA)
Abukhaled, Marwan& Sadek, Ibrahim S.. A Galerkin-Parameterization Method for the Optimal Control of Smart Microbeams. Mathematical Problems in Engineering. 2009. Vol. 2009, no. 2009, pp.1-15.
https://search.emarefa.net/detail/BIM-479070
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-479070