Wavelets approach for the optimal control of vibrating plates by piezoelectric patches

The optimal control for vibration suppression of a plate by distributed piezoelectric actuators is considered. A performance index in the form of a weighted quadratic functional of the dynamic response of a rectangular simply supported plate will be minimized within a prescribed time duration using...

Full description

Saved in:
Bibliographic Details
Published in:Journal of vibration and control 2018-03, Vol.24 (6), p.1101-1108
Main Authors: Abualrub, Taher, Abukhaled, Marwan, Jamal, Binish
Format: Article
Language:English
Subjects:
Boundary conditions
Control systems
Dynamic response
Equations of motion
Lumped parameter systems
Mathematical programming
Optimal control
Optimization
Parameterization
Patches (structures)
Performance indices
Piezoelectric actuators
Piezoelectricity
Plates (structural members)
Queuing theory
Structural vibration
Trajectory control
Vibration
Vibration control
Wavelet analysis
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The optimal control for vibration suppression of a plate by distributed piezoelectric actuators is considered. A performance index in the form of a weighted quadratic functional of the dynamic response of a rectangular simply supported plate will be minimized within a prescribed time duration using piezoelectric patches (voltages). The minimization of the performance index over these voltages is subject to the equation of motion governing the plate's structural vibration and a set of initial and boundary conditions. The solution method is a combination of modal space expansion and direct state parameterization. Modal space expansion will transform the optimal control of a distributed parameter system into the optimal control of a lumped parameter system. Using Legendre wavelets, the quadratic optimization problem is transformed into a mathematical programming problem, where the objective is to minimize a set of unknown coefficients to obtain the optimal trajectory and the optimal control. Numerical examples will be provided to illustrate the effectiveness and the efficiency of the proposed method.
ISSN:1077-5463
1741-2986
DOI:10.1177/1077546316657781